Search

In this paper we consider the generalized quasilinear Schrödinger equations − div (g 2 (u) ∇ u) + g (u) g ′ (u) | ∇ u | 2 + V (x) u = h (x , u) , x ∈ R N , where V and h are periodic in x i , 1 ⩽ i ⩽ N. By using variational methods, we prove the existence of ground state solutions, i.e., nontrivial solutions with least possible energy. [ABSTRACT FROM AUTHOR]

We consider a nonlinear coefficient inverse problem of reconstructing the density and the memory matrix of a viscoelastic medium by probing the medium with a family of wave fields excited by moment tensor point sources. A spatially non-overdetermined formulation is investigated, in which the manifolds of point sources and detectors do not coincide and have a total dimension equal to three. The requirements for these manifolds are established to ensure the unique solvability of the studied inverse problem. The results are achieved by reducing the problem to a chain of connected systems of linear integral equations of the M. M. Lavrentiev type. [ABSTRACT FROM AUTHOR]

We extend the Calderón–Zygmund theory for nonlocal equations to strongly coupled system of linear nonlocal equations ℒ A s ⁢ u = f {\mathcal{L}^{s}_{A}u=f} , where the operator ℒ A s {\mathcal{L}^{s}_{A}} is formally given by ℒ A s ⁢ u = ∫ ℝ n A ⁢ ( x , y ) | x - y | n + 2 ⁢ s ⁢ ( x - y ) ⊗ ( x - y ) | x - y | 2 ⁢ ( u ⁢ ( x ) - u ⁢ ( y ) ) ⁢ 푑 y . \mathcal{L}^{s}_{A}u=\int_{\mathbb{R}^{n}}\frac{A(x,y)}{|x-y|^{n+2s}}\frac{(x-% y)\otimes(x-y)}{|x-y|^{2}}(u(x)-u(y))\,dy. For 0 < s < 1 {0 0 {\inf_{x\in\mathbb{R}^{n}}A(x,x)>0} , then for f ∈ L loc p {f\in L^{p}_{\rm loc}} , for p ≥ 2 {p\geq 2} , the solution vector u ∈ H loc 2 ⁢ s - δ , p {u\in H^{2s-\delta,p}_{\rm loc}} for some δ ∈ ( 0 , s ) {\delta\in(0,s)} . [ABSTRACT FROM AUTHOR]

We derive an exponential decay rate of energy for the cubic Schrödinger equation on a dissipative waveguide with a damping term that is effective locally on a neighborhood at the boundary and at infinity. In this paper, we give a new example for which the geometric control condition is sufficient to obtain an exponential decay of energy Schrödinger equation. The proof is based on Strichartz's estimates and the smoothing effects argument associated with the linear Schrödinger equation(LS). [ABSTRACT FROM AUTHOR]

The dynamic response of a double-layered circular region under anti-plane linear loads is investigated using the complex function method. The scattering wave functions for each layer are provided, and the total wave field functions for each layer are formulated through the superposition principle. By establishing an infinite linear equation system with unknown coefficients based on the boundary conditions, finite term truncation is performed to obtain the dynamic stress concentration coefficient of the circular hole defect. Furthermore, a specific example is presented to discuss both the validity of the theory and numerical results regarding this factor. [ABSTRACT FROM AUTHOR]

This paper revisits the set-invariance for linear delay-difference equations and proposes novel delay-dependent notions in contrast with the existing delay-independent constructions available in the literature. The main tool in this endeavour is the model transformation by means of a matrix parametrization, which opens the way to the elaboration of delay-dependent conditions for set invariance. For the class of polyhedral sets, it will be shown how these transformed models enable particularly structured invariance conditions. Aside from the mathematical developments, a discussion of the delay-dependent conditions with respect to the confinement of the state trajectories of the original system will be presented. The relationship will be established by means of constraints involving the initial states for the time-delay systems. The characterization of this set of admissible initial conditions can be analysed in terms of complexity and conservativeness with respect to the classical delay-independent set-invariance. An illustrative example is provided to underline that confinement of state trajectories in a set can be achieved even though this is not invariant according to the classical definition. [ABSTRACT FROM AUTHOR]

Iteration is one of the most important topics in computer science and attentions are paid to functional equations involving iterates, one of which is the linear combination of alternative iterates. Recently existence, uniqueness and dependence for increasing Lipschitzian solutions were obtained for linear combination of alternative iterates on $ [0, 1] $ [ 0 , 1 ] and $ \mathbb {R} $ R in the case that all given functions are strictly increasing. In this paper we work in various cases of monotonicity (increasing and decreasing) among given functions and the unknown function. [ABSTRACT FROM AUTHOR]

It is known that many physical systems undergoing (nuclear, atomic, etc.) decay do not obey the standard decreasing exponential formula which corresponds to the solution of a first-order, linear ODE having constant coefficients. We propose and solve a new functional equation mathematical model whose solutions are consistent with current experimental data. The basis of our functional representation is centred on the critical role played by the concept of the decay half-life. [ABSTRACT FROM AUTHOR]

