While the simple model of the total atmospheric carbon sink effect as a linear function of concentration has provided excellent prediction results, several problems remained to be investigated and solved. The most obvious open issue is the correct treatment of land use change emssions. It turns out that the model improves by mostly neglecting them after 1959. This effectively implies that land use change emissions have been constant and small since then. The key investigation starts with the observation, that the total carbon sink has a short term component which be explained by temperature changes commonly known as El Nin˜o. The apparent paradox is analysed and explained, why contrary to the short term changes no temperature caused trend can be detected in the model, despite the fact that several contributing processes exhibit temperature dependency. The result of this analysis leads to the model extension, where the total effect of sinks and natural emissions are a linear function of concentration and temperature. This model not only explains current measurements but also paleo climate from ice-core time series.

As society becomes more reliant on Lithium-ion (Li-ion) batteries, state-of-health (SOH) estimation will need to become more accurate and reliable. Therefore, SOH modelling is in the process of shifting from using simple and continuous charge/discharge profiles, to more dynamic profiles constructed to mimic real operation, when ageing the Li-ion batteries. However, in most cases, when ageing the batteries, the same exact profile is just repeated until the battery reaches its end-of-life. Using data from batteries aged in this fashion to build a model, there is a very real possibility that the model will rely on the built-in repetitiveness of the profile. Therefore, this work will examine the dependence of the performance of a multiple linear regression on the number of charges used to train the model, and their location within the profile used to age the batteries. The investigation shows that it is possible to build models using randomly selected partial charges while still reaching errors as low as 0.5%. Furthermore, it shows that only two randomly sampled partial charges are needed to achieve errors of less than 1%. Lastly, as the number of randomly sampled partial charges used to create the model increases, then the dependence on particular partial charges tends to decrease.

This research aims to explore factors that influence sustainable music learning system from psychological perspective, and innovatively constructs a combination of qualitative and quantitative approaches. For first time, combines nonlinear system and identifies relevant factors affecting music learning by establishing data system for questionnaire answering and a quantitative model for actual academic performance. Existing research mainly looks at several factors that affect fragmented music learning system from perspective of teachers' teaching rules, emphasizing phased teaching state and learning goals of teachers as main body, thus ignoring music learning students, who are a large group of music learning objects. The research fills gap in this type of research object, focusing on sustainable music learning system from emotional perspective and students who occupy a dominant position in music learning, so as to more accurately explore impact of their emotional influencing factors on music learning system. The most prominent innovation of this study lies in construction of stochastic nonlinear system for psychological influencing factors of student music learning and a quantitative model for actual learning effect. Through analysis of nonlinear system, weight values of several negative emotions on music learning system are obtained. The comprehensive impact of emotional factors and practical learning on music learning system can be obtained by weighting them together.

Nonlocal theories are gaining prominence because they can solve problems which lead to unphysical conclusions in standard models. This study presents a novel fractional boundary element method (BEM) solution for nonlinear nonlocal thermoelastic problems of anisotropic fibrous polymer nanomaterials. This broad BEM solution combines two solutions: anisotropic fibrous polymer nanomaterials problem solution and nonlinear nonlocal thermoelasticity problem solution. The nonlinear nonlocal thermoelasticity problem solution divides the displacement field into complementary component and particular component. The overall displacement is generated using the boundary element technique, which is the solution to a Navier type problem, while the particular displacement is derived using local radial point. The New Modified Shift-Splitting (NMSS) approach, which reduces memory and processing time requirements, was used to solve linear systems created by BEM. Figures demonstrate the numerical findings, which show the effects of fractional and graded parameters on the thermal stresses of nonlinear nonlocal thermoelastic problems of anisotropic fibrous polymer nanomaterials. The numerical results indicate the consistency and efficiency of the proposed methodology.

Degradation is an inevitable companion in the operation of solid oxide fuel cell (SOFC) systems since it directly deteriorates the reliability of the system’s operation and the system’s durability. Both are seen as barriers that limit the extensive commercial use of SOFC systems. Therefore diagnosis and prognosis are valuable tools that can contribute to raising the reliability of the system operation, efficient health management, increased durability and implementation of predictive maintenance techniques. Remaining useful life (RUL) prediction has been extensively studied in many areas like batteries and proton-exchange membrane fuel cell (PEM) systems, and a range of different approaches has been proposed. On the other hand, results available in the domain of SOFC systems are still relatively limited. Moreover, methods relying on detailed process models and models of degradation turned out to have limited applicability for in-field applications. Therefore, in this paper, we propose an effective, data-driven approach to predicting RUL where the trend of the health index is modelled by an adaptive linear model, which is updated at all times during the system operation. This allows for a closed-form solution of the probability distribution of the RUL, which is the main novelty of this paper. Such a solution requires no computational load and is as such very convenient for the application in ordinary low-cost control systems. The performance of the approach is demonstrated first on the simulated case studies and then on the data obtained from a long-term experiment on a laboratory SOFC system. From the tests conducted so far it turns out that, the quality of the RUL prediction is usually rather low at the beginning of the system operation, but then gradually improves while the system is approaching the end-of-life (EOL), making it a viable tool for prognosis.

Soil secondary salinization has seriously affected the greenhouse vegetable production in China. To improve the secondary salinization greenhouse soil and enhance the soil physical-chemical properties in an eco-environmental way, different organic amendments (straw, straw biochar, Trichoderma bio-organic manure, commercial organic manure) were applied using pot experiment for 60 day to comprehensively screen the optimal remediation method. In this study, soil nutrient condition and salt movement were assessed, and predictive models using multi-linear regression (MLR) and Random Forest (RF) were developed to estimate soil salinization parameters. The findings indicated a significant decrease in soil salt content following the application of organic materials compared to the control treatment. Specifically, the addition of straw at a rate of 250g/kg resulted in a 59.38% reduction in soil salt levels after 60 days (P < 0.05). Furthermore, the main salt ions exhibited dynamic changes over the course of the experiment, with reductions observed in Na+, Ca2+, Cl-, and NO3- content under the 250 g/kg straw treatment by 83.63%, 74.67%, 63.26%, 59.07%, respectively, compared to CK (P < 0.05). In addition, the SO42- content under 125 g/kg commercial organic manure amendment reduced by 48.94%, respectively (P < 0.05). Contrary to expectations, the addition of organic materials significantly increased the levels of total nutrients (N/P/K) and available potassium (AK) and phosphorus (AP) in the soil. Specifically, the addition of straw at a rate of 250 g/kg resulted in increases of 18.02%-87.38% in total potassium (TK), 66.67%-200% in total phosphorus (TP), and 142.87%-367.8% in AK after a period of sixty days (P < 0.05). Ultimately, the treatment involving the addition of 250 g/kg of straw demonstrated the most pronounced impact on the physical and chemical properties of the soil. The random forest method shows promise in accurately predicting soil salt and soil sodium adsorption ratio (SAR)indicators, thereby providing a valuable tool for estimating soil properties.

This research aims to explore factors that influence sustainable music education from a psychological perspective, and innovatively constructs a combination of qualitative and quantitative approaches. For first time, combines stochastic nonlinear system of control theory and identifies relevant factors affecting sustainable music learning by establishing a data system for questionnaire answering and a quantitative model for actual academic performance. Existing research mainly looks at several factors that affect fragmented music education from perspective of teachers' teaching rules, emphasizing phased teaching state and learning goals of teachers as main body, thus ignoring sustainable music education and students, who are a large group of music learning objects. The research fills gap in this type of research object, focusing on sustainable music education from an emotional perspective and students who occupy a dominant position in music learning, so as to more accurately explore impact of their emotional influencing factors on sustainable music learning. The most prominent innovation of this study lies in construction of stochastic nonlinear system for psychological influencing factors of sustainable student music learning and a quantitative model for actual learning effect. Through analysis of nonlinear system, weight values of several negative emotions on sustainable music learning are obtained.

In this paper, we propose a system of nonlinear mixed variational inequality problems, which consists of two elliptic mixed variational inequality problems on Banach spaces. Under suitable assumptions, using the Kakutani-Ky Fan fixed point theorem and Minty techniques, we prove the solution set to the system of nonlinear mixed variational inequality problem is nonempty, weakly compact and unique. Additionally, we suggest a stability result for the system of nonlinear mixed variational inequality problem by perturbing the duality mappings. Furthermore, we present an optimal control problem governed by the system of nonlinear mixed variational inequality problems and establish a solvability result.

Cancer is a disease caused by the abnormal growth of cells in different parts of body is one of the top causes of death globally. Microarray gene expression data plays a critical role in the identification and classification of cancer tissues. Due to recent advancements in Machine Learning (ML) techniques, researchers are analyzing gene expression data using a variety of such techniques to model the progression rate &amp; treatment of cancer patients with great effect. But high dimensionality alongside the presence of highly correlated columns in gene expression datasets leads to computational difficulties. This paper aims to propose the use of ML classification techniques- Linear Discriminant Analysis (LDA) &amp; Random Forest (RF) for classifying five types of cancer (breast cancer, kidney cancer, colon cancer, lung cancer and prostate cancer) based on high dimensional microarray gene expression data. Principal component analysis (PCA) was used for dimensionality reduction, and principal component scores of the raw data for classification. Six distinct categorization performance measures were used to evaluate these approaches; RF method provided us with higher accuracy than LDA method. The method and results of this article should be helpful to researchers who are dealing with many genes in microarray data.

Reliable prediction of infectious disease is an essential need for public health organizations to minimize or prevent the disease's spread. With the increase of data growth in the healthcare sector, accurate analysis of such data helps for early disease detection and better patient care. With the availability of huge data, it is a great deal for predicting and handling an epidemic occurrence. To control the epidemic disease, a new Artificial Intelligence called Manhattan Hessian Linear Feature Embedding Based Tucker Congruence Deep Convolutional Network (MHLFE-TCDCN) is introduced with higher accuracy and minimum time consumption. The MIoT device is used to collect the data from the patient body. The proposed MHLFE-TCDCN includes two major processes namely feature selection and classification with multiple layers such as input, two hidden layers, and one output layer. First, the feature selection process is performed using the Manhattan Hessian Locally Linear Embedding technique in the first hidden layer to minimize the dimensionality and time complexity. After selecting the feature, the classification is performed using the Tucker coefficient of congruence regression. The Tucker coefficient of congruence measures the similarity between the training and testing disease data. A positive similarity level is used to accurately identify the disease at the output layer based on the similarity measure. Experimental assessment is carried out with various parameters such as accuracy, precision, recall, F-measure, and computational time concerning several numbers of patient data. The quantitative results and discussion that the proposed MHLFE-TCDCN technique achieves higher accuracy with minimal computation time as compared to the conventional methods.

Scattering of a probe laser pulse by an intense light spring in QED vacuum is considered. This new scattering configuration can be seen as the vacuum equivalent to the process originally associated with scattering of light by a rotating black hole, usually called Penrose superradiance. Here the rotating object is an intense laser beam containing two different components of orbital angular momentum. Due to these two components with slightly different frequencies, the energy profile of the intense laser beam rotates with a frequency that depends on the frequency difference. The nonlinear properties of quantum vacuum are described by first order Euler-Heisenberg Lagrangian. It is shown that, in such a configuration, nonlinear photon-photon coupling leads to scattered radiation, with frequency shift and angular dispersion. These two distinct properties, of frequency and propagation direction, could eventually be favourable for possible experimental observations. In principle, this new scattering configuration can also be reproduced in a nonlinear optical medium.

Time series forecasting has been a challenging area in the field of Artificial Intel-ligence. Various approaches such as linear Neural Networks, Recurrent Linear Neural Networks, Convolutional Neural Networks and recently Transformers have been attempted for the time series forecasting domain. Although, Trans-former-based architectures have been outstanding in the Natural Language Pro-cessing domain, especially in autoregressive language modeling, the initial at-tempts to use transformers in the time series arena have met with mixed success. One of the recent papers demonstrated that modeling the multi-variate time se-ries problem as independent channels on a transformer architecture produced lower mean square and mean absolute errors on benchmarks, however, another recent paper claimed that a simple linear neural network out-performs previous approaches including transformer-based designs. We investigate this paradox in detail comparing the linear Neural Network and Transformer based designs, provide insights to why a certain approach may be better for a particular type of problem. We also improve upon the recently proposed simple linear Neural Network based architecture by using dual pipelines with batch normalization and reversible instance normalization. Our enhanced architecture outperforms all existing architectures for time series forecasting on majority of the popular benchmarks.

