In real-life scenario, there are many mathematical tools to handle the incomplete and imprecise data. One of them is the fuzzy approach. This article aims to contribute to the literature of fuzzy multi-objective dynamic programming issues involving the fuzzy objective functions. The piecewise quadratic fuzzy numbers characterize these fuzzy parameters. Some basic notions in the problem under the α-pareto optimal solution concept is redefined and analyzed to study the stability of the problem. Furthermore, a technique, named as enhancing decomposition approach, is presented for achieving a subset for the parametric space that contains the sameα-pareto optimal solution. For a better understanding and comprehension of the suggested concept, a numerical example is provided.

Nonlinear rheological properties of chiral crystal cholesteryl oleyl carbonate (COC) in blue phase III are investigated under different shear deformations; large amplitude oscillatory shear, step shear deformation, and continuous shear flow. Rheology of the liquid crystal is significantly affected by structural rearrangement of defects under shear flow. One of the examples on the defect-mediated rheology is the blue phase rheology. Blue phase is characterized by three dimensional network structure of the disclination lines. It has been numerically studied that the rheological behavior of the blue phase is dominated by destruction and creation of the disclination networks. In this study, we find that the nonlinear viscoelasticity of BPIII is characterized by the fracture of the disclination networks. Depending on the degree of the fracture, the nonlinear viscoelasticity is divided into two regimes; the weak nonlinear regime where the disclination network locally fractures but still show elastic response, and the strong nonlinear regime where the shear deformation breaks up the networks, which results in a loss of the elasticity. Continuous shear deformation reveals that a series of the fracture process delays with shear rate. The shear rate dependence suggests that force balance between the elastic force acting on the disclination lines and the viscous force determines the fracture behavior.

In this article, the usual factorials and binomial coefficients have been generalized and extended to the negative integers. Basing on this generalization and extension, a new kind of polynomials has been proposed, which led directly to the non-classical hypergeometric orthogonal polynomials and the non-classical second-order hypergeometric linear DEs. The resulting polynomials can be used in non-relativistic and relativistic QM, particularly, in the case of the Schrödinger equation, and Dirac equations for an electron in a Coulomb potential field.

We present a method to turn results of model-based optimisations into resilient and comprehensible control strategies. Our approach is to define priority lists for all available technologies in a district energy system. Using linear discriminant analysis and the results of the optimisations, these are then assigned to discrete time steps using a set of possible steering parameters. In contrast to the model-based optimisations, the deduced control strategies do not need perfect foresight but solely rely on data about the present. Our result indicate that the results of the control strategies obtained using the proposed method are comparable to the results of the linear optimisations, in our case in terms of emissions and prices.

To obtain an accurate and reproducible experimental results in microbial fuel cell (MFC), it is important to know ‘anode maturation biofilm’ to produce a stable and maximum performance. For this purpose, four single chamber MFCs were tested in this study. The linear sweep voltammetry (LSV) polarization tests illustrated that maximum power densities of three MFCs became stable after 9 weeks. Although there were variations afterwards, such variations were negligible. Average maximum power densities from the 9th to the 17th week were 2,990 mW/m2 (MFC-4), 2,983 mW/m2 (MFC-2), 2,368 mW/m2 (MFC-3) and 837 mW/m2 (MFC-1). Polarization resistance shows that MFC-1 had much larger anode resistance (36.6-85.4 Ω) than the other MFCs (1.7-11.6 Ω). Anodic cyclic voltammetry (CV) shows that current production increased over time and MFC-1 had much smaller current production (24.4 mA) than the other MFCs (31.0-34.9 mA) at 17th week. The increased current production indicates anode biofilm became more mature over time, but overall cell performance did not increased accordingly. Possibly due to the bad inoculation, MFC-1 showed the lowest performance. However, its performance was restored to the initial performance and anode resistance was reduced by 47% at 17th week. This study shows that the optimum anode maturation time is 9 weeks and that bioanode performance is a key factor for MFC performance. This study also shows than LSV polarization and CV tests are accurate and non-destructive measurement methods for diagnosing anode performance.

A four-parameter kinematic model for the position of a fluid parcel in a time-varying ellipse is introduced. For any ellipse advected by an arbitrary linear two-dimensional flow, the rates of change of the ellipse parameters are uniquely determined by the four parameters of the velocity gradient matrix, and vice-versa. This result, termed ellipse/flow equivalence, provides a stronger version of the well-known result that a linear velocity field maps an ellipse into another ellipse. Moreover, ellipse/flow equivalence is shown to be a manifestation of Stokes' theorem. This is done by deriving a matrix-valued relationship, called the geometric Stokes' theorem, that involves a spatial integral over the velocity gradient tensor, thus accounting for the two strain terms in addition to the divergence and vorticity. General expressions for various physical properties of an elliptical ring of fluid are also derived. The ellipse kinetic energy is found to be composed of three portions, associated respectively with the circulation, the rate of change of the moment of inertia, and the variance of parcel angular velocity around the ellipse. A particular innovation is the use of four matrices, termed the IJKL basis, that greatly facilitate the required calculations.

Satellite Image Time Series (SITS) is a data set which includes satellite images across several years with a high acquisition rate. Radiometric normalization is a fundamental and important preprocessing method for remote sensing applications using SITS due to the radiometric distortion caused by noise between images. Normalizing the subject image based on the reference image is a general strategy when using traditional radiometric normalization methods to normalize multi-temporal imagery (usually two scenes or three scenes in different time phases). However, these methods are not suitable for calibrating SITS because they cannot minimize the radiometric distortion between any pair of images in SITS. The existing relative radiometric normalization methods for SITS are based on linear assumptions which cannot effectively reduce nonlinear radiometric distortion caused by continuously changing noise in SITS. To overcome this problem and obtain a more accurate SITS, this study proposed a Nonlinear Radiometric Normalization Model (named NMAG) for SITS based on Artificial Neural Networks (ANN) and Greedy Algroithm (GA) . In this method, GA was used to determine the correction order of SITS and calculate the error between the image to be corrected and normalized images, which avoided the selection of a single reference image. ANN was used to obtain the optimal solution of error function, which minimized the radiometric distortion between different images in SITS. SITS composed of 21 Landsat-8 images in Tianjin City from October 2017 to January 2019 were selected to test the method. We compared NMAG with other two contrasting method (refered as CM1 and CM2), and found that the average of root mean square error $(\mu_{RMSE})$ of NMAG $(497.22)$ was significantly smaller than those of CM1 $(641.39)$ and CM2 $(543.47)$, and the accuracy of normalized SITS obtained by using NMAG has increased by 22.4\% and 8.5\% toward CM1 and CM2, respectively. These experimental results confirmed the effectiveness of NMAG in the reduction of radiometric distortion caused by continuously changing noise between images in SITS.

Non-intrusive load monitoring (NILM) is a core technology for demand response (DR) and energy conservation services. Traditional NILM methods are rarely combined with practical applications, and most studies aim to decompose the whole loads in a household, which leads to low identification accuracy. In this paper, an NILM approach based on multi-feature integrated classification (MFIC) is explored, which combines some non-electrical features such as ON/OFF duration, usage frequency of appliances, and usage period to improve load differentiability. The implementation of MFIC algorithm is consistent with traditional event-based method. The uniqueness of our algorithm is that it designs an event detector based on steady-state segmentation and a linear discriminant classifier group based on multi-feature global similarity. Simulation results using an open-access dataset demonstrate the effectiveness and high accuracy of MFIC algorithm, with the state-of-the-art NILM methods as benchmarks.

Based on the fractional order of nonlinear system for love model with a periodic function as an external force, analyzed the characteristics of the chaotic dynamic in this study. The relationship between the chaotic dynamic of the fractional-love model with the external force and the fractional-order system was analyzed when the parameters are fixed. Further, we also studied the relationship between the chaotic systemic dynamic and the parameters when the fractional-order system is fixed. The results show that when the parameters are fixed, the fractional-order system exhibited segmented chaotic states for the different fractional orders of the system. When fixed the fractional-order system, the system exhibited the periodic and chaotic states as parameter changes.

Recently a new class of experiments in the field of surface gravity waves has emerged. These experiments serve as demonstration of an analogy to a broad variety of phenomena in optics and quantum mechanics. In particular, experiments involving Airy water-wave packets were carried out. The Airy wave packets have attracted tremendous attention in optics and quantum mechanics owing to their unique properties, spanning from an ability to propagate along parabolic trajectories without spreading, and to accumulating a phase that scales with the cubic power of time. Non-dispersive Cosine-Gauss wave packets and self-similar Hermite-Gauss wave packets, also well known in the field of optics and quantum mechanics, were recently studied using surface gravity waves as well. These wave packets demonstrated self-healing properties in water wave pulses as well, preserving their width despite being dispersive. Finally, this new approach also allows to observe diffractive focusing from a temporal slit with finite width.

The Lamiaceae belong to the species-richest families of flowering plants and harbor many species used as herbs or for medicinal applications, such as Basils or Mints. Evolution of this group has been driven by chemical speciation, mainly of Volatile Organic Compounds (VOCs). The commercial use of these plants is characterized by a large extent of adulteration and surrogation. To authenticate and discern the species, is, thus, relevant for consumer safety, but usually requires cumbersome analytics, such as Gas Chromatography, often to be coupled with Mass Spectroscopy. We demon-strate here that quartz-crystal microbalance (QCM)-based electronic noses provide a very cost-efficient alternative, allowing for a fast, automated discrimination of scents emitted from leaves of different plants. To explore the range of this strategy, we used leaf material from four genera of Lamiaceae along with Lemongrass as similarly scented, but non-related outgroup. In order to unambiguously differentiate the scents from the different plants, the output of the 6 different SURMOF/QCM sensors was analyzed using machine learning (ML) methods, together with a thorough statistical analysis. The exposure and purging datasets (4 cycles) obtained from a QCM-based, low-cost homemade portable e-Nose were analyzed with Linear Discriminant Analysis (LDA) classification model. Prediction accuracies with repeating test measurements reached values of up to 90%. We show that it is not only possible to discern and identify plants on the genus level, but even to discriminate closely related sister clades within a genus (Basil), demonstrating that e-Noses are a powerful technology to safeguard consumer safety against the challenges of globalized trade.

Ocean surface waves have been utilized as fundamental information in various fields of oceanic research. In this paper, we suggest a simulation and modelling technique for generating an ocean surface wave using an inverse Fast Fourier Transform (iFFT), and we subsequently verify the wave’s accuracy. The conventional method, linear superposition, requires recursive calculation because of the double summation and the time variable; to circumvent this issue, the new algorithm is presented. The Joint North Sea Wave Project (JONSWAP) spectrum is utilized for the ocean surface wave simulation example, and the parameters are the significant wave height (HS) and the zero-crossing wave period (TZ). A coordinate transform for the wavenumber domain was used to apply the inverse FFT algorithm. To verify the accuracy of the simulation result, the relative error between the input condition and the analysis result was calculated. The result for TZ is below 4% relative error, and the maximum relative error for HS is 7%. To avoid the Nyquist frequency for wave-field analysis and simulation, the minimum grid size was calculated by twice applying the maximum wavenumber.

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.

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.

In this paper, design of optical spectral filters based on mode coupling of optical fibers is presented. The finite difference method is applied to find the dispersion characteristics of optical fiber coupler constructing from two fibers as a composite multi-dielectric waveguide with different cores but the same cladding. Also, the field distribution for both fibers as a separate and as a composite waveguide. The spectral characteristics of the filters are investigated depending on the coupling of two linear polarized modes LP01 and LP11. The dependence of the transmission coefficient on operating wavelengths is illustrated. Finally, the spectral bandwidth of filter as a function of the distance between the two cores is addressed.

Neural networks models are mostly represented by oriented graphs where only the components, constitutive elements of the graph, are transcribed into mathematical xpression. Indeed, accurate knowledge of the full expression of the model is required in certain situations such as selecting among several reference models, the one that best fits the available data or comparing the explanatory and predictive performance of an established model with respect to some reference models. In this paper, we establish a formalism of the mathematical expression for multilayer perceptron neural network in a general framework, MLP-p-n-q, with p, n and q natural integers and show its restriction to cases where one has a hidden layer and multivariate outputs (MLP-p-1-q), and then a single output (MLP-p-1-1). Then, we give some specific cases of the most commonly used models. An application case is presented in the context of solving a nonlinear regression problem.

Crop production is a major livelihood activity of smallholders in Ethiopia. However, it is often characterized by low performance. In an effort to improve crop production, a series of agricultural extension programs have been running in Ethiopia since the 1950s. Nevertheless, the performance of agriculture is still low. In this study, it is argued that the limited attention given to cropland allocation methodologies is one of the major causes of low performance of crop production and increased environmental degradation. This study used linear programming to examine the role and impacts of cropland allocation methods on performance of crop production. The data for this study was drawn from household survey of 75 randomly selected households combined with focus-grouped discussion, key informant interview, and secondary data. In the current conventional cropland allocation, households were not able to meet their household consumption. The average profitability of farms under current practice was found significantly below than estimated optimal level of profit that could be realized using linear programming. In addition, it uncovered that low performance of crop production (in terms of meeting household consumption demand and profitability) is the primary cause that limited the effort of households to participate in environmental and natural resource management. This study suggests the use of linear programming-based cropland allocation to enhance the profit performance of smallholder crop production, meeting household consumption requirement, and thereby promote sustainable utilization of natural and environmental resources.

DGJ (Daftardar-Gejii-Jafaris) method is used to obtain numerical solution of the third order fractional differential equation. Providing the DGJ method converges, the approximate solution is a good and effective numerical result which is close to the exact solution or the exact solution. For this,the examples of the explaning the method are presented. The proposed method is implemented for the approximation solution of the third order nonlinear fractional partial differential equations. The method was shown to be unsuitable and inconsistent for an example of a nonlinear fractional partial differential equation depend on initial-boundary value conditions. The fact that these numerical results are not consistent can be explained by the fact that the method is not convergent.

The remaining capacity can only be measured with offline method. This brings great challenge for the online prediction of Li-ion battery’s RUL. A novel online prediction method for Li-ion battery’s RUL was proposed, which is based on multiple health indicators (HIs) and can be derived from the batteries’ historical operation data. Firstly, four indirect HIs were built according to the battery’s operation current, voltage and temperature data respectively. On that basis, a generalized regression neural network (GRNN) was developed to estimate the battery’s remaining capacity, and the non-linear autoregressive approach (NAR) was utilized to predict the battery’s RUL based on the estimated capacity value. Furthermore, to reduce the interference, twice wavelet denoising were performed with different thresholds. A case study is conducted with a NASA battery dataset to demonstrate the effectiveness of the method. The result shows that the proposed method can obtain Li-ion batteries’ RUL effectively.

Regression models form the core of the discipline of econometrics. One of the basic assumptions of classical linear regression model is that the values of the explanatory variables are fixed in repeated sampling. However, in most of the real life cases, particularly in economics the assumption of fixed regressors is not always tenable. Under a non-experimental or uncontrolled environment, the dependent variable is often under the influence of explanatory variables that are stochastic in nature. There is a huge literature related to stochastic regressors in various aspects. In this paper, a historical perspective on some of the works related to stochastic regressor is being tried to pen down based on literature search.

Since the electro-hydraulic servo shaking table exists many nonlinear elements, such as, dead zone, friction and blacklash, its acceleration response has higher harmonics which result in acceleration harmonic distortion, when the electro-hydraulic system is excited by sinusoidal signal. For suppressing the harmonic distortion and precisely identify harmonics, a combination of the adaptive linear neural network and least mean M-estimate (ADALINE-LMM), is proposed to identify the amplitude and phase of each harmonic component. Namely, the Hampel’s three-part M-estimator is applied to provide thresholds for detecting and suppressing the error signal. Harmonic generators are used by this harmonic identification scheme to create input vectors and the value of the identified acceleration signal is subtracted from the true value of the system acceleration response to construct the criterion function. The weight vector of the ADALINE is updated iteratively by the LMM algorithm, and the amplitude and phase of each harmonic, even the results of harmonic components, can be computed directly online. The simulation and experiment are performed to validate the performance of the proposed algorithm. According to the experiment result, the above method of harmonic identification possesses great real-time performance and it has not only good convergence performance but also high identification precision.

One of the non-linear phenomena that affect high bandwidth and long reach communication systems is the non-linear phenomenon called four-wave mixing (FWM). Unfortunately, the simulation of such systems aiming to obtain their design parameter limitations require more time as the number of channels increases. In this paper, we propose a new high-performance computational model to obtain optimal design parameters in a multi san Dense Wavelength Division Multiplexing (DWDM) system, limited by FWM and the intrinsic Amplified Spontaneous Emission (ASE) noise of optical amplifiers employed in each segment. The simulation in this work provides a complete optical design characterization and compares the efficiency and speed improvement of the proposed parallelization model versus a previous sequential model. Additionally, an analysis of the computational complexity of parallel model is presented, where two parallel implementations are used. First, Open Multi−Processing (OpenMP), based on the use of a central, multi-core processing unit is used and secondly the Compute Unified Device Arquitecture (CUDA), which is based on the use of graphics processing unit. Results show that parallelism improves to up to 40 times the performance of the simulation when nested parallelization with CUDA is used, over de sequential method and up to 6 times compared with the implementation with OpenMP using 12 processors. Within our parallel implementation, it is possible to simulate with an increased number of channels, that was unpractical in the sequential simulation.