We consider the problem of tracking arbitrary free nutating trajectories of the Lagrange top using linear feedback. The equations of motion of the top are linearised about the desired trajectories. Due to the inherent symmetries, this yields a system of linear equations with periodically varying coefficients governing the error dynamics. It is shown that the higher-order dynamics of the Lagrange top leads to nuances in the implementation of the control. Two different control strategies are implemented in the present work. These are applicable for impulsive and short-duration disturbances, respectively. The control effort is in the form of a body-fixed torque input about the symmetry axis and a vertical space-fixed force input. In both the proposed control strategies, the iterative application of the control effort over multiple periods is shown to stabilise the error. These strategies are shown to work for significantly large errors. [ABSTRACT FROM AUTHOR]

In this study, we investigate the transport properties of Airy and Hermit-Gaussian wavepackets traveling through a Gaussian potential well in the standard and fractional media. We use a split step Fourier method to solve the corresponding two-dimensional fractional nonlinear linear Schrodinger equation. We study the interference phenomenon, Huygens principle and trapping properties of the system in different situations. For this purpose, the position of the system has also selected inside the potential well to consider the wavepacket evolution. Then, the effect of the well and incident wavepackets parameters on the evolution the transport properties of employed wavepackets have properly been considered. [ABSTRACT FROM AUTHOR]

In this work, a theoretical analysis of bulk wave interaction with a sliding layer has been considered. The layer is assumed to be sliding with a constant velocity. The effect of the sliding velocity on the reflection and transmission behaviors has been studied. A low loss viscoelastic property is considered for the layer, which is held between two identical grounded elastic half-spaces. The governing equations for the dilatoric and deviatoric wave components in the viscoelastic layer are derived. The problem is solved using a coordinate transform based on an appropriate change in the wave velocities. The solutions are then used to calculate the reflection and transmission coefficients by solving the system of linear equations. The coefficients are observed to be affected remarkably by the sliding velocity of the layer. The effects of incidence angle and frequency of an incoming wave on the reflection and transmission characteristics are studied. The conditions for the existence of critical incidence are also discussed. This work gives some theoretical understanding of the wave characteristics in a sliding medium, which is expected to be useful in applications related to wave-based actuation and manipulation. [ABSTRACT FROM AUTHOR]

Integral equations with infinite delay are considered as functional equations in a Banach space. Two types of Hyers–Ulam stability criteria are established. First, it is shown that a linear autonomous equation is Hyers–Ulam stable if and only if it has no characteristic value with zero real part. Second, it is proved that the Hyers–Ulam stability of a linear autonomous equation is preserved under sufficiently small nonlinear perturbations. The proofs are based on a recently developed decomposition theory of linear integral equations with infinite delay. [ABSTRACT FROM AUTHOR]

Heroism serves as the banner showcasing the sublime spirit of the Chinese nation, and constructing a societal identity rooted in heroism is a crucial reference for the successful continuation of heroism in the new era. Moreover, media consumption plays a pivotal role in influencing public identification with heroism. From the perspective of cultivation theory, this study surveyed 511 respondents nationwide, utilizing quantitative measurements and empirical analysis through linear regression equations. The results indicate that there is a significant positive correlation between the media usage of the Chinese public and their social identification with heroism, impacting cognitive, emotional, and behavioral dimensions differently. Additionally, traditional media is the main force in shaping this identification. Concurrently, there are evident generational differences in the public's heroic social identity, with the memory of heroes in the new media era showing a trend of "intergenerational decline." Future research should explore how to effectively use media to transmit the spirit of heroism and promote value integration. This includes optimizing media content, formats, and communication strategies to meet the needs of different audiences and enhancing the public's deep understanding and recognition of heroism. [ABSTRACT FROM AUTHOR]

We study a version of the randomized Kaczmarz algorithm for solving systems of linear equations where the iterates are confined to the solution space of a selected subsystem. We show that the subspace constraint leads to an accelerated convergence rate, especially when the system has approximately low-rank structure. On Gaussian-like random data, we show that it results in a form of dimension reduction that effectively increases the aspect ratio of the system. Furthermore, this method serves as a building block for a second, quantile-based algorithm for solving linear systems with arbitrary sparse corruptions, which is able to efficiently utilize external knowledge about corruption-free equations and achieve convergence in difficult settings. Numerical experiments on synthetic and realistic data support our theoretical results and demonstrate the validity of the proposed methods for even more general data models than guaranteed by the theory. [ABSTRACT FROM AUTHOR]

We study a type of correlated queue in which its inter-arrival and service times are correlated, with their joint distribution being characterized by a copula function. This characterization allows for very generally correlated inter-arrival and service times. For such a queue, we first derive an infinite system of linear equations for the moments of the waiting time, based on which we design an algorithm to calculate the moments of the waiting time. In contrast with traditional methods, our algorithm incorporates a recursive procedure which is computationally much more efficient. Furthermore, we show how the moments and covariances of the inter-departure times of the queue can be obtained based on the moments of the waiting time. Numerical experiments are provided to validate our method. [ABSTRACT FROM AUTHOR]

