Search

Stochastic cellular automata for rock-paper-scissors games are related to Lotka-Volterra model. Simulations are usually performed by two methods local and global interactions. It is well known that the population dynamics with local interaction is stable, where all species coexist. In contrast, global interaction leads to extinction. So far, theories such as mean-field theory and pair approximation have been presented, but they never explained the stable dynamics in local simulation. In the present article, we apply effective medium approximation (EMA) which has been developed in Physics. The effective medium is determined in a self-consistent way. The EMA theory well predicts the stability of population dynamics. Moreover, it fairly explains the aggregation of each species observed in the stationary state. [ABSTRACT FROM AUTHOR]

Summarizes the construction of paper folding. Method for approximating rational subdivisions or arbitrary angles and line segments; Angle-folding algorithm; Approximating angles, regular polygons and star polygons; Dissection of angles into equal parts.

This paper deals with global well-posedness of the solution to the complex short pulse equation. We first use regularized technology and the approximation argument to prove the local existence and uniqueness of this equation. Then, based on conserved quantities and energy analysis, we show that the solution can be extended globally in time for suitably small initial data. [ABSTRACT FROM AUTHOR]

Let H be a separable Hilbert space and let { x n } be a sequence in H that does not contain any zero elements. We say that { x n } is a Bessel-normalizable or frame-normalizable sequence if the normalized sequence { x n ‖ x n ‖ } is a Bessel sequence or a frame for H, respectively. In this paper, several necessary and sufficient conditions for sequences to be frame-normalizable and not frame-normalizable are proved. Perturbation theorems for frame-normalizable sequences are also proved. As applications, we show that the Balazs–Stoeva conjecture holds for Bessel-normalizable sequences. Finally, we apply our results to partially answer the open question raised by Aldroubi et al. as to whether the iterative system { A n x ‖ A n x ‖ } n ≥ 0 , x ∈ S associated with a normal operator A : H → H and a countable subset S of H, is a frame for H. In particular, if S is finite, then we are able to show that { A n x ‖ A n x ‖ } n ≥ 0 , x ∈ S is not a frame for H whenever { A n x } n ≥ 0 , x ∈ S is a frame for H. [ABSTRACT FROM AUTHOR]

In this paper, we describe an algorithm for fitting an analytic and bandlimited closed or open curve to interpolate an arbitrary collection of points in R 2 . The main idea is to smooth the parametrization of the curve by iteratively filtering the Fourier or Chebyshev coefficients of both the derivative of the arc-length function and the tangential angle of the curve and applying smooth perturbations, after each filtering step, until the curve is represented by a reasonably small number of coefficients. The algorithm produces a curve passing through the set of points to an accuracy of machine precision, after a limited number of iterations. It costs O(N log N) operations at each iteration, provided that the number of discretization nodes is N. The resulting curves are smooth, affine invariant, and visually appealing and do not exhibit any ringing artifacts. The bandwidths of the constructed curves are much smaller than those of curves constructed by previous methods. We demonstrate the performance of our algorithm with several numerical experiments. [ABSTRACT FROM AUTHOR]

We present a scheme for finding all roots of an analytic function in a square domain in the complex plane. The scheme can be viewed as a generalization of the classical approach to finding roots of a function on the real line, by first approximating it by a polynomial in the Chebyshev basis, followed by diagonalizing the so-called “colleague matrices.” Our extension of the classical approach is based on several observations that enable the construction of polynomial bases in compact domains that satisfy three-term recurrences and are reasonably well-conditioned. This class of polynomial bases gives rise to “generalized colleague matrices,” whose eigenvalues are roots of functions expressed in these bases. In this paper, we also introduce a special-purpose QR algorithm for finding the eigenvalues of generalized colleague matrices, which is a straightforward extension of the recently introduced structured stable QR algorithm for the classical cases (see Serkh and Rokhlin 2021). The performance of the schemes is illustrated with several numerical examples. [ABSTRACT FROM AUTHOR]

Singular integral operators play an important role in approximation theory and harmonic analysis. In this paper, we consider a weighted Lebesgue space L p , w , define a modified Gauss–Weierstrass singular integral on it, and study direct and inverse approximation properties of the operator followed by a Korovkin-type approximation theorem for a function f ∈ L p , w . We use the modulus of continuity of the functions to measure the rate of convergence. [ABSTRACT FROM AUTHOR]