Remote sensing is one of the modern methods that have significantly developed over the last two decades and nowadays provides a new means for forest monitoring. High spatial and temporal resolutions are demanded for accurate and timely monitoring of forests. In this study multi-spectral Unmanned Aerial Vehicle (UAV) images were used to estimate canopy parameters (definition of crown extent, top and height as well as photosynthetic pigment contents). The UAV images in Green, Red, Red-Edge and NIR bands were acquired by Parrot Sequoia camera over selected sites in two small catchments (Czech Republic) covered dominantly by Norway spruce monocultures. Individual tree extents, together with tree tops and heights, were derived from the Canopy Height Model (CHM). In addition, the following were tested i) to what extent can the linear relationship be established between selected vegetation indexes (NDVI and NDVIred edge) derived for individual trees and the corresponding ground truth (e.g., biochemically assessed needle photosynthetic pigment contents), and ii) whether needle age selection as a ground truth and crown light conditions affect the validity of linear models. The results of the conducted statistical analysis show that the two vegetation indexes (NDVI and NDVIred edge) tested here have a potential to assess photosynthetic pigments in Norway spruce forests at a semi-quantitative level, however the needle-age selection as a ground truth was revealed to be a very important factor. The only usable results were obtained for linear models when using the 2nd year needle pigment contents as a ground truth. On the other hand, the illumination conditions of the crown proved to have very little effect on the model’s validity. No study was found to directly compare these results conducted on coniferous forest stands. This shows that there is a further need for studies dealing with a quantitative estimation of the biochemical variables of nature coniferous forests when employing spectral data acquired by the UAV platform at a very high spatial resolution.

The goal of this paper is to propose a dual version of the direct cosine simplex algorithm (DDCA) for general linear problems. Unlike the two-phase and the big-M methods, our technique does not involve artificial variables. Our technique solves the dual Klee-Minty problem in two iterations and solves the dual Clausen’s problem in four iterations. The utility of the proposed method is evident from the extensive computational results on test problems adapted from NETLIB. Preliminary results indicate that this dual direct cosine simplex algorithm (DDCA) reduces the number of iterations of two-phase method.

A real-time two-way direct load control (TWDLC) of central air-conditioning chillers in wide area is proposed to provide demand response. The proposed TWDLC scheme is designed to optimize the load shedding ratio of every customer under control to ensure the target load to be shed is met at every scheduling period. In order to overcome the load reduction uncertainties of TWDLC, an innovative solution is proposed by applying a certain degree of loosening on the constraint of the actual shed load. Fuzzy linear programming is utilized to solve the optimization problem with fuzzy constraints. The proposed fuzzy linear programming problem is solved by delicately transforming it into a regular liner programming problem. A selection scheme used to obtain the feasible candidates set for load shedding at every sampling interval of TWDLC is also designed along with the fuzzy linear programming.

This study addresses an alternative use of viscous dampers (VDs) associated with buckling restrained braces (BRBs) as the innovative seismic protection devices. For this, 4, 8 and 12 storey steel frames were designed with 6.5 m equal span length and 4 m storey height. Thereafter, the VDs and BRBs were placed over the height of each frame considering three different configurations. The structures were modeled using SAP2000 finite element program and evaluated by the nonlinear time history analyses subjected to the six natural accelerograms (1976 Gazlı, 1978 Tabas, 1987 Superstition Hills, 1992 Cape Mendocino, 1994 Northridge and 1999 Chi-Chi). The structural response of the structures with and without VDs and BRBs were studied in terms of variation in the displacement, interstorey drift, absolute acceleration, maximum base shear, time history of roof displacement. The results clearly indicated that the application of VDs and BRBs had remarkable improvement in the earthquake performance of the case study frames by reducing the local/global deformations in the main structural systems and satisfied the serviceability.

Endothelial disorders are related to various diseases. An initial endothelial injury is characterized by endothelial glycocalyx injury. We aimed to evaluate endothelial glycocalyx injury by measuring serum syndecan-1 concentrations in patients during comprehensive medical examinations. A single-center, prospective, observational study was conducted at Asahi University Hospital. The participants enrolled in this study were 1313 patients who underwent comprehensive medical examinations at Asahi University Hospital from January 2018, to June 2018. One patient undergoing hemodialysis was excluded from the study. At enrollment, blood samples were obtained, and study personnel collected demographic and clinical data. No treatments or exposures were conducted except for standard medical examinations and blood sample collection. Laboratory data were obtained by collection of blood samples at the time of study enrolment. According to nonlinear regression, the concentrations of serum syndecan-1 were significantly related to age (p = 0.016), aspartic aminotransferase concentration (AST, p = 0.020), blood urea nitrogen concentration (BUN, p = 0.013), triglyceride concentration (p < 0.001), and hematocrit (p = 0.006). These relationships were independent associations. Endothelial glycocalyx injury, which is reflected by serum syndecan-1 concentrations, is related to age, hematocrit, AST concentration, BUN concentration, and triglyceride concentration.

This study presents the substantiation, development, and analysis of a technique for planning the autonomous vehicle (AV) motion reference parameters. The trajectory plan, speed and acceleration distributions, including other AV's kinematic parameters, are determined using sequential optimization. The study objectives are based on an analysis of the fundamental problems of AV motion planning summarized in this area's latest publications. The proposed approach combines the basic principles of the finite element method (FEM) and nonlinear optimization with nonlinear constraints. First, the generalization on representing an investigated function by finite elements (FE) is briefly described. A one-dimension FE with two nodes and three degrees of freedom (DOF) in a node was chosen as the basic one, corresponding to the 5th-degree polynomial. Next, a method for determining the motion trajectory is presented. The following are considered: formation of a restricted space for the AV's allowable maneuvering, the geometry of motion trajectory and its relation with vehicle steerability parameters, cost functions and their influences on the desirable trajectory's nature, compliance of nonlinear restrictions of the node parameters with the motion area boundaries. At the second stage, a technique for optimizing AV speed and acceleration redistribution is presented. The model considers possible combinations of cost functions, conditions of limiting the kinematic parameters with the tire slip critical speed, maximum speed level, maximum longitudinal acceleration, and critical lateral acceleration. In the simulation section, several variants of trajectories were searched and compared. Several versions of distributing the longitudinal speed and acceleration curves are determined, and their comparative analysis is fulfilled. At the end of the paper, the advantages and drawbacks of the proposed technique are noted. The conclusion is made regarding the options for improving the method in further studies.

In this paper we introduce the hypo-q-norms on a Cartesian product of algebras of bounded linear operators on Hilbert spaces. A representation of these norms in terms of inner products, the equivalence with the q-norms on a Cartesian product and some reverse inequalities obtained via the scalar reverses of Cauchy-Buniakowski-Schwarz inequality are also given. Several bounds for the norms δ_p, ϑ_p and the real norms η_r,p and θ_r,p are provided as well.

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.

This article aims to solve the problem of robust supervision of a reverse osmosis desalination system (RO-DS) with two models, external model and bond graph model. The structure of an industrial system from the point of view of the external model operates according to several modes of operation (degraded and normal). For this external model, we cannot locate the faults since we are talking about a global operation of the system. The possible solution for the development of research was to use the multidisciplinary model called bond graph. This model by its graphic nature and using a unified language makes it possible to model the industrial system element by element from where it helps the user not only to detect the faults but also to locate them when they appear in the system. The results suggest that the use of the bond graph model for alarm 02 is a reverse osmosis error (RO1); these phenomena are readable on the bond graph model and can be quantified by equations. The equation of the model of this reverse osmosis (RO1) is found in the residual equations (r5, r6 and r7), so that these residues will be sensitive to this rupture. The possible solution during research development was to use the bond graph model to supplement information with physical knowledge and to locate faults. This article also describes the operating safety (by minimizing false alarms and non-detections as well as delays in fault detection) of the desalination system by using the bond graph model described in Linear Fractional Transformation (LFT) form for enable it to manage the robust supervision of a desalination system. An approach based on (LFT-BG) is developed to monitor tank leakage (Cu) and reverse osmosis (RO1 and RO2) faults or valve level (V1 and V2) closures and membrane clogging reverse osmosis (Rm1 and Rm2) that can occur in the reverse osmosis desalination system (RO-DS).

Electrode is a key component in a microbial electrolysis cell (MEC) and it needs significant improvement for practical implementation of MEC. For effective development of electrode technology, accurate and reproducible analytical methods are very important. Linear sweep voltammetry (LSV) is an essential analytical method for evaluating electrode performance; however, it has not been firmly established yet in the MEC field. In this study, biological brush (BB), abiotic brush (AB), Pt wire (PtW), stainless steel wire (SSW) and mesh (SSM)) were tested to explore the most suitable counter electrode in different medium conditions. Coefficient of variation (CV) for Imax of LSV were comparatively analyzed. In BB-anode LSV, SSW (0.48%) and SSM (2.17%) showed higher reproducibility as a counter electrode. In SSM-cathode LSV, BB (1.76%) and PtW (2.01%) produced more reproducible results. In the Ni-AC-SSM-cathode LSV, PtW (3.54%) and BB (8.81%) produced more reproducible result. It shows electrode used in the operation is an appropriate counter electrode in the acetate-added condition. However, in the absence of acetate, PtW (1.24%) and BB (1.71%) produced more reproducible results in SSM cathode and PtW (0.61%) and SSW (1.21%) did in the Ni-AC-SSM-cathode, showing PtW is an appropriate counter electrode. These results also shows that PtW is an appropriate counter electrode in cathode LSV.

In this paper, we proposed a new model of non-linear electrodynamics with parameter. Firstly, we study the weak limit approximation and by using the Gauss Bonnet theorem, we obtain the deflection angle of photon from magnetized black hole and effect of bnon-linear electrodynamics. In doing so, we find the corresponding optical metric after that we calculate the Gaussian curvature which is used in Gauss Bonnet theorem. Then we show the deflection angle in the leading order terms. We also analyzed that our results reduces into Maxwell's electrodynamics and RN solution with the reduction of parameters. Moreover, we also investigate the graphical behavior of deflection angle w.r.t correction parameter, black hole charge and impact parameter.