The use of a beneficiation machine for mineral soring can increase the content of target minerals, optimize resource utilization, and improve production efficiency, winch is of great significance and value in the mining field. However, during the soring process, the ore images obtained through X-ray transmission technology may have target adhesion and overlap, which will seriously affect the efficiency and accuracy of mineral soring. Obtaining an independent ore image is a necessary condition for using the method to identify, locate and sort the ore. To improve the accuracy and efficiency of mineral soring, a concave point detection and matching algorithm based on polygon fitting is proposed for segmenting adhesive ore images. Firstly, fitting a binary image of the ore into a polygon image and identifying concave points from the turning point of the image. Secondly, constructing a linear equation by using a turning point to form a detection area, searching the to-be-connected points of the concave points in the area, and completing concave point matching. Finally, the computer view is transferred from the binary image to the gray image, and the gray value of the region to be segmented is analyzed to determine whether the region is the actual adhesion between ores, so as to determine whether to execute the segmentation operation. The results show that the overall segmentation accuracy of the algorithm on the adhesive ore dataset is 93.60%, the concave noise rate is only 5.23%, and the average calculation time for processing images with a size of 281x336 is as low as 5.13 ms. Its noise concave filtering ability, concave detection accuracy, segmentation accuracy, and algorithm running speed are all better than those of similar algorithms. It shows strong segmentation stability for ore images with different adhesive quantities and forms. [ABSTRACT FROM AUTHOR]

The present study aims to assess the responses of growth, development, and yield of summer maize to the effects of drought–flood abrupt alternation through comparative tests under single flood, single-drought, and drought–flood abrupt alternation treatments with varying degrees from the elongation to the tasseling stage during the 2021 and 2022 growing seasons. In addition, a water production function model for summer maize was preliminarily established based on the results obtained under the drought–flood abrupt alternation scenarios. The results indicated that drought–flood abrupt alternation with early moderate drought had a certain restricting effect on summer maize, while early moderate drought followed by waterlogging had a compensation effect on the cultivated summer maize. Furthermore, both mild and severe drought followed by waterlogging exert a significant combined constraint on the normal growth and development of summer maize, leading to a sharp decline in maize yield, necessitating a shorter timeframe for mitigating and reducing the effects of waterlogging. Additionally, the water production function model established through a multiple linear regression equation exhibits a high degree of fit and demonstrates a strong linear relationship. This study provides crucial insights for agricultural practices and water resource management strategies, particularly in the evaluation of the integrated impacts of drought and waterlogging on crop yields and the formulation of effective disaster risk reduction and mitigation measures in response to these impacts. [ABSTRACT FROM AUTHOR]

Runoff prediction is of great importance to water utilization and water-project regulation. Although sun activity has been considered an important factor in runoff, little modeling has been constructed. This study put forward a forecast heuristic combining back propagation neural network (BPNN) and particle swarm optimization (PSO) for annual runoff based on sunspot number and applied it to the Yellow River of China for the period 1956–2016 and assessed the contribution of the sunspot number by placing sole BPNN modeling on the time series as a contrast. First, the heuristic is made up of BPNN calibration and PSO optimization: (1) we use historical data to calibrate BPNN models and obtain a prediction of the sunspot number for training and testing stages; (2) we use the PSO to minimize the difference between the predicted runoff of both BPNN and a linear equation for forecasting stage. Second, the application offers interesting findings: (1) while BPNN calibration obtains first-class forecasting with the ratio >85% with <20% absolute error in training and testing stages, the PSO can achieve similar performance in the forecasting stage; (2) the heuristic can achieve better prediction in years with a lower sunspot number; (3) besides the influence of the sun activity, atmospheric circulation, water usage, and water-project regulation do play important roles on the measured or natural runoff to some extent. This study could provide useful insights into further forecasting of measured and natural runoff under this forecast heuristic in the world. [ABSTRACT FROM AUTHOR]

A new solution for the analysis of slitted parallel‐plate waveguide is proposed using the method of Kobayashi Potential (KP). The interior and exterior problems are studied for the TE and TM polarizations. Simplified forms of Weber‐Schafheitlin (WS) integrals are utilized for problem formulation. The Fourier function space is exploited to construct the governing linear system of equations. A simple strategy is suggested for the evaluation of the required integrals. Numerical results are validated through convergence analysis and available reports based on the Moment Method (MM). It is shown that the KP is superior to the conventional MM in the sense of tracking edge singularities, especially when the radiation problem is of interest. Key Points: A new solution for the analysis of slitted parallel‐plate waveguides is proposed using the method of Kobayashi PotentialA direct numerical integration method is proposed to efficiently evaluate semi‐infinite integralsSupersedes the conventional moment method for the problem at hand due to precise tracking of edge singularities [ABSTRACT FROM AUTHOR]

For a one dimensional 2-lattice we write down the momentum equation and the equation ruling the shift vector for the dynamic case as a first order system and characterize it in terms of its hyperbolicity. We use similar arguments for problems of increasing difficulty and tackle: one dimensional 3-lattices, three dimensional 2-lattices, three dimensional 3-lattices and finally the most general case of three dimensional (n + 1) -lattices. Our approach is confined to the geometrically and materially linear elastodynamic theory and is valid for generic anisotropic materials that have the multilattice structure. The main finding is that, with the assumptions adopted, the presence of each shift vector is related with zero eigenvalues when the system is written as a first order system. [ABSTRACT FROM AUTHOR]