Volatile organic compounds (VOCs) released from plants have been correlated with disease-status. Analysis of VOCs using GC-MS is time-consuming, laboratory-based, and requires specialist training. Electronic nose devices (E-nose) provide a portable alternative. Three different E-nose devices were compared to assess how accurately they could detect Mango Twig Tip Dieback and Panama disease in banana. The devices were initially trained on known volatiles, then pure cultures of Pantoea sp., Staphylococcus sp., and Fusarium odoratissimum, and finally, on infected and healthy mango leaves and field-collected, infected banana pseudo-stems. The experiments were repeated three times with six replicates for each host-pathogen pair. The variation between healthy and infected host materials was evaluated by principal component and linear discriminant analysis, cross-validation and chemometric data analysis. GC-MS analysis was conducted contemporaneously and identified an 80% similarity between healthy and infected plant material. The portable C 320 was 100% successful in discriminating known volatiles but had a low capability in differentiating healthy and infected plant substrates. The advanced devices (PEN 3 / MSEM 160) successfully detected healthy and diseased samples with a high variance. The results suggest that E-nose devices are more sensitive and accurate in detecting changes of VOCs between healthy and infected plants compared to headspace GC-MS.

Let $n \geq 2$ be a fixed integer and $\mathcal{A}$ be a $C^*$-algebra. A permuting $ n $-linear map $ \mathcal{G} : \mathcal{A} ^{n} \rightarrow \mathcal{A} $ is known to be symmetric generalized $n$-derivation if there exists a symmetric $n$-derivation $ \mathfrak{D} : \mathcal{A} ^{n} \rightarrow \mathcal{A} $ such that $ \mathcal{G} \left(x_{1}, x_{2}, \ldots, x_{i} x_{i}^{\prime}, \ldots, x_{n}\right)= \mathcal{G} \left(x_{1}, x_{2}, \ldots, x_{i}, \ldots, x_{n}\right) x_{i}^{\prime}+x_{i} \mathfrak{D} (x_{1}, x_{2},\ldots, x_{i}^{\prime}, \ldots, x_{n})$ holds for all $x_{i}, x_{i}^{\prime} \in \mathcal{A} $. In this paper, we investigate the structure of $C^*$-algebras involving generalized linear $n$-derivations. Moreover, we describe the forms of traces of linear $n$-derivations satisfying certain functional identity.

Abstract—The static and fatigue analysis of plates with holes, made of 2D woven roving composites, is conducted. The parametrization of convex holes is proposed. Experimental results of specimens without holes and with different shapes of notches are discussed. The fatigue behaviour is considered with the use of the low cycle fatigue method. The analysis is supplemented by the numerical finite element modeling. The present work is an extension of the results discussed in the literature. The finite element modeling of plates with holes is presented in details in Ref [1-3] including also the problems of the accuracy. The experimental results and the form of specimens are shown in Ref [4]. Two parametrical description of static and fatigue behaviour of plates with holes characterizes the goal and the novelty of the paper. The fuzzy approach is employed to reduce the number of experimental data [5].

Understanding the optimal strategy for a real estate investment and how performance changes based on characteristics is crucial for optimising the achievable return. This is prominent in tourist areas such as Paphos where there is no clear distinction as to whether short or long-term approaches are optimal. The study aimed to develop a model for predicting the optimal rental strategy whilst assessing which model performed best and which property attributes impacted its return the greatest. Short-term data was collected from AirDNA and long-term data was manually collected from real estate agents websites. Furthermore, Random Forest, K-Nearest Neighbour and Multiple Linear Regression models were created to predict the highest and best use for each property. Model accuracy varied between data sets with the best performing model for short-term properties being Random Forest (R-Squared: 0.843), and Distance-Based Multiple Linear Regression for long-term approach (R-Squared: 0.843). The study demonstrated that accurate models could be created to predict the optimal rental strategy with the number of bedrooms being the main driver for rental income, followed by luxury finishes and the presence of a pool. It found that locational characteristics didn’t impact the returns significantly assuming that the property was located within a tourist area.

The penetrability and directivity of ultrasound in different media is of interest in engineering and medical applications (imaging, nondestructive testing, sonochemistry, among others). The nonlinearity of a liquid can be used in the parametric antenna framework to generate low-frequency components with particular features from several ultrasonic signals at the source. Bubbly liquids are dispersive liquids in which a small amount of tiny gas bubbles leads to the increase of the nonlinear parameter of the media over certain frequency ranges. Parametric antenna applied to this huge nonlinear media gives rise to low-frequency components with relatively small intensity at the source. The evolution of a low-frequency component (difference-frequency component obtained from two primary signals) during its propagation in a bubbly liquid is somehow unknown. It is thus interesting to analyse its characteristics to establish whether this component can benefit from the quality of its own frequency and from the primary frequencies in terms of directivity and penetrability into the medium. It must be noted that no such study in bubbly liquids exists in the litterature, but only for homogeneous media. To this end, several numerical models developed previously are used here to analyse the difference-frequency component obtained from a parametric antenna emitting from two ultrasonic signals at the source in one and two-dimensional domains. These models allow us to observe the behavior of this frequency component. An angle that measures the directivity of a beam is also defined. Our results show a point hardly found in the literature: the high directivity and the huge penetrability of the secondary beam associated to the difference-frequency component into the bubbly liquid, compared to the same frequency signal excited directly from the source in the bubbly liquid and to the parametric acoustic array in homogeneous fluids.

This paper presents two control design strategies for voltage regulation in a single inductor dual output (SIDO) DC-DC Buck converter system. Based on a nominal multiple input multiple output (MIMO) plant model and performance requirements, both an LQR and a decoupled PI control laws are designed to control the power converter system, under parametric uncertainties such as voltage source variation, CPL power variation, and load resistance variation. Therefore, the SIDO converter can cascade operating, which may cause the undesired effects of voltage oscillation and reduce the system's stability margin. The control performance was assessed under both uncertainties resistive loading and power variation of a constant power load (CPL). A SIDO DC-DC Buck converter board has been developed for experimental tests. The experimental results show that the LQR strategy, compared to the PI strategy, presented a robust performance in the presence of parametric uncertainties in the resistive loads being, however, sensitive to uncertainties due to the presence of CPL loads.

This article describes an approach for optimising sensor-controlled systems through minimal intervention, utilising Fuzzy Linear Systems of Equations (FLSE). Staring with a generalised model of the system behaviour, incorporating an array of control units, environmental sensors, and an expert knowledge base. The described problems of detecting the level of intervention needed to change the system state to another is handled with the help of developed methods for solving the inverse problem for FLSE. By achieving minimal intervention, we ensure that system adjustments effective, economically optimal and non-intrusive. A MATLAB-based implementation is presented.

The article presents a model for optimizing biomass supply chains using the linear programming framework integrated with a Geographic Information System. Based on the distance from a given type of biomass resource, its calorific value, price, and transportation costs, the model identifies the optimal source of biomass, allowing it to cover the demand for the required total energy value with the lowest possible costs. The case study includes the Połaniec power plant in southeastern Poland and potential sources of forest biomass and agricultural straw within 100 km of the plant. Unit costs of biomass varied depending on biomass availability and energy demands. For energy demand on the level of 1 PJ yearly, the lowest unit costs of biomass (4.08 €/MJ) were when all kinds of biomass were available, and the highest (5.47 €/MJ) was when only stacked wood was available. As energy demand increased, unit costs increased, and the ability to meet this demand with just one type of biomass decreased. The energy biomass sector can utilize the model to benefit both biomass producers and their final buyers.

In this project the EEG – electroencephalogram - channel(s) will be characterized to diagnose PTSD – Post-traumatic stress disorder – cases. For this aim, we applied boosting methods including a combination of K-mean and Support Vector Machine (SVM) models to find the feature weights to detect the PTSD cases. We classified 32 channels of 12 subjects including 6 PTSD and 6 healthy controls using a 6-mean classifier. The linear SVM found the weights of distinguished channels within each subject for each cluster. It was found that the significant SVM weights of F4, F8, and Pz are smaller in PTSD than in healthy subjects. This new method can be used as a tool to better understand the interaction of EEG signals and diagnosis.

Silver eel were sampled in 1981 and 1983 in River Brede, Denmark, with outlet to the North Sea. Yellow eel in River Køge-Lellinge, Denmark, with outlet to the Baltic Sea were sampled 1965-1968. Silver eel were aged by burning the otoliths. Silver male ages varied from 4 to 25 years, lengths 30.8 to 45.3 cm, and female silver eel varied from 7 to 25 years, lengths 42.3 to 77.3 cm. von Bertalanffy trajectories of length-at-age of male and female yellow eel were calculated in both rivers. Younger yellow eel had significantly higher annual growth rate compared to older age groups, and females grew significantly faster than males. Two models for natural mortality M were used to estimate number of glass eel needed to produce number of silver eel for each sex and silver age group. Annual silver eel production from River Brede Å was 49.2 kg ha-1, demanding 2,894 glass eel ha-1 and in River Køge-Lellinge, the silver eel production was 48.5 kg ha-1, demanding 5,570 glass eel ha-1. It was calculated that one (0.29 g) thousand glass eel contribute to 8.8 kg silver eel in River Køge-Lellinge, and 17.0 kg silver eel in River Brede. To fulfill the Danish EMP in rivers requires annual stocking of 33 tons or 9.4 million reared on-grown eel (3.5 g) to compensate for 183 tons lost silver eel.

Soccer is the leading cause of all sports-related ocular injuries in Europe and Israel and leads to blindness at a disproportionately high rate, especially among children (Thompson et al., 2019). With soccer being the most popular sport in the world, it is surprising the only solution to ocular injuries are sports glasses which can cause direct damage to the eye and impair peripheral vision by 15%, calling for an alternative (Smith & Jones, 2020). This work, based on an imported facial model, focuses on both the qualitative and quantitative aspects of building a personalized, low-cost (through optimizing material needed), superior apparatus to conventional sports glasses. The quantitative side examines a modified and model-validated (through a SRS of thirty unique extrapolated points) multivariate linear regression equation, based on horizontal and vertical rotation angles (n=60) trained with residual and computer simulation data, that can accurately extrapolate and quantify ocular impact from all horizontal and vertical rotation angles and a modified Hertzian Contact Stress Equation to determine the thickness of the apparatus using the elasticity modulus, impact force, and geometrical facial and soccer-ball features. The qualitative side examines where firstly, ocular impact is most prevalent, and secondly, where most impact is seen from rotating the ball horizontally and vertically through analysis of Pearson’s Correlation Coefficient at the supraorbital, medial canthus, infraorbital, and lateral canthus regions from both regression equations as well as a cost-benefit analysis for comparison with conventional sports glasses. The findings discovered in this work lay the groundwork for future research to build a customized low-cost ocular injury prevention device which can simultaneously ensure complete ocular safety while enhancing athletic performance for over 250,000,000 players (Johnson & Garcia, 2022).

Density functional theory (DFT) calculations of hydrogen adsorption on titanium nitride had previously shown that hydrogen may adsorb on both titanium and nitrogen sites with a moderate adsorption energy. Further, the diffusion barrier was also found to be low. These findings may qualify TiN, a versatile multifunctional material with electronic conductivity, as electrode material for the hydrogen evolution reaction (HER). This was the main impetus of this work which aims to experimentally and theoretically investigate the electrocatalytic properties of TiN-layers that were processed on Ti substrate using reactive ion sputtering. The properties are discussed focusing on the role of oxygen defects introduced during the sputtering process on the HER. Based on DFT calculations, it is shown that these oxygen defects alter the electronic environment of the Ti atoms which entails a low hydrogen adsorption energy in the range of -0.1 eV; this leads to HER performances that match those of Pt-NPs in acidic media. When a few nanometr thick layer of Pd-NPs is sputtered on-top of the TiN-layer, the performance is drastically reduced. This is interpreted in terms of oxygen defects being scavenged by the Pd-NPs near the surface which is thought to reduce the hydrogen adsorption sites.

The goal was to model the irrigated (IBY) and rainfed (RBY) bean yields, as a function of essential climatic variables (ECVs), in the center (Culiacán) and south (Rosario) from Sinaloa. In Sinaloa, and for the period 1982–2013 (October–March), the following were calculated: a) temperatures. b) average degree days for the bean, c) cumulative potential evapotranspiration and d) cumulative effective precipitation. For ECVs, from the European Space Agency, e) daily soil moisture. f) IBY and RBY, from the Agrifood and Fisheries Information Service. Multiple linear regressions were applied, which modeled IBY–RBY (dependent variables), as a function of ECVs (independent variables). Then, to establish each Pearson correlation (PC) as significantly different from zero, a hypothesis test was applied: PC vs Pearson's critical correlation (CPC). The four models obtained were significantly predictive: IBY–Culiacán (PC = 0.590 > CPC = |0.349|), RBY–Culiacán (PC = 0.734 > CPC = |0.349|), IBY–Rosario (PC = 0.621 > CPC = |0.355|) and RBY–Rosario (PC = 0.532 > CPC = |0.349|). This study is the first in Sinaloa to predict IBY and RBY based on ECVs, contributing to the production of sustainable food.

In this paper, we propose a method to find all efficient solutions of an interval multiple objective linear programming (IMOLP) problem with interval coefficients in the objective functions, the constraint matrix and the right-hand side vector. The set of all efficient solutions of an IMOLP problem can completely supply information to the decision makers in finding their most preferred solutions but, up to now, not all solutions of an IMOLP problem can be found by known methods. A numerical example is given to illustrate the working of the proposed method.

Remote sensing technologies are critical for analyzing the escalating impacts of global climate change and increasing urbanization, providing vital insights into land surface temperature (LST), land use and cover (LULC) changes, and the identification of urban heat island (UHI) and surface urban heat island (SUHI) phenomena. This research focuses on the nexus between LULC alterations and variations in LST and air temperature (Tair), with a specific emphasis on the intensified SUHI effect in Kharkiv, Ukraine. Employing an integrated approach, the study analyzes time-series data from Landsat and MODIS satellites, alongside Tair climate records, utilizing machine learning techniques and linear regression analysis. Key findings indicate a statistically significant upward trend in Tair and LST during summer months from 1984 to 2023, with a notable positive correlation between Tair and LST across both datasets. MODIS data exhibit a stronger correlation R² = 0.879, compared to Landsat R² = 0.663. The application of supervised classification through Random Forest algorithms and vegetation indices on LULC data reveals significant alterations, manifested as a 70.3% increase in urban land, concurrently with a decrement in vegetative cover, especially 15.5% reduction in dense vegetation and a 62.9% decrease in sparse vegetation. Change detection analysis elucidates a 24.6% conversion of sparse vegetation into urban land, underscoring a pronounced trajectory towards urbanization. Temporal and seasonal LST variations across different LULC classes were analyzed using kernel density estimation (KDE) and boxplot analysis. Urban areas and sparse vegetation had the smallest average LST fluctuations, at 2.09°C and 2.16°C, respectively, but recorded the most extreme LST values. Water and dense vegetation classes exhibited slightly larger fluctuations of 2.30°C and 2.24°C, with the bare land class showing the highest fluctuation 2.46°C, but fewer extremes. Quantitative analysis with the application of Kolmogorov-Smirnov tests across various LULC classes substantiated the normality of LST distributions p &gt; 0.05 for both monthly and annual data sets. Conversely, the Shapiro-Wilk test validated the normal distribution hypothesis exclusively for monthly data, indicating deviations from normality in the annual data. Thresholded LST classifies urban and bare lands as warmest classes with 39.51°C, 38.20°C and water by 35.96°C and dense vegetation 35.52°C, sparse vegetation 37.71°C as coldest, a trend consistent annually and monthly. The analysis of SUHI effects demonstrates an increasing trend in UHI intensity, with statistical trends indicating a growth in average SUHI values over time. This comprehensive study underscores the critical role of remote sensing in understanding and addressing the impacts of climate change and urbanization on local and global climates, emphasizing the need for sustainable urban planning and green infrastructure to mitigate UHI effects.

Unmanned aerial vehicle (UAV), or drone is recognized for its potential to improve efficiency and address last-mile delivery issues. As a result, there has been a lot of activity in recent years in the field of drone scheduling and routing. Unlike the vehicle routing problem, drone route design is difficult due to several operational characteristics, such as speed optimization, multitrip operation, and energy consumption estimation. On the one hand, drone energy consumption is a complex nonlinear function of both speed and payload in practice. On the other hand, the high operating speed of drones can significantly curtail the drone range, thereby limiting the efficiency of drone delivery systems. Most of the existing drone delivery models either assume constant drone speed or do not consider the effect of drone speed and parcel weight on energy consumption, leading to costly or energy-infeasible routes. This paper addresses the trade-off between speed and flight range in a multi-trip drone routing problem with variable flight speeds (DRP-VFS), in which a team of homogeneous drones is employed for delivery services. We propose a new model to particularly consider energy constraints using a nonlinear energy consumption model and treat drone speeds as decision variables so that various drone speeds can be adopted in applications. The DRP-VFS is initially formulated as mixed-integer linear programming (MILP) to minimize total energy consumption. To solve large-scale instances, we propose a three-phase adaptive large neighborhood search (ALNS) algorithm. The experimental results demonstrate that suboptimal solutions can be found effectively in practical scenarios using the proposed method. Furthermore, results indicate that operating drones at variable speeds leads to about 21% of energy savings compared to fixed speeds, boasting advantages in cost-savings and range extensions.

Objective: To evaluate the variables influencing the length of stay (LoS) for COVID-19 ICU patients at Tygerberg Hospital (Cape Town) and to identify the covariates that significantly influenced it and any potential risk factors associated with LoS. Methods and Results: Poisson, negative binomial (NB), Hurdle–Poisson, and Hurdle–NB regression models were used to model the LoS in this prospective cohort study. The fitted models were compared using the Akaike information criterion (AIC), Vuong’s test criteria, and Rootograms. Based on the chosen performance criteria, the NB model provided the best fit outperforming other candidate models. The baseline LoS count was 8 days. On average, antibiotics reduced LoS by 0.74-fold (95% CI 0.62-0.89) compared to not taking antibiotics. The second wave had a significant effect on the average LoS, which decreased by 0.36-fold (95% CI 0.14-0.93) compared to the first wave. Average LoS increased by 1.01-fold (95% CI 1.01-1.02) for every one-year increase in the age of the patient and by 1.02-fold (95% CI 1.01-1.03) for every 1 unit increase in neutrophils. A 1 ng/L increase in log (TropT) levels decreased the average LoS by 0.87-fold (95% CI 0.81-0.93) similarly, a unit increase in the PF ratio decreased the average LoS by 0.998-fold (95% CI 0.997-0.999) respectively. Conclusion: The study identified common clinical characteristics associated with length of stay in ICU for COVID-19 patients, including age at admission, PF ratio, neutrophils, TropT, Wave, and antibiotic use. These results can aid in identifying risk factors for increased length of stay, assist in healthcare systems planning, and aid in evaluating different models for analysing this type of data.

Herein, we examined the effects of weather parameters and individual clinicodemographic risk factors on hemorrhagic stroke (HS) incidence, severity on admission, and disability at discharge in a harsh desert climate. In a retrospective design we studied patients admitted to a stroke unit in Arab Emirates in 2016-2019. With a distributed lag nonlinear model we explored immediate and delayed effects of weather on stroke incidence. Supervised machine learning was used to build models predictive of scores in NIHSS and mRS scales. We assessed model performance by calculating ROC AUC, F1 scores, specificity, and sensitivity. HS risk increased after a significant change in any weather parameter. The risk was reduced below baseline after 1-week adjustment to environmental changes. Climate input from the previous 3 days yielded reliable classification models. Humidex was a better predictor of severity than air temperature, whereas body mass index, age, and time of day at stroke onset were the strongest clinical predictors. Weather parameters before admission were stronger predictors of disease severity than individual clinical factors. We addressed limitations of previous studies by analyzing a full set of climate parameters: ambient temperature, relative humidity, humidex, atmospheric pressure, and wind speed. Predictive models may help to optimize patient management and develop preventative strategies.

The susceptible-infected-recovered-vaccinated-deceased (SIRVD) epidemic compartment model extends the SIR model to include the effects of vaccination campaigns and time-dependent fatality rates on epidemic outbreaks. It encompasses the SIR, SIRV, SIRD, and SI models as special cases, with individual time-dependent rates governing transitions between different fractions. We investigate a special class of exact solutions and accurate analytical approximations for the SIRVD and SIRD compartment models. While the SIRVD and SIRD equations pose complex integro-differential equations for the rate of new infections and the fractions as a function of time, a simpler approach considers determining equations for the sum of ratios for given variations. This approach enables us to derive fully exact analytical solutions for the SIRVD and SIRD models. For nonlinear models with a high-dimensional parameter space, such as the SIRVD and SIRD models, analytical solutions, exact or accurately approximative, are of high importance and interest: not only as suitable benchmarks for numerical codes, but especially as they allow us to understand the critical behavior of epidemic outbursts as well as the decisive role of certain parameters. In the second part of our study, we apply a recently developed analytical approximation for the SIR and SIRV models to the more general SIRVD model. This approximation offers accurate analytical expressions for epidemic quantities, such as the rate of new infections and the fraction of infected persons, particularly when the cumulative fraction of infections is small. The distinction between recovered and deceased individuals in the SIRVD model affects the calculation of the death rate, which is proportional to the infected fraction in the SIRVD/SIRD cases but often proportional to the rate of new infections in many SIR models using a posteriori approach. We demonstrate that the temporal dependence of the infected fraction and the rate of new infections differs when considering the effects of vaccinations and when the real-time dependence of fatality and recovery rates diverge. These differences are highlighted for stationary ratios and gradually decreasing fatality rates. \Revised{The case of stationary ratios allows one to construct a new powerful diagnostics method to extract analytically all SIRVD model parameters from measured COVID-19 data of a completed pandemic wave.

The Planetary Roller Screw Mechanisms (PRSMs), alongside Ball Screw Mechanisms (BSMs) and Electromechanical Actuators (EMAs), occupies a pivotal role in advancing the precision and efficiency of various industrial applications, including aerospace, automotive, and high-precision machining tools. Despite their critical advantages such as high load capacity, superior precision, and extended lifespan, the deployment of PRSMs in complex operational conditions reveals a landscape rife with challenges and opportunities for further research. This comprehensive review endeavors to dissect the multifaceted aspects of PRSMs, focusing on their mechanics and dynamics, tribology and thermal behavior, and the paramount importance of reliability and condition monitoring. By synthesizing current research findings, this paper highlights the significant advancements in understanding the static and dynamic characteristics of PRSMs, the intricate interplay between lubrication conditions and wear mechanisms, and the critical role of thermal effects on operational performance. Moreover, it delves into the dynamic models that address the impact of manufacturing imperfections, such as waviness and defects, on the reliability of these mechanisms. Despite the strides made, the review identifies critical gaps in the existing literature, particularly under conditions of extreme temperatures, large deformations, and multifaceted loads, advocating for a holistic approach to research. By proposing integrated thermo-mechanical models and emphasizing the need for empirical validations, this paper outlines a roadmap for future studies aimed at facilitating the development of more robust and reliable PRSMs, capable of meeting the demands of complex operational scenarios and advancing the field of high-precision applications in aerospace, robotics, and beyond.

Different types of resonators are used to create acoustic metameterials and metasurfaces. Recent studies focused on the use of multiple resonators of dipole, quadrupole, octupole and even hexadecapole types. This paper considers the theory of an acoustic metasurface, which is a flat surface with a periodic arrangement of multiple resonators. The sound field reflected by the metasurface is determined. If the distance between the resonators is less than a half the wavelength of the incident plane wave, the far field can be described by a reflection coefficient that depends on the angle of incidence. This allows to characterize the acoustic properties of the metasurface by a homogenized boundary condition, which is a high order tangential impedance boundary condition. The tangential impedance depending on the multiple order of the resonators is introduced. In addition, we analyze sound absorption properties of these metasurfaces, which are a critical factor in determining their performance. The paper presents a theoretical model that accounts for the multiple orders of resonators and their impact on sound absorption. The maximum absorption coefficient for a diffuse sound field, as well as the optimal value for the homogenized impedance, are calculated for arbitrary multipole orders.

The numerical implementation of the controllers allows the use of very complex algorithms with ease. However, in practice, due to its proven advantages, the PID controller (and its variants) is widely used in industrial control systems as well as in many other applications that require continuous control. Most of the methods for tuning the parameters of PID controllers are based on time-invariant linear models of the processes, which in practice can lead to poor performance of the control system. The paper presents an application of reinforcement learning algorithms in tuning of PID controllers for the control of some classes of continuous nonlinear systems. Tuning the parameters of PID controllers is done with the help of Twin Delayed Deep Deterministic Policy Gradients (TD3) algorithm which presents a series of advantages compared to other similar methods from Machine Learning dedicated to continuous state and action spaces. TD3 algorithm is an off-policy Actor-Critic based method and was used as it does not require a system model. The presented technique is applied for control of a biotechnological system which has a strongly nonlinear dynamic. The proposed tuning method is compared to the classical tuning methods of PID controllers. The performance of the tuning method based on the TD3 algorithm is demonstrated through simulation illustrating the effectiveness of the proposed methodology.