Full-order state-space models represent the starting point for the development of advanced control methods for wind turbine systems (WTSs). Regarding existing control-oriented WTS models, two research gaps must be noted: (i) There exists no full-order WTS model in form of one overall ordinary differential equation that considers all dynamical effects which significantly influence the electrical power output; (ii) all existing reduced-order WTS models are subject to rather arbitrary simplifications and are not validated against a full-order model. Therefore, in this paper, two full-order nonlinear state-space models (of 11th and 9th-order in the (a, b, c)- and (d, q)-reference frame, resp.) for variable-speed variable-pitch permanent magnet synchronous generator WTSs are derived. The full-order models cover all relevant dynamical effects with significant impact on the system’s power output, including the switching behavior of the power electronic devices. Based on the full-order models, by a step-by-step model reduction procedure, two reduced-order WTS models are deduced: A non-switching (averaging) 7th-order WTS model and a non-switching 3rd-order WTS model. Comparative simulation results reveal that all models capture the dominant system dynamics properly. The full-order models allow for a detailed analysis covering the high frequency oscillations in the instantaneous power output due to the switching in the power converters. The reduced-order models provide a time-averaged instantaneous power output (which still correctly reflects the energy produced by the WTS) and come with a drastically reduced complexity making those models appropriate for large-scale power grid controller design.

Damage detection based on modal parameter changes becomes popular in the last decades. Nowadays are available robust and reliable mathematical relations to predict the natural frequency changes if damage parameters are known. Using these relations, it is possible to create databases containing a large variety of damage scenarios. Damage can be thus assessed by applying an inverse method. The problem is the complexity of the database, especially for structures with more cracks. In this paper, we propose two machine learning methods, namely the random forest (RF) and the artificial neural network (ANN) as search tools. The databases we developed contain damage scenarios for a prismatic cantilever beam with one crack and ideal and non-ideal boundary conditions. The crack assessment is made in two steps. First, a coarse damage location is found from the networks trained for scenarios comprising the whole beam. Afterward, the assessment is made involving a particular network trained for the segment of the beam on which the crack is previously found. Using the two machine learning methods, we succeed to estimate the crack location and severity with high accuracy for both simulation and laboratory experiments. Regarding the location of the crack, which is the main goal of the practitioners, the errors are less than 0.6%. Based on these achievements, we concluded that the damage assessment we propose, in conjunction with the machine learning methods, is robust and reliable.

In this paper, we are interested in a model of exact asymptotically flat charged hairy black holes in the background of dilaton potential. We study the weak gravitational lensing in the spacetime of hairy black hole in Einstein-Maxwell theory with a non-minimally coupled dilaton and its non-trivial potential. In doing so, we use the optical geometry of the flat charged hairy black hole for some range of parameter $\gamma$. For this purpose, by using Gauss-Bonnet theorem, we obtain the deflection angle of photon in a spherically symmetric and asymptotically flat spacetime. Moreover, we also investigate the impact of plasma medium on weak gravitational lensing by asymptotically flat charged hairy black hole with a dilaton potential. Our analytically analyses show the effect of the hair on the deflection angle in weak field limits.

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.

We present a new mathematical model of disease spread reflecting specialties of covid-19 epidemic by elevating the role social clustering of population. The model can be used to explain slower approaching herd immunity in Sweden, than it was predicted by a variety of other mathematical models; see graphs Fig. \ref{GROWTH2}. The hierarchic structure of social clusters is mathematically modeled with ultrametric spaces having treelike geometry. To simplify mathematics, we consider homogeneous trees with $p$-branches leaving each vertex. Such trees are endowed with algebraic structure, the $p$-adic number fields. We apply theory of the $p$-adic diffusion equation to describe coronavirus' spread in hierarchically clustered population. This equation has applications to statistical physics and microbiology for modeling {\it dynamics on energy landscapes.} To move from one social cluster (valley) to another, the virus (its carrier) should cross a social barrier between them. The magnitude of a barrier depends on the number of social hierarchy's levels composing this barrier. As the most appropriate for the recent situation in Sweden, we consider {\it linearly increasing barriers.} This structure matches with mild regulations in Sweden. The virus spreads rather easily inside a social cluster (say working collective), but jumps to other clusters are constrained by social barriers. This behavior matches with the covid-19 epidemic, with its cluster spreading structure. Our model differs crucially from the standard mathematical models of spread of disease, such as the SIR-model. We present socio-medical specialties of the covid-19 epidemic supporting our purely diffusional model.

We report the results of an analysis of the functional capabilities of the KTP crystal and its isomorphs for nonlinear-optical frequency conversion of all types of interaction in the transparency range of the crystal. The possibility of implementing angle-, wavelength- (frequency-) and temperature-noncritical phase matching is shown.

The present article addresses the long-standing problem of the polymer brush bilayers under stationary shear flow at non-linear response regime where the system gets a non-Newtonian fluid. The main idea behind this research would be the fact that the immense lubricity of the polymer brush bilayers originates from a global restructuring that takes place at large shear rates. It is shown here that physical quantities like, stress tensor, viscosity tensor, the friction coefficient and the chain extensions could become dependent on the shear rate at non-Newtonian regime. Apparently, the sub-linear scaling of the physical quantities at large shear rates is solely due to the fact that the chains stretch in the shear direction.

3D city models are being extensively used in applications such as evacuation scenarios and energy consumption estimation. The main standard for 3D city models is the CityGML data model which can be encoded through the CityJSON data format. CityGML and CityJSON use polygonal modelling in order to represent geometries. True topological data structures have proven to be more computationally efficient for geometric analysis compared to polygonal modelling. In a previous study, we have introduced a method to topologically reconstruct CityGML models while maintaining the semantic information of the dataset, based solely on the combinatorial map (C-Map) data structure. As a result of the limitations of C-Map's semantic representation mechanism, the resulting datasets could suffer either from semantic information loss or the redundant repetition of them. In this article, we propose a solution for a more efficient representation of both geometry, topology and semantics by incorporating the C-Map data structure in the CityGML data model and implementing a CityJSON extension to encode the C-Map data. In addition, we provide an algorithm for the topological reconstruction of CityJSON datasets to append them according to this extension. Finally, we apply our methodology to three open datasets in order to validate our approach when applied to real-world data. Our results show that the proposed CityJSON extension can represent all geometric information of a city model in a lossless way, providing additional topological information for the objects of the model.

Studies have shown that in many practical applications, data interpolation by splines leads to better approximation and higher computational efficiency as compared to data interpolation by a single polynomial. Data interpolation by splines can be significantly improved if knots are allowed to be free rather than at a priori fixed locations such as data points. In practical applications, the smallest possible curvature is often desired. Therefore, optimal splines are determined by minimizing a derivative of continuously differentiable functions comprising the spline of the required order. The problem of obtaining an optimal spline is tantamount to minimizing derivatives of a nonlinear differentiable function over a Banach space on a compact set. While the problem of data interpolation by quadratic splines has been accomplished analytically, interpolation by splines of higher orders or in higher dimensions is challenging. In this paper, to overcome difficulties associated with the complexity of the interpolation problem, the interval over which data points are defined, is discretized and continuous derivatives are substituted by their discrete counterparts. It is shown that as the mesh of the discretization approaches zero, a resulting near-optimal spline approaches an optimal spline. Splines with the desired accuracy can be obtained by choosing an appropriate mesh of the discretization. By using cubic splines as an example, numerical results demonstrate that the linear programming (LP) formulation, resulting from the discretization of the interpolation problem, can be solved by linear solvers with high computational efficiency and resulting splines provide a good approximation to the optimal splines.

We report enhanced nonlinear optics in complementary metal-oxide-semiconductor (CMOS) compatible photonic platforms through the use of layered two-dimensional (2D) graphene oxide (GO) films. We integrate GO films with silicon-on-insulator nanowires (SOI), high index doped silica glass (Hydex) and silicon nitride (SiN) waveguides and ring resonators, to demonstrate an enhanced optical nonlinearity including Kerr nonlinearity and four-wave mixing (FWM). The GO films are integrated using a large-area, transfer-free, layer-by-layer method while the film placement and size are controlled by photolithography. In SOI nanowires we observe a dramatic enhancement in both the Kerr nonlinearity and nonlinear figure of merit (FOM) due to the highly nonlinear GO films. Self-phase modulation (SPM) measurements show significant spectral broadening enhancement for SOI nanowires coated with patterned films of GO. The dependence of GO’s Kerr nonlinearity on layer number and pulse energy shows trends of the layered GO films from 2D to quasi bulk-like behavior. The nonlinear parameter of GO coated SOI nanowires is increased 16 folds, with the nonlinear FOM increasing over 20 times to FOM > 5. We also observe an improved FWM efficiency in SiN waveguides integrated with 2D layered GO films. FWM measurements for samples with different numbers of GO layers and at different pump powers are performed, achieving up to ≈7.3 dB conversion efficiency (CE) enhancement for a uniformly coated device with 1 layer of GO and ≈9.1 dB for a patterned device with 5 layers of GO. These results reveal the strong potential of GO films to improve the nonlinear optics of silicon, Hydex and SiN photonic devices.

This article, we study the sufficient conditions for the controllability of second-order impulsive partial neutral evolution differential systems with infinite delay in Banach spaces by using the theory of cosine families of bounded linear operators and fixed point theorem.

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.

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.

In spite of numerous predictions, the natural herd immunity for covid-19 visru had not been approahed anywhere in the world. Thus, the traditional mathematical models of disease spread demonstrated their inability to describe adequately the covid-19 pandemic. In author's works, the novel model of the disease spread was developed. This model reflects the basic features of the covid-19 pandemic: a) the social clustering character of virus spread, b) . Social clustering is mathematically modelled with ultrametric spaces having the treelike geometry encoding hierarchy of the regulation constraints. The virus spread is described by ultrametric diffusion or random walk on the hierarchic energy landscape. In contrast to the standard models which are characterized by the exponential decrease of the probability to become infected - at the stage of approaching of the herd immunity, the ultrametric model is characterized by the power law. Moreover, the model gives the possibility to quantify the influence of restriction measures up to the lockdown. Our main result is that the play with restrictions, including lockdowns, is counterproductive and leads to the essential slowdown of approaching the herd immunity or even makes this impossible.

The fifth Generation (5G) mobile networks use millimeter Waves (mmWaves) to offer giga bit data rates. However, unlike microwaves, mmWave links are prone to user and topographic dynamics. They easily get blocked and end up forming irregular cell patterns for 5G. This in turn cause too early, too late, or wrong handoffs (HOs). To mitigate HO challenges, sustain connectivity and avert unnecessary HO, we propose a HO scheme based on Jump Markov Linear System (JMLS) and Deep Reinforcement Learning (DRL). JMLS is widely known to account for abrupt changes in system dynamics. DRL likewise emerges as an artificial intelligence technique for learning highly dimensional and time-varying behaviors. We combine the two techniques to account for time-varying, abrupt, and irregular changes in mmWave link behaviour by predicting likely deterioration patterns of target links. The prediction is optimized by meta training techniques that also reduces training sample size. Thus, the JMLS-DRL platform formulates intelligent and versatile HO policies for 5G. Results show our proposed prediction scheme about target link behavior post HO to be highly reliable. The scheme also averts unnecessary HOs thus ably supports longer dew time.

We write the mutual information between an input speech utterance and its reconstruction by a Code-Excited Linear Prediction (CELP) codec in terms of the mutual information between the input speech and the contributions due to the short term predictor, the adaptive codebook, and the fixed codebook. We then show that a recently introduced quantity, the log ratio of entropy powers, can be used to estimate these mutual informations in terms of bits/sample. A key result is that for many common distributions and for Gaussian autoregressive processes, the entropy powers in the ratio can be replaced by the corresponding minimum mean squared errors. We provide examples of estimating CELP codec performance using the new results and compare to the performance of the AMR codec and other CELP codecs. Similar to rate distortion theory, this method only needs the input source model and the appropriate distortion measure.

Integrated photonic devices operating via optical nonlinearities offer a powerful solution for all-optical information processing, yielding processing speeds that are well beyond that of electronic processing as well as providing the added benefits of compact footprint, high stability, high scalability, and small power consumption. The increasing demand for high-performance nonlinear integrated photonic devices has facilitated the hybrid integration of novel materials to address the limitations of existing integrated photonic platforms, such as strong nonlinear optical absorption or an inadequate optical nonlinearity. Recently, graphene oxide (GO), with its large optical nonlinearity, high flexibility in altering its properties, and facile fabrication processes, has attracted significant attention, enabling many hybrid nonlinear integrated photonic devices with improved performance and novel capabilities. This paper reviews the applications of GO to nonlinear integrated photonics. First, an overview of GO’s optical properties and the fabrication technologies needed for its on-chip integration is provided. Next, the state-of-the-art GO nonlinear integrated photonic devices are reviewed, together with comparisons of the nonlinear optical performance of different integrated platforms incorporating GO. Finally, the challenges and perspectives of this field are discussed.

The relative dislocation density of aluminum and copper samples is quantitatively measured using linear Resonant Ultrasound Spectroscopy (RUS). For each metallic group, four samples were prepared with different thermomechanical treatments in order to induce changes in their dislocation densities. The RUS results are compared with Nonlinear Resonant Ultrasound Spectroscopy (NRUS) as well as Second Harmonic Generation (SHG) measurements. NRUS has a higher sensitivity by a factor of two to six and SHG by 14% to 62%. The latter technique is, however, faster and simpler. As main a result we obtain a quantitative relation between the changes in the nonlinear parameters and the dislocation density variations, which in a first approximation is a linear relation between these differences. We also present a simple theoretical expression that explains the better sensitivity to dislocation content of the nonlinear parameters with respect to the linear ones. X-Ray diffraction measurements, although intrusive and less accurate, support the acoustics results.

In this study, we investigate the performance of the saddlepoint approximation of the probability mass function and the cumulative distribution function for the weighted sum of independent Poisson random variables. The goal is to approximate the hazard rate function for this complicated model. The better performance of this method is shown by numerical simulations and comparison with a performance of other approximation methods.

Cellular Nonlinear Networks (CNN) are a concept introduced in 1988 by Leon Chua and Lin Yang as a bio-inspired architecture, capable of massively parallel computation. Later on, CNN have been enhanced by incorporating designs that incorporate memristors to profit from their processing and memory capabilities. In addition, Stochastic Computing (SC) can be used to optimize the quantity of required processing elements; thus it provides a lightweight approximate computing framework, quite accurate and effective, though. In this work, we propose utilization of SC in designing and implementing a memristor-based CNN. As a proof of the proposed concept, an example of application is presented. This application combines Matlab and a FPGA in order to create the CNN. The implemented CNN has then been used to perform three different real-time applications on a 512x512 gray-scale and a 768x512 color image: storage of the image, edge detection, and image sharpening. It has to be pointed out that the same CNN has been used for the three different tasks, with the sole change of some programmable parameters. Results show an excellent capability with significant accompanying advantages, like the low number of needed elements further allowing for a low cost FPGA-based system implementation, something confirming the system’s ability for real time operation.

Since December 2019, the coronavirus disease (COVID-19) has rapidly spread worldwide. The Mexican government has implemented public safety measures to minimize the spread of the virus. In this paper, the authors use statistical models in two stages to estimate the total number of coronavirus (COVID-19) cases per day at the state and national level in Mexico. Two types of models are proposed: first, a polynomial model of the growth for the first part of the outbreak until the inflection point of the pandemic curve and then a second nonlinear growth model is used to estimate the middle and the end of the outbreak. Model selection will be performed using Vuong’s test. The proposed models show overall fit similar to predictive models (e.g. time series, and machine learning); however, the interpretation of parameters is less complex for decision-makers and the residuals follow the expected distribution when fitting the models without autocorrelation being an issue.

Reverse-order laws for generalized inverses of matrix products is a classic object of study in the theory of generalized inverses. One of the well-known reverse-order laws for a matrix product AB is (AB)^(i,...,j) = B^(i,...,j)A^(i,...,j), where (·)^i,...,j denotes an {i,...,j}-generalized inverse of matrix. Because {i,...,j}-generalized inverse of a general matrix is not necessarily unique, the relationships between both sides of the reverse-order law can be divided into four situations for consideration. In this article, we first introduce a linear mixed model y = AB β + Aγ + ε, present two least-squares methodologies to estimate the fixed parameter vector in the model, and describe the connections between the two least-squares estimators and the reverse-order laws for generalized inverses of the matrix product AB. We then prepare some valued matrix analysis tools, including a general theory on linear or nonlinear matrix identities, a group of expansion formulas for calculating ranks of block matrices, two groups of explicit formulas for calculating the maximum and minimum ranks of B^(i,...,j)A^(i,...,j), as well as necessary and sufficient conditions for B^(i,...,j)A^(i,...,j) to be invariant with respect to the choice of A^(i,...,j) and B^(i,...,j). We then present a uni ed approach to the 512 set inclusion problems {(AB)^(i,...,j) ⊇ {B^(i,...,j)A^(i,...,j)}for the eight commonly-used types of generalized inverses of A, B, and AB using the block matrix representation method (BMRM), matrix equation method (MEM), and matrix rank method (MRM), where {(·)^(i,...,j)} denotes the collection of all {i,...,j}-generalized inverse of a matrix.

This paper reviews the low-resilience problem in many cities, poor designs of cities to cope with disasters, and the need for tolerance of urban constructions. It explores answers concerning the question of how shall we build cities resiliently? The method of this applied research is a multiphase process that considers all physical and socioeconomic elements of a city. It introduces six indicator groups of urban management (M), economy (E), built environments (U), Infrastructures (I), natural environments (N), and health protection (H). The groups include 55 indicators as variables in the mathematical calculations in this paper. This paper builds a mathematical model to maximize the profitability of resilient buildings by optimizing investments in the required projects. The projects will upgrade the firmness and tolerance of cities against nature-based and human-made dangers and risks. There is a linear programming in 55 variables to select optimal solutions from fifty-five factorial alternatives. Then, the programming will develop into non-linear programming. The unique innovation of this paper is its linear programming interpretation by non-linear to give optimal solutions for the problem. Applying the Lagrange function in the Kuhn-Tucker conditions proves the accuracy of the hypothesis that post-COVID urbanization requires maximum resilience. Only in this way, the urban economies will be free of risks. Outcomes in this paper will assist in the pre-planning, design, and building of built environments everywhere resilient and sustainable.