This paper deals with the experimental procedures of lock-in thermography (LIT) for polyetheretherketone (PEEK), which is used as a lightweight material in various industrial fields. The LIT has limitations due to non-uniform heating by external optic sources and the non-uniformity correction (NUC) of the infrared (IR) camera. It is generating unintended contrast in the IR image in thermal imaging inspection, reducing detection performance. In this study, the non-uniformity effect was primarily improved by producing an equivalent array halogen lamp. Then, we presented absolute temperature compensation (ATC) and temperature ratio compensation (TRC) techniques, which can equalize the thermal contrast of the test samples by compensating for them using reference samples. By applying compensation techniques to data acquired from the test samples, defect detectability improvement was quantitatively presented. In addition, binarization was performed and detection performance was verified by evaluating the roundness of the detected defects. As a result, the contrast of the IR image was greatly improved by applying the compensation technique. In particular, raw data were enhanced by up to 54% using the ATC compensation technique. Additionally, due to improved contrast, the signal-to-noise ratio (SNR) was improved by 7.93%, and the R2 value of the linear trend equation exceeded 0.99, demonstrating improved proportionality between the defect condition and SNR. [ABSTRACT FROM AUTHOR]

From the perspective of Social cognitive theory (SCT), this study investigates the influence of responsible leadership (RL) on employee ethical voice (EV) and the RL mechanism using the data collected from 298 full-time employees in three phases. Linear regression equations and Bootstrap methods were used for empirical testing. The results show that RL significantly influences employee EV behavior, that ethical efficacy (EE) partially mediates between the two, and that moral identity (MI) moderates the relationship between RL and EE as well as the mediating role of EE. The paper reveals the psychological mechanisms of RL's EV to employees, as well as important practical implications for organizations to improve employees' EV behavior. [ABSTRACT FROM AUTHOR]

We introduce the notion of porous invariants for multipath affine loops over the integers. These are invariants definable in (fragments of) Presburger arithmetic and, as such, lack certain tame geometrical properties, such a convexity and connectedness. Nevertheless, we show that in many cases such invariants can be automatically synthesised, and moreover can be used to settle reachability questions for various non-trivial classes of affine loops and target sets. For the class of Z -linear invariants (those defined as conjunctions of linear equations with integer coefficients), we show that a strongest such invariant can be computed in polynomial time. For the more general class of N -semi-linear invariants (those defined as Boolean combinations of linear inequalities with integer coefficients), such a strongest invariant need not exist. Here we show that for point targets the existence of a separating invariant is undecidable in general. However we show that such separating invariants can be computed either by restricting the number of program variables or by restricting from multipath to single-path loops. Additionally, we consider porous targets, represented as Z -semi-linear sets (those defined as Boolean combinations of equations with integer coefficients). We show that an invariant can be computed providing the target spans the whole space. We present our tool porous, which computes porous invariants. [ABSTRACT FROM AUTHOR]

The primary aim of this article is to explore the approximate controllability of second-order impulsive hemivariational inequalities with initial conditions in Hilbert space. The mild solution was initially derived using the properties of the cosine and sine family of operators, Clarke's subdifferential, and the fact that the related linear equation has an evolution operator. The results of the approximate controllability of the considered systems are then taken into account using the fixed-point theorem method. An application is provided to support our theoretical findings. [ABSTRACT FROM AUTHOR]

In this paper, we study physics-informed neural networks (PINN) to approximate solutions to one-dimensional boundary value problems for linear elliptic equations and establish robust error estimates of PINN regardless of the quantities of the coefficients. In particular, we rigorously demonstrate the existence and uniqueness of solutions using the Sobolev space theory based on a variational approach. Deriving L 2 -contraction estimates, we show that the error, defined as the mean square of the differences between the true solution and our trial function at the sample points, is dominated by the training loss. Furthermore, we show that as the quantities of the coefficients for the differential equation increase, the error-to-loss ratio rapidly decreases. Our theoretical and experimental results confirm the robustness of the error regardless of the quantities of the coefficients. [ABSTRACT FROM AUTHOR]

Background & Objectives: Estimation of stature from the incomplete skeletal remains have importance in personal identification in the events of murders, accidents or natural disasters and considered as one of the biggest challenges of forensic science. Objectives: To study the relationship of stature in relation with hand dimensions and to derive a mathematical model to predict the stature from hand dimensions. Methods: This cross-sectional study was done among 50 medical students studying at a medical college in South Tamilnadu. Age, gender, hand dimensions and height of all the subjects were noted. Pearson correlation was done to find the correlation between hand dimensions and height. Linear regression was used to derive the equations to predict the stature of an individual using various dimensions of hands. Results: The mean age of the study population was 20.06 ± 1.28 years. Regression equations were derived to predict the stature of an individual with length and breadth of right and left hand. There was statistically significant positive correlation between stature and dimensions of both right and left hand. Linear regression equations were derived to predict the stature of an individual with any of the hand dimensions. Interpretation & Conclusion: Hand dimensions have statistically significant positive correlation with the stature. The length or breadth of the right or left hand can be used to predict the stature of an individual. [ABSTRACT FROM AUTHOR]