The paper is concerned with the mathematical theory and numerical approximation of systems of partial differential equations (pde) of hyperbolic, pseudo-parabolic type. Some mathematical properties of the initial-boundary-value problem (ibvp) with Dirichlet boundary conditions are first studied. They include the weak formulation, well-posedness and existence of traveling wave solutions connecting two states, when the equations are considered as a variant of a conservation law. Then, the numerical approximation consists of a spectral approximation in space based on Legendre polynomials along with a temporal discretization with strong stability preserving (SSP) property. The convergence of the semidiscrete approximation is proved under suitable regularity conditions on the data. The choice of the temporal discretization is justified in order to guarantee the stability of the full discretization when dealing with nonsmooth initial conditions. A computational study explores the performance of the fully discrete scheme with regular and nonregular data. [ABSTRACT FROM AUTHOR]

In this paper, a one-step block of optimized hybrid schemes for the numerical integration of second-order initial value problems (IVP) of ordinary differential equations (ODE) is constructed via collocation techniques. The developed scheme is obtained by considering two intra-step nodal points as hybrid points, which are chosen in order to achieve optimized errors of the main formulae approximating the solution such that 0 < v1 < v2 < 1 where v1 and v2 are defined as hybrid points. The characteristics of the developed scheme are analyzed. Application of the new scheme on some second-order IVPs shows the accuracy and effectiveness of the scheme compared with some existing methods. [ABSTRACT FROM AUTHOR]

In his famous paper [15] Ibragim Ibishievich Ibragimov has given asymptotic valucs of the best uniform approximation of functions of the form (a - χ)s lnm(a - χ), (a ≥ 1). These results have led to the developmcnt of a series of new directions in approximation theory, including the following ones, to which we devote this paper. • Constructive characterization of approximation of functions on a closed interval. • Babenko spaces. • Ditzian-Totik moduli of smoothness. • Constructive characterization of approximation of functions on the sets of complex plane. • Shape preserving approximation. In particular, we will show how we have used the results by I. I. Ibragimov in our recent paper in Constructive Approximation. [ABSTRACT FROM AUTHOR]

Abstract: A physical model of a continuous paper pulp digester is simplified and two subprocesses selected from the digester are modelled by coupled linear partial differential equations. This study focuses on the parameter identification of the simplified linear models. Finite-dimensional approximation of the model is made and a software package developed for identification of distributed parameter processes is applied. This identification system is developed for flexibility to allow identification for different choices of subprocesses and process variables. Unknown parameters of the subprocess models are estimated and the results are illustrated by process simulation and model validation. [Copyright &y& Elsevier]

Abstract: In this note, we point out an error in the recently published article [R.K. Mohanty, M.K. Jain, D. Dhall, A cubic spline approximation and application of TAGE iterative method for the solution of two-point boundary value problems with forcing function in integral form, Appl. Math. Model. 35 (2011) 3036–3047] and then correct it. [Copyright &y& Elsevier]

Abstract: Ahn, Lee, Park and Yoo proved that the best constrained degree reduction of a polynomial f in -norm equals the best weighted Euclidean approximation of the Bernstein–Bézier coefficients of f in a paper, published in the journal, Computer Aided Geometric Design 21 (2) (2004) 181–191. In this note, we point out an error in their paper and give the correct result. [Copyright &y& Elsevier]

In the design of antenna arrays which require fast and robust flat‐top beam synthesis, computationally efficient methods are preferred. This feature is usually met by analytical techniques or simple optimisation procedures. On the other hand, in the flat‐top beam synthesis, a common requirement is the ability to control beamwidth or sidelobe level. However, this can result in a high dynamic range ratio (DRR) of array's excitation coefficients. In this paper, a straightforward method for the design of symmetrical flat‐top arrays with controllable sidelobe level or DRR is proposed. The method is based on quadratic and cubic transforms of Gaussian excitations. In addition, the method utilises zero coefficients whose positions are used to control the DRR, including the ability to achieve its minimum. Compared to other flat‐top arrays with analytically shaped beams, the proposed arrays have lower DRRs for the same sidelobe level. [ABSTRACT FROM AUTHOR]