Laser reduced graphene oxide (LRGO) on a PET substrate was prepared in one-step to obtain the LRGO grid electrode for sensitive carbaryl determination. The grid form results in a grid distribution of different electrochemically active zones affecting the electroactive substance diffusion towards to the electrode surface and increasing the electrochemical sensitivity for carbaryl determination. Carbaryl is electrochemically irreversibly oxidized by the secondary amine moiety of the molecule with the loss of one proton and one electron in the pH range from 5 to 7 by LSV on the LRGO grid electrode with a scan rate of 300 mV/s. Some interference of the juice matrix molecules did not significantly affect the LSV oxidation current of carbaryl on the LRGO grid electrode after adsorptive accumulation without applied potential. The LRGO grid electrode can be used for LSV determination of carbaryl in fruit juices in the concentration range from 0.25 to 128 mg/L with LOD of 0.1 mg/L by. The fabrication of the LRGO grid electrode opens up possibilities for further inexpensive monitoring of carbaryl in other fruit juices and fruits.

Purpose: Prostate cancer remains the 2nd leading cancer killer of men, yet it is also a disease with a high rate of overtreatment. Diffusion weighted imaging (DWI) has shown promise as a reliable, grade-sensitive imaging method, but it is limited by low image quality. Currently, DWI image quality is directly related to low gradient ampli-tudes, since weak gradients must be compensated with long echo times. Methods: We propose a new type of MRl accessory, an "inside-out" and nonlinear gradient, whose sole purpose is to deliver diffusion encoding to a region of interest. Performance was simulated in OPERA and the resulting fields were used to simulate DWI with two compartment and kurtosis models. Experiments with a nonlinear head gradient prove the accuracy of DWI and ADC maps diffusion encoded with nonlinear gradients. Results: Simulations validated thermal and mechanical safety while showing a 5 to 10-fold increase in gradient strength over prostate. With these strengths, lesion CNR in ADC maps approximately doubled for a range of anatomical positions. Proof-of-principle experiments show that spatially varying b-values can be corrected for accurate DWI and ADC. Conclusions: Dedicated nonlinear diffusion encoding hardware could improve prostate DWI.

Indirect imaging methods involve at least two steps, namely optical recording, and computational reconstruction. The optical recording process uses an optical modulator that transforms the light from the object into a typical intensity distribution. This distribution is numerically processed to reconstruct the object’s image corresponding to different spatial and spectral dimensions. There have been numerous optical modulation functions and reconstruction methods developed in the past years for different applications. In most cases, a compatible pair of optical modulation function and reconstruction method gives optimal performance. A new reconstruction method termed non-linear reconstruction (NLR) was developed in 2017 to reconstruct the object image in the case of optical scattering modulators. During the years, it was revealed that the NLR could reconstruct an object’s image modulated by an axicons, bifocal lenses and even exotic spiral diffractive elements, which generate deterministic optical fields. Apparently, NLR seems to be a universal reconstruction method for indirect imaging. In this review, the performance of NLR has been investigated for many deterministic and stochastic optical fields. Simulation and experimental results for different cases are presented and discussed.

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 study investigated the trends of registered Death and Birth in Nigeria using Generalized Linear Models. Annual data on Death and Birth was collected from National Population Commission for the period of 2004 to 2017. The Natural increase calculated revealed a positive trend in the natural increase in Nigeria from 2004 to 2017. Evidence from summary statistics revealed some level of over dispersion (variance > mean). This study explored Poisson Regression Models and Negative Binomial Regression Models using two links (identity and log). The results revealed a positive increase in registration of birth and death rates in Nigeria and among the competing the models, Negative Binomial regression model with identity link emerged as the best model for modeling birth and death rates registration in Nigeria. Data on numbers of deaths and causes of death are essential if countries are to determine priorities, formulate and monitor policies for public health care as well as other government policies that may be based on such data

In this paper, we generalize the problems of finding simple polygons with the minimum area, maximum perimeter and maximum number of vertices so that they contain a given set of points and their angles are bounded by $\alpha+\pi$ where $\alpha$ ($0\leq\alpha\leq \pi$) is a parameter. We also consider the maximum angle of each possible simple polygon crossing a given set of points, and derive an upper bound for the minimum of these angles. The correspondence between the problems of finding simple polygons with the minimum area and maximum number of vertices is investigated from a theoretical perspective. We formulate the three generalized problems as nonlinear programming models, and then present a Genetic Algorithm to solve them. Finally, the computed solutions are evaluated on several datasets and the results are compared with those from the optimal approach.

Damage in concrete structures initiates as the growth of diffuse microcracks that is followed by damage localisation and eventually leads to structural failure. Weak changes such as diffuse microcracking processes are failure precursors. Identification and characterisation of these failure precursors at an early stage of concrete degradation and application of suitable precautionary measures will considerably reduce the costs of repair and maintenance. To this end, a reduced order multiscale model for simulating microcracking-induced damage in concrete at the mesoscale levelis proposed. The model simulates the propagation of microcracks in concrete using a two-scale computational methodology. First, a realistic concrete specimen that explicitly resolves the coarse aggregates in a mortar matrix was generated at the mesoscale. Microcrack growth in the mortar matrix is modelled using a synthesis of continuum micromechanics and fracture mechanics. Model order reduction of the two-scale model is achieved using clustering technique. Model predictions are calibrated and validated using uniaxial compression tests performed in the laboratory.

The article analyzes Bernoulli 's binary sequences in representation of empirical events about the distribution of natural resources and population sizes. Considering the event as a nonlinear system, and consisting of two dependent random variables, with memory and probabilities in maximum finite or infinite lengths, constant and equal to ½ for both variables (stationary process). The expressions of the possible trajectories remain constant in sequences that are repeated alternating the presence or absence of one of the variables at each iteration (asymmetric). There are constant oscillations in the event except if the variables X₁ and X₂ are regulated as a function of time Y. It is observed that the variables X₁ and X₂ assume in time T_k → ∞ specific behaviors (geometric variable) that can be used as management tools for random systems. In this way, the article seeks to know from this analyzes, the maximum entropy of information in the system by a theoretical view and how to model resources distribution or containment in the given problem.

For a dynamical system, it is known that the existence of a Lyapunov density implies almost global stability of an equilibrium. It is then natural to ask whether the existence of a common Lyapunov density for a nonlinear switched system implies almost global stability, in the same way as a common Lyapunov function implies global stability for nonlinear switched systems. In this work, the answer to this question is shown to be affirmative as long as switchings satisfy a dwell-time constraint with an arbitrarily small dwell time. As a straightforward extension of this result, we employ multiple Lyapunov densities in analogy with the role of multiple Lyapunov functions for the global stability of switched systems. This gives rise to a minimum dwell time estimate to ensure almost global stability of nonlinear switched systems, when a common Lyapunov density does not exist. The results obtained for continuous-time switched systems are based on some sufficient conditions for the almost global stability of discrete-time non-autonomous systems. These conditions are obtained using the duality between Frobenius-Perron operator and Koopman operator.

In this paper, mean-field type games between two players with backward stochastic dynamics are defined and studied. They make up a class of non-zero-sum differential games where the players' state dynamics solve backward stochastic differential equations (BSDEs) that depend on the marginal distributions of player states. Players try to minimize their individual cost functionals, also depending on the marginal state distributions. Under some regularity conditions, we derive necessary and sufficient conditions for existence of Nash equilibria. Player behavior is illustrated by numerical examples, and is compared to a centrally planned solution where the social cost, the sum of player costs, is minimized. The inefficiency of a Nash equilibrium, compared to socially optimal behavior, is quantified by the so-called price of anarchy. Numerical simulations of the price of anarchy indicate how the improvement in social cost achievable by a central planner depends on problem parameters.

Searching, recognizing and retrieving a video of interest from a large collection of a video data is an instantaneous requirement. This requirement has been recognized as an active area of research in computer vision, machine learning and pattern recognition. Flower video recognition and retrieval is vital in the field of floriculture and horticulture. In this paper we propose a model for the retrieval of videos of flowers. Initially, videos are represented with keyframes and flowers in keyframes are segmented from their background. Then, the model is analysed by features extracted from flower regions of the keyframe. A Linear Discriminant Analysis (LDA) is adapted for the extraction of discriminating features. Multiclass Support Vector Machine (MSVM) classifier is applied to identify the class of the query video. Experiments have been conducted on relatively large dataset of our own, consisting of 7788 videos of 30 different species of flowers captured from three different devices. Generally, retrieval of flower videos is addressed by the use of a query video consisting of a flower of a single species. In this work we made an attempt to develop a system consisting of retrieval of similar videos for a query video consisting of flowers of different species.

We experimentally demonstrate enhanced spectral broadening of femtosecond optical pulses after propagation through silicon-on-insulator (SOI) nanowire waveguides integrated with two-dimensional (2D) graphene oxide (GO) films. Owing to the strong mode overlap between the SOI nanowires and the GO films with a high Kerr nonlinearity, the self-phase modulation (SPM) process in the hybrid waveguides is significantly enhanced, resulting in greatly improved spectral broadening of the femtosecond optical pulses. A solution-based, transfer-free coating method is used to integrate GO films onto the SOI nanowires with precise control of the film thickness. Detailed SPM measurements using femtosecond optical pulses are carried out, achieving a broadening factor of up to ~4.3 for a device with 0.4-mm-long, 2 layers of GO. By fitting the experimental results with theory, we obtain an improvement in the waveguide nonlinear parameter by a factor of ~3.5 and the effective nonlinear figure of merit (FOM) by a factor of ~3.8, relative to the uncoated waveguide. Finally, we discuss the influence of GO film length on the spectral broadening and compare the nonlinear optical performance of different integrated waveguides coated with GO films. These results confirm the improved nonlinear optical performance for silicon devices integrated with 2D GO films.

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.

The extensive deployment of wireless infrastructure provides a low-cost way to track mobile users in indoor environment. This paper demonstrates a prototype model of an accurate and reliable room location awareness system in a real public environment, where three typical problems arise. First, a massive number of access points (APs) can be sensed leading to a high-dimensional classification problem. Second, heterogeneous devices record different received signal strength (RSS) levels due to the variations in chip-set and antenna attenuation. Third, APs are not necessarily visible in every scanning cycle leading to missing data. This paper presents a probabilistic Wi-Fi fingerprinting method in a hidden Markov model (HMM) framework for mobile user tracking. Considering the spatial correlation of the signal strengths from multiple APs, a Multivariate Gaussian Mixture Model (MVGMM) is fitted to model the probability distribution of RSS measurements in each cell. Furthermore, the unseen property of invisible AP has been investigated in this research, and demonstrated the efficiency of differentiation between cells. The proposed system is able to achieve comparable localization performance. The filed test results present a reliable 97% localization room level accuracy of multiple mobile users in a real university campus WiFi network without any prior knowledge of the environment.

A variable annuity is a popular life insurance product that comes with financial guarantees. Using Monte Carlo simulation to value a large variable annuity portfolio is extremely time-consuming. Metamodeling approaches have been proposed in the literature to speed up the valuation process. In metamodeling, a metamodel is first fitted to a small number of variable annuity contracts and then used to predict the values of all other contracts. However, metamodels that have been investigated in the literature are sophisticated predictive models. In this paper, we investigate the use of linear regression models with interaction effects for the valuation of large variable annuity portfolios. Our numerical results show that linear regression models with interactions are able to produce accurate predictions and can be useful additions to the toolbox of metamodels that insurance companies can use to speed up the valuation of large VA portfolios.

The non-linear analysis of hollow-core concrete slabs requires the use of advanced numerical techniques, proper constitutive models both for concrete and steel as well as particular computational skills. If prestressing, cracking, crack opening, material softening, etc. are also to be taken into account, then the computational task can far exceed the capabilities of an ordinary engineer. In order for the calculations to be carried out in a traditional design office, simplified calculation methods are needed. Preferably based on the linear finite element (FE) method with a simple approach that takes into account material nonlinearities. In this paper the simplified analysis of hollow-core slabs based on the generalized nonlinear constitutive law is presented. In the proposed method a simple decomposition of the traditional iterative linear finite element analysis and the non-linear algebraic analysis of the plate cross-section is used. Through independent analysis of the plate cross-section in different deformation states, a degraded plate stiffness can be obtained, which allows iterative update of displacements and rotations in the nodes of the FE model. Which in turn allows to update the deformation state and then correct translations and rotations in the nodes again. The results obtained from the full detailed 3D nonlinear FEM model and from the proposed approach are compared for different slab cross-sections. The obtained results from both models are consistent.

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.

We construct a family of two-step optimal fourth order iterative methods for finding single root of non-linear equations. We generalize these methods to simultaneous iterative methods for determining all the distinct as well as multiple roots of single variable non-linear equations. Convergence analysis is present for both cases to show that the order of convergence is four in case of single root finding method and is twelve for simultaneous determination of all roots of non-linear equation. The computational cost, Basin of attraction, efficiency, log of residual and numerical test examples shows, the newly constructed methods are more efficient as compared to the existing methods in literature.

Scattering has been always considered a problem in most of the imaging and holography systems. In this project, a 3D imaging system has been developed based on scattering against common beliefs. The 3D imaging system consists of only two components namely a scattering lens, fabricated by grinding the surface of a convex lens using sandpaper and a web camera. The point spread function (PSF) in the form of speckle distribution was recorded using a laser source in the first step. A synthetic object was selected which was convolved with the PSF in a computer to generate the object intensity distribution. The image of the object was reconstructed by processing the PSF and object intensity distribution using a computational reconstruction method called non-linear reconstruction. The recorded PSF was scaled and the process was repeated for a different synthetic object. The concept was extended to 3D by summing the object intensity distributions generated using PSFs with different scaling factors. The image at different planes can be reconstructed using the PSFs corresponding to that plane.

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.

We report a large third-order nonlinear optical response of palladium diselenide (PdSe₂) films – a two-dimensional (2D) noble metal dichalcogenide material. Both open-aperture (OA) and closed-aperture (CA) Z-scan measurements are performed with a femtosecond pulsed laser at 800 nm to investigate the nonlinear absorption and nonlinear refraction, respectively. In the OA experiment, we observe optical limiting behaviour originating from large two photo absorption (TPA) in the PdSe₂ film of β = 3.26 ×10^-8 m/W. In the CA experiment, we measure a peak-valley response corresponding to a large and negative Kerr nonlinearity of n₂ = -1.33×10^-15 m²/W – two orders of magnitude larger than bulk silicon. We also characterize the variation of n₂ as a function of laser intensity, observing that n₂ decreases in magnitude with incident laser intensity, becoming saturated at n₂ = -9.96×10^-16 m²/W at high intensities. These results verify the large third-order nonlinear optical response of 2D PdSe₂ as well as its strong potential for high performance nonlinear photonic devices.

The framework of product life cycle (PLC) cost analysis is one of the most important evaluation tools for a contemporary high-tech company in an increasingly competitive market environment. The PLC-purchasing strategy provides the framework for a procurement plan and examines the sourcing strategy of a firm. The marketing literature emphasizes that ongoing technological change and shortened life cycles are important elements in commercial organizations. From a strategic viewpoint, the vendor has an important position between supplier, buyer and manufacturer. The buyer seeks to procure the products from a set of vendors to take advantage of economies of scale and to exploit opportunities for strategic relationships. However, previous studies have seldom considered vendor selection (VS) based on PLC cost (VSPLCC) analysis. The purpose of this paper is to solve the VSPLCC problems considering the situation of a single-buyer-multiple-supplier. For this issue, a new VSPLCC procurement model and solution procedure are derived by this paper to minimize net cost, rejection rate, late delivery and PLC cost subject to vendor capacities and budget constraints. Moreover, a real case in Taiwan is provided to show how to solve the VSPLCC procurement problem.

We review some new approaches to the description of the evolution of states of many-particle quantum systems by means of the correlation operators. Using the de nition of marginal correlation operators within the framework of dynamics of correlations governed by the von Neumann hierarchy, we establish that a sequence of such operators is governed by the nonlinear quantum BBGKY hierarchy. The constructed nonperturbative solution of the Cauchy problem to this hierarchy of nonlinear evolution equations describes the processes of the creation and the propagation of correlations in many-particle quantum systems. Moreover, we consider the problem of the rigorous description of collective behavior of many-particle quantum systems by means of a one-particle (marginal) correlation operator that is a solution of the generalized quantum kinetic equation with initial correlations, in particular, correlations characterizing the condensed states of systems.

In present work an opportunity of nearly single-cycle THz pulse generation in aperiodically poled lithium niobate (APPLN) crystal is studied. A radiating antenna model is used to simulate the THz generation from chirped APPLN crystal pumped by a sequence of femtosecond laser pulses with chirped delays m (m = 1, 2, 3 …) between adjacent pulses. It is shown that by appropriative choosing m it is possible to obtain temporally overlap of all THz pulses generated from positive (or negative) domains. It results in the formation of a nearly single-cycle THz pulse, if the chirp rate of domain length  in the crystal is sufficiently large. In opposite case, a few cycle THz pulses are generated with the number of the cycles depending on . The closed form expression for THz pulse form is obtained. The peak THz electric field strength of 0.3 MV/cm is predicted for APPLN crystal pumped by the sequence of laser pulses with peak intensity of the separate pulse in the sequence about 20 GW/cm2. By focusing the THz beam and by increasing the pump power the field strength can reach values of an order of few MV/cm.

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.

In this paper, we study the third order semilocal convergence of the Newton-like method for finding the approximate solution of nonlinear operator equations in the setting of Banach spaces. First, we discuss the convergence analysis under ω-continuity condition, which is weaker than the Lipschitz and Hölder continuity conditions. Second, we apply our approach to solve Fredholm integral equations, where the first derivative of involved operator not necessarily satisfy the Hölder and Lipschitz continuity conditions. Finally, we also prove that the R-order of the method is 2p + 1 for any p $\in$ (0,1].

Driving simulators are widely used for understanding human-machine interaction, driver behavior and in driver training. The effectiveness of simulators in these process depends largely on their ability to generate realistic motion cues. Though the conventional filter-based motion cueing strategies have provided reasonable results, these methods suffer from poor workspace management. To address this issue, linear MPC-based strategies have been applied in the past. However, since the kinematics of the motion platform itself is non-linear and the required motion varies with the driving conditions, this approach tends to produce sub-optimal results. This paper presents a nonlinear MPC-based algorithm which incorporates the nonlinear kinematics of the Stewart platform within the MPC algorithm in order to increase the cueing fidelity and utilize maximum workspace. Further, adaptive weights-based tuning is used to smoothen the movement of the platform towards its physical limits. Full-track simulations were carried out and performance indicators were defined to objectively compare the response of the proposed algorithm with classical washout filter and linear MPC-based algorithms. The results indicate a better reference tracking with lower root mean square error and higher shape correlation for the proposed algorithm. Lastly, the effect of the adaptive weights-based tuning was also observed in the form of smoother actuator movements and better workspace utilization.

The quality of dietary patterns can be optimized using a mathematical technique known as linear programming (LP). LP methods have rarely been applied to individual meals. The present LP models optimized the breakfast meal for those participants in the nationally representative National Health and Nutrition Examination Survey 2011-2014 who ate breakfast (n=11,565). The Nutrient Rich Food Index (NRF9.3) was a measure of diet quality. Breakfasts in the bottom tertile of NRF9.3 scores (T1) were LP-modeled to meet nutrient requirements without deviating too much from current eating habits. Separate LP models were run for children and for adults. The LP-modeled breakfasts resembled the existing ones in the top tertile of NRF9.3 scores (T3), but were more nutrient-rich. Favoring fruit, cereals, and dairy, the LP-modeled breakfasts had less meat, added sugars and fats but more whole fruit and 100% juices, more whole grains, and more milk and yogurt. LP modeling methods can build on existing dietary patterns to construct food-based dietary guidelines and identify individual meals and/or snacks that need improvement.

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.

Given a quasi-definite linear functional u in the linear space of polynomials with complex coefficients let us consider the corresponding sequence of monic orthogonal polynomials (SMOP in short) (Pn)n≥0. For the Christoffel transformation u˜=(x−c)u with SMOP (P˜n)n≥0, we are interested to study the relation between u˜ and u(1)˜, where u(1) is the linear functional for the associated orthogonal polynomials of the first kind (Pn(1))n≥0 and u(1)˜=(x−c)u(1) is its Christoffel transformation. This problem is also studied for the Geronimus transformations.

Any effort to combat corruption can benefit from an examination of past and projected worldwide trends. In this paper, we forecast the level of corruption in countries by integrating an artificial neural network modeling and time series analysis. The data were obtained from 113 countries from 2007 to 2017. The study is carried out at two levels: (a) global level where all countries are considered as a monolithic group; and (b) cluster level, where countries are placed into groups based on their development-related attributes. For each cluster, we use the findings from our previous study on the cluster analysis of global corruption using machine learning methods that identified the four most influential corruption factors, and we use those as independent variables. Then, using the identified influential factors, we forecast the level of corruption in each cluster using a nonlinear autoregressive recurrent neural network with exogenous inputs (NARX), an artificial neural network technique. The NARX models were developed for each cluster, with the objective function in terms of the Corruption Perceptions Index (CPI). For each model, the optimal neural network is determined by finetuning the hyperparameters. The analysis was repeated for all countries as a single group. The accuracy of the models is assessed by comparing the mean square errors (MSE) of the time series models. The results suggest that the NARX artificial neural network technique yields reliable future values of CPI globally or for each cluster of countries. This can assist policymakers and organizations in assessing the expected efficacies of their current or future corruption control policies from a global perspective as well as for groups of countries.

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.

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.

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.

The Eliezer and Gray physical interpretation of the Ermakov-Lewis invariant is applied as a guiding principle for the derivation of the special relativistic analog of the Ermakov-Milne-Pinney equation and associated first integral. The special relativistic extension of the Ray-Reid system and invariant is obtained. General properties of the relativistic Ermakov-Milne-Pinney are analyzed. The conservative case of the relativistic Ermakov-Milne-Pinney equation is described in terms of a pseudo-potential, reducing the problem to an effective Newtonian form. The non-relativistic limit is considered as well. A relativistic nonlinear superposition law for relativistic Ermakov systems is identified. The generalized Ermakov-Milne-Pinney equation has additional nonlinearities, due to the relativistic effects.

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.

The overrun of transient power quality index caused by the large-capacity electric arc furnace (EAF) has become a prominent problem affecting the safe and stable operation of the power system. (1) In this paper, the relationship between arc furnace volt-age and current is derived based on the different stages of arc combustion, and the random variation of chaotic phenomenon of the arc voltage are simulated. Established an EAF model suitable for the study of transient power quality problems. (2) Take 50t AC EAF as an example to analyze the reactive power impact and the influence on the point of common coupling (PCC) voltage caused by the three-phase short circuit of the electrode. The results show that the experimental results are consistent with the theoretical analysis, verifying the correctness and effectiveness of the model. (3) When the three-phase short-circuit occurs, the reactive power impact is nearly 6 times that of normal operation, the short-circuit current is 2.66 times that of normal operation, and the effective value of the PCC voltage has dropped by 40.37%, which provides a theoretical basis for real-time compensation of impulsive reactive power and improvement of the transient power quality of the EAF.

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.

Free volume is an extremely important intrinsic defect in polymers. Structurally, the free volume is the randomly distributed holes in the polymer molecular chain segments. From the perspective of molecular movement, it is also the space needed for the movement of molecular segments. In proton exchange membrane fuel cells, the free volume is also the space needed for the directional conduction of protons. Irradiation grafting sulfonated polyvinylidene fluoride (PVDF) is one of the methods to produce proton exchange membrane with good proton channel rate. Using the LYS-1 program, based on the linear absorption coefficient and backscatter coefficient models, the percentage of annihilated positrons in PVDF in the two-layer model and the three-layer model was studied, and comparing the two fitting results it is determined that the model closest to the positron annihilation percentage required by the PALS experiment is the two-layer model, which allows the percentage of positrons that are annihilated in PVDF films with a thickness of 100 μm to reach 46% using the high energy positron source ⁴⁴Ti without using the positron moderator. Using positron annihilation lifetime spectrum (PALS) analysis methods, based on Eldrup's classical model of free volume, the influence of absorbed doses of α particles on the free volume and crystallinity of PVDF was investigated, respectively. Based on the two test results the model of cross-linking and degradation of polyvinylidene fluoride irradiated by α particles was determined. Afterwards, X-ray diffraction (XRD) methods was used to study the change of PVDF crystal area before and after irradiation. The XRD results are consistent with the results measured by PALS.

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 short note we present a technique using which one attributes frequency and wavevector to (almost) arbitrary scalar fields. Our proposed definition is then applied to the classical wave equation to yield a novel nonlinear PDE.

The instability of traveling pulses in nonlinear diffusion problems is inspected on the example of Gunn domains in semiconductors. Mathematically the problem is reduced to the calculation of the "energy" of the ground state in Schrödinger equation with a complicated potential. A general method to obtain the bottom-part spectrum of such equations based on the approximation of the potential by square wells is proposed and applied. Possible generalization of the approach to other types of nonlinear diffusion equations is discussed.

We consider a model of predator-prey interaction at fractional-order where the predation obeys the ratio-dependent functional response and the prey is linearly harvested. For the proposed model, we show the existence, uniqueness, non-negativity as well as the boundedness of the solutions. Conditions for the existence of all possible equilibrium points and their stability criteria, both locally and globally, are also investigated. The local stability conditions are derived using the Magtinon's theorem, while the global stability is proven by formulating an appropriate Lyapunov function. The occurance of Hopf bifurcation around the interior point is also shown analytically. At the end, we implement the Predictor-Corrector scheme to perform some numerical simulations.

The PI3K/mTOR signalling pathway plays a central role in the governing of cell growth, survival and metabolism. As such, it must integrate and decode information from both external and internal sources to guide efficient decision-making by the cell. To facilitate this, the pathway have evolved an intricate web of complex regulatory mechanisms and elaborate crosstalk with neighbouring signalling pathways, making it a highly non-linear system. Here, we describe the mechanistic biological details that underpin these regulatory mechanisms, covering a multitude of negative and positive feedback loops, feed-forward loops, competing protein interactions, and crosstalk with major signalling pathways. Further, we highlight the non-linear and dynamic network behaviours that arise from these regulations, uncovered through both computational and experimental studies. Given the pivotal role of the PI3K/mTOR network in cellular homeostasis and its frequent dysregulation in pathologies including cancer and diabetes, a coherent and systems-level understanding of the complex regulation and consequential dynamic signalling behaviours within this network is imperative for advancing biology and development of new therapeutic approaches.