Linear-width is a well-regarded width parameter in graph theory. The constructs of linear loose tangle and linear tangle present obstacles to attaining linear-width. In this succinct paper, our primary focus will be the exploration of maximal linear loose tangles.

For a nonzero normed linear space X‎, ‎we will define some different classes of fuzzy norms on X generated by linear and bounded linear functionals‎. ‎Also separate continuity of the elements of each class are investigated‎. ‎The aim of this research is to introduce a source of examples and counterexamples in the field of fuzzy normed spaces‎.

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.

In this paper, a 3 DOF gyrscope position control have been designed and controlled using optimal control theory. An input torque has been given to the first axis and the angular position of the second axis have been analyzed while the third axis are kept free from rotation. The system mathematical model is controllable and observable. Linear Quadratic Integral (LQI) and Linear Quadratic State Feedback Regulator (LQRY) controllers have been used to improve the performance of the system. Comparison of the system with the proposed controllers for tracking a desired step and random angular position have been done using Matlab/Simulink Toolbox and a promising results has been analyzed.

This paper presents the application of optimal control problem in modeling of stirred tank heater temperature control. The analysis of the open loop system shows that the system is not efficient without a controller. Linear Quadratic Gaussian (LQG) and Linear Quadratic Integral (LQI) controllers are used to increase the performance of the system. Comparison of the closed loop system with the proposed controllers have been done with Matlab/Simulink Toolbox and a promising results have been analyzed.

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.

Quantum computing has attracted significant interest in the optimization community because it potentially can solve classes of optimization problems faster than conventional supercomputers. Several researchers proposed quantum computing methods, especially Quantum Interior Point Methods (QIPMs), to solve convex optimization problems, such as Linear Optimization, Semidefinite Optimization, and Second-order Cone Optimization problems. Most of them have applied a Quantum Linear System Algorithm at each iteration to compute a Newton step. However, using quantum linear solvers in QIPMs comes with many challenges, such as having ill-conditioned systems and the considerable error of quantum solvers. This paper investigates how one can efficiently use quantum linear solvers in QIPMs. Accordingly, an Inexact Infeasible Quantum Interior Point Method is developed to solve linear optimization problems. We also discuss how we can get an exact solution by Iterative Refinement without excessive time of quantum solvers. Finally, computational results with a QISKIT implementation of our QIPM using quantum simulators are analyzed.

The potential of quantum computing for scientific and industrial breakthroughs is immense, however, we are still in the Noisy Intermediate-Scale Quantum (NISQ) era, where the currently available quantum devices contain small numbers of qubits, are very sensitive to environmental conditions and prone to quantum decoherence. Even so, existing NISQ computers have already been shown to outperform conventional computers on specific problems and the key question is how to make use of today’s NISQ devices to achieve quantum advantage in the field of computational science and engineering (CSE). In this direction, this work proposes a hybrid computing formulation by combining quantum computing with machine learning for accelerating the solution of parameterized linear systems in NISQ devices. In particular, it focuses on the Variational Quantum Linear Solver (VQLS), which is a hybrid quantum- classical algorithm for solving linear systems of equations. VQLS employs a short-depth quantum circuit to efficiently evaluate a cost function related to the system solution. The algorithm’s circuit consists of a quantum gate sequence (unitary operators) that involves a set of tunable parameters. Then, well-established classical optimizers are utilized to tune the parameters of the sequence in order to minimize the cost function, which is equivalent to finding the system solution at an acceptable level of accuracy. In this work, it is demonstrated that machine learning tools such as feed-forward neural networks and nearest-neighbor interpolation techniques can be successfully employed to accelerate the convergence of the VQLS algorithm towards the optimal values for the circuit parameters when applied to parameterized linear systems that need to be solved for multiple parameter instances.

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.

We present a new perspective of the link between QED and Maxwell's equations. We demonstrate that the interpretation of $\mathbf{D}=\varepsilon_{0} \mathbf{E}$ as vacuum polarization is consistent with QED. A free electromagnetic field polarizes the vacuum, but the polarization and magnetization currents cancel giving zero source current. The speed of light is a universal constant, while the fine structure constant, which couples the electromagnetic field to matter, runs as it should.

MicroRNAs (miRNA) exert regulatory actions via base-pairing with their binding sites on target mRNAs. Cooperative-binding, i.e., synergism, among binding sites on a mRNA is biochemically well-characterized. We studied whether this synergism is reflected in global relationship between miRNA-mediated regulatory activity and miRNA-binding-site count on the target mRNAs, i.e., leading to a non-linear relationship between the two. Recently, using our own and public datasets, we have enquired into miRNA regulatory actions: first, we analyzed the power-law distribution pattern of miRNA binding sites; second, strikingly, mRNAs for core miRNA regulatory apparatus proteins have extra-ordinarily high binding site counts, forming self-feedback-control loops; third, we revealed that tumor suppressor mRNAs generally have more sites than oncogene mRNAs; and fourth, we characterized enrichment of miRNA target mRNAs in translationally less-active polysomes relative to more-active polysomes. In these four studies, obvious correlation was observed qualitatively between the extent to which a mRNA is miRNA-regulated and its binding sites count. This paper summarizes the used datasets. We also re-analyzed the correlation by comparative linear and non-linear regression analyses. The results support a non-linear, instead of linear, relationship between the two parameters, conceivably a transcriptome-level reflection of cooperative-binding/synergism among miRNA binding sites on a target mRNA.

This study aimed to apply different complexity-based methods to surface electromyography (EMG) in order to detect neuromuscular changes after realistic warm-up and stretching procedures. Sixteen volunteers conducted two experimental sessions. They were tested before, after a standardized warm-up, and after a stretching exercise (static or neuromuscular nerve gliding technique). Tests included measurements of the knee flexion torque and EMG of biceps femoris (BF) and semitendinosus (ST) muscles. EMG was analyzed using the root mean square (RMS), sample entropy (SampEn), percentage of recurrence and determinism following a recurrence quantification analysis (%Rec and %Det) and a scaling parameter from a detrended fluctuation analysis. Torque was significantly greater after warm-up as compared to baseline and after stretching. RMS was not affected by the experimental procedure. In contrast, SampEn was significantly greater after warm-up and stretching as compared to baseline values. %Rec was not modified but %Det for BF muscle was significantly greater after stretching as compared to baseline. The a scaling parameter was significantly lower after warm-up as compared to baseline for ST muscle. From the present results, complexity-based methods applied to the EMG give additional information than linear-based methods. They appeared sensitive to detect EMG complexity increases following warm-up.

Refinery planning optimization is a challenging problem as regards handling the nonconvex bilinearity mainly due to pooling operations in processes such as crude oil distillation and product blending. This work investigates the performance of several representative piecewise-linear (or piecewise-affine) relaxation schemes (referred to as McCormick, bm, nf5, nf6t, and de (which is a new approach proposed based on eigenvector decomposition) that mainly give rise to mixed-integer optimization programs to convexify a bilinear term using predetermined univariate partitioning for instances of uniform and non-uniform partition sizes. Computational results show that applying these schemes give improved relaxation tightness than only applying convex and concave envelopes as estimators. Uniform partition sizes typically perform better in terms of relaxation solution quality and convergence behavior. It is also seen that there is a limit on the number of partitions that contributes to relaxation tightness, which does not necessarily correspond to a larger number of partitions, while a direct relation between relaxation size and tightness does not always hold for non-uniform partition sizes.

Near-fault ground motions can cause severe damage to civil structures, including bridges. Safety assessment of these structures for near fault ground motion is usually performed through Non-Linear Dynamic Analyses, while faster methods are often used. IMPAb (Incremental Modal Pushover Analysis for Bridges) permits to investigate the seismic response of a bridge by considering the effects of higher modes, which are often relevant for bridges. In this work, IMPAb is applied to a bridge case study considering near-fault pulse-like ground motion records. The records were analyzed and selected from the European Strong Motion Database and the pulse parameters were evaluated. In the paper results from standard pushover procedures and IMPAb are compared with nonlinear Response-History Analysis (NRHA), considering also the vertical component of the motion, as benchmark solutions and incremental dynamic analysis (IDA). Results from the case study demonstrate that the vertical seismic action has a minor influence on the structural response of the bridge. Therefore IMPAb, which can be applied considering vertical motion, remains very effective conserving the original formulation of the procedure, and can be considered a well performing procedure also for near-fault events.

A vast majority of the countries is under the economic and health crises due to the current epidemic of coronavirus disease 2019 (COVID-19). The present study analyzes the COVID-19 using time series, which is an essential gizmo for knowing the enlargement of infection and its changing behavior, especially the trending model. We have considered an autoregressive model with a non-linear time trend component that approximately converted into the linear trend using the spline function. The spline function split the COVID-19 series into different piecewise segments between respective knots and fitted the linear time trend. First, we obtain the number of knots with its locations in the COVID-19 series and then the estimation of the best-fitted model parameters are determined under Bayesian setup. The results advocate that the proposed model/methodology is a useful procedure to convert the non-linear time trend into a linear pattern of newly coronavirus case for various countries in the pandemic situation of COVID-19.

Amaranth has the potential to support Malawi's food and nutrition security, income generation and livelihoods, and climate change resilience efforts. Due to the high genetic variability of Ama-ranth, there is a need to develop stable and high-yielding genotypes for sustainable production. To determine the degree of genetic stability in different environments, five Amaranth accessions were subjected to stability analysis. The experiment was carried out at three sites (Bunda, Bembeke, and Chipoka) for two seasons in 2020-2021 in the central region of Malawi. It was laid out in Ran-domized Complete Block Design (RCBD) with four replicates. Eberhart and Russell linear regres-sion model was used for stability analysis and Pearson correlation was used to test the relationship between variables. Environmental variance + (genotype x environment) was significant for four of the parameters studied, namely grain yield, plant height, leaf length, and leaf width, indicating the presence of a remarkable interaction between genotypes and environment. The results of a pooled analysis of variance showed significant differences at a 5% significance level among the Amaranth accessions, indicating inherent genetic variability. Using the linear regression model of Eberhart and Russell, accessions PE-LO-BH -01 and LL-BH -04 were identified as the highest yielding stable genotypes for leaf and grain yield, respectively. In addition, Bembeke site was the most favourable environment for all the accessions. Thus, to enhance the production of amaranth in Malawi, LL-BH-04 and PE-LO-BH-01 were put forward for release as varieties for grain and leaf respectively. These results will also guide and support for future breeding programs.

The motion of a circular elastic plate floating on the surface is investigated in the time–domain. The solution is found from the single frequency solutions and the method to solve for the circular plate is given using the eigenfunction matching method. Simple plane incident waves with a Gaussian profile in wavenumber space are considered and a more complex focused wave group is considered. Results are given for a range of plate and incident wave parameters are investigated. Code is provided to show how to simulate the complex motion.

Quantum computers are machines that are designed to use quantum mechanics in order to improve upon classical computers by running quantum algorithms. One of the main applications of quantum computing is solving optimization problems. For addressing optimization problems, we can use linear programming. Linear programming is a method to obtain the best possible outcome in a special case of mathematical programming. Application areas of this problem consist of resource allocation, production scheduling, parameter estimation, etc. In our study, we look at quantum speedup ratios of HHL Algorithm for different scenarios of linear programming. In a first scenario we look quantum speedup ratio (S(N)) as a function of phase transition and the ratio (κ) between the greatest and smallest eigenvalues of the matrix in linear equation system. As a second scenario, we investigate the changes in S(N) as a function of κ and s, which is the coefficient for defining the matrix as s-sparse.

Quantum computers are machines that are designed to use quantum mechanics in order to improve upon classical computers by running quantum algorithms. One of the main applications of quantum computing is solving optimization problems. For addressing optimization problems we can use linear programming. Linear programming is a method to obtain the best possible outcome in a special case of mathematical programming. Application areas of this problem consist of resource allocation, production scheduling, parameter estimation, etc. In our study, we looked at the duality of resource allocation problems. First, we chose a real world optimization problem and looked at its solution with linear programming. Then, we restudied this problem with a quantum algorithm in order to understand whether if there is a speedup of the solution. The improvement in computation is analysed and some interesting results are reported.

As known all physical properties of solids are described well by the system of quantum linear harmonic oscillators. It is shown in the present paper that the system consisting of classical linear harmonic oscillators having temperature dependent masses or (and) frequencies has the same partition function as the system consisting of quantum linear harmonic oscillators having temperature independent masses and frequencies while the means of the square displacements of the positions of the oscillators from their mean positions for the system consisting of classical linear harmonic oscillators having: the temperature dependent masses; temperature dependent frequencies; and temperature dependent masses and frequencies differ from each other and from that of the system consisting of quantum linear harmonic oscillators, and hence, the system consisting of classical linear harmonic oscillators describes well the thermodynamic properties of the system consisting of quantum linear harmonic oscillators and solids.

Recently, a large number of Transformer-based solutions have emerged for the trajectory prediction task, but there are shortcomings in the effectiveness of Transformers in trajectory prediction. Specifically, while position encoding preserves some of the ordering information, the self-attention mechanism at the core of the Transformer has its alignment invariance that leads to the loss of temporal information, which is crucial for trajectory prediction. For this reason, we design a simple and efficient strategy for temporal information extraction and prediction of trajectory sequences using the self-attention mechanism and linear layers. Experimental results show that the strategy we designed can effectively combine the advantages of the linear layer and self-attention mechanisms, compensating for the shortcomings of the Transformer. Additionally, we conducted an empirical study to explore the effectiveness of the linear layer and sparse self-attention mechanisms in trajectory prediction.

Education is generally considered to be a great equalizer as well as a tool the young generation can use in becoming the nation’s future leaders. It is imperative that today’s young people are well equipped with good quality education to better lead a country into the future. As a consequence, it is also important that we find out the factors that affect the learning success of the youth, since knowing these factors, either positive or negative will help the government in designing programs that can help propagate the positives and rectify the negatives. This study utilized data from the elementary and high school students of a private educational institution in the Philippines. Multiple linear regression using lin-lin model was used to analyze the data. Results indicated both the over-all significance of the model and the absence of violations regarding the basic assumptions of CLRM. Three variables English proficiency, Math proficiency, and time spent in playing video games turned out to be significant. This study adds to the existing body of knowledge by showing that time spent in commuting between house and school can also at times to be used to study resulting and impacting Cumulative Grade Point Average positively.

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.

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.

We study the atom-field interaction at finite temperature and in the dispersive regime. We show that the master equation for this sytem may be solved with the use of superoperator techniques. We calculate the linear entropy in case the field is initially in a coherent state and the atom in a superposition of its ground and excited states.

To verify the reliability of the proposed stitching linear scan method for roundness measurement of small cylindrical workpieces, measurement uncertainties of the workpieces with various dimension are conducted. The cross-sectional circle of a cylindrical workpiece is divided into several equal arcs to be measured. Thus, the arc profile can be characterized according to the measured arcs. The roundness profile of the cylindrical part can be obtained by stitching these arc profiles together. Firstly, the measurement uncertainty of the workpiece with a diameter 1.5 mm and length 5.8 mm is evaluated to be 0.095 μm which can meet the uncertainty target of 0.1 μm. Considering the uncertainty of θx and θz which are the alignment around X-axis and Z-axis respectively changing with workpiece dimension changing, relevant uncertainties are carried out. As a result, there is no limitation with respect to workpiece diameter theoretically If the alignment can reach θz = θx = ±0.1° without considering the measurable range of the machine.

The Circular Economy of plastics is a promising concept that has the potential to reduce pollution and close the loop on plastic waste. However, further research is needed to develop more efficient and environmentally friendly methods of recycling plastic. This review article discusses the Circular Economy of plastics, its potential benefits and drawbacks, and the challenges that need to be addressed to make it a reality. Some case studies are also examined to explore how the Circular Economy of plastics has been implemented across the globe.

Recently, most countries suffering from global warming due to the waste gases coming out of the combustion engines used to generate electric power by traditional methods. Therefore, many countries are currently trying to find alternative solutions to this problem by using renewable energies such as solar energy, wind energy, and energy generated from the waves of the ocean and sea to overcome pollution problems. The waves of the seas and oceans have enormous and largely untapped energy, so this work presents an efficient way to use the energy of sea waves to generate electricity. And also, trying to be a way to produce electricity from wave energy in the future. The best suitable places along the shores of Jizan city were inspected to install the buoy system to revenue advantage of the wave supreme height to achieve the height amount of electrical energy. A mathematical model was made to analyze the wave energy and convert it into energy extracted by mechanical force. The mathematical analyzes used the data collected from satellite maps of the numerous severe waves in the Red sea of the Jazan area, and the data published in previous research along that area. It was found that the beach of the Al Shuqaiq area is the greatest for installing the buoy and obtaining the highest electrical energy due to the presence of the highest wave intensity, followed by the beach of the Baysh and Al Morgan area. Also, one of the objectives of this research is to study the design of a device powered by a buoy to use the waves of the Red Sea to generate electric power. The influence of the buoy system design parameters such as the buoy diameter, length of the cylinder, and the length of the connecting rod on the electrical energy generation from wave energy was investigated. The current device is designed with a gearbox to produce continuous power with a single electric generator. A floating mooring device uses the rise and fall of bulges to convert sea wave energy into electrical energy. The device consists of a float, arm, two wheels of different diameters, a gear set, and an electric generator. The effect of the design of several factors on the performance of the device for converting the sea waves energy into electrical energy, including the length of the buoy arm, the wave height by changing the cam diameter, and the conversion ratios between the gear set, to optimize the output power of the wave energy.

An image consisting of (m, n) pixels can be seen as a matrix of m × n size. Based on the formula of angles between two subspaces, a pair of angles can be defined between two matrices, by utilizing column spaces and row spaces of the two matrices. The singular values of each matrix can be used to calculate distances. Thus, a distance representation is obtained, and a pair of angles between 2 matrices of the same size.

In this paper, modelling design and analysis of a triple inverted pendulum have been done using Matlab/Script toolbox. Since a triple inverted pendulum is highly nonlinear, strongly unstable without using feedback control system. In this paper an optimal control method means a linear quadratic regulator and pole placement controllers are used to stabilize the triple inverted pendulum upside. The impulse response simulation of the open loop system shows us that the pendulum is unstable. The comparison of the closed loop impulse response simulation of the pendulum with LQR and pole placement controllers results that both controllers have stabilized the system but the pendulum with LQR controllers have a high overshoot with long settling time than the pendulum with pole placement controller. Finally the comparison results prove that the pendulum with pole placement controller improve the stability of the system.

From the linear Nash-Green fluctuations of background metric, we present the perturbation equations in an embedded four space-time. In the context of a five-dimensional bulk, we show that the perturbations are only propagated by the gravitational tensorial field equation. In a Newtonian conformal gauge, we study the matter density evolution in sub-horizon regime and on how such scale may be affected by the extrinsic curvature. We use the "extended Gold 2018'' growth dataset with 25 datapoints and the best fit Planck2018/LambdaCDM parameters. Hence, we determine the evolution equation for the density growth delta(a) as a result from the embedded equations of the background geometry. By using solar constraints, we analyse the evolution of the effective Newtonian constant G_eff and showing that applying Taylor expansion to G_eff (a) under the constraint of time-derivative of G_eff(0)=G at a= 1 in matter domination era, we get an agreement with Big Bang Nucleosynthesis (BBN) and also an alleviation of the 3-sigma tension to 1-sigma contour between (sigma8-Omega_m) of the observations from Cosmic Microwave Background (CMB) and Large Scale Structure (LSS) probes.

Increasingly, genomics is being used for the prediction of specific traits and diseases (phenotypes) among humans. Wider availability of genomics data through multiple research projects (such as International HapMap Project1 and 1000 Genomes2) has been a catalyst in that direction. With the recent advances in machine learning and big data analysis, data computation resources and data models needed for genomics data analysis are readily available. However, the prediction of traits and diseases has its own challenges in terms of computational requirements and computational analysis, statistical analysis (example: confounding variables), and limited quality of data collection. Linear Mixed Models (LMM, a type of linear regression) is a common approach for Genome-wide Association Studies (GWAS) for the prediction of common traits among humans using genomics. This paper researches the existing LMM-based approaches for Genome-wide Association Studies (GWAS), describes the experiment performed on FaST-LMM approach from Microsoft Research, and then proposes an enhanced approach (called LMM-22) on how to address computational and statistical issues. LMM-22 focuses on the parallelization of LMM computations and execution of LMM-22 on General Purpose Graphics Processing Units (GPU) as against CPUs to accelerate the LMM approach for GWAS studies.

The goal of this contribution is an application of the Linear General Model Predictive Control (LGMPC). In this paper, stability of the LGMPC is proven by means of a demonstration of a Theorem stating a sufficient and constructive condition. This condition can be applied for calculating the weight matrices of the cost function in the optimisation problem in LGMPC. Lower bounds conditions are found for one of these matrices and then a system with saturation is taken into consideration. The conditions could be interpreted and discussions through physical aspects. The obtained results were tested by means of computer simulations and an example with a recover water process is considered.

We present a new method of estimating fitness of countries and complexity of products by exploiting a non-linear non-homogeneous map applied to the publicly available information on the goods exported by a country. The non homogeneous terms guarantee both convergence and stability. After a suitable rescaling of the relevant quantities, the non homogeneous terms are eventually set to zero so that this new method is parameter free. This new map reproduces the findings of the method proposed by Tacchella et al. [1], and allows for an approximate analytic solution in case of actual binarized matrices based on the Revealed Comparative Advantage (RCA) indicator. This solution is connected with a new quantity describing the neighborhood of nodes in bipartite graphs, representing in this work the relations between countries and exported products. Moreover, we define the new indicator of country net-efficiency quantifying how a country efficiently invests in capabilities able to generate innovative complex high quality products. Eventually, we demonstrate analytically the local convergence of the algorithm.

Anomalous waves and rogue events are closely associated with irregularities and unexpected events occurring at various levels of physics, such as in optics, in oceans and in the atmosphere. Mathematical modeling of rogue waves is a highly actual field of research, which has evolved over the last four decades into a specialized part of mathematical physics. The applications of the mathematical models for rogue events is directly relevant to technology development for prediction of rogue ocean waves, and for signal processing in quantum units. In this manuscript, a comprehensive view of the most recent development in conventional methods for representing rogue waves is carried out, along with discussion of the devised forms and solutions. The standard nonlinear Schrödinger equation, the Hirota equation, the MMT equation and further to other models are discussed, and their properties highlighted. This review shows that the most recent advancement in modeling rogue waves give models which can be used to establish methods for prediction of rogue waves at open seas, which is important for the safety and activity of marine vessels and installations. The study further puts emphasis on the difference between the methods, and how the resulting models form a basis for representing rogue waves.

Background: In the functional data analysis (FDA), the hybrid or mixed data are scalar and functional datasets. The semi-functional partial linear regression model (SFPLR) is one of the first semiparametric models for the scalar response with hybrid covariates. Various extensions of this model are explored and summarized. Methods: Two first research articles, including “semi-functional partial linear regression model”, and “Partial functional linear regression” have more than 300 citations in Google Scholar. Finally, only 106 articles remained according to the inclusion and exclusion criteria such as 1) including the published articles in the ISI journals and excluding 2) non-English and 3) preprints, slides, and conference papers. We use the PRISMA standard for systematic review. Results: The articles are categorized into the following main topics: estimation procedures, confidence regions, time series, and panel data, Bayesian, spatial, robust, testing, quantile regression, varying Coefficient Models, Variable Selection, Single-index model, Measurement error, Multiple Functions, Missing values, Rank Method and Others. There are different applications and datasets such as the Tecator dataset, air quality, electricity consumption, and Neuroimaging, among others. Conclusions: SFPLR is one of the most famous regression modeling methods for hybrid data that has a lot of extensions among other models.

The study presents the conceptual development and simulation of a robotic exoskeleton for ankle rehabilitation. The device is designed for ankle rehabilitation in patients with musculoskeletal disorders, injuries, or neurological diseases. The exoskeleton is equipped with three linear electric actuators that provide precise control of joint movements in multiple planes, allowing dorsiflexion and plantar flexion, inversion, and eversion. By utilizing a screw drive, the exoskeleton provides smooth and controlled movements, significantly reducing the risk of re-injury and improving rehabilitation. Simulation of the device and simulation results showed its high compatibility with the biomechanical features of the ankle joint. Virtual testing confirmed that the exoskeleton provides the smooth, controlled movements necessary for effective rehabilitation. Due to its ability to adapt to the individual physical capabilities of the patient, the device can be used in both active and passive forms of movement support. The results of the study demonstrate the potential of the exoskeleton in clinical applications, including its use in rehabilitation centers and at home. Its cost-effectiveness, ease of use, and high accuracy of movement control make this device a promising solution for restoring the functions of the lower extremities in patients with various musculoskeletal disorders.

The primary objective of this paper is to establish connections between two well-known but previously independently developed theories: the theory of violator spaces and the theory of greedoids. Violator spaces were introduced by Matoušek et al. in 2008 as a generalization of linear programming problems. Greedoids were introduced by Korte and Lovász in 1981 in an effort to characterize combinatorial structures where greedy algorithms yield optimal solutions. In this work, we explore the relationships between violator spaces and greedoids, demonstrating that greedoids can be defined using a variant of a violator operator. These interrelations provide a new characterization of antimatroids.

This work investigates the stability conditions for linear systems with time-varying delays via augmented Lyapunov-Krasovskii functional(LKF). Two types of augmented LKFs with cross terms in integral are suggested to improve the stability conditions for interval time-varying linear systems. Through this work, the compositions of the LKFs are considered to enhance the feasible region of stability criterion for linear systems. Mathematical tools such as Wirtinger-based integral inequality(WBII), zero equalities, reciprocally convex approach, and Finsler’s lemma are utilized to solve the problem of stability criteria. Two sufficient conditions are derived to guarantee the asymptotic stability of the systems using linear matrix inequality(LMI). First, asymptotic stability criteria are induced by constructing the new augmented LKFs in Theorem 1. And then simplified LKFs in Corollary 1 are proposed to show the effectiveness of Theorem 1. Second, asymmetric LKFs are shown to reduce the conservatism and the number of decision variables in Theorem 2. Finally, the advantages of the proposed criteria are verified by comparing maximum delay bounds in two examples. Two numerical examples show that the proposed Theorem 1 and 2 obtained less conservative results than existing outcomes. Also, Example 2 shows that the asymmetric LKF methods of Theorem 2 can provide larger delay bounds and fewer decision variables than Theorem 1’s in some specific systems.

The fractional advection-dispersion equation FADE plays an important role, especially in explaining the process of solute-transport in natural porous media with different degrees of heterogeneity. However, studies of the flow and transport of contaminants in the underground environment are based on the knowledge of many functional parameters of the subsoil. The delay factor caused by nonlinear absorption is one of these parameters inheriting significant ambiguities in its estimation in heterogeneous media. In the study, a fractional advection-dispersion FADE model was developed by the implicit Euler method, based on a Grunwald and Caputo-Liousville approximation to explicitly evaluate and simulate the transport mechanism of contaminants in media with unsaturated porous materials subjected to a nonlinear sorption model. Better solute mass retention was observed for fractional advection-dispersion FADE model. Moreover, the absorption parameter of the retardation coefficient has a better impact on the motion of the solute in a saturated porous medium. In other words, it has a significant effect on the dispersion of pollutants in aquifers. This study highlights the need to characterize the aquifer to predict solute transport in porous media.

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 the context of reinforcement learning (RL), ensuring both safety and performance is crucial, especially in real-world scenarios where mistakes can lead to severe consequences. This study aims to address this challenge by integrating temporal logic constraints into RL algorithms, thereby providing a formal mechanism for safety verification. We employ a combination of theoretical and empirical methods, including the use of temporal logic for formal verification and extensive simulations to validate our approach. Our results demonstrate that the proposed method not only maintains high levels of safety but also achieves comparable performance to traditional RL algorithms. Importantly, our approach fills a critical gap in existing literature by offering a solution that is both mathematically rigorous and empirically validated. The study concludes that the integration of temporal logic into RL offers a promising avenue for developing algorithms that are both safe and efficient. This work lays the foundation for future research aimed at generalizing this approach to various complex systems and applications.

We solve the And\^{o} dilation problem for linear maps on vector space asked by Krishna and Johnson in \textit{[Oper. Matrices, 2022]}. More precisely, we show that any commuting linear maps on vector space can be dilated to commuting injective linear maps.

In this paper, we address the problem of stabilization of switched linear systems. The idea is to look for a state feedback control law using evolutionary algorithms (EA) in order to assure the stability of the switched linear systems under control constraints. In some cases when states are not available and only outputs are measurable, the previous method is applied to design an output feedback controller which stabilizes the system. Both stabilizing controllers are developed using deferential evolution and genetic algorithm. Two numerical examples illustrate our proposed theory and point out the effectiveness of our proposed approaches.

Introduced in 2009, Bitcoin has demonstrated a huge potential as the world’s first digital currency and has been widely used as a financial investment. Our research aims to uncover the relationship between Bitcoin prices and people’s sentiments about Bitcoin on social media. Among various social media platforms, micro-blogging is one of the most popular. Millions of people use micro-blogging platforms to exchange ideas, broadcast views, and to provide opinions on different topics related to politics, culture, science, and technology. This makes them a potentially rich source of data for sentiment analysis. Therefore we chose one of the busiest micro-blogging platforms, Twitter, to perform sentiment analysis on Bitcoin. We used ELMo embedding model to convert Bitcoin-related tweets into a vector form and SVM classifier to divide the tweets into three sentiment categories - positive, negative, and neutral. We then used the sentiment data to find its relation with Bitcoin price fluctuation using the linear mixed model.

This dissertation is a rigorous study of ecology and macrocellular biology as a subfield of abstract algebra. We begin with the creation of an axiomatic paradigm, then move onto constructing a universal genetic code of biology. We use this to define increasingly complex algebraic structures (ecosystem, evolving populations, etc.). We prove a variety of theorems regarding to the members of the previous mathematical constructs, notably the following three: 1. There is one unique phenotypic representation of each organism. For example, if you subdivide any piece of genetic code into its phenotypic components, then two identical organisms have identical decomposed DNA 2. There are a finite number of indivisible phenotypic traits. 3. The three sophioid-definitions are equivalent: (a) dynamical evolutionary enlargement of the medial temporal lobe and frontal lobe, (b) reliance upon intelligence, (c) the existence of an intellectually- or socially-hierarchical society. Much has yet to be done on this work, but as a first draft, it stands as a jumping point for future exploits; I am working on an entirely revised second draft.

This work examines drought and pluvial events based on Standardized Precipitation-Evapotranspiration Index (SPEI) over Kenya from 1981 to 2016. Spatiotemporal analysis of dry and wet events is conducted for 3 and 12-month SPEI. The drought incidences were observed during the period 1984, 1987, 2000, 2006, 2009, 2015, and 2016 for SPEI-3 whilst the SPEI-12 demonstrated the manifestation of drought during the year 2000 and 2006. SPEI clearly shows the wettest period, 1997 and 1998 coinciding with the El Nino event in both time steps. SPEI -3 shows a reduction in moderate drought events while severe and extreme cases were on increase towards the end of the twentieth century. Conversely, SPEI-12 depicts an overall severe drought occurrence over the study location with observed intensity of -1.54 and cumulative frequency of 64 months during the study period. The trend of wet events is upwards in the western and central highlands while the rest of the regions show increase in dry events during the study period. Moreover, moderate dry/wet events predominate whilst extreme events occur least frequent across all grid cells. It is apparent that the study area experiences mild extreme dry events in both categories although moderately severe dry events dominate most parts of the study area. High intensity and frequency of drought is noted in SPEI-3 while least occurrences of extreme events are recorded in SPEI-12. Although drought event prevails across the study area, there is evidence of extreme flood conditions over the recent decades.

In this paper, we present a framework to study the spatial structure of noctilucent clouds formed by ice particles in the upper atmosphere at mid and high latitude during summer. We study noctilucent cloud activity in optical images taken from three different locations and under different atmospheric conditions. In order to identify and distinguish noctilucent cloud activity from other objects in the scene, we employ linear discriminant analysis (LDA) with feature vectors ranging from simple metrics to higher-order local autocorrelation (HLAC), and histogram of oriented gradients (HOG). Finally, we propose a Convolutional Neural Networks (CNN) based method for the detection of noctilucent clouds. The results clearly indicate that the CNN based approach outperforms LDA based methods used in this article. Furthermore, we outline suggestions for future research directions to establish a framework that can be used for synchronizing the optical observations from ground based camera systems with echoes measured with radar systems like EISCAT in order to obtain independent additional information on the ice clouds.

This study tries to focusing on applying information communication technology for economic importance of Mid Oil Company (MDOC), which is among contemporary oil companies in Iraq. Since ICT forms a significant aspect of achieving organizational economic objectives, most of public and private bodies seek to utilize ICT tool and techniques to improve work efficiencies. The emerging growth in ICT has made it process and service automation possible in managing organizational activities. To determine this effect of ICT on organizations, this study formulated statistical research model at MDOC through using fifteen questionnaires, which were distributed on three axes. The outcome of the questionnaire analysis revealed that there is inadequate comprehensive infrastructure to suitably support ICT within the selected organization management. In addition, it revealed that there are no ideal standards to maintain and sustain internet networks. Based on these revelations, the study presents recommendation for the adoption of ICT with the aim of minimizing cost, enhancing communication and managing infrastructure. Also recommends the need to support IT department within an organization, with essential equipment, in terms of man and machine, for better efficiency to employ the key of ICT Impact in Iraqi governmental oil companies.

In this study, we describe quark confinement in terms of linear interaction potentials and solve the problem of the net spin of a proton. The three quarks in a proton are assumed to revolve around a common center, and their masses are determined assuming they are Dirac particles. On the basis of these assumptions, the magnetic moment of a proton can be derived. Moreover, the rotation of the quarks is considered, in which an electrical current induces a magnetic field. Thus, the scalar product of the magnetic moment and field describes the linear interaction potential between the quarks, and the mass of the proton can be obtained. The proton mass predicted by this physical model is consistent with experimental values, and no numerical or fitting calculations are required. Furthermore, using the newly derived spins and angular momentum of the three quarks, we derived the net spin of a proton. Additionally, we predicted the mass of a pi-meson from the same model, which agrees with the experimental values.

This research work focused on the risks we are faced with on our day to day activities, either directly or indirectly, which can gradually accumulates and results to communal crisis, religious crisis, socio-economic agitations and tribal crises. Nasarawa Eggon Local Government Area of Nasarawa State was used as case study and a well structure close–ended questionnaire was used for data collection as it relates to Controlled Self Risk Assessment (CSRA) and linear programming technique was used to analyze. The results proved that many of this processes were neglected in these communities, making them to be prone to incessant communal crisis. The study recommend that Government should strongly, as a matter of urgency address the unemployment rate, distribution of political position, schools, primary health care and equip security personnel with the modern technology facilities, which happen to record the highest risk level.

Fusarium graminearum causes head blight in wheat and corn, and produces chemicals harmful for humans and other animals. It is important to understand how it grows in order to prevent outbreaks. There are 3 well-known growth models for microorganisms and they seem applicable to molds: linear, Gompertz and Baranyi. This study aimed to see which could better represent F. graminearum growth. Three replicates were grown in yeast extract agar (YEA) for 20 days. The Feret’s radius was measured in ImageJ software, and then related to the models. Linear model was the most closely correlated to the actual growth. Thus, considering that it was the most representative of the reality and it is easier to use, it seems to be the best logical choice for F. graminearum growth studies.

The main contribution of this paper is to develop a graphical tool to evaluate the suitability of a candidate parametric model to fit a data set. The practical motivation is to check the adequacy of the so called SAINT model proposed in Jarner and Kryger (2011). This model has been implemented in practice by an important European pension fund concerned with setting annuity reserves for all current or former employees of Denmark. So, one particular relevant question is whether this mortality model is actually fitting old-age. Our graphical test can be described as follows. First we transform the data by means of the parametric model which is being evaluated. Should the model be correct, the transformed data will be in accordance with an Exponential distribution with rate 1. Then we construct a family of local linear hazard estimates based on the data on the transformed scale. Finally we use the statistical tool SiZer to assess the goodness-of-fit of the Exponential distribution to the data on the transformed scale. If the model is correct the SiZer map should not reveal any significant feature in the family of kernel estimates. Our method allow us to establish a diagnostic regarding the validity of the SAINT model when describing mortality patterns in four different countries.

This paper conducts an extensive literature review focusing on the utilisation of crack tip plasticity as a crucial parameter in determining and enhancing crack growth models. The review encompasses a comprehensive analysis of various methodologies, predominantly emphasising numerical simulations of crack growth models while also considering analytical approaches. Although experimental investigations are not the focus of this review, their relevance and interplay with numerical and analytical methods are acknowledged. The paper critically examines these methodologies, providing insights into their advantages and limitations. Ultimately, this review aims to offer a holistic understanding of the role of crack tip plasticity in the development of effective crack growth models, highlighting the synergies and gaps between theoretical, experimental, and simulation-based approaches.

In the framework of the self-consistent Maxwell-Pauli theory, the non-linear Pauli equation is obtained. Stationary and nonstationary solutions of the nonlinear Pauli equation for the hydrogen atom are studied. We show that spontaneous emission and the related rearrangement of the internal structure of an atom, which is traditionally called a spontaneous transition, have a simple and natural description in the framework of classical field theory without any quantization and additional hypotheses. The behavior of the intrinsic magnetic moment (spin) of an electron wave in an external magnetic field is considered. We show that, according to the self-consistent Maxwell-Pauli theory, in a weak magnetic field, the intrinsic magnetic moment of an electron wave is always oriented parallel to the magnetic field strength vector, while in a strong magnetic field, depending on the initial orientation of the intrinsic magnetic moment, two orientations are realized: either parallel or antiparallel to the magnetic field strength vector.

The goal is the optimal synthesis of the parameters of the control law for a nonlinear satellite attitude control system under constraints related to the saturation effect of reaction wheels. The maximum stability degree of the control system is considered as a criterion for the optimality of the parameters of the control law, and the absolute values of the control torques and angular velocities of the reaction wheels, achievable within the limits of the physical characteristics of the drives, are considered as constraints. The solution to the optimal synthesis problem is based on the transformation of the nonlinear control system model into a linear model, within the framework of the problem of global asymptotic stability of the control system is also guaranteed. The problem is decomposed into a subproblems of obtaining the optimal transient process shape in the control system and considering the constraints. A method of synthesizing the optimal transient process shape based on the criterion of maximum stability degree had been developed. An analytical method of determining the optimal values of the control law parameters, based on decomposing the normalized characteristic polynomial in the linear model into three identical factors had been proposed. A method with regards to the constraints of the control torque and angular speed of the reaction wheels, based on transitioning from relative to real time is developed. An algorithm for calculation of the transition scale from relative to real time, ensuring the fulfillment of all constraints in the optimal synthesis problem, is proposed. An example demonstrating the efficiency and simplicity of the proposed methods and algorithm for targeted selection of technical characteristics of the control system, considering the maximum absolute values of angular speeds and control torques of the reaction wheels, is provided.

Linear Hashing is an important algorithm for many key-value stores. Spiral Storage was invented to overcome the poor fringe behavior of Linear Hashing, but after an influential study by Larson, seems to have been discarded. Since almost 50 years have passed, we repeat Larson’s comparison with in-memory implementation of both to see whether his verdict still stands. Our study shows that Spiral Storage has slightly better look-up performance, but slightly poorer insert performance.

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.

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.

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.

Lateral vehicle control is a high importance in automated vehicles as it directly influences the vehicle’s performance and safety during operation. The Linear Quadratic Regulator (LQR) controller stands out due to its high-performance characteristics and is used in the open source for self driving functions. However, a notable limitation of the current approach is the manual calibration of LQR controllers based on the experience and intuition of the designers, leading to empirical uncertainties. To address this issue and enhance the lateral control performance, this paper concentrates on refining the LQR by employing three optimization algorithms: Artificial Bee Colony Optimization (ABC), Genetic Algorithm (GA), and Particle Swarm Optimization (PSO). These algorithms aim to overcome the reliance on empirical methods and enable a data-driven approach to LQR calibration. By comparing the outcomes of these optimization algorithms to the manual LQR controller within an offline multibody simulation as testing platform, the study highlights the superiority of the best-performing optimization approach. Following this, the optimal algorithm is implemented on a real-time system for the full vehicle level, revealing the Model-in-the-Loop and the Hardware-in-the-Loop gap up to 78,89% with lateral velocity when we use Relative Error Criterion (REC) method to validate and 2.35m with lateral displacement when considering by maximum absolute value method.

This article presents the impact analysis of space harmonics (SH) presence on a single-sided three-phase linear induction motor, along with a comprehensive parametric investigation. The presence of SH often reduces the LIM performances. The electromagnetic phenomena are governed by Maxwell's equations associated with equivalent circuit modelling. The chosen mathematical model uses 2D formulation with magnetic vector potential A. The model implementation is performed with finite element method on Gmsh-GetDP free platform. The electromagnetic thrust is calculated in current excitation case by a numerical model (FEM) with and without term generating SH in order to highlight the effect of SH. The adaptation to voltage supply operation is obtained by equivalent electric circuits (EEC), through calculation of the operational impedance. The main objective of the study consists in a comparative exploration of SH presence using two numerical models (single and multi-harmonics), and an assessment of parameters effect on space harmonic presence and various machine characteristics such as thrust, efficiency, and power factor. The motor’s characteristics (ie: thrust, efficiency and power factor) strongly depend on parameters such as the pole pair number and conductivity. Improving the operation and maximizing the performances of such a machine for a given specification requires the use of optimization algorithms.

The paper presents the relationship between the efficiency of the process of skin onion peeling and its effect in the form of waste. The research was carried out on a pilot test stand for onion peeling. The process variables were compressed air with a pressure of (p) and valve controlling opening time of flow (t). The experiment took into account the influence of the onion diameter (d0) and its hardness (H). The obtained results were subjected to statistical analysis. Standard deviations were of the percentage loss of onion mass in the form of the skin removed of onion peeling in the process in relation to obtained aver-age values. Tukey's multiple comparison test was performed in order to identify the importance of individual process variables on the final effect of onion peeling. This was the basis for the development of a predictive model in the form of a nonlinear regression Mp=f(p,t,d0,H), which is a mathematical description of the peeling onion skin process . Finally, the response surface area of relationship between analyzed variables was determined. The results of research showed the peeling efficiency of the onion and waste of skin mass depend on the compressed air pressure. Extending the onion blowing time does not improve the process efficiency, while the hardness and size of the onion are irrelevant to the process.

Abstract: Theoretical and non-dimensional investigations have been performed to study the vibration control potential of approaches that can be based on viscoelastic but also on endochronic elements. The latter are known from the endochronic theory of plasticity and provide the possibility to establish rate-independent schemes for vibration control. The main question that has to be answered is: Can rate-independent damping be efficiently used to reduce mechanical vibrations? To answer this question non-dimensional models for dynamical systems are derived and analyzed numerically in time-domain as well as in frequency-domain. The results are used to compare the performance of an optimally tuned endochronic absorber to the performance of an optimally tuned dynamic absorber with viscoelastic damping. Based on a novel closed form representation for non-linear systems with endochronic elements, it has been possible to prove that rate-independent control of vibration results in an overall control profit that is close to the control profit obtained by the application of well-established approaches. It has also been found that the new concept is advantageous if anti-resonances have to be considered in broadband vibration control. Based on these novel findings, a practical realization in the context of active vibration control is proposed in which the rate-independent control law is implemented on an appropriate signal processing hardware.

Background: Cochlear implantation is an efficient treatment for postlingually deafened adults who do not benefit sufficiently from acoustic amplification. Implantation is indicated when it can be foreseen that speech recognition with a cochlear implant (CI) is superior to that with a hearing aid. Especially for subjects with residual speech recognition it is desirable to predict CI outcome on the basis of preoperative audiological tests. Purpose: The purpose of the study was to extend and to refine a previously developed model for CI outcome prediction for subjects with preoperative word recognition to include subjects with no residual hearing by incorporat-ing additional results of routine examinations. Results: By introducing the duration of unaided hearing loss (DuHL) the median absolute error (MAE) of the prediction was reduced. While for subjects with preoperative speech recognition the model modification did not change the MAE, for subjects with no residual speech recognition before surgery, the MAE decreased from 23.7% with the previous model to 17.2% with the extended model. Conclusions: Prediction of word recognition with CI is possible within clinically relevant limits. Outcome prediction is particu-larly important for preoperative counselling and in CI aftercare, to support systematic monitor-ing of CI fitting.

The quantile estimation of extreme wind speed is needed in various environmental fields such as climatology, design of structures, renewable energy sources and agricultural operations. These calculations are crucial for the coding of wind speed. In this study, the required wind speed series of 16 stations in Khyber Pakhtunkhwa, Pakistan, was obtained from the NASA official website and measured in meters per second (m/s) at a 10-meter distance. A Regional Frequency Analysis of 16 AMWS stations was performed using L-moments. The quantile estimates of extreme wind speed are needed for various areas of interest using Regional Frequency Analysis (RFA) and extreme value theory. These calculations are crucial for the coding of wind speed. The data was taken from the NASA official website at a 10-meter distance and measured in meter per second (m/s). A Regional Frequency Analysis of AMWS using L-moments is performed utilizing wind speed data from sixteen sites (16) in Pakistan's Khyber Pakhtunkhwa province. There are no sites that are found to be discordant. The wards method is used to construct a homogenous region and make two homogenous regions from 16 sites. The heterogeneity test justifies that both clusters are homogeneous. The most appropriate probability distribution from the Generalized Normal (GNO), Generalized Logistic (GLO), Pearson Type-3 (P3), Generalized Pareto (GPA), and Generalized Extreme Value (GEV) distributions are chosen to calculate regional quantiles. According to the L-moments diagram and Z statistics, GEV for Cluster- Ι and GLO for Cluster- ΙΙ are the best suggestions from the others. Both clusters’ robustness is measured utilizing Relative Bias (RB) and Relative Root Mean Square Error (RRMSE). Overall, GEV distribution is fit for cluster-Ι, and the GLO distribution is fit for cluster-ΙΙ. Utilizing the site mean and median as index parameters, we can also find at-site quantiles from regional quantiles. The study’s quantile estimates can be employed in codified structural designs with policy consequences.

The paper portrays a linear model for synchronous prediction of the dissolved oxygen (DO) level in a protected urban lake by using independent variables in real-time monitoring of the water quality parameters. Multi-linear regression and machine learning techniques were applied to the Dissolved Oxygen (DO) using the basic four parameters of Water Quality Index (WQI). Three real-time industry standard sensors PHEHT, CTZN, OPTOD were used for sampling, data was then interpolated through ArcGIS kriging method. 25 correlations were checked through the ML algorithm, a correlation heat map was produced and the top five relations were taken under consideration and validated by r-score and root mean squared error (RMSE) to develop the linear regression model. The performance of the model was validated through the RMSE, mean squared error (MSE), and mean absolute error (MAE) the r2 accuracy came to 0.983 when it is checked against the sample data. The suggested model can be used as a technique for unknown or malfunctioned sensor’s null DO data prediction.

Human ether-a-go-go-related gene (hERG) potassium channel is well-known contributor to drug-induced cardiotoxicity and therefore an extremely important target when performing safety assessments of drug candidates. Ligand-based approaches in connection with quantitative structure active relationships (QSAR) analyses have been developed to predict hERG toxicity. Availability of the recent published cryogenic electron microscopy (cryo-EM) structure for the hERG channel opened the prospect for using structure-based simulation and docking approaches for hERG drug liability predictions. In recent time, the idea of combining structure- and ligand-based approaches for modeling hERG drug liability has gained momentum offering improvements in predictability when compared to ligand-based QSAR practices alone. The present article demonstrates uniting the structure-based SILCS (site-identification by ligand competitive saturation) approach in conjunction with physicochemical properties to develop predictive models for hERG blockade. This combination leads to improved model predictability based on Pearson’s R and percent correct (represents rank-ordering of ligands) metric for different validation sets of hERG blockers involving diverse chemical scaffold and wide range of pIC50 values. The inclusion of the SILCS structure-based approach allows determination of the hERG region to which compounds bind and the contribution of different chemical moieties in the compounds to blockade, thereby facilitating the rational ligand design to minimize hERG liability.

In this note, we provide some effective treatments of a general linear model with adding-up restrictions via algebraic operations of given vectors and matrices in the model, including analytic expressions of the well-known ordinary least-squares estimator (OLSE) and the best linear unbiased estimator (BLUE) of the unknown parameters in the model.

In surveying engineering tasks, close-range photogrammetry belongs to leading technology considering different aspects like the achievable accuracy, availability of hardware and software, accessibility to measured objects, or the economy. Hence, constant studies on photogrammetric data processing are desirable. Especially in industrial applications, the control points for close-range photogrammetry are usually measured using total stations. In the case of small objects, more precise positions of control points can be obtained by deploying and adjusting a three-dimensional linear network set up on the object. The article analyzes the accuracy of the proposed method, based on the measurement of the linear network using a tape with a precision of ±1 mm. The experiment shows that the adjusted positions of the network control points can be determined with high, one-millimeter accuracy. The photogrammetric 3D model derived referring to such control points and stereo-images captured with a non-metric camera is also characterized by the highest possible precision, which qualifies the presented method to accurate measurements used in surveying engineering. The authors prove that the distance between two randomly optional points derived from the 3D model of a dimensioned object is equal to the actual distance measured directly on it with one-millimeter accuracy.

This paper will discuss the application of statistic modeling to interpret a health system crisis in Sri Lanka due to COVID- 19.A strong focus on the preventive approach and the contact tracing with the utilization of available resources in a rational manner describes Sri Lanka’s response towards COVID- 19 prevention and mitigation. The early contact tracing, preemptive quarantining, isolation, and treatment were implemented as a concerted effort. This approach, proven efficient during the early phase of the pandemic, was sustainable when there was a rapid increase in the COVID- 19 patients since July 2021, exceeding the health system capacity.The country’s COVID- 19 situation during the period from 01st of August 2021 to 31st of October 2021 was taken into consideration. Variables used for analysis were; total number of cases, recovered cases, comorbid and O₂ dependent patients, ICU patients, and deaths. The regression model was applied to analyze the data by using the EViews 12 (x64) software application.The correlation coefficients of all the independent variables under consideration implies that they have a strong positive relationship with the number of deaths occurred during the said period. According to the computed multiple linear regression model, the number of positive cases and O₂ dependents have a positive relationship with the dependent variable. Further, the Durbin- Watson stat value of the model and multicollinearity test reflect that it is free from serial correlation thereby the model is fit. From the perspective of epidemiological control, these findings highlight the importance of keeping the number of cases within the limits of health system capacity.

This addendum contains clarifications and a sharpening of some of the results on the VIT transform framework developed in [1]. The focus is on the right-coefficient and left- coefficient forms of the transform, the extraction of a first-order term from a left polynomial fraction, and the application to linear time-varying systems.

Epidermal growth factor receptor (EGFR) is a receptor tyrosine kinase that instigates several signaling cascades, including the NF-kB signaling pathway, to induce cell differentiation and proliferation. Overexpression and mutations of EGFR are found in up to 30% of solid tumors and correlate with a poor prognosis. Although it is known that EGFR-mediated NF-kB activation is involved in tumor development, the signaling axis is not well elucidated. Here, we found that PKP2 and the LUBAC complex were required for EGFR-mediated NF-kB activation. Upon EGF stimulation, EGFR recruited PKP2 to the plasma membrane, and PKP2 bridged HOIP, the catalytic E3 ubiquitin ligase in the LUBAC, to the EGFR complex. The recruitment activated the LUBAC complex and the linear ubiquitination of NEMO, leading to IkB phosphorylation and subsequent NF-kB activation. Furthermore, EGF-induced linear ubiquitination was critical for tumor cell proliferation and tumor development. Knockout of HOIP impaired EGF-induced NF-kB activity and reduced cell proliferation. HOIP knockout also abrogated the growth of A431 epidermal xenograft tumors in nude mice by more than 70%. More importantly, the HOIP inhibitor, HOIPIN-8, inhibited EGFR-mediated NF-kB activation and cell proliferation of A431, MCF-7, and MDA-MB-231 cancer cells. Overall, our study reveals a novel linear ubiquitination signaling axis of EGFR, and perturbation of HOIP E3 ubiquitin ligase activity is potential targeted cancer therapy.

In this paper, we consider with a class of system of differential equations whose argument transforms are involution. In this an initial value problem for a differential equation with involution is reduced to an initial value problem for a higher order ordinary differential equation. Than either two initial conditions are necessary for a solution, the equation is then reduced to a boundary value problem for a higher order ODE.

This paper reports applying Minimax principle and impulsive differential inequality to derive the existence of multiple stationary solutions and the global stability of a positive stationary solution for a delayed feedback Gilpin-Ayala competition model with impulsive disturbance. The conclusion obtained in this paper reduces the conservatism of the algorithm compared with the known literature, for the impulsive disturbance is not limited to impulsive control.

This paper answers the need to plan a cost-minimizing charging schedule for electric buses and proposes a three-stage procedure, which is oriented around the participation of electric buses aggregator in a day-ahead energy auction. First, optimization models are provided to determine charging availability expressed as minimum and maximum hourly energy requirements taking into account detailed, minutely characteristics and constraints of the charging equipment and the buses. Next, the auction model is formulated by considering aggregated bids submitted by the electric buses aggregator once the charging availability is determined. Hence, the day-ahead prices reflect the optimal schedules of auction participants, and the bus aggregator is safe against peak-hour charging. Finally, hourly auction-based schedules are disaggregated into optimal minutely charging schedules. Mixed-integer linear programming models are formulated for aggregation-disaggregation stages investigated in this paper, while the variables and constraints introduced into the auction model are linear. The proposed methodology has been verified on a recently published case study of a real-world bus service operated on The Ohio State University campus. We show that the auction-based charging of all 22 buses outperforms as-soon-as-possible schedules by 7% to even 28% of daily cost savings. Using the aggregated bids, buses can flexibly shift charges between high- and low-price periods while preserving constraints of the charging equipment and timetables.

This review describes the subjective experience of visual aura in migraine, outlines theoretical models of this phenomenon, and explores how these may be linked to neurochemical, electrophysiological and psychophysical differences in sensory processing that have been reported in migraine with aura. Reaction-diffusion models have been used to model the hallucinations thought to arise from cortical spreading depolarisation and depression in migraine aura. One aim of this review is to make the underlying principles of these models accessible to a general readership. Cortical spreading depolarisation and depression in these models depends on the balance of the diffusion rate between excitation and inhibition, and the occurrence of a large spike in activity to initiate spontaneous pattern formation. We review experimental evidence, including recordings of brain activity made during the aura and attack phase, self-reported triggers of migraine, and psychophysical studies of visual processing in migraine with aura, and how these might relate to mechanisms of excitability that make some people susceptible to aura. Increased cortical excitability, increased neural noise, and fluctuations in oscillatory activity across the migraine cycle are all factors likely to contribute to the occurrence of migraine aura. There remain many outstanding questions relating to the current limitations of both models and experimental evidence. Nevertheless, reaction-diffusion models, by providing an integrative theoretical framework, support the generation of testable experimental hypotheses to guide future research.

In this work, fluorinated graphene nanoscrolls (FGN) were synthesized via facile chemical methods under simple and mild conditions. Interestingly, the formation of the featured FGN was significantly solvent sensitive. Experimental results indicated that in the presence of aprotic solvent, for example, N,N dimethylformamide (DMF), the reaction system inclined to form the interesting FGN nanostructures. The structure and morphology of the prepared FGN were detailed characterized by atomic force microscopy (AFM), transmission electron microscopy (TEM), scanning electron microscopy (SEM) and X-ray diffraction (XRD) etc. The obtained FGN was used as a cathode material for primary lithium ion batteries with superior discharge specific capacity (eg. 979.3 mAhg-1), stable discharge platform and high energy density (eg. 2287.9 Wh kg-1), which fosters it a high density, low cost and durable candidate for cathode material for lithium ion batteries..

In this paper, an electromechanical mass lifter system is designed, analyzed and compare using optimal and robust control theories. LQR and μ -synthesis controllers are used to improve the lift displacement by comparison method for tracking the desired step and sinusoidal wave signals input. Finally, the comparison simulation result prove the effectiveness of the electromechanical mass lifter system with μ -synthesis controller for improving the rise time, percentage overshoot, settling time and peak value of tracking the desired step displacement signal and improving the peak value for tracking the desired sinusoidal displacement signal with a good performance.

Tidal stream energy, due to its high level of consistency and predictability, is one of the feasible and promising type of renewable energy for future development and investment. Applicability of Blade Element Momentum (BEM) method for modeling the interaction of turbines in tidal arrays has been proven in many studies. Apart from its well-known capabilities, yet there is scarcity of research using BEM for the modeling of tidal stream energy farms considering full scale rotors. In this paper, a real geographical site for developing a tidal farm in the southern coasts of Iran is selected. Then, a numerical methodology is validated and calibrated for the selected farm by analyzing array of turbines. A linear equation is proposed to calculate tidal power of marine hydrokinetic turbines. This methodology narrows down the wide range of turbine array configurations, reduces the cost of optimization and focuses on estimating best turbine arrangements in a limited number of positions.

The purpose of this study is to ascertain whether implementation difficulty can be used in slot allocation model as a new mechanism for slightly weakening grandfather right. According to which, a linear integer programming model is designed to compare and analyze displacement, implementation difficulty and priority with different weights. Test results show that the implementation difficulty can be significantly reduced without causing excessive displacement and disruption of existing priorities, by weight setting while declared capacity is cleared. In addition to this, whether the movements are listed in order of descending priority or not have great impact on displacement and implementation difficulty within slot allocation model. Capacity is surely a key factor affecting displacement and implementation difficulties. This study contributes to propose a new mechanism for slightly weakening grandfather right, which can help decision makers to upgrade slot allocation policies.

The purpose of this study is to assess the concentration-response relations between conjunctivitis and exposure to ambient ozone. This retrospective study includes emergency department (ED) visits for conjunctivitis in Edmonton, Canada, for the period April 1992–March 2002. Daily average levels of ozone (range: 1.2–50.9, ppb), of temperature, and of relative humidity were estimated and used for the period of the study. For each of the considered exposure lags, (from 0 to 9 days), six different models were fitted to estimate the concentration-response function. The goodness of fit was assessed using the Akaike information criterion. During the period of the study, 17,211 ED visits for conjunctivitis were recorded and used. For all subjects together, a positive statistically significant association was obtained for the exposure lagged by 5 days. For female subjects, lags 1, 3, and 9 had positive statistically significant associations (lag 2 had negative associations). For male subjects, only lag 5 had a positive statistically significant association. The estimated non-linear concentration-response functions for the considered groups (all, males, females) and lags, revealed the associations along the exposure levels. The fitted shapes are described by algebraic functions and may have various forms. The estimated functions are useful to determine the risk associated with exposure to ground-level ozone.

The fatty-acid profiles of five main commercial pistachio cultivars, including Ahmad-Aghaei, Akbari, Chrok, Kalle-Ghouchi and Ohadi, were determined by gas chromatography: palmitic (C16:0), palmitoleic (C16:1), stearic (C18:0), oleic (C18:1), linoleic (C18:2), linolenic (C18:3) arachidic (C20:0) and gondoic (C20:1) acid. Based on the oleic to linoleic acid (O/L) ratio, a quality index was determined for these five cultivars: Ohadi (2.40) < Ahmad-Aghaei (2.60) < Kale-Ghouchi (2.94) < Chrok (3.05) < Akbari (3.66). Principal component analysis (PCA) of the fatty-acid data yielded three significant PCs, which together account for 80.0% of the total variance in the data set. A linear discriminant analysis (LDA) model evaluated with cross validation correctly classified almost all samples: the average percent accuracy for the prediction set was 98.0%. The high predictive power for the prediction set shows the ability to indicate the cultivar of an unknown sample based on its fatty-acid chromatographic fingerprint.

A numerical application of linear-molecule symmetry properties, described by the D_∞h point group, is formulated in terms of lower-order symmetry groups D_nh with finite n. Character tables and irreducible representation transformation matrices are presented for D_nh groups with arbitrary n-values. These groups are subsequently used in the construction of symmetry-adapted ro-vibrational basis functions for solving the Schrödinger equations of linear molecules as part of the variational nuclear motion program TROVE. The TROVE symmetrisation procedure is based on a set of "reduced" vibrational eigenvalue problems with simplified Hamiltonians. The solutions of these eigenvalue problems have now been extended to include the classification of basis-set functions using ℓ, the eigenvalue (in units of ℏ) of the vibrational angular momentum operator ${\widehat{L}}_z$ . This facilitates the symmetry adaptation of the basis set functions in terms of the irreducible representations of D_nh. ¹²C₂H₂ is used as an example of a linear molecule of D_∞h point group symmetry to illustrate the symmetrisation procedure.

We generalize the idea of quantum clock time to quantum spacetime reference frame via physical realization of a reference system by quantum rulers and clocks. Omitting the internal degrees of freedom (such as spins) of the physical rulers and clocks, only considering their metric properties, the spacetime reference frame is described by a bosonic non-linear sigma model (NLSM). We study the quantum behavior of the system under approximations, and obtain (1) a cosmological constant valued (2/π)ρ_c0 (ρ_c0 the critical density at near current epoch) which is very close to the observations; (2) an effective Einstein-Hilbert term; (3) the ratio of variance to mean-squared of spacetime interval tends to a universal constant 2/π in the infrared region. This effect is testable by observing a linear dependence between the inherent quantum variance and mean-squared of the redshifts from cosmic distant spectral lines. The proportionality is expected to be the observed percentage of the dark energy. The equivalence principle is also generalized to the quantum level.

Linear regression is a basic tool in mobile robotics, since it enables accurate estimation of straight lines from range-bearing scans or in digital images, which is a prerequisite for reliable data association and sensor fusing in the context of feature-based SLAM. This paper discusses, extends and compares existing algorithms for line fitting applicable also in case of strong covariances between the coordinates at each single data point, which must not be neglected if range-bearing sensors are used. Besides, particularly the determination of the covariance matrix is considered, which is required for stochastic modeling. The main contribution is a new error model of straight lines in closed form for calculating fast and reliably the covariance matrix dependent on just a few comprehensible and easily obtainable parameters. The model can be applied widely in any case when a line is fitted from a number of distinct points also without a-priori knowledge of the specific measurement noise. By means of extensive simulations the performance and robustness of the new model in comparison to existing approaches is shown.

The polarised emission from AGN jets carries information about the physical conditions at the emitting plasma elements while its temporal evolution probes the physical processes that introduce variability and dynamically modify the local conditions. Here we present the analysis of multi-frequency radio linear and circular polarisation datasets with the aim to exactly quantify the conditions in blazar jets. Our analysis includes both the careful treatment of observational datasets and numerical modelling for the reproduction of synthetic polarisation curves that can be compared to the observed ones. In our approach the variability is attributed to traveling shocks. The emission from the cells of our jet model is computed with radiative transfer of all Stokes parameters. The model also accounts for Faraday effects which map the low-energy particle populations. We present two extreme cases in terms of the significance of Faraday conversion in the production of circular polarisation. As we show, in both regimes the model gives realistic reproduction of the observed emission.

Recent research on fractional order control laws has introduced the fractional calculus concept into the field of control engineering. As described herein, we apply fractional order LQR control to a current-controlled attractive-force type magnetic levitation system, which is a strongly nonlinear and unstable system, to investigate its control performance through experimentation. First, to design the controller, a current-controlled attractive-force type magnetic levitation system expressed as an integer-order system is extended to a fractional order system expressed using fractional order derivatives. Then target value tracking control of levitated objects is achieved by adding states, described by the integrals of the deviation between the output and the target value, to the extended system. Next, a fractional order LQR controller is designed for the extended system. For state-feedback control such as fractional order servo LQR control, which requires information of all states, a fractional order state-observer is configured to estimate fractional order states. Simulation results demonstrate that fractional order servo LQR control can achieve equilibrium point stabilization and enable target-value tracking. Finally, to verify the fractional order servo LQR control effectiveness, experiments using the designed fractional order servo LQR control law are done with comparison to conventional integer-order servo LQR control.

A large number of bridges are designed and built without considering seismic actions and, differently from buildings, there are currently no comprehensive guidelines to evaluate existing bridges without performing, as in the well known incremental dynamic analysis (IDA), complex non linear dynamic analyses (RHA). Bridges are structurally very different from building but, at the same time, are sensitive to higher modes as well as many multi-storey buildings that inspired innovative pushover procedures such as the well known modal pushover analysis (MPA). In the present study the incremental modal pushover analysis (IMPA), a pushover based approach already proposed and applied on buildings by the same authors, is revised and proposed for bridges (IMPAβ). IMPAβ accounts for the effects of higher modes in order to accurately estimate the seismic response of bridges; the effect of higher modes is considered by introducing a suitable number of modes to ensure the participation of a predefined total effective modal mass. The efficiency of the proposed method is demonstrated by conducting a study on two bridges, one regular and one irregular, and the IDA analysis is employed as reference solution. Numerical results indicate good accuracy of the proposed method in assessing the seismic response and a very good accuracy if compared to other available pushover procedures available in the literature.

Optimizing faculty workload in higher education institutions is essential for enhancing faculty satisfaction, student learning, and institutional productivity. Traditional workload management approaches tend to simplify the realities of academic work, creating distortions that undermine the quality of the academic system. In this paper, we present the simplex method, a linear programming technique that can be used as a sophisticated technological solution for optimizing faculty workload. Using a comprehensive mathematical model and a Python code outline, we demonstrate the effective use of the simplex method to balance the teaching loads across the faculty. The obtained results indicate that this method is superior to traditional approaches in terms of efficiency and satisfaction. By doing this, we not only explore new horizons in scholarly discourse on faculty workload but also offer a practical tool for higher education institutions to enhance their operational efficiency and faculty functioning.

We deal with Ulam stability of second order periodic linear differential equations with periodic damping. Necessary and sufficient condition for the Ulam stability of second order periodic linear differential equations is obtained by giving an Ulam stability theorem and an Ulam instability theorem. These results extend the conclusions in relevant literature. In addition, for the situation of constant coefficients, the minimum Ulam constant is given.

This article develops duality principles applicable to originally non-convex primal variational formulations. More specifically, as a first application, we establish a convex dual approximate variational formulation for a non-linear Kirchhoff-Love plate model. The results are obtained through basic tools of functional analysis, calculus of variations, duality and optimization theory in infinite dimensional spaces. We emphasize such a convex dual approximate formulation obtained may be applied to a large class of similar models in the calculus of variations. Finally, in the last section, we present a duality principle and respective convex dual formulation for a Ginzburg-Landau type equation.

Two approaches are being proposed to complements existing practical implementations of quantum information processing; (a) Multiplexed Michelson interferometry for Linear Optical quantum computation which should in principle split further an initially split beam to yield new sets of beams which are scalable to multiple interferometric outputs beyond just the dual output in Mach Zehnder interferometry. Generally Interferometry is applied in quantum computation particularly linear optical quantum computation schemes such as K.L.M protocol using the Mach-Zehnder interferometer, however a multiplexed Michelson interferometry enables the production of scalable cross-correlated beams making it suitable for optical multi-qubit operations. (b) Coupled LDR Circuits for Quantum emulation which can model cross correlation and probabilistic qubit states to enable parallelization and Gating on Classical electrical circuits. The system is to be designed as a network of electrical circuits coupled to each other using electrical coupling elements and are equipped with a light dependent resistor (LDR) alternatively referred to as photo-resistor to provide variable resistance in response to varied intensity of incident light. The maximum threshold current state which is being defined for the circuit and a minimum current state corresponds to 1 and 0 binary states respectively, however an intermediate current state models a superposition of 1 & 0. Likewise varying the intermediate current values closer to either 1 or 0 is akin to a probability rotation of the qubit states which is achieved by varying resistance using the LDR where the multi-circuit coupling interaction helps emulates cross-correlation of multi-qubit systems. The proposed system can be useful at least as a tool for informative applications in a classical framework.

In recent years, transformer-based models have gained prominence in multivariate long-term time series forecasting (LTSF), demonstrating significant advancements despite facing challenges such as high computational demands, difficulty in capturing temporal dynamics, and managing long-term dependencies. The emergence of LTSF-Linear, with its straightforward linear architecture, has notably outperformed transformer-based counterparts, prompting a reevaluation of the transformer's utility in time series forecasting. In response, this paper presents an adaptation of a recent architecture termed extended LSTM (xLSTM) for LTSF. xLSTM incorporates exponential gating and a revised memory structure with higher capacity that has good potential for LTSF. Our adopted architecture for LTSF termed as xLSTMTime surpasses current approaches. We compare xLSTMTime's performance against various state-of-the-art models across multiple real-world datasets, demonstrating superior forecasting capabilities. Our findings suggest that refined recurrent architectures can offer competitive alternatives to transformer-based models in LTSF tasks, potentially redefining the landscape of time series forecasting.

A single-track magnetic code tape based absolute position sensor system is demonstrated. Unlike traditional dual-track systems, our method simplifies manufacturing and avoids crosstalk between tracks, offering higher tolerance to alignment errors. The sensing system employs an array of magnetic field sensing elements that recognize the bit sequence encoded on the tape. This approach allows for accurate position determination even when the number of sensing elements is fewer than the number of bits covered, and without the need for specific spacing between sensing elements and bit length. We demonstrate the system's ability to learn and adapt to various magnetic code patterns, including those that are irregular or have been altered. Our method can identify and localize the sensed magnetic field pattern directly within a self-learned magnetic field map, providing robust performance in diverse conditions. This self-adaptive capability enhances operational safety and reliability, as the system can continue functioning even when the magnetic tape is misaligned or has undergone changes.

The increase in population and the challenges caused by it are always among the concerns of decision-makers and policymakers in large countries. One of the most serious concerns is in the field of energy consumption. Optimizing energy use is one of the most effective ways to manage limited resources and energy. Energy consumption in residential houses constitutes a significant percentage of the total energy consumption worldwide; therefore, current research focusing on mathematical models aims to provide a predictive multi-objective linear mathematical model for residential house consumption. For this purpose, the consumption of water, electricity, and gas for 80 residential houses, including 10 household appliances and equipment on a weekly basis, has been considered. The results showed that the mixed-integer multi-objective predictor model is able to optimize household consumption plans compared to the actual state of household energy consumption. Since the goals of household satisfaction and energy consumption costs in the model conflict with each other, the influence coefficient was calculated to demonstrate the simultaneous achievement of these goals. The optimal value achievable with the default model for the model's purposes is 69%.

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.

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.

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.