In the paper the discrete linear quadratic optimization problem, where, over a certain part of the time interval, some coordinates of the control actions are known constants. These equalities in the form of a penalty function with a certain weight are added to the quadratic functional and the corresponding discrete Euler-Lagrange equation is constructed, the solution of which is constructed using a discrete fundamental matrix. Then, an explicit expression of control actions over the entire time interval is given. The results are illustrated using the example of the vertical motion of a flying vehicle. [ABSTRACT FROM AUTHOR]

This study empirically investigates the causal relationship that exist between innovators and internal ecosystem factors driving technological innovation among small and medium-sized enterprises (SMEs) across the European region using the linear equation model. Our analysis is based on firm-level panel data from the European Innovation Survey conducted by the European Union from 2011–2018 with 296 SMEs across Europe. The results show that, human resources, research systems, financial support, firm investments, linkages, and employment impact was positively related to technological innovation performance. However, the outcome of an innovation-free environment and sales impacts as contextual factors had an insignificant influence on SMEs' innovation performance. The results imply that effective human resource approach coupled with good governmental policies are important factors that can increase SMEs' innovation performance. Based on this study results, SMEs' managers can provide effective and sustainable policies that would provide both direct and support roles on the main drivers of regional and economic development. The outcome of this research indicates that firms need to pay greater attention to external factors such as governmental policies governing SMEs, considering customers' needs, product specification and ensuring that they deliver quality product to satisfy consumers. [ABSTRACT FROM AUTHOR]

Affine subspaces are translates of linear subspaces, and hyperplanes are well-known instances of affine subspaces. In basic linear algebra, one encounters the explicit formula for projecting onto a hyperplane. An interesting—and relevant for applications—question is whether or not there is a formula for projecting onto the intersection of two hyperplanes. The answer turns out to be yes, as demonstrated recently by Behling, Bello-Cruz, and Santos, by López, by Needell and Ward, and by Ouyang. Most of these authors also provided formulas for projecting onto the intersection of an affine subspace and a hyperplane. In this note, we present an alternative approach which has the advantage of being more explicit and more elementary. Our results also provide useful information in the case when the two sets don't intersect. Luckily, the material is fully accessible to readers with a basic background in linear algebra and analysis. Finally, we demonstrate the computational efficiency of our formula when applied to an image reconstruction problem arising in Computed Tomography, and we also present a new formula for the projection onto the set of generalized bistochastic matrices with a moment constraint. [ABSTRACT FROM AUTHOR]

We are considered with the following nonlinear Schrödinger equation: −Δu+(λa(x)+1)u=f(u),x∈V,$$ -\Delta u+\left(\lambda a(x)+1\right)u=f(u),x\in V, $$on a locally finite graph G=(V,E)$$ G=\left(V,E\right) $$, where V$$ V $$ denotes the vertex set, E$$ E $$ denotes the edge set, λ>1$$ \lambda >1 $$ is a parameter, f(s)$$ f(s) $$ is asymptotically linear with respect to s$$ s $$ at infinity, and the potential a:V→[0,+∞)$$ a:V\to \left[0,+\infty \right) $$ has a nonempty well Ω$$ \Omega $$. By using variational methods, we prove that the above problem has a ground state solution uλ$$ {u}_{\lambda } $$ for any λ>1$$ \lambda >1 $$. Moreover, we show that as λ→∞$$ \lambda \to \infty $$, the ground state solution uλ$$ {u}_{\lambda } $$ converges to a ground state solution of a Dirichlet problem defined on the potential well Ω$$ \Omega $$. [ABSTRACT FROM AUTHOR]

This study purposes to extract some fractional analytical solutions of the Peyrard-Bishop-Deoxyribo-Nucleic-Acid (β -PBDNA) dynamic model with the beta-derivative by the unified Riccati equation expansion method (UREEM). Furthermore, we examine the role of various parameters of the fractional model on the soliton dynamic. The research focuses on computational biophysics and materials science, examining the impact of various parameters on the fractional model. This paper contributes to understanding soliton solutions and the β -PBDNA dynamic model, demonstrating the applicability of the UREEM method to various fractional models. Some soliton solutions of the model are successfully generated by applying the UREEM. Implementing the UREEM, we take a fractional wave transformation to convert the model into a nonlinear ordinary differential equation. So, a linear equation system is generated. After the system is solved, the soliton solutions are gained for the appropriate solution sets. Finally, 3D, 2D and contour graphs of diverse solutions are depicted at suitable values of parameters. In addition, this paper presents 3D, 2D and contour graphs of various solutions with suitable parameter values. The results are beneficial for interpreting the model in future work and confirm that UREEM is effectively applicable to diverse fractional models, coupled with a comprehensive graphical analysis of how different parameters influence these solutions. [ABSTRACT FROM AUTHOR]

The solution approximation for partial differential equations (PDEs) can be substantially improved using smooth basis functions. The recently introduced mollified basis functions are constructed through mollification, or convolution, of cell‐wise defined piecewise polynomials with a smooth mollifier of certain characteristics. The properties of the mollified basis functions are governed by the order of the piecewise functions and the smoothness of the mollifier. In this work, we exploit the high‐order and high‐smoothness properties of the mollified basis functions for solving PDEs through the point collocation method. The basis functions are evaluated at a set of collocation points in the domain. In addition, boundary conditions are imposed at a set of boundary collocation points distributed over the domain boundaries. To ensure the stability of the resulting linear system of equations, the number of collocation points is set larger than the total number of basis functions. The resulting linear system is overdetermined and is solved using the least square technique. The presented numerical examples confirm the convergence of the proposed approximation scheme for Poisson, linear elasticity, and biharmonic problems. We study in particular the influence of the mollifier and the spatial distribution of the collocation points. [ABSTRACT FROM AUTHOR]

The given text is a technical document discussing mathematical equations and algorithms related to remote sensing and linear equation systems. It provides a precise definition of the rhombus convergence property and discusses the enhancement of Algorithm 2 for calculating vectors. The document demonstrates the application of algorithms to solve diagonal QUBO problems and includes examples using exact rational expressions. While the text may not be directly relevant to specific research topics, it may be useful for researchers studying remote sensing and mathematical algorithms. [Extracted from the article]

Using modified f(T) gravity and the diagonal tetrad, we propose a new kind of analytical solution to describe anisotropic charged stellar structures in this study. We obtain precise solutions by applying the linear form of f(T) as f(T) = γT + δ in the framework of Tolman–Kuchowicz physically sound metric potentials. The stellar structures of the compact star EXO 1785-248 are then investigated using the model by incorporating a linear equation of state relating the radial pressure pr and the matter density ρ. We computed the closed-form expressions for the model parameters and illustrated their characteristics. The comprehensive graphical analysis demonstrates the scientific plausibility, causality, and dynamical stability of the model describing charged anisotropic stars. Finally, using the M-R curve, we estimate the numerical values of mass for different values of γ. The observational data of the neutron star candidates 4U 1820-30, PSR J1614-2230, and PSR J2215 + 5135 are covered by the maximum allowable masses for different values of γ additionally, when γ = 2.5, the charged compact star’s maximum permissible mass is calculated to be 2.56M⊙, which could indicate the secondary component of the GW190814 event discovered by LIGO/VIRGO experiments. [ABSTRACT FROM AUTHOR]

Objective: The aim was to investigate the association between baseline coexistence of hypertension (HTN) and arthritis, HTN alone, or arthritis alone, and their impact on longitudinal physical function measures among community-dwelling older adults over 5 years of follow-up. Methods: Ours was a longitudinal prospective cohort study from the second wave (2010–2011) and third wave (2015–2016) of the National Social Life, Health, and Aging Project (NSHAP). Data for older adults were used. Participants were categorized based on self-reported diagnoses into four groups: coexisting HTN and arthritis, HTN only, arthritis only, or neither. Physical performance measures included walking speed using the 3-Meter Walk Test and the Five Times Sit-to-Stand Test (FTSST). Multiple generalized estimating equations with linear regression analyses were conducted, adjusting for age, sex, race, body mass index (BMI) educational level, pain severity, and baseline use of pain and hypertension medications. Results: Data for 1769 participants were analyzed. Slower walking speed was only associated with coexisting HTN and arthritis (B = −0.43, p < 0.001) after accounting for covariates. The coexisting HTN and arthritis group showed no significant association with FTSST (B = 0.80, p = 0.072) after accounting for covariates. Conclusions: The coexistence of baseline HTN and arthritis in older adults is associated with a gradual decline in only walking speed as a physical performance measure in older adults. [ABSTRACT FROM AUTHOR]

Underground parking garages are enclosed spaces not directly exposed to the exterior. A smoke control system is typically required to facilitate occupants’ safe evacuation/relocation and assist in firefighting/rescue. Currently, there is a lack of guidelines for designing such systems in primary codes/standards. Only a limited number of local authorities have developed amendments to address this issue. These amendments either rely on outdated approaches, such as air change method, or simply repurpose carbon monoxide ventilation systems for smoke control without conducting additional engineering analysis and providing justification. The intent of this study is to examine the adopted approaches and explore an effective and efficient approach for garage smoke control. According to the study’s findings, it is discovered that garage floor height significantly impacts the performance of smoke control system. Additionally, structural components (beams) also influence the performance of smoke control system. Moreover, this study derives a linear equation to ascertain available safe egress time (ASET) when utilizing the carbon monoxide ventilation system or typical air change methods. Taking cost into consideration, the study concludes that for effective and cost-efficient smoke control in large underground garages, employing a carbon monoxide ventilation system is preferable to the traditional or equivalent air change method. [ABSTRACT FROM AUTHOR]

We consider the inhomogeneous semilinear wave equation with linear damping ∂ttu−Δu+∂tu=|u|p+w(t,x) in (0,∞)×RN, where p>1 and w≢0. A general criterium for the nonexistence of global weak solutions is established. In the particular case w=ω(x), we obtain the critical exponent in the sense of Fujita (first critical exponent) and the critical exponent in the sense of Lee and Ni (second critical exponent) for the considered problem. Namely, we show that, if 1p∗(N), then a global solution exists, for some ω>0 and suitable initial values. Moreover, when N ≥ 3 and p>p∗(N), we prove that for σ0 with ω(x) ≤ C|x|−σ for |x| large, and suitable initial values. Next, we extend our study to the case of systems. [ABSTRACT FROM AUTHOR]

The solution of large linear systems of equations with sparse matrices is a critical component of finite element analyses. Three linear solvers are investigated here: MUMPS, UMFPACK, and Intel DSS (PARDISO). Often, these solvers are employed as "black boxes." However, some caveats in their implementation must be observed. For instance, the solvers may yield incorrect results or perform extremely poorly in a multithread environment. These issues are demonstrated, and suggestions to fix them are provided. Some performance benchmarks are also presented with a focus on the multithreaded behavior. [ABSTRACT FROM AUTHOR]

We propose an efficient approach for time integration of Klein–Gordon equations with highly oscillatory in time input terms. The new methods are highly accurate in the entire range, from slowly varying up to highly oscillatory regimes. Our approach is based on splitting methods tailored to the structure of the input term which allows us to resolve the oscillations in the system uniformly in all frequencies, while the error constant does not grow as the oscillations increase. Numerical experiments highlight our theoretical findings and demonstrate the efficiency of the new schemes. [ABSTRACT FROM AUTHOR]

Electrical anisotropy has a significant impact on the observation data of the magnetotelluric (MT) method; therefore, it is necessary to develop forward and inverse methods in electrical anisotropic media. Based on the axis anisotropic electric field control equations, forming a large linear equation through staggered finite difference approximation, adding boundary conditions, and using the quasi-minimum residual method to solve the equation, this study obtained MT forward modeling results in axis anisotropic media. The correctness of the algorithm was verified by comparing it with the 2D quasi-analytic solution. By designing several sets of axis anisotropic 3D models, the characteristics of the apparent resistivity tensor and tipper were analyzed. The results indicated that the py, p^y and Tzy are sensitive to changes in resistivity in the X direction of the anomalous body, whereas the pyx, paxx and Tzx are sensitive to changes in resistivity in the Y direction. The apparent resistivity tensor and tipper are insensitive to changes in resistivity in the Z direction of the anomalous body. For exploration of anisotropic media, the apparent resistivity tensor and tipper of MT can identify the changes in resistivity in two horizontal axes directions and the boundaries of the anomalous body, which has the advantages for exploration. [ABSTRACT FROM AUTHOR]

Intense methane emission from permafrost soil into the atmosphere has long been observed in Arctic shelf and coastal zones. Due to the potential danger of this phenomenon for the environment and infrastructure, there is a need for periodic monitoring of gas pockets, including by means of land seismic exploration. In the present paper, this process is studied using numerical simulation methods. In order to reflect the main specific features of the region, a model of layered permafrost sandy soil with curved boundaries between the layers is constructed. Vertical and horizontal gas migration is represented by an increase in the number of methane reservoirs. The hyperbolic equations of linear elasticity are used as a governing system. The problem is solved by applying the grid-characteristic method in the two-dimensional case. The elastic parameters of the layers are specified in each grid cell. Wave structures exhibited by the resulting synthetic wave patterns and seismograms are analyzed in detail, allowing the direction of gas migration to be determined. The results can be used to interpret similar in situ measurements. [ABSTRACT FROM AUTHOR]

This paper outlines a numerical method called the Bernstein operational matrix of derivative (BOMD) of order two and order three with the approach of the Chebyshev collocation technique to solve boundary value problems (BVP). BOMD with suitable collocation points is implemented to solve the BVP using the linear combination of Bernstein polynomials with unknown coefficients to approximate the solutions. The derivatives featured in the problem sets will be approximated by utilizing the matrix. The subsequent examination involves a mathematical analysis of the proposed method, including evaluating its order, absolute error metrics and comparative assessments with alternative methodologies. Four problems involving linear and non-linear equations and systems, along with practical real-world problems, are addressed to assess the reliability of the proposed method. [ABSTRACT FROM AUTHOR]

The increasing availability and scale of biobanks and "omic" datasets bring new horizons for understanding biological mechanisms. PathGPS is an exploratory data analysis tool to discover genetic architectures using Genome Wide Association Studies (GWAS) summary data. PathGPS is based on a linear structural equation model where traits are regulated by both genetic and environmental pathways. PathGPS decouples the genetic and environmental components by contrasting the GWAS associations of "signal" genes with those of "noise" genes. From the estimated genetic component, PathGPS then extracts genetic pathways via principal component and factor analysis, leveraging the low-rank and sparse properties. In addition, we provide a bootstrap aggregating ("bagging") algorithm to improve stability under data perturbation and hyperparameter tuning. When applied to a metabolomics dataset and the UK Biobank, PathGPS confirms several known gene–trait clusters and suggests multiple new hypotheses for future investigations. [ABSTRACT FROM AUTHOR]

The least-squares ReLU neural network (LSNN) method was introduced and studied for solving linear advection-reaction equation with discontinuous solution in [4, 5]. The method is based on an equivalent least-squares formulation and [5] employs ReLU neural network (NN) functions with ⌈log2 (d + 1)⌉ + 1-layer representations for approximating solutions. In this paper, we show theoretically that the method is also capable of accurately approximating non-constant jumps along discontinuous interfaces that are not necessarily straight lines. Theoretical results are confirmed through multiple numerical examples with d = 2, 3 and various non-constant jumps and interface shapes, showing that the LSNN method with ⌈log2 (d + 1)⌉ + 1 layers approximates solutions accurately with degrees of freedom less than that of mesh-based methods and without the common Gibbs phenomena along discontinuous interfaces having non-constant jumps. [ABSTRACT FROM AUTHOR]

The restricted mean survival time (RMST) is often of direct interest in clinical studies involving censored survival outcomes. It describes the area under the survival curve from time zero to a specified time point. When data are subject to length-biased sampling, as is frequently encountered in observational cohort studies, existing methods cannot estimate the RMST for various restriction times through a single model. In this article, we model the RMST as a continuous function of the restriction time under the setting of length-biased sampling. Two approaches based on estimating equations are proposed to estimate the time-varying effects of covariates. Finally, we establish the asymptotic properties for the proposed estimators. Simulation studies are performed to demonstrate the finite sample performance. Two real-data examples are analyzed by our procedures. [ABSTRACT FROM AUTHOR]

Fuzzy linear matrix equations are generally applicable in signal processing, control, and system theory since most time-dependent models can be represented as linear or nonlinear dynamical systems. This paper presents a uniform method to find the classical solution of fuzzy linear matrix equations developed from He et al. (Soft Comput 22:6515–6523, 2018), Mikaeilvand et al. (Mathematics 8(5):850, 2020). As an applications of the method, numerical methods to solve fuzzy generalized Lyapunov matrix equation are presented. As suggested by large scale numerical tests, the method proposed here perform much faster than other methods and can solve large scale examples that other methods fail to do. [ABSTRACT FROM AUTHOR]

Takagi–Sugeno fuzzy neural network (TSFNN) has been widely used in intelligent prediction. The prediction accuracy of TSFNN is impacted by its model parameter choices. However, the manual selection of parameters is hard to ensure the prediction accuracy of TSFNN. Therefore, we propose a Particle Swarm Optimization with Result Precision Enhancement strategy, PSO-RPE, to automatically generate highly optimized parameters to improve the prediction accuracy of TSFNN. In PSO-RPE, we present memory enhancement technology to direct the evolution of particles and accelerate the search process for the solution. Next, our PSO-RPE strategy employs a customized linear dynamic equation to balance the global and local search capabilities. Moreover, the elite strategy is applied to produce better feasible parameters with high probability. Moreover, the analysis of the convergence on 12 benchmarks is given to verify the superiority of PSO-RPE. Finally, our experiments in predicting water quality based on TSFNN demonstrate that the PSO-RPE strategy is effective in the generation of optimized parameters. [ABSTRACT FROM AUTHOR]

The author proposes algorithms for constructing a prebasis and the basis of the set of solutions to systems of linear constraints in the form of equalities and inequalities in the domains of integers, which are based on combined coefficients of constraints. The article considers the algorithm for constructing the prebasis and basis of systems of linear equations and algorithms for constructing the fundamental system of solutions to systems of linear homogeneous and linear inhomogeneous inequalities. [ABSTRACT FROM AUTHOR]

The primary goal of this article is to extend the reciprocal LASSO for applications to binary and survival outcomes. We consider the least squares approximation (LSA) as a solver for the reciprocal LASSO problem. The LSA is a general theoretical framework that includes generalized linear models, Cox regression, and many others as special cases. By applying LSA to reciprocal LASSO regularization, we transfer the original reciprocal LASSO problem into an asymptotically equivalent least squares problem. While the existing literature on reciprocal LASSO has mostly focused on linear models, our algorithm can be easily implemented for general likelihoods, providing a flexible framework for variable selection using reciprocal penalties. To handle the computational burden of implementing the resulting procedure, we employ a scalable stochastic search method called Simplified Shotgun Stochastic Search with Screening (S5), which is easy to implement, without requiring any sophisticated optimization package other than a linear equation solver. We examine the effectiveness of our procedure through Monte Carlo simulations and real data analyses. [ABSTRACT FROM AUTHOR]

In this review, the thermoelectric properties in nodal‐point semimetals with two bands are discussed. For the two‐dimensional (2D) cases, it is shown that the expressions of the thermoelectric coefficients take different values depending on the nature of the scattering mechanism responsible for transport, by considering examples of short‐ranged disorder potential and screened charged impurities. An anisotropy in the energy dispersion spectrum invariably affects the thermopower quite significantly, as illustrated by the results for a node of semi‐Dirac semimetal and a single valley of graphene. The scenario when a magnetic field of magnitude B$B$ is applied perpendicular to the plane of the 2D semimetal is also considered. The computations for the three‐dimensional (3D) cases necessarily involve the inclusion of nontrivial Berry phase effects. In addition to demonstrating the expressions for the response tensors, the exotic behavior observed in planar Hall and planar thermal Hall set‐ups is discussed. [ABSTRACT FROM AUTHOR]