With the use of linear regression modeling, this study sought to forecast and analyze rainfall patterns in Ethiopia. The dataset included historical rainfall data as well as pertinent independent variables. The R-squared score and mean squared error (MSE) were used to assess the effectiveness of the linear regression model. The results showed that the model's ability to forecast and analyze rainfall patterns was not very good. Only around 5.3% of the variance in rainfall could be explained by the chosen independent variables, according to the R-squared score of 0.053. This low number indicated that there was little correlation between the selected variables and rainfall, and that a sizable percentage of the variation in the dependent variable was not captured by the model. The model's accuracy in forecasting rainfall was shown to be quite low by the MSE error, with significant squared discrepancies between the expected and actual amounts. These results support the notion that the linear regression model as it is now designed is not appropriate for studying or forecasting Ethiopia's rainfall patterns. Alternative modeling approaches, the inclusion of other pertinent factors, and the assurance of the availability of high-quality data that faithfully captures the intricate dynamics of rainfall in the area all require more investigation.

German noise action plans aim to reduce negative health outcomes from noise exposure and identify quiet areas free of noise pollution. Quiet area identification in German noise action plans is based primarily on noise mapping and spatial analysis and not empirical or qualitative data about acoustic environments, thus leaving a gap in the understanding of the quality of formally recognized quiet areas in noise action plans. This work presents a comparative empirical case study in Dortmund, Germany, with the aim to describe the diurnal dB(A) and biophonic properties of quiet areas versus noise 'hot spots'. Sound observations were collected (n=282,764) in five different natural or recreational land use patch types larger than four acres within 33 proposed quiet areas in Dortmund (n=70) and 23 noise hot spots between April 27^th, 2022 and March 2^nd, 2023. We find that quiet areas are on average more than 20 dB(A) quieter than noise hot spots almost every hour of the day. Forests, managed tree stands, cemeteries, and agriculture diel patterns are dominated by dawn dusk chorus in spring and summer, whereas sport and recreation as well as noise hot spots are dominated by traffic and human noise. A novel composite biophony mapping procedure is presented that finds distinct temporal distribution of biophony in forested and agriculture peri-urban locations positively associated with patch size, distance away from LDEN > 55, proximity to water, and the number of vegetation layers in the plant community. Anthrophony distribution dominates urban land uses in all hours of the day, but expands during day and evening and contracts at night and in dusk hours. The procedures presented here illustrate how qualitative information regarding quiet areas can be integrated into German noise action planning.

Most works related to the identification of mathematical nonlinear systems make one suppose that such approaches can always be directly applied to any nonlinear system. This misconception produces a great deal of discouragement when the obtained results are not the expected ones. Thus, the current work hypothesizes that the most information one has about the mathematical structure of the model, the most precise the identification result should be. Therefore, a variant of the Sparse Identification of Nonlinear Dynamics (SINDY) approach is presented to obtain the full mathematical nonlinear model of a high-order system with coupled dynamics, namely, a commercial quadcopter. Furthermore, due to its high sensitivity to inputs, a control system is devised using the identified model to stabilize the quadcopter. This illustrates the effectiveness of the proposed identification method.

This paper aims to address the exponential stability and stabilization problems for a class of delayed nonlinear Markov jump systems under randomly occurring Denial-of-Service (DoS) attack and packet loss. Firstly, the stochastic characteristics of DoS attack and packet loss are depicted by the attack success rate and packet loss rate. Secondly, a Period Observation Window (POW) method and a hybrid-input strategy are proposed to compensate for the impact of DoS attack and packet loss on the system. Thirdly, A Dynamic Event-triggered Mechanism (DETM) is introduced to save more network resources and ensure the security and reliability of systems. Then, by constructing a general common Lyapunov functional and combining with the DETM and other inequality analysis techniques, the less conservative stability and stabilization criteria for the underlying systems are derived. In the end, the effectiveness of our result is verified through a numerical example.

This paper proposed an optimal tracking control scheme through adaptive dynamic programming(ADP) for a class of partially unknown discrete-time nonlinear systems based on radial basis function neural network(RBF-NN). In order to acquire the unknown system dynamics, we use two RBF-NNs, the one is used to construct the identifier, and the another is used to directly approximate the steady-state control input, where a novel adaptive law is proposed to update neural network weights. While the optimal feedback control and the cost function are derived via feedforward neural networks approximating, it is proposed to regulate the tracking error, the critic network and the actor network are then trained online to obtain the solution of the associated Hamilton–Jacobi–Bellman (HJB) equation being built under the ADP framework. Simulations verify the effectiveness of the optimal tracking control technique using the neural networks.

Byers Peninsula is considered one of the largest ice-free areas in Maritime Antarctica. Since 2006, the Spanish Polar Program has taken part in a large number of environmental studies involving effects of climate changes in lives cycles, limnology and microbiology. Soils from maritime Antarctica are generally weakly developed and have chemical, physical and morphological characteristics strongly influenced by the parent material. However, biological activity during the short Antarctic summer promotes intense transference of nutrients and organic matter in areas occupied by different species of birds and marine mammals. To mapping and monitoring those areas with high biological occupation, could be very useful to have models of edaphic properties prepared from satellite images. In this approach, Deep Learning and Linear Regression models of soil properties and spectral indexes as explicative variables were performed. We training models of soil properties closely related to biological activity such as Dissolved Organic Carbon (DOC) and the iron fraction associated with organic matter (Fe). We tested the best approach to model the spatial distribution of DOC, Fe and pH by training models of Linear Regression and Deep Learning over Sentinel2 and WorldView2 images. The most robust models were used to track possible areas with ornithogenic soils as well as areas of the Byers Peninsula that could support the highest biological development.

This work introduces a new architecture for a time-domain feedback-based beamformer designed to meet real-time processing demands. The primary goal of this design is to locate reflective sources by estimating their direction of arrival (DOA) and signal range. Incorporating a feedback mechanism in this architecture is a unique aspect that refines localization precision. We conduct an in-depth analysis highlighting their respective benefits and limitations to compare the effectiveness of time-domain feedback beamforming against conventional time-domain methods. Our evaluation of the proposed architecture, based on critical performance indicators such as peak-to-sidelobe ratio, mainlobe width, and directivity factor, demonstrates its ability to improve beamformer effectiveness significantly.

We explores the hydrodynamical limit of a homogeneous electron gas, considering the interplay between the infrared limit and phenomenological hydrodynamics. Our study involves interactions generated by non-linear coordinate transformations. The focus begins with an analysis of non-linear coordinate transformations and their impact on normal modes in a harmonic system. The Lagrangian for a harmonic oscillator is used as an illustrative example, highlighting the role of position-dependent effective mass in preventing certain coordinate values. Moving beyond single degrees of freedom, we extend the discussion to a system with several harmonic degrees of freedom, introducing a collective variable. The effective dynamics of this collective variable are defined through a Lagrange multiplier term, emphasizing linearity in the description. Our study extends to the Current Two-Point function (CTP) formalism, introducing matrices and their inverses, such as $\hD$ and $\hD^{-1}$. Further, we delve into the dynamics of current in a homogeneous electron gas at finite density and zero temperature. Green's functions are generated using a functional integral approach, and the effective action is constructed via functional Legendre transformation. The quadratic part of the generator functional is expanded to derive the effective action, leading to the Maxwell equation and the subsequent elimination of the photon field. The resulting effective action for current dynamics is expressed in terms of the Current Two-Point function, paving the way for further exploration of the hydrodynamical aspects of the electron gas. Our study combines theoretical developments and mathematical formalism to provide insights into the hydrodynamical behavior of homogeneous electron gases.

We propose a theoretical method for the deterministic shaping of quantum light via photon number state selective interactions. Nonclassical states of light are an essential resource for high precision optical techniques that rely on photon correlations and noise reshaping. Notable techniques include quantum enhanced interferometry, ghost imaging, and generating fault tolerant codes for continuous variable optical quantum computing. We show that a class of nonlinear-optical resonators can transform many-photon wavefunctions to produce structured states of light with nonclassical noise statistics. The devices, based on parametric down conversion, utilize the Kerr effect to tune photon number dependent frequency matching, inducing photon number selective interactions. With a high amplitude coherent pump, the number selective interaction shapes the noise of a two-mode squeezed cavity state with minimal dephasing, illustrated with simulations. We specify the requisite material properties to build the device and highlight the remaining material degrees of freedom which offer flexible material design.

Polymer electrolyte was used as a medium for testing the performance of microband electrodes under conditions of linear diffusion. Cyclic voltammetry and chronoamperometry experiments were performed in such viscous medium, where diffusion rates are much slower than in fluid solutions. Confirmation of the existence of such conditions from the log i vs. log v or log i vs. log t relationships in the current equation always yielded values lower than the expected value of 0.5. This could indicate impure linear diffusion profile, i. e. some contribution from radial diffusion (edge effect). However, performing these tests in monomeric solvents of similar viscosities, such as glycerol or propylene glycol, gave the desired value of 0.5. These results lead to the conclusion that current equations which are based on Fick’s laws may not be applicable for polymer electrolytes, where various obstruction to diffusion make it a more complicated process than in monomeric solvents.

Rebar cages form the skeletal framework of reinforced concrete structural members. They comprise longitudinal and transverse reinforcing bars, usually connected by tie wires. Past studies have identified tie-wire connections as the "weak links" in large, prefabricated rebar cages, leading to their failure during site handling and construction stages. Recent research has explored the use of mechanical U-bolt connectors to bolster stability and safety of rebar cages while reducing their vulnerability and risk of failure. This paper presents a comprehensive experimental and numerical investigation of a new type of mechanical connector, referred to as "Cage Clamp", to enhance rebar cage stability and safety. Component-level experimental tests are conducted to determine the force-displacement response of Cage Clamp connectors for crossbar connections in different degrees of freedom. The results highlight the remarkable strength and stiffness of Cage Clamp connectors, significantly outperforming traditional tie-wire connections. Furthermore, full-scale experimental tests are performed on a circular underground pile-shaft rebar cage with Cage Clamp connectors to assess its behavior under various site handling conditions. The data obtained from these experiments are used to construct and refine detailed 3D finite element models of the rebar cages, capable of capturing the complex behavior of rebar cages with Cage Clamp connectors. Using the numerical model, a sensitivity analysis is performed to assess the effect of the number of Cage Clamps on the deflection and stability of the rebar cage. The findings show that using cage clamps to connect pick-up rebar with lateral reinforcement at every 8 to 10 feet is sufficient to ensure the stability of the cage during typical site handling conditions. The results of this study serve as a basis for establishing analysis, design, fabrication, and handling guidelines for rebar cages, contributing to safe and efficient construction practices.

We show that Universe inflation occurs when Einstein's gravity couples to nonlinear electromagnetic fields with cosmic stochastic magnetic fields background. Nonlinear electrodynamics with two parameters is used. The strength of magnetic fields to have the Universe inflation is obtained. It is shown that singularities of the energy density and pressure are absent for any scale factors. At large scale factors one arrives at equation of state for ultra-relativistic case. It is demonstrated that the curvature invariants do not have singularities. By computing the deceleration parameter we show that graceful exit takes place with reasonable e-folding number. The duration of Universe inflation as a function of model parameters is obtained. The classical stability and causality are analyzed by calculating the speed of the sound.

Over the last decades, an important number of regional and global Digital Elevation Models (DEMs) have been released publicly. As a consequence, researchers need to choose between several of these models to perform their studies and to use these DEMs as third-party data to compute derived products (e.g., for orthorectification). However, the comparison of DEMs is not trivial. For most quantitative comparisons, DEMs require to be expressed in the same Coordinate Reference System (CRS), sampled over the same grid (i.e., be at the same ground sampling distance with the same pixel-is-area or pixel-is-point convention), and with heights relative to the same Vertical Reference System (VRS). Thankfully, many open tools allow us to perform these transformations precisely and easily. Despite these rigorous transformations, local or global planimetric displacements may still be observed from one DEM to another. These displacements, or disparities, may lead to significant biases in comparisons of DEM elevations or derived products such as slope, aspect or curvature. Therefore, the control of DEM planimetric accuracy is certainly the most important task to perform at first before any comparison. This paper presents the disparity analysis method enhanced to achieve a sub-pixel accuracy, by interpolating the linear regression coefficients computed within an exploration window. This new method is significantly faster than oversampling the input data because it uses the correlation coefficients that have been already computed in the disparity analysis. To demonstrate the robustness of this algorithm, artificial displacements have been performed in a 11x11 grid with a 0.1-pixel step in both directions. The Copernicus DEM GLO-30 has been interpolated by a “classical” bicubic to achieve these 11x11 displacements. This validation method has been applied in four 10 km x 10 km DEMIX tiles showing different height distributions. Globally, this new sub-pixel accuracy method is robust. Artificial displacements have been retrieved with with typical errors (e_b) ranging from 12 to 20 % of the pixel size (worst case in Croatia).These errors in displacement retrievals are not constant in the 11x11 grid and the overall error E_b depends on the roughness (altimetry variations) encountered in the different tiles. The second idea of this paper is to assess the impact of the bicubic parameter (slope of the weight function at a distance d=1 of the interpolated point) on the accuracy of the displacement retrieval. By considering E_b as a quality indicator, tests have been performed in the four DEMIX tiles making the bicubic parameter vary between -1.5 and 0.0 by step of 0.1. For each DEMIX tile, the best bicubic (BBC) parameter b* is interpolated from the four E_b minimal values. This BBC parameter b* is low for flat areas (around -0.95) and higher in mountainous areas (around -0.75). The roughness indicator is the standard deviation of the slope norms computed from all the pixels of a tile. A logarithmic regression analysis performed between the roughness indicator and the BBC parameter b* computed in 67 DEMIX tiles shows a high correlation (r=0.717). The logarithmic regression formula estimating the BBC parameter from the roughness indicator is generic and may be applied to estimate the displacements between two different DEMs. This formula may also be used to set up a future Adaptative Best BiCubic (ABBC) that will estimate the local roughness in a sliding window to compute a local BBC.

Commuting is a vital travel channel for college students throughout their higher education career; nevertheless, excessive commute time negatively impacts students’ school satisfaction, academic achievement, health, and quality of life. Meanwhile, few studies have explored students’ commute time, covering a large population and scope. Therefore, this study analyzes the dwelling type that influences college and graduate students’ school commute times in the Seoul Metropolitan Area, using data from the 2016 Household Travel Diary Survey. This study uses spatial data on housing development to classify five dwelling types (i.e., new town, housing site development, Seoul, Incheon, and Gyeonggi-do). A multiple linear regression model empirically analyses students’ household and personal characteristics. The results reveal that dwelling type significantly affects students’ commute time. Specifically, Students living in Seoul have a shorter commute to school than those living in new towns. Socioeconomic characteristics have less effect on college and graduate students' school commute time. This study discusses the problem of excessive commuting of college and graduate students in new towns.

Online teaching is considered an important approach for achieving sustainable learning and education, and college teachers’ attitude and behavioral intention are essential for the sustainable adoption of online teaching practice in higher education institutions. To examine the influencing factors that sustain teachers’ attitude toward online teaching and behavioral intention, we conducted a cross-sectional study based on a sample of 1,102 college teachers in central China, using hierarchical linear regression analysis to explore possible influencing factors in four levels: individual experience, environmental support, self-perception, and technology acceptance. The study results show that the subjective norms, readiness, beliefs, and perceived usefulness of online teaching had a significant impact on teachers’ attitude toward online teaching and behavioral intention. Nevertheless, the effect varied with factors like online-teaching load and teachers’ technology self-efficacy, as their influence seemed to be singular, affecting the teachers’ attitude toward online teaching or behavioral intention exclusively. In contrast, previous online-teaching experience did not notably affect either. The findings of this study reveal the complex interactions of factors that influence college teachers’ disposition toward and decisions about online-teaching practices and emphasize the need for targeted strategies to maintain and enhance online education in the post-pandemic era.

Tail-sitters aim to combine the advantages of fixed-wing and rotor-craft, but demand a robust and fast stabilization strategy to perform vertical maneuvers and transitions to and from aerodynamic flight. The research conducted in this work intends to assess the performance of nonlinear control strategies to stabilize the attitude of a X-Vert VTOL aircraft when hovering, comparing existing solutions to applications of Nonlinear Dynamics Inversion (NDI) and its incremental version, INDI. Such controllers are implemented and tuned in simulation in order to stabilize a model of the tail-sitter , complemented by estimation methods that allow to feed back the necessary variables. These estimators and controllers are then implemented in a microcontroller, validating them in a Hardware-in-the-Loop (HITL) scenario, with simple maneuvers in vertical flight. Lastly, the developed control solutions are used to stabilize the aircraft in experimental flight, being monitored by a motion capture system. The experimental results allow to validate the model of the X-Vert and compare the effectiveness of the different control solutions in stabilizing it, with the INDI presenting itself as a more robust control strategy, with better tracking capabilities and less actuator demands.

In addition to their importance in statistical thermodynamics, probabilistic entropy measurements are crucial for understanding and analyzing complex systems, with diverse applications in time series and one-dimensional profiles. However, extending these methods to two- and three-dimensional data still requires further development. In this study, we present a new method to classify spatiotemporal processes based on entropy measurements. To test and validate the method, we selected four classes of similar processes related to the evolution of random patterns: dynamic colored noises ((i)~white and (ii)~red); (iii)~weak turbulence from reaction-diffusion; (iv)~hydrodynamic fully developed turbulence, and (v)~plasma turbulence from MHD. Considering seven possible ways to measure entropy from a matrix, we present the method as a parameter space composed of the two best separating measures of the five selected classes. The results highlight better combined performance of Shannon Permutation Entropy ($S^p_H$) and a new approach based on Tsallis Spectral Permutation Entropy ($S^s_q$). Notably, our observations reveal the segregation of reaction terms in this $S^p_H \times S^s_q$ space, a result that identifies specific sectors for each class of dynamic process, and can be used to train machine learning models for automatic classification of complex spatiotemporal patterns.

Remotely sensed data play a crucial role in monitoring the El-Niño/La-Niña Southern Oscillation (ENSO), which is an oceanic-atmospheric phenomenon occurring quasi-periodically with several impacts worldwide, such as specific biological and global climate responses. Since 1980, Earth has witnessed three strong ENSO events (1982–1983, This study aims, 2015-2016). In September 2022, La-Niña entered its third year and was unlikely to continue through 2023. Instead, since 2022 forecasts pointed to a transition from La-Nina to a Neutral phase in summer or late 2023. The onset of the El-Niño occurred around April 2023, and it is anticipated by sophisticated models to be a strong event through the Northern Hemisphere winter (December 2023 - February 2024). The aim of this study is to demonstrate the ability of the combination of two new methods to improve the accuracy of the above claim because El-Niño apart from climate anomalies, significantly impacts Earth’s ecosystems and human societies, regulating the spread of diseases by insects (e.g., malaria and dengue fever), and influencing nutrients, phytoplankton biomass, and primary productivity. This is done by exploring first the previous major El-Niño events in the period January 1876-July 2023. Our calculations show that the ongoing 2023-2024 El-Niño will not be the strongest.

The thick functionally graded material (FGM) circular cylindrical shells with advanced varied shear correction coefficient and third-order shear deformation theory (TSDT) under advanced thermal vibration are studied by the method of generalized differential quadrature (GDQ). The coefficient of displacement model of TSDT is applied to derive the equations of motion for the thick FGM circular cylindrical shells. The stiffness in simpler forms of thick FGM circular cylindrical shells and temperature rise in linear expression of the heat conduction equation are used. The differential equations in dynamic equilibrium state of thick FGM circular cylindrical shells can be obtained and rewritten into displacements and shear rotations in partial derivative expressions under dynamic thermal loads in partial derivative expressions. Parametric effect studies including advanced nonlinear varied shear correction coefficient, nonlinear coefficient c1 value, power law index and thermal temperature difference of external heating loads on the displacements and stresses of thick FGM cylindrical shells under thermal dynamic vibration are investigated.

This paper presents a mathematical modeling approach utilizing a fuzzy modeling framework for fixed wing aircraft systems with the goal of creating a highly desirable mathematical representation for model-based control design applications. The starting point is a mathematical model comprised of fifteen non-linear ordinary differential equations representing the dynamic and kinematic behavior applicable to a wide range of fixed wing aircraft systems. Here the proposed mathematical modeling framework is applied to the AIRBUS A310 model developed by ONERA. The proposed fuzzy modeling framework takes advantage of sector non-linearity techniquesto recast all the non-linear terms from the original model to a set of combined fuzzy rules. The result of this fuzzification is a more suitable mathematical description from the control system design point of view. Therefore, the combination of this fuzzy model and the wide range of control techniques available in the literature for such kind of models will enable us to avoid common control design methods, such as gain scheduling, where stability issues can be extremely challenging.

In this study, different configurations based on linear fiber lasers were proposed and experimentally demonstrated to measure the concentration of paracetamol liquid solutions in a range of 52.61 to 201.33 g/kg. The optical gain was provided by a commercial bidirectional Erbium-Doped Fiber Amplifier (EDFA) and the linear cavity was obtained using two commercial Fiber Bragg Gratings (FBGs). The main difference of each configuration was the coupling ratio of the optical coupler used to extract the system signal. The sensing head corresponded to a Single-Mode Fiber (SMF) tip that worked as an intensity sensor. The results reveal that, despite the optical coupler used (50:50, 60:40, 70:30 or 80:20), all the configurations reached the laser condition, however, the concentration sensing was only possible using a laser drive current near to the threshold value. The configurations using a 70:30 and an 80:20 optical coupler allowed to perform paracetamol concentration measurements with a higher sensitivity of (-3.00±0.24) pW/(g/kg). In terms of resolution, the highest value obtained was 1.75 g/kg, when it was extracted 20% of the output power to the linear cavity fiber laser configuration.

The goal of this article is to provide a review of the experimental techniques and procedures using vibration methods for the Structural Health Monitoring (SHM) of Polymer-Matrix Composites (PMC). It aims to be a guide for any researchers to carry out vibration experiments. The linear methods are first introduced. But as PMC is a complex material, these classic methods showed some limits, such as low accuracy for small damages, and a high environmental dependency. This is why the nonlinear methods are secondly studied, considering that the complexity of PMC induces a nonlinear behavior of the structure after damage occurrence. The different damage mechanisms are well explained in order to evaluate the potential of each vibration method to detect them.

Non-Linear Simulation by Harmonic Balance Techniques of Load Modulated Power Amplifier Driven by Random Modulated Signals. Comparison with measured results.

In this paper we address the approximation of the coupling problem for the wave equation and Maxwell's equations of electromagnetism in the time domain in terms of the electric field, by means of a nodal linear finite-element discretization in space, combined with a classical'explicit finite-difference scheme for the time discretization. Our study applies to the particular case where the dielectric permittivity has a constant value outside a sub-domain, whose closure does not intersect the boundary of the domain where the problem is defined. Inside this sub-domain Maxwell's equations hold. Outside this sub-domain the wave equation holds, which may correspond to the Maxwell's equations with a constant permittivity under certain conditions. We consider as a model the case of first order absorbing boundary conditions. Optimal error estimates that hold in natural norms under reasonable assumptions are given, among which lies a typical CFL condition for hyperbolic equations.

Electrospun fiber scaffolds are widely used in small diameter vascular tissue engineering because they mimick organizational structure and biological function of natural extracellular matrix. However, there is still one problem of low patency rate in the long term. The main reasons are the mismatch of compliance and the easy formation of thrombus. Therefore, it is very important to promote the rapid endothelialization of small diameter tissue engineering blood vessels by regulating the topological structure and biological properties of electrospun fiber scaffolds. Firstly, crimped polylactic acid (PLA) fibers were prepared by heat treatment to mimick the crimped structure and nonlinear mechanical properties of the elastic membrane of blood vessel wall. It improved effectively the aspect ratio of human umbilical vein endothelial cells (HUVECs) and promoted lateral alignment and growth. Then, crimped PLA fibers with three levels of pore structure were prepared by thermal induced phase separation, vapor induced phase separation and laser ablation to enhance the degree of HUVECs infiltrarion and realize patterned cell growth. Crimped PLA fibers with three levels of pore structure promote rapid endothelialization of blood vessels, which is of great significance to achieve long term patency rate of small diameter tissue engineering blood vessels.

Building energy demand impacts a myriad of interconnected economic, societal, and environmental aspects. As a result, Buildings Energy Models (BEM) play an important role in the process of urban design and planning. While previous studies have investigated the effects of building interventions on energy efficiency, their applicability may be limited due to the BEM’s high computational complexity. This limits their ability to systematically study important aspects of energy demand on a large scale. The development of Machine Learning Models (MLM) allows to design the required detailed analysis and solutions, while reducing the computational burden, making MLM attractive for urban designers. The capability of MLM to generalize well for multiple contexts (in our case, multiple buildings) is a crucial contributor to their applicability. However, the validation process in a wider context is often overlooked, therefore its generalization capabilities are not quantified. In this paper, we present a framework to train and validate a surrogate model derived from a physics-based BEM. Our method employs a Multiple Linear Regression model to predict Energy Use Intensity (EUI) for office buildings in Singapore using 36 input parameters (covariates), based on a training dataset of 23,000 samples. Model validation is performed by comparing the results of the Surrogate Model (SM) to a widely used BEM for a sample of 120 buildings. Our results indicate that the SM has an accuracy of NRMSE of 13%, NMBE of −3.56%, and R2 of 0.92, which suggests it can effectively and accurately predict building EUI. We also conduct a sensitivity analysis, which indicates that the parameters associated with internal loads and internal space usage are the most influential. Additionally, we present a reduced order model trained with only the 11 most influential parameters, which exhibits negligible loss in accuracy compared to the full SM while providing reduced complexity. Finally, we demonstrate an application of our SM to evaluate energy efficiency under uncertainty scenarios. The analytically derived results indicate a potential reduction of EUI of offices in Singapore from 227kWh/m2 to 99kWh/m2 by altering the building parameters that were identified as most influential.

This paper introduces an innovative nanotechnology-based approach that provides a pathway to enhance the energy release efficiency of nanoenergetic materials (nEMs) by harnessing self-synchronized collective atomic vibrations and phonon wave resonance within the transition domains between nanocomponents, without altering the material composition. The key innovation involves incorporating finely-tuned 2D-ordered linear-chain carbon-based multilayer nano-enhanced interfaces as programmable nanodevices into the transition domains using advanced multistage processing and assembly techniques. These programmable nanodevices enable precise control over self-synchronized collective atomic vibrations and phonon wave propagation, leading to synergistic effects. To activate and optimize these effects, a combination of various methods is employed, including energy-driven initiation of allotropic phase transformations, surface acoustic wave-assisted micro/nano-manipulation, heteroatom doping, directed self-assembly using high-frequency electromagnetic fields, and data-driven inverse design approaches. By leveraging a data-driven inverse design strategy and uncovering hidden structure-property relationships, we maximize energy release efficiency using the carbon nano-materials genome approach derived from multifactorial neural network-based predictive models. This approach not only unlocks new functionalities in nEMs but also improves environmental performance and safety levels. By pioneering transformative pathways for nEMs through harnessing phonon wave resonance in low-dimensional nanocarbon transition interfaces, this research brings significant advancements in the field.

In this paper, we consider an epidemiological Susceptible-Infected-Susceptible (SIS) model in which the individuals cured from the infection return back into the group of people endangered by the infection. Delay differential equations were introduced to create more realistic models since many processes depend on past history. Many different mathematical methods, including the Susceptible-Infected-Recovered (SIR) model as well as derivatives thereof, can be used to prognose the spread of many various infectious diseases, including Covid-19.We use a nonlinear differential system with time delay as a mathematical formulation of this model. It is examined by the existence of a positive solution which is bounded by two functions $k_1, k_2\in C([t_0,\infty),(0,\infty))$ with constants $\lambda_1 > 0,\,\lambda_2 > 0$ where $0<\lambda_1\leq \lambda_2$. The conditions are put in place for existence of a positive solution that approaches zero in infinity, if $t\to\infty$. Infectious diseases accompany a person throughout their entire life, and in the history of mankind often appeared in frequent epidemics caused high mortality. The occurrence of infectious diseases in the population represents a serious health, social and economic problem. There is a lot of ambiguity concerning the time span and final spread of the epidemic thus making it very demanding for the governing bodies, healthcare institutions, and economic sector to precisely judge the future development.Several examples are shown at the end of this paper.

In the discussion on environmental policies, the notion of eco-efficiency is often used. Eco-efficiency is defined as the delivery of products and services with competitive values, while reducing the ecological impacts and satisfying human needs. In an environment of great competitiveness in which the companies operate, the improvements in the productive process is one of the differentiating factors for guaranteeing a strong competition. Also it is essential rationalizing energy consumption and natural resources. For this it is necessary to understand the main operations and dynamics of the company. This work presents an empirical study of a Portuguese company in the industrial sector. The problematic here presented is based on the company’s growing concern to reduce the amount of scrap produced. From the literature research that was performed, a strong dependence relation between the different variables in the extrusion process was found. The main objective of this work is to model the aluminium extrusion process, with the aim of minimizing the production of scrap. For this several variables involved in the process are taking into account. Using statistical techniques, in particular multiple linear regressions, it was possible to identify the importance of the variables under study for the scrap production.

To study the coupling mechanism and dynamic response of the end-face movable gear trans-mission system under complex excitation, a specific configuration of end-meshing movable gear reduction mechanism was used to achieve predetermined rigid thrust transmission and mis-matched gear meshing functions, which solved the inherent defects of traditional harmonic gear mechanism thin-wall flexible wheel easy to be damaged by fatigue. Considering the phenomenon of elastic deformation of live teeth accompanied by significant changes in meshing characteristics in the transmission process of end-meshing harmonic reducer, the influence of dynamic meshing parameters, live tooth deformation, time-varying stiffness of tooth meshing, and time-varying backlash on nonlinear dynamic performance was explored, as well as the mechanism of mul-ti-parameter coupling on transmission performance. The nonlinear dynamics model of the end-meshing harmonic reducer is established to solve the chattering prediction problem. Finally, a comprehensive test bed for the transmission system of harmonic reducer with meshing type with adjustable characteristic end was built to verify the correctness of the theoretical model and provide the theoretical and technical basis for exploring the optimal parameter selection of pas-sive vibration suppression problem.

The exceptional performance of graphene has driven the advancement of its preparation technique and application. Laser-induced graphene (LIG), as a novel graphene preparation technique, has been applied in various fields. Graphene periodic structures created by LIG technique exhibit superhydrophobic characteristics and can be used for deicing and anti-icing applications, which are significantly influenced by the laser parameters. The laser surface treatment process was simulated by a finite element software analysis (COMSOL Multiphysics) to optimize the scanning parameter range, and the linear array surface structure were subsequently fabricated by the LIG technique. The generation of graphene was confirmed by Raman spectroscopy, and energy-dispersive X-ray spectroscopy. The periodic linear array structure were observed by Scanning electron microscopy (SEM) and confocal laser imaging (CLSM). In addition, CLSM testings, contact angle measurements, and delayed icing experiments were systematically performed to investigate the effect of scanning speed on surface hydrophobicity. The results show that the high quality and uniform graphene can be achieved using the laser scanning speed of 125 mm/s. The periodic linear array structures can obviously increase the contact angle and suppress delayed icing. Furthermore, these structures have the enhanced ability of the electric heating deicing, which can reach 100°C and 240°C within 15 s and within 60 s under the DC voltage power supply ranging from 3 to 7 V, respectively. These results indicate that the LIG technique can be developed to provide an efficient, economical, and convenient approach for preparing graphene and the hydrophobic surface array structure based on LIG has considerable potential for deicing and anti-icing applications.

To identify the exchange coefficients of a nonlinear polynomial tricompartmental general system of α+β , we follow the procedure; firstly, the recommended solution is to introduce an adequate time t*&gt;0 in a determinable manner. That is, after injecting quantity a into the main compartment, wait a moment for the exchange in the polynomial α+β order nonlinear general system to settle, and then compare this compartment to compartment 2 at t*. Secondly, applying the Taylor formula will linearize the system and identify the exchange coefficients. Finally, we will prove that the linearization method is stable.

Abdominal aortic aneurysm (AAA) is a chronic disease in which the abdominal aorta expands until it ruptures. AAA incidence: 10 million/year (India), deaths: 40%-90% (13th leading cause of death in the USA). Current treatment methods make diagnosis difficult due to the lack of noticeable symptoms and inaccurately planned operations. Rupture Scope is a mathematical model to dramatically reduce AAA deaths and improve treatment efficiency. Using a case-specific replica/simulation of real-time abdominal aortic blood flow for monitoring without frequent imaging scans and a novel derived mathematical linear regression model to predict rupture date and expansion rate with an overall accuracy of 95.64%.

Carbon fiber reinforced polymer (CFRP) bending structure is widely used in the aviation field. The occurrence and propagation of delamination damage will reduce the safety of in-service bending structures. As a detection tool with high damage sensitivity, Lamb wave can effectively identify delamination damage. In this study, the signal difference coefficient (SDC) was introduced to quantify delamination damage and evaluate the sensitivity of A0 and S0 mode lamb waves to delamination damage. The simulation results show that compared with the S0 mode Lamb wave, the A0 mode Lamb wave exhibits higher delamination damage sensitivity. The delamination damage can be quantified based on the strong correlation between the SDC and the delamination damage size. The control effect of the linear array PZT phase time-delay method on Lamb wave mode was investigated by simulation. The phase time-delay method realizes the generation of a single-mode Lamb wave, which can separately excite the A0 mode and S0 mode Lamb wave to identify delamination damage of different sizes. The A0 mode Lamb wave was excited by the developed one-dimensional linear comb transducer (LCT), which was used to conduct the detection experiment on the CFRP bending plate with delamination damage sizes of Φ6.0 mm, Φ10.0 mm, and Φ15.0 mm. The experimental results verify the correctness of the simulation. According to the Hermite interpolation results of the finite-element simulation data, the relationship between the delamination damage size and the SDC was fitted by the Gaussian function, which can accurately quantify the delamination damage. The absolute error of the delamination damage quantification with fitting expression is not larger than 0.8 mm, and the percentage error is not more than 8%.

Vectorial Boolean functions and codes are closely related, and each corresponding domain gives been to each other. On the one hand, various requirements of binary linear codes are needed for their theatrical interests but, more importantly, for their practical applicants (such as few-weight codes or minimal codes for secret sharing, locally recoverable codes for storage, etc.). On the other hand, various criteria and tables have been introduced to analyse the security of S-boxes that are related to vectorial Boolean functions, such as the Differential Distribution Table (DDT), the Boomerang Connectivity Table (BCT), and the Differential-Linear Connectivity Table (DLCT). In previous years, two new tables have been proposed for which the literature was pretty abundant: the $c$-DDT to extend the DDT and the $c$-BCT to extend the BCT. In the same vein, we propose extended concepts to study further the security of vectorial Boolean functions, especially the $c$-Walsh transform, the $c$-autocorrelation, and the $c$-differential-linear uniformity, and its accompanying table, the $c$-Differential-Linear Connectivity Table ($c$-DLCT). We study these properties of the novel functions at their optimal level concerning these concepts and describe the $c$-DLCT of the crucial inverse vectorial (Boolean) function case. Finally, the derived functions could lead to new families of binary minimal codes, as the recent achievements on minimal codes from low differential uniformity. We draw new avenues for future research toward linear code designs.

In wireless sensor networks (WSNs) deployed in smart agriculture systems, accurately determining the locations of sensor nodes is crucial for efficient monitoring and control. However, in many cases, the exact positions of certain sensor nodes may be unknown. To address this challenge, this paper presents a novel method for localizing unknown sensor nodes in WSN-based smart agriculture systems using range measurements. The proposed method utilizes the Levenberg-Marquardt optimization algorithm to solve a nonlinear least squares problem and minimize the error in estimating the unknown node locations. By leveraging the known positions of a subset of sensor nodes and the inexact distance measurements between pairs of nodes, the localization problem is transformed into a nonlinear optimization problem. To validate the effectiveness of the approach, extensive simulations and experiments were conducted. The results demonstrate that the proposed method achieves accurate localization of the unknown sensor nodes, effectively enhancing the overall performance of the WSN-based smart agriculture system. Furthermore, the method demonstrates robustness against measurement noise and scalability for large-scale networks. The practical implications of this research extend beyond smart agriculture systems, as the proposed method can be applied to various WSN applications where precise node localization is essential.

The design of thin-walled structures is commonly based on the solutions of linear boundary-valued problems, formulated within well-developed theories for elastic plates and shells. However, in modern appliances, especially in MEMS design, it is necessary to take into account non-linear mechanical effects that become decisive for flexible elements. Among substantial non-linear effects, that significantly change the deformation properties of thin plates, are the effects of residual stresses caused by incompatibility of deformations, which inevitably arise during the manufacture of ultra-thin elements. The development of new methods of mathematical modeling of residual stresses and incompatible finite deformations in plates is the subject of the paper. To this end the local unloading hypothesis is used. It makes possible to define smooth fields of local deformations (inverse implant field) for the mathematical formalization of incompatibility. The main outcomes are field equations, natural boundary conditions and conservation laws, derived from least action principle and variational symmetries with account of implant field. The derivations were carried out in the framework of elasticity theory for simple materials and, over and above, within the Cosserat’s theory of a two-dimensional continuum. As illustrative examples the distributions of incompatible deformations in a circular plate are considered.

The influence of applied loads on free vibrations analysis of plates and shells panels made of functionally graded materials is analyzed in the present work. Formulations for the static analysis considering geometrically nonlinear behavior, as well as linear buckling and free vibrations analyses are considered. The calculation of the through-thickness stress distribution is also performed. A finite element model based on a higher order shear deformation theory and using a non-conforming triangular flat plate/shell element with 3 nodes, and 8 degrees of freedom per node is used in the numerical implementation. The results obtained with this numerical model are presented, discussed, and compared with alternative solutions published by other authors in some benchmark applications.

This article presents a concise survey of basic discrete and semi-discrete nonlinear models which produce two- and three-dimensional (2D and 3D) solitons, and a summary of main theoretical and experimental results obtained for such solitons. The models are based on the discrete nonlinear Schrödinger (DNLS) equations and their generalizations, such as a system of discrete Gross-Pitaevskii (GP) equations with the Lee-Huang-Yang corrections, the 2D Salerno model (SM), DNLS equations with long-range dipole-dipole and quadrupole-quadrupole interactions, a system of coupled discrete equations for the second-harmonic generation with the quadratic (χ⁽²⁾) nonlinearity, a 2D DNLS equation with a superlattice modulation opening mini-gaps, a discretized NLS equation with rotation, a DNLS coupler and its PT-symmetric version, a system of DNLS equations for the spin-orbit-coupled (SOC) binary Bose-Einstein condensate, and others. The article presents a review of basic species of multidimensional discrete modes, including fundamental and vortex solitons, their bound states, gap solitons populating mini-gaps, symmetric and asymmetric solitons in the conservative and PT-symmetric couplers, cuspons in the 2D SM, discrete SOC solitons of the semi-vortex and mixed-mode types, 3D discrete skyrmions, and some others.

The R23Cu7Mg4 (R = Ca, Eu) intermetallics, studied by single crystal X-ray diffraction, were found to be isostructural with the Yb23Cu7Mg4 prototype (hP68, k4h2fca, space group P63/mmc), forming a small group inside the bigger 23:7:4 family, otherwise adopting the hP68-Pr23Ir7Mg4 crystal structure. The observed structural peculiarity is connected with the divalent character of the R component and with a noticeable volume contraction, resulting in a clear clustering of title compounds inside the whole 23:7:4 family. The occurrence of fragments typical of similar compounds, particularly Cu-centered trigonal prisms and Mg-centered core-shell polyicosahedral clusters with R at vertices, induced the search of significant structural relationships. In this work, a description of the hexagonal crystal structure of the studied compounds is proposed as a linear intergrowth along the c-direction of the two types of slabs R10CuMg3 (parent type: hP28-kh2ca, SG 194) and R13Cu6Mg (parent type: hR60-b6a2, SG 160). The ratio of these slabs in the studied structure is 2:2 per unit cell, corresponding to the simple equation 2XR10CuMg3 + 2XR13Cu6Mg = 2XR23Cu7Mg4. This description assimilates the studied compounds to the (Ca,Eu,Yb)4CuMg ones, where the same slabs (of p3m1 layer symmetry) are stacked in a different way/ratio, and constitutes a further step towards a structural generalization of R-rich ternary intermetallics.

Reservoir computing (RC) systems can efficiently forecast chaotic time series using nonlinear dynamical properties of an artificial neural network of random connections. The versatility of RC systems has motivated further research on both hardware counterparts of traditional RC algorithms and more efficient RC-like schemes. Inspired by the nonlinear processes in a living biological brain and using solitary waves excited on the surface of a flowing liquid film, in this paper we experimentally validate a physical RC system that substitutes the effect of randomness for a nonlinear transformation of input data. Carrying out all operations using a microcontroller with a minimal computational power, we demonstrate that the so-designed RC system serves as a technically simple hardware counterpart to the `next-generation’ improvement of the traditional RC algorithm.

A robust explicit model predictive control (EMPC)-based frequency adaptive grid voltage sensorless control is developed for a grid-connected inverter (GCI) via a linear matrix inequality (LMI) approach under the model parameter uncertainties and non-ideal grid environment. The control scheme is achieved by an enhanced prediction model rather than the conventional prediction model provided by fixed parameters to maintain the quality of grid currents injected into the grid when the model parameters are varied. Furthermore, an LMI-based observer is integrated with the disturbance observer to improve the reference tracking performance and reject disturbances. The proposed observer is employed for the grid frequency adaptive control without need of grid voltage sensors. The proposed current controller and observer employ the LMI scheme to maintain a stable and robust operation of the GCI. The discrete-time frequency response and pole-zero map analyses are used to investigate system stability and robustness against parameter uncertainties. Comprehensive simulation, experimental results and analyses clearly demonstrate the robustness of the proposed control scheme under various adverse test conditions with unexpected grid and system uncertainties.

In this paper, we present a three-step sixth-order iterative schemes to estimate the solutions of a nonlinear systems of equations, for predicting the shear strength of a reinforced concrete beam. This procedure is designed by means of a weight function technique. The values for the parameters of this system were randomly selected inside the prescribed ranges by technical standards for structural concrete; moreover, some of this parameters were fixed taking into consideration the solvability region of the adopted steel constitutive model. The efficiency of the new class is compared with other current schemes, with very good results.

This paper investigates reachable set estimation and state-feedback controller design for linear time-delay control system with bounded disturbances. First, by constructing an appropriate Lyapunov-Krasovskii functional, we obtained a delay-dependent condition, which determed the admissible bounding ellipsoid for the reachable set of the system we considered. Then, a sufficient condition in form of liner matrix inequalities is given to solve the problem of controller design with reachable set estimation. Finally, by minimizing the volume of the ellipsoid and solving the liner matrix inequality, we obtain the desired ellipsoid and controller gain. A comparative numerical example is given to verify the usefulness of our result.

Power sources that can consistently deliver high levels of energy over extended periods are crucial for various space applications. Among the many methods of energy generation, direct heat-to-electricity conversion without intermediate steps or moving components shows particular promise but also presents significant challenges. The aim of this research is to address these challenges by enhancing the energy efficiency of thermionic conversion, which transforms thermal energy into electrical energy, through the development and utilization of a novel class of emission nanomaterials known as multilayer carbyne-enriched 3D-shaped nano-interfaces. By manipulating the topological, physicochemical, and functional characteristics of these interfaces, we seek to optimize their thermionic conversion capabilities. Building on the recent discovery of collective atomic vibrations called phonon waves within transition domains of multilayer nanostructures, we have devised a new approach to enhance the efficiency of thermionic energy converters. This involves unlocking the predictive functionality of 2D-ordered linear-chain carbon-based multilayer emitters through the excitation and fine-tuning of collective atomic vibrations and nanoarchitecture. To achieve this, we propose employing a combination of techniques that leverage interface effects, enable phonon wave propagation, facilitate energy exchange, and capitalize on synergistic effects offered by the multilayer nano-enhanced interfaces. The resulting devices for thermionic energy conversion have the potential to significantly surpass the efficiency of existing plasma thermionic converters by several orders of magnitude. Moreover, these electricity-generating sources based on thermionic conversion represent fundamental options for the advancement of Lunar and Martian research missions, opening up possibilities for sustainable energy production in extraterrestrial environments.

The presence of escaped fish in aquaculture facilities as a result of harsh meteorological conditions (more pressing in a face of climate change) requires a better understanding of these dynamical behaviour through vigilant monitoring and validated numerical models. In this context, data from strain, stress sensors as well as meteorological and current sensors installed at an aquaculture farm in the Region of Murcia (Spain) were collected, processed and analysed. Among them, first results about the relationship between load and currents sensors are presented. Due to the complexity of the time series, various analyses were conducted to examine their interrelation, encompassing regression analysis of raw data and data segmented into different time intervals. Through this analysis, it was observed that employing distinct time windows better elucidated the data variability. Furthermore, an optimal data window of 240 data was identified, demonstrating significantly improved explanatory power, with the coefficient of determination (R2) increasing by approximately 0.8 depending on the section. This pave the way for optimizing the monitoring features that must be carried out to relate cause-and-effect variables in the behaviour of these off-shore infrastructures.

The traditional receiver employs scalar tracking loops, resulting in degraded navigation performance in weak signal and high dynamic scenarios. An innovative design of a vector tracking receiver based on nonlinear Kalman filter (KF) tracking loops is proposed in this paper, which combines the strengths of both vector tracking and KF tracking loops. Firstly, a comprehensive description of the vector tracking receiver model is presented, and unscented Kalman filter (UKF) is applied to nonlinear tracking loop. Secondly, to enhance the stability and robustness of the KF tracking loop, we introduce square root filtering and an adaptive mechanism. The tracking loop based on square root UKF (SRUKF) can dynamically adjust its filtering parameters based on signal noise and feedback Doppler error. Finally, the proposed method is implemented on a software-defined receiver (SDR), and the field vehicle experiment demonstrates the superiority of this method over other receivers in complex dynamic environments.

: Low-temperature growth of diamond films by chemical vapor deposition (CVD) method is not so widely reported and especially its initial periods of nucleation and growth phenomenon are of particular interest to the researchers. Four sets of substrates were selected for growing diamond films by linear antenna microwave plasma enhanced CVD (LA-MPCVD). Among them, silicon and sapphire substrates were pre-treated with detonation nanodiamond (DND) seeds before diamond growth for enhancement of its nucleation. On the other hand, carbon nanotube (CNT) films on Si substrates were also used as another template for LA-MPCVD diamond growth. In order to enhance the diamond nucleation during CVD growth, some of the CNT films were again pre-treated by electrophoretic deposition (EPD) of diamond nanoparticles. All these substrates were then put inside the LA-MPCVD chamber for growing diamond films under variable processing conditions. Microwave input powers (1100 – 2800 W), input power modes (pulse or continuous), antenna to stage distances (5 - 6.5 cm), process gas recipes (with or without CO2), methane gas percentages (3 - 5%), deposition times (11 – 120 minutes) were altered to investigate their effect on the growth of diamond film on the pre-treated substrates. The substrate temperatures were found to vary from as low as 170oC to a maximum of 307oC during the alteration of the different processing parameters. Contrary to the conventional MPCVD, it was observed that during the first hour of LA-MPCVD diamond growth, DND seeds or the nucleating structures, do not coalesce together to make a continuous film. Deposition time was the most critical factor in fully covering the substrate surfaces with diamond film, since the substrate temperature could not become stable during the first hour of LA-MPCVD. CNT was found to be oxidised rapidly under LA-MPCVD plasma conditions; therefore, a CO2-free process gas recipe was used to reduce CNT burning. Moreover, EPD-coated CNT was found to be less oxidised by the LACVD plasma during diamond growth.

We consider an autonomous heat engine in simultaneous contact with a hot and a cold reservoir, and described within a linear-irreversible framework. In the tight-coupling approximation, the rate of entropy generation is effectively written in terms of a single thermal flux which is a homogeneous function of the hot and cold fluxes. The specific algebraic forms of the effective flux are deduced in scenarios containing internal and external irreversibilities for the typical example of a thermoelectric generator.

In this paper, a swarm trajectory planning method is proposed for multiple autonomous surface vehicles (ASVs) in an unknown and obstacle-rich environment. Specifically, based on the point cloud information of the surrounding environment obtained from local sensors, a kinodynamic path searching method is used to generate a series of waypoints in the discretized control space at first. Next, after fitting B-spline curves to the obtained waypoints, a nonlinear optimization problem is formulated to optimize the B-spline curves based on gradient-based local planning. Finally, a numerical optimization method is used to solve the optimization problems in real-time to obtain collision-free, smooth and dynamically feasible trajectories relying on a shared network. Simulation results demonstrate the effectiveness and efficiency of the proposed swarm trajectory planning method for a network of ASVs.

The susceptible-infected-recovered/removed-vaccinated (SIRV) epidemics model is an important generalization of the SIR epidemics model as it accounts quantitatively for the effects of vaccination campaigns on the temporal evolution of epidemics outbreaks. Additional to the time-dependent infection ($a(t)$) and recovery ($\mu (t)$) rates, regulating the transitions between the compartments $S\to I$ and $I\to R$, respectively, the time-dependent vaccination rate $v(t)$ accounts for the transition between the compartments $S\to V$ of susceptible to vaccinated fractions. An accurate analytical approximation is derived for arbitrary and different temporal dependencies of the rates which is valid for all times after the start of the epidemics for which the cumulative fraction of new infections $J(t)\ll 1$. As vaccination campaigns automatically reduce the rate of new infections by transferring susceptible to vaccinated persons, the limit $J(t)\ll 1$ is even better fulfilled than in the SIR-epidemics model. The comparison of the analytical approximation for the temporal dependence of the rate of new infections $\jt(t)=a(t)S(t)I(t)$, the corresponding cumulative fraction $J(t)$, and $V(t)$, respectively, with the exact numerical solution of the SIRV-equations for different illustrative examples proves the accuracy of our approach. The considered illustrative examples include the cases of stationary ratios with a delayed start of vaccinations, and an oscillating ratio of recovery to infection rate with a delayed vaccination at constant rate. The proposed analytical approximation is self-regulating as the final analytical expression for the cumulative fraction $\jinf $ after infinite time allows us to check the validity of the original assumption $J(t)\le \jinf \ll 1$.

Stratified Taylor Couette Flow (STCF) undergoes transient growth. Recent studies have shown that there exists transient amplification in the linear regime of counter-rotating STCF. It is reported that as Gr increases, the maximum amplification factor ($G_0$) initially decays before it eventually starts growing after reaching a certain critical value Gr$_{c}$. Assuming other parameters of the model are kept constant, the value Gr$_{c}$ changes with respect to different speed ratios of the cylinders. The observed decay/growth pattern of $G_0$ is attributed to the interplay between the induced shear and buoyancy. In this study, the mechanism that triggers this observed pattern is investigated. The kinetic budget of the optimal transient perturbation is analysed numerically to simulate the interaction of the shear production (SP), buoyancy production (BP) and other energy components that contributes to the total optimal transient kinetic energy. These contributions affect the total energy by influencing the perturbation to extract kinetic energy (KE) from the mean flow. The decay of $G_0$ resulted from the positive amplification of both BP and SP, while the growth is attributed to the negative and positive amplification of BP and SP, respectively. The optimal SP is positively amplified, implying that there is the possibility of constant linear growth. These findings agree with the linear growth rate for increasing values of Gr.

The Spearman rank correlation coefficient is a non-parametric (distribution-free) rank statistic proposed by Charles Spearman as a measure of the strength of the relationship between two variables. It is a measure of a monotonic relationship that is used when the distribution of the data makes Pearson's correlation coefficient undesirable or misleading. The Spearman coefficient is not a measure of the linear relationship between two variables. It assesses how well an arbitrary monotonic function can describe the relationship between two variables, without making any assumptions about the frequency distribution of the variables. Unlike Pearson's product-moment (linear) correlation coefficient, it does not require the assumption that the relationship between variables is linear, nor does it require that the variables be measured on interval scales; it can be applied to variables measured at the ordinal level. The purpose of this study is to compare the values of Pearson's product-moment correlation coefficient (treating the data in a quantitative way) and Spearman's rank correlation coefficient (treating the same data in a somewhat "qualitative" way) and their statistical significance for six Pinus sylvestris L. traits (original – for Pearson's coefficient and ranked – for Spearman's coefficient) estimated from all observations, object means (for trees) and medians. The results show that the linear and rank correlation coefficients are consistent (as to direction and strength). In cases of divergence in the direction of correlation, the correlation coefficients were not statistically significant, which does not imply consistency in decision-making. Estimation of correlation coefficients based on medians is robust to outlier observations and factors that linear correlation is then very similar to rank correlation.

Recent studies have shown that the mechanical properties of bioinspired periodic composite materials can be strongly influenced by finite deformation effects, leading to highly nonlinear static and dynamic behaviors at multiple length scales. For instance, in porous periodic nacre-like microstructures, microscopic and macroscopic instabilities may occur for a given uniaxial loading process and, as a consequence, wave attenuation properties may evolve as a function of the microstructural evolution, giving it the designation of metamaterials. The numerical outcomes provide new opportunities to design bioinspired soft composite metamaterials characterized by high deformability and enhanced elastic wave attenuation capabilities given by the insertion of voids and lead cores.

We demonstrate a method for realization of highly nonlinear optical 4-(4-dimethylaminostyryl)-1-methylpyridinium tosylate (DAST) two-dimensional structures by a double step technique. The desired polymeric structures have been first fabricated by using the multiple-exposure of two-beam interference technique, and the DAST nanoscrystals were then prepared inside the air-voids of these photoresist templates, resulting in nonlinear periodic structures. The nonlinear properties were characterized by optical and scanning microscopies, as well as by second-harmonic generation technique. This nonlinear modulation is very promising for the enhancement nonlinear conversion rates, such as terahertz generation, by using the quasi-phase matching technique.

The study’s objective is to analyse the mechanical properties of steel pipe piles as a part of a trestle bridge subjected to five years of natural marine corrosion degradation. Sixteen tensile specimens were extracted from the steel pipe piles in the splash, tidal, and immersion zones. The experimental tensile test results are used to establish regression equations defining elastic modulus, yield strength, strain hardening index, and strength coefficient for the true stress-strain curves of the three regions. A non-linear time-dependent mathematical model is exploited to identify the corrosion degradation using the data from one single corrosion degradation measurement campaign. The analysis indicated that the splash zone experiences the most severe corrosion degradation, and there are progressive losses in the mechanical properties of each zone as the corrosion degradation progresses. The established relationships of the mechanical properties, as a function of the ratio of corroded plate thickness to the as-built one, can be used as a fast-engineering approach to identify the mechanical properties of severely corroded piles. The corrosion degradation allowance is also defined using the First Order Reliability Method, accounting for existing uncertainties covered by the partial safety factors. By examining the impact of marine corrosion on the mechanical properties of marine structures and developing predictive models to assess the corrosion’s effect on material strength and corrosion allowance, the study aims to improve offshore structures’ safety, design, and maintenance.

This paper provides a proof of concept for a linear electric generator that can be used to harvest energy from various sources of linear motion, such as vibrations, free-piston engines and wave energy. The generator can be used to power small electronic devices, such as sensors, or charge household batteries. Literature was reviewed to develop an understanding about the applications, control methods, excitation methods and mechanics of rotating and linear electric machines. A bidirectional, two-sided linear machine was designed with two stator cores and a single mover core. The stator windings and mover winding can be independently excited, allowing for three modes: no mover excitation, DC excited mover, and AC excited mover. Simulations results showed that the magnetic flux generated by DC excited stator cores were concentrated in the centre of the mover core. The use of two stator cores eliminates lateral flux in the mover core when it is not excited, minimising attraction and repulsion forces. Parametric analysis showed that flux cutting occurred in all operation modes, verifying that the generator will produce power when operating. Hardware tests produced an output current when the machine is electrically and mechanically excited, verifying the proposed design.

The Langmuir isotherm is a widely used model for analyzing adsorption equilibrium data. This study evaluated the efficiency and accuracy of all four linear forms of the Langmuir isotherm and its non-linear form using 67 experimental data sets selected from the literature. The results showed that only if all four linear forms simultaneously show high accuracy, then the non-linear form also shows high accuracy, and therefore it can be said that the process probably follows the Langmuir isotherm. On the contrary, when at least one of the four linear forms of the Langmuir isotherm has low accuracy, it means that the non-linear form also has low accuracy, and it can be concluded that this process does not follow the Langmuir isotherm. This research suggests that all four linear forms of the Langmuir isotherm should be evaluated simultaneously to conclude whether the studied system follows the Langmuir isotherm or not. In other words, relying on only one of the four linear forms of the Langmuir isotherm to model adsorption and calculate the Langmuir constant and maximum adsorption capacity is an incomplete approach, contrary to the conventional approach.

In this paper, experimental results about the performance of a Takagi-Sugeno Fuzzy Controller (TSFC) for an EV3 Ballbot Robotic System (EV3BRS) are reported. The physical configuration for the EV3BRS has the form of an inverted pendulum mounted on a ball. The EV3BRS is an underactuated robotic system with four outputs and two control torques. The Takagi-Sugeno Fuzzy Model (TSFM) design comes from linearization of the nonlinear model around two operation points near from the upright position of the EV3BRS's body. The Parallel Distributed Compensation (PDC) approach is used to the design of the TSFC. The Linear Matrix Inequalities (LMIs) approach is used to get the feedback gains for every local linear controller guaranteeing global asymptotically stability, via a more relaxed stability condition, of the overall fuzzy control system. Measurement and control data from and to the EV3BRS are transferred via telecontrol and telemetry.

This paper considers the direction of arrival (DOA) estimation problem of phase ambiguity for unfolded coprime linear array (UCLA). The existing most common stacking subarray-based method can tackle the phase ambiguity problem. However, the method is not always true. For a given DOA, it has its corresponding steering vector, but if there are two DOAs which have the same steering vectors with the given DOA for different subarrays, the phase ambiguity problem still arises. A modified method, which defines a decision variable and uses the classic beamforming technique to estimate the DOAs is proposed. However, this method needs additional algorithm to distinguish the true DOAs besides multiple signal classification (MUSIC) spectrum. And sometimes this method is not reliable if the decision variable is not chosen appropriately. Therefore, based on the UCLA, we reconstruct the array to design an improved UCLA called IUCLA. With moving the reference element, the linear relationship among the directional vectors can be broken. In this way, we can directly utilize the MUSIC algorithm to estimate with no additional algorithm. The proposed method can solve the phase ambiguity problem and it does not demand other technique to decrease the complexity. Moreover, the Cramer-Rao Bound (CRB), as the lower bound of the unbiased estimation, is provided and numerical simulations are given to demonstrate the effectiveness and superiority of the proposed method.

This paper investigated reliability modeling for systems subject to dependent competing risks considering that the variation of failure threshold is not considered in most studies on competing failure reliability. Firstly, the variation of degradation quantity under shocks was analyzed, and the variation of threshold was considered on this basis. Secondly, the cumulative degradation under the influence of the random shock process was analyzed. The attractive property of copula is symmetry. Then, A linear Wiener process model is applied to model performance degradation failure, and a multi-performance-degradation correlated-competition model based on a Copula function is constructed, which considers the correlated competition between multiperformance degradation failures. Lastly, the micromotor system is used to analyze the applicability of the proposed model for bivariate instances. demonstrating the rationality and effectiveness of the proposed model.

Gradual disability worsening in Multiple Sclerosis (MS) is indicative of confirmed progression that mostly involves progression independent of relapse activity (PIRA) and is associated with neurodegeneration. Insights from pathology reveal grey matter involvement (neocortex, hippocampus, spinal cord, and deep grey matter structures) and microglia activation in early stages of MS. Cortical lesions result in thinning and atrophy and are considered accurate predictors of disability progression and cognitive decline.Neuroimaging biomarkers, such as high-resolution 7T MR images and TSPO-PET, have been examined for the detection of cortical pathology linked to cognitive deficits and thus progression, but are limited in clinical practice due to availability, time constraints, and cost.Electroencephalography (EEG) emerges as a non-invasive, cost-effective tool that reflects cortical activity in MS. Its potential in monitoring cognitive impairment is explored by focusing on nonlinear EEG analysis. The MuST PREDICT^TM project aims to extract linear and nonlinear EEG features, investigating their role in predicting disease progression and optimizing treatment. The study employs retrospective, cross-sectional, and prospective designs, utilizing EEGs from various MS forms, cognitive assessments, serum/cerebrospinal fluid biomarkers and neuroimaging. The methodology involves time-based and spectral feature extraction, employing artificial intelligence classifiers and brain criticality-based approaches.The conceptual framework of an innovative modality is herein presented, that would EEG for early MS progression detection. Standardization of the methodology could lead to the creation of a digital tool for better prognostication and treatment strategy optimization.

Fractional calculus is defined by expanded integer order integration and differentiation. In this paper, multiple mathematical models of a nonlinear dual tank device are precisely formulated by fractional calculus. Using the accurate model, multivariable Fractional-Order Controller is designed for the nonlinear device. The merits of the fractional-order design include: 1) Control of multivariable nonlinearities, 2) Compensation of uncertainties, 3) Elimination of coupling effects. Simulations and experiments are conducted to verify the precision of the fractional order models and the effectiveness of the multivariable fractional-order control design.

The various methods used to choose the profile shift coefficients, primarily the so-called equalizations, were based on assumed advantages without physical evidence proving them. In this paper a new calculation method is presented for determining profile shift coefficient. The procedure gives the pair of values ​​of the profile shift coefficients, in which case, under the given load, the resulting bending stress will be of the lowest possible value.

To investigate the variation patterns of spectral characteristics of main branches in fruit trees due to uneven distribution of growth, pruning, and fruit quality, as well as to determine the optimal fruit vi-bration harvesting, a vibration differential model of tree branches was constructed using the concen-trated mass method. A three-dimensional model of the fruit tree was built using finite element software. The spectral characteristics of each branch were obtained using the linear sweep frequency method. The method of changing the mass of each branch was employed to simulate the variation in branch mass. The frequency of occurrence, mean acceleration, and coefficient of variation of the inherent frequencies were used as evaluation indicators. The results revealed that when the vibration frequency of the fruit tree was at the peak frequency in the tree trunk spectrum, the frequency of occurrence and mean accel-eration were optimal. And the coefficient of variation of branch acceleration was less than 1, indicating a moderate dispersion. Additionally, reducing the branch mass resulted in an increase in the peak fre-quency of the tree trunk spectrum. Therefore, the growth, pruning, and uneven distribution of the branches in fruit trees can alter the spectral characteristics. When harvesting fruit by vibration, selecting the peak frequency in the trunk vibration spectrum as the excitation force frequency yields the best fruit detachment.

Exercising surds to represent figures is a common practice in scientific and Engineering fields, especially in scripts where calculators are banned or unapproachable. Peter Chew Theorem make result becomes simple when dealing with converting Quadratic Surds. The substance of the Peter Chew Theorem lies in enabling the forthcoming generation to simple break problems related to Quadratic Surds more effectively, easing a direct comparison with contemporary results. By employing the Peter Chew Theorem, one can streamline the tutoring and literacy of math, particularly concerning second- order direct equations with constant portions. This theorem's objective aligns with Albert Einstein's famed quotation Everything should be made as simple as possible, but not simpler.