Hadamard type fractional calculus involves logarithmic function of an arbitrary exponent as its convolutional kernel, which causes challenge in numerical treatment. In this paper we present a spectral collocation method with mapped Jacobi log orthogonal functions (MJLOFs) as basis functions and obtain an efficient algorithm to solve Hadamard type fractional differential equations. We develop basic approximation theory for the MJLOFs and derive a recurrence relation to evaluate the collocation differentiation matrix for implementing the spectral collocation algorithm. We demonstrate the effectiveness of the new method for the nonlinear initial and boundary problems, i.e, the fractional Helmholtz equation, and the fractional Burgers equation. [ABSTRACT FROM AUTHOR]

In this paper, we provide a new framework for studying continued fractions (CFs) by means of the backwards continued fraction (BCF). We develop an approximation theory for BCFs based on taking expansions of a fixed length, show the correspondence between continued fractions and their BCFs counterpart, and illustrate a rich approximation theory for continued fractions based off the methods of the approximation theory for the backwards case. In particular, we construct explicit functions that are sharp bounds for the BCF or CF error infinitely often over any BCF or CF cylinder set, and work out the details to pass seamlessly between the BCF and CF expansion of any real number. [ABSTRACT FROM AUTHOR]

The transmission eigenvalue problem arising from the inverse scattering theory is of great importance in the theory of qualitative methods and in the practical applications. In this paper, we study the FEM for the transmission eigenvalue problem for anisotropic inhomogeneous media in Ω ⊂ R d (d = 2 , 3). Using the T -coercivity and the spectral approximation theory, we derive an a posteriori estimator of residual type and prove its effectiveness and reliability for eigenfunctions. In addition, we also prove the reliability of the estimator for transmission eigenvalues. The numerical experiments indicate our method is efficient and can reach the optimal order D o F − 2 m / d by using piecewise polynomials of degree m for real and complex eigenvalues. [ABSTRACT FROM AUTHOR]

The Picard iterative approach used in the paper to derive conditions under which nonlinear ordinary differential equations based on the derivative with the Mittag-Leffler kernel admit a unique solution. Using a simple Euler approximation and Heun's approach, we solved this nonlinear equation numerically. Some examples of a nonlinear linear differential equation were considered to present the existence and uniqueness of their solutions as well as their numerical solutions. A chaotic model was also considered to show the extension of this in the case of nonlinear systems. [ABSTRACT FROM AUTHOR]

This paper is interested in studying the one-phase Stefan problem. For this purpose, we use the nonlinear sentinel method, which relies typically on the approximate controllability and the Fanchel-Rockafellar duality of the minimization problem, to prove the existence and uniqueness of a solution to this problem. In particular, our research focuses on the application of the nonlinear sentinel method to the single-phase Stefan problem. This approach aids in identifying an unspecified boundary section within the domain undergoing a liquid-solid phase transition. We track the evolution of the temperature profile in the liquid-solid material and the corresponding movement of its interface over time. Eventually, the local convergence used for the iterative numerical scheme is demonstrated. [ABSTRACT FROM AUTHOR]

We study extremal problems related to the best joint polynomial approximation of functions analytic in the unit disk and belonging to the Bergman space . The problem of joint approximation of periodic functions and their derivatives by trigonometric polynomials was considered by Garkavy [1] in 1960. Then, in the same year, Timan [2] considered this problem for classes of entire functions defined on the entire axis. The problem of joint approximation of functions and their derivatives is considered in more detail in Malozemov's monograph [3], where some classical theorems of the theory of approximation of functions are presented and generalized. In the present paper, a number of exact theorems are obtained and sharp upper bounds for the best joint approximations of a function and its successive derivatives by polynomials and their respective derivatives on some classes of complex functions belonging to the Bergman space are calculated. [ABSTRACT FROM AUTHOR]

Quite often (e.g., using numerical methods), we are only able to find approximate solutions of some equations, and it is necessary to know the size of the difference between such approximate solutions and the mappings that satisfy the equation exactly. This issue is the main subject of the theory of Ulam stability, and it is related to other areas of research such as, e.g., shadowing, optimization, and approximation theory. In this expository paper, we present several selected outcomes on Ulam stability of difference equations, show possible extensions of them and indicate further directions for research. We also present and discuss some simple methods that allow improvement of several already known results concerning Ulam stability of some difference equations in normed or metric spaces and extend them to b-metric and 2-normed spaces. Our results show that the noticeable symmetry exists between the outcomes of this type in normed and metric spaces and those obtained by us for other spaces. In particular, we extend the result of Pólya and Szegö concerning the stability of equation x n + m = x n + x m for m , n ∈ T , where T means either the set of integers Z or the set of positive integers N. We also consider the stability of equation x n + p + a 1 x n + p − 1 + ... + a p x n + b n = 0 (with a fixed positive integer p) and of two more general difference equations. [ABSTRACT FROM AUTHOR]

We shall give an elementary proof for Lemma 2.4 and correct some errors in Table 1 of the author's paper of the title. Moreover, we shall extend this table up to integers below 232. [ABSTRACT FROM AUTHOR]

Fuzzy rough set theory has been successfully applied to many attribute reduction methods, in which the lower approximation set plays a pivotal role. However, the definition of lower approximation used has ignored the information conveyed by the upper approximation and the boundary region. This oversight has resulted in an unreasonable relation representation of the target set. Despite the fact that scholars have proposed numerous enhancements to rough set models, such as the variable precision model, none have successfully resolved the issues inherent in the classical models. To address this limitation, this paper proposes an unsupervised attribute reduction algorithm for mixed data based on an improved optimal approximation set. Firstly, the theory of an improved optimal approximation set and its associated algorithm are proposed. Subsequently, we extend the classical theory of optimal approximation sets to fuzzy rough set theory, leading to the development of a fuzzy improved approximation set method. Finally, building on the proposed theory, we introduce a novel, fuzzy optimal approximation-set-based unsupervised attribute reduction algorithm (FOUAR). Comparative experiments conducted with all the proposed algorithms indicate the efficacy of FOUAR in selecting fewer attributes while maintaining and improving the performance of the machine learning algorithm. Furthermore, they highlight the advantage of the improved optimal approximation set algorithm, which offers higher similarity to the target set and provides a more concise expression. [ABSTRACT FROM AUTHOR]

In this paper, we present a two-grid scheme of fully discrete finite element approximation for optimal control problems governed by parabolic integro-differential equations. The state and co-state variables are approximated by a piecewise linear function and the control variable is discretized by a piecewise constant function. First, we derive the optimal a priori error estimates for all variables. Second, we prove the global superconvergence by using the recovery techniques. Third, we construct a two-grid algorithm and discuss its convergence. In the proposed two-grid scheme, the solution of the parabolic optimal control problem on a fine grid is reduced to the solution of the parabolic optimal control problem on a much coarser grid; additionally, the solution of a linear algebraic system on the fine grid and the resulting solution maintain an asymptotically optimal accuracy. Finally, we present a numerical example to verify the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper we investigate an iterated function system that defines a fractal interpolation function, where ordinate scaling, that is Lipschitz constant in Banach contraction principle is substituted by real-valued control function. In such a manner, fractal interpolation functions associated with Matkowski contractions are obtained and provide a new framework of approximating experimental data. Furthermore, given a data generating function f , we study a new class of fractal interpolation functions which converge to f. [ABSTRACT FROM AUTHOR]

The traces used in side-channel analysis are essential to breaking the key of encryption and the signal quality greatly affects the correct rate of key guessing. Therefore, the preprocessing of side-channel traces plays an important role in side-channel analysis. The process of side-channel leakage signal acquisition is usually affected by internal circuit noise, external environmental noise, and other factors, so the collected signal is often mixed with strong noise. In order to extract the feature information of side-channel signals from very low signal-to-noise ratio traces, a hybrid threshold denoising framework using singular value decomposition is proposed for side-channel analysis preprocessing. This framework is based on singular value decomposition and introduces low-rank matrix approximation theory to improve the rank selection methods of singular value decomposition. This paper combines the hard threshold method of truncated singular value decomposition with the soft threshold method of singular value shrinkage damping and proposes a hybrid threshold denoising framework using singular value decomposition for the data preprocessing step of side-channel analysis as a general preprocessing method for non-profiled side-channel analysis. The data used in the experimental evaluation are from the raw traces of the public database of DPA contest V2 and AES_HD. The success rate curve of non-profiled side-channel analysis further confirms the effectiveness of the proposed framework. Moreover, the signal-to-noise ratio of traces is significantly improved after preprocessing, and the correlation with the correct key is also significantly enhanced. Experimental results on DPA v2 and AES_HD show that the proposed noise reduction framework can be effectively applied to the side-channel analysis preprocessing step, and can successfully improve the signal-to-noise ratio of the traces and the attack efficiency. [ABSTRACT FROM AUTHOR]

In this work, a Bayesian Regularization Network based Geometric Deviation Control (BRN-GDC) algorithm is developed to mitigate thermal distortion in 3D printing. Inspired by points registration in computer vision and function approximation theory, the Bayesian regularization network method is used to quantify thermal distortion in 3D printed products. Because of "shallow" regularization network architecture, the BRN-GDC method is training-free and does not require lots of data. Due to the lack of one-to-one correspondence between the design point data and the scan point data in 3D printing, conventional point set registration methods, e.g. Coherent Point Drift method, may fail in finding the global geometric deviation field, while the Bayesian regularization network approach works. In the two experiments presented in this paper, we showed that the BRN-GDC algorithm has the capability to control the thermal distortion in 3D printing that is parameter- and location-dependent. [ABSTRACT FROM AUTHOR]

The Laplace operator is a differential operator which is used to detect edges of objects in digital images. This paper presents the properties of the most commonly used fifth-order pixels Laplace filters including the difference schemes used to derive them (finite difference method - FDM and finite element method - FEM). The results of the research concerning third-order pixels matrices of the convolution Laplace filters used for digital processing of images were presented in our previous paper: The mathematical characteristic of the Laplace contour filters used in digital image processing. The third order filters is presented byWinnicki et al. (2022). As previously, the authors focused on the mathematical properties of the Laplace filters: their transfer functions and modified differential equations (MDE). The relations between the transfer function for the differential Laplace operator and its difference operators are described and presented here in graphical form. The impact of the corner elements of the masks on the results is also discussed. A transfer function, is a function characterizing properties of the difference schemes applied to approximate differential operators. Since they are relations derived in both types of spaces (continuous and discrete), comparing them facilitates the assessment of the applied approximation method. [ABSTRACT FROM AUTHOR]

In this paper, control analysis of a stochastic lagging discrete ecosystem is investigated. Two-dimensional stochastic hysteresis discrete ecosystem equilibrium points with symmetry are discussed, and the dynamical behavior of equilibrium points with symmetry and their control analysis is discussed. Using the orthogonal polynomial approximation theory, the stochastic lagged discrete ecosystems are approximately transformed as its equivalent deterministic ecosystem. Based on the stability and bifurcation theory of deterministic discrete systems, through mathematical analysis, asymptotic stability and Hopf bifurcation are existent in the ecosystem, constructing control functions, controlling the behavior of the system dynamics. Finally, the effects of different random strengths on the bifurcation control and asymptotic stability control are verified by numerical simulations, which validate the correctness and effectiveness of the main results of this paper. [ABSTRACT FROM AUTHOR]

In the field of reinforcement learning, we propose a Correct Proximal Policy Optimization (CPPO) algorithm based on the modified penalty factor β and relative entropy in order to solve the robustness and stationarity of traditional algorithms. Firstly, In the process of reinforcement learning, this paper establishes a strategy evaluation mechanism through the policy distribution function. Secondly, the state space function is quantified by introducing entropy, whereby the approximation policy is used to approximate the real policy distribution, and the kernel function estimation and calculation of relative entropy is used to fit the reward function based on complex problem. Finally, through the comparative analysis on the classic test cases, we demonstrated that our proposed algorithm is effective, has a faster convergence speed and better performance than the traditional PPO algorithm, and the measure of the relative entropy can show the differences. In addition, it can more efficiently use the information of complex environment to learn policies. At the same time, not only can our paper explain the rationality of the policy distribution theory, the proposed framework can also balance between iteration steps, computational complexity and convergence speed, and we also introduced an effective measure of performance using the relative entropy concept. [ABSTRACT FROM AUTHOR]

This paper aims to fuzzify the width problem of classical approximation theory. New concepts of fuzzy Kolmogorov n-width and fuzzy linear n-width are introduced on the basis of α -fuzzy distance which is induced by the fuzzy norm. Furthermore, the relationship between the classical widths in linear normed space and the fuzzy widths in fuzzy linear normed space is discussed. Finally, the exact asymptotic orders of the fuzzy Kolmogorov n-width and fuzzy linear n-width corresponding to a given fuzzy norm in finite-dimensional space and Sobolev space are estimated. [ABSTRACT FROM AUTHOR]

The investigations of the discrete and fast linear canonical transform (LCT) are becoming one of the hottest research topics in modern signal processing and optics. Among them, the fast calculation of LCT for non-uniform data is one of key problems. Focus on this problem, a new fast algorithm of the LCT has been proposed in this paper firstly by interpolation and approximation theory. The proposed algorithms can calculate quickly the LCT of the data, whether the input or output data is uniform. Secondly, the complexity and precision of derived algorithms have been analyzed for different situations. Finally, the experimental results are presented to verify the correctness of the obtained results. [ABSTRACT FROM AUTHOR]

This study focuses on the problem that the multiobjective optimization decision-making process of the design scheme under the cloud service model fails to fully consider the needs of users' diversity, due to the lack of research on quantitative modeling and evaluation methods of designers' ability. It affects the reasonable matching between complex design tasks and design ability and hinders the socialized aggregation of design ability. Based on the competency model, facing the industrial designers in the cloud manufacturing model, our paper constructs the design capability evaluation system from the perspectives of Yuan Shengren capability, industry technology competency, design task competency, and learning capability competency and discusses the design capability evaluation method based on a network analysis method. Through the design capability evaluation of the industrial design cloud service platform, feasibility and scientificity of the method in this paper are verified. This paper proposes a design scheme optimization decision-making method combining quality function configuration and rough set theory. Based on the analysis of the cloud service model, this method introduces the design decision-making process model of user participation and fuzzy evaluation mechanism to carry out cluster analysis and the intelligent transformation of user requirements. A design scheme evaluation index system oriented to user requirements is established, and the importance of design scheme evaluation indexes in the process of networked collaborative design is accurately quantified. Following the principle of combining scientificity and systematicness, a third-order decision-making model for design scheme optimization under the cloud service model is proposed. The model is solved by combining the rough set theory and rough approximation ideal solution. [ABSTRACT FROM AUTHOR]

In this paper, we propose the Bayes estimators of unknown parameters of power function distribution in the context of double censoring. The maximum-likelihood estimators (MLEs) for the power function parameters are derived. Bayes estimators are derived using the squared error loss function, entropy loss function, and linex loss function using the Lindley approximation and the importance sampling procedures. We also introduced sample prediction estimates using Bayesian techniques. Finally, we perform a simulation study to compare all the proposed estimation methods and analyze a real-life data set for illustration purposes. [ABSTRACT FROM AUTHOR]

The Oberbeck–Boussinesq approximation is the most commonly employed theoretical scheme for the study of natural or mixed convection flows. However, the misunderstanding of this approximated framework is a possibility that may cause the emergence of paradoxes or, at least, incorrect conclusions. In this paper, the basic features of the Oberbeck–Boussinesq approximation are briefly recalled and three simple examples where this theoretical scheme may be misused are provided. Such misuses of the approximation lead to erroneous conclusions that, in the examples presented in this note, entail violations of the principle of mass conservation. A discussion about the Oberbeck–Boussinesq approximation as an asymptotic theory obtained by letting the product of the thermal expansion coefficient and the reference temperature difference tend to zero is also presented. [ABSTRACT FROM AUTHOR]

Wavelet expansions are a powerful tool for constructing adaptive approximations. For this reason, they find applications in a variety of fields, from signal processing to approximation theory. Wavelets are usually derived from refinable functions, which are the solution of a recursive functional equation called the refinement equation. The analytical expression of refinable functions is known in only a few cases, so if we need to evaluate refinable functions we can make use only of the refinement equation. This is also true for the evaluation of their derivatives and integrals. In this paper, we detail a procedure for computing integrals of wavelet products exactly, up to machine precision. The efficient and accurate evaluation of these integrals is particularly required for the computation of the connection coefficients in the wavelet Galerkin method. We show the effectiveness of the procedure by evaluating the integrals of pseudo-splines. [ABSTRACT FROM AUTHOR]

Many of the new M V -valued fuzzy structures, including intuitionistic, neutrosophic, or fuzzy soft sets, can be transformed into so-called almost M V -valued fuzzy sets, or, equivalently, fuzzy sets with values in dual pair of semirings (in symbols, (R , R *) -fuzzy sets). This transformation allows any construction of almost M V -valued fuzzy sets to be retransformed into an analogous construction for these new fuzzy structures. In that way, approximation theories for (R , R *) -fuzzy sets, rough (R , R *) -fuzzy sets theories, or F-transform theories for (R , R *) -fuzzy sets have already been created and then retransformed for these new fuzzy structures. In this paper, we continue this trend and define, on the one hand, the theory of extensional (R , R *) -fuzzy sets defined on sets with fuzzy similarity relations with values in dual pair of semirings and power sets functors related to this theory and, at the same time, the theory of cuts with relational morphisms of these structures. Illustratively, the reverse transformations of some of these concepts into new fuzzy structures are presented. [ABSTRACT FROM AUTHOR]

The weak L1 -space meets in many areas of mathematics. For example, the conjugate functions of Lebesgue integrable functions belong to the weak L1 -space. The difficulty of working with the weak L1 -space is that the weak L1 -space is not a normed space. Moreover, infinitely differentiable (even continuous) functions are not dense in this space. Due to this, the theory of approximation was not produced in this space. In the present paper, we introduced the concept of the modulus of continuity of the functions from the weak L1 -space, studied its properties, found a criterion for convergence to zero of the modulus of continuity of the function from the weak L1 -space, and proved in this space an analogue of the Jackson-type theorem. [ABSTRACT FROM AUTHOR]

Introduction: Silica nanoparticles (SNP) are extremely promising tools in nanotechnology and nano medicine. In most of applications such as capture and release of bacteriophage viruses the nano-structures of silica are coated by bio-compatible groups such as amine compounds. The presence of amino groups on the surface of the biosensors enables the installation of analyte receptors and antifouling agents such as oligo (ethylene oxide). Therefore, in this study, the electronic and structural properties of Core-Shell aminoSilica Nanoparticles are investigated. Material and Methods: In this investigation, we aim at obtaining the optimized structures and evaluate the geometries of the ground state for (SiO2) n (n=16, 20) nanoclusters. The electronic properties computed by density functional theory with GGA approximation and SCC-DFTB with hybrid Slater-Koster files are investigated and the effect of functionalization on such properties is discussed. Results: Solvolysis of studied structures is examined and it is shown that the highest occupied and lowest unoccupied molecular orbital states shift to obviously higher energy levels, which lead to more stable hydrogenated nanoclusters. The stability of nanoclusters rises by functionalization with amino and methylamine groups. Charge analysis of functionalized systems indicates the reactivity of nanoclusters. The results obtained in this paper are useful for chemical and biochemical applications of silica nanostructures. Conclusion: Results show that the length of amine hydrocarbon chain can control the electronic and magnetic properties of studied silica nanocluster (SNP) with different number of SiO2 unit. Pure ultra-small nanocluster shows the impressive spin splitting around the Fermi level, which is due to the spin splitting of outer silicon atoms. This feature of silica nanoclusters may be notable for applications in electronics. [ABSTRACT FROM AUTHOR]

This paper discusses a class of nonlinear singular perturbation problems with Robin boundary values in critical cases. By using the boundary layer function method and successive approximation theory, the corresponding asymptotic expansions of small parameters are constructed, and the existence of uniformly efficient smooth solutions is proved. Meanwhile, we give a concrete example to prove the validity of our results. [ABSTRACT FROM AUTHOR]

Standard PN-EN 1992-1-1 for designing reinforced concrete structures gives a major priority to the issues relating to second-order effects, but presents in detail only two approximate calculation methods: the nominal stiffness method and the nominal curvature method. As regards the general method, only certain requirements and suggestions are provided. In typical situations, when the appropriate assumptions are satisfied, the approximate methods yield satisfactory results. However, in engineering practice one can come across several cases (e.g. very tall columns, columns with a cantilever for a gantry girder, and floor joists) in which the approximate methods will prove unreliable. This paper presents and discusses a procedural algorithm for analysing second-order effects using the general method. The algorithm is employed to perform exemplary calculations and their results are compared with the results yielded by the approximate methods commonly used by engineers. Moreover, areas in which the approximate methods can be unreliable are indicated. The analyses have confirmed the significant advantage of the general method over the approximate methods. Therefore it is worth popularizing this method, the more so that its calculation procedures can be to a large extent automated and dedicated computer programs can be developed. [ABSTRACT FROM AUTHOR]

In survey sampling, the errors which are mostly studied during estimation are sampling errors. However, the properties of estimators are more influenced by non-sampling errors than sampling errors. This paper addresses the problem of estimating the finite population mean of the study variable y using auxiliary information in sample surveys in the presence of non-response. We have proposed an estimator for estimating the population mean of study variable when the parameter of auxiliary variable x is known. The bias and mean squared error (MSE) of the proposed estimator are obtained to the first degree of approximation. The minimum mean square error of the proposed estimator is also obtained. A Simulation study has been carried out to support the theoretical results. The comparison of the proposed estimator with other estimators is made to show that our proposed estimator is more efficient than the other estimators in terms of percent relative efficiency (PRE). [ABSTRACT FROM AUTHOR]

Extriangulated categories were introduced by Nakaoka and Palu as a simultaneous generalization of exact categories and triangulated categories. In this paper, we first introduce the concept of left Frobenius pairs on an extriangulated category C , and then establish a bijective correspondence between left Frobenius pairs and certain cotorsion pairs in C . As an application, some new admissible model structures are established from left Frobenius pairs under certain conditions, which generalizes a result of Hu et al. (J. Algebra 551 (2020) 23–60). [ABSTRACT FROM AUTHOR]

Power flow solvers typically start from an initial point of power injection. This paper constructs a system of multiple initial points (SMIP) to enable selection of an appropriate initial point, with the objective to achieve a balanced improvement in the solution speed and accuracy, for problems with a large number of power flows. The intent is to recover time cost of forming the SMIP through the improvements to each power flow. The SMIP is tested on a time series based Monte Carlo study of Electric Vehicle (EV) hosting capacity in a low voltage distribution network, which has 5.4 million power flows. SMIP is applied to two power flow solvers: a Taylor series approximation and a Z-bus method. The accuracy of the quadratic Taylor series approximation was improved by a factor of 30 with a 27% increase in the solve time when compared against a single no-load initial point. A Z-bus solver with SMIP, limited to two iterations, gave the best performance for the EV hosting capacity case study. [ABSTRACT FROM AUTHOR]

Abstract: A comment on a recent paper about the combined effects of radiation and viscous dissipation on the convection in an annular porous enclosure has raised the problem of the role played by the viscous dissipation and the pressure work contributions in buoyant flows. The aim of this further comment is to show that the criticism expressed by Costa on the model of the viscous dissipation effect employed in the paper by Badruddin and co-workers is unjustified. [ABSTRACT FROM AUTHOR]

In recent years, significant advancements have been made in neural beamforming, leveraging spectral and spatial cues to enhance their performance in multi-channel speech enhancement. When the frame-wise processing mechanism is required, there exists a trade-off between performance and algorithmic delay for existing all-neural beamformers. However, from the perspective of multi-source information fusion, the network is often encapsulated into a black box to entangle and fuse the spatial and spectral features into a non-linear feature space, which hinders our understanding of how they work collaboratively for target speech extraction. In this regard, this paper proposes to decouple the spatial and spectral domain processing inspired by Taylor's approximation theory. Specifically, we reformulate the time-variant beamforming defined in the spatial domain into the adaptive weighting and mixing of different beam components in the beamspace domain. This reformulation enables us to model the recovery of target speech as a weighted sum operation in the beamspace domain, where each beam component is associated with an introduced unknown term for residual interference cancellation. By virtue of Taylor's series expansion, the recovery process can be decomposed into the superimposition of the 0th-order non-derivative and high-order derivative terms, where the former acts as spatial filtering in the spatial domain, and the latter serves as a residual interference canceller in the spectral domain. We conduct extensive experiments on the spatialized LibriSpeech and L3DAS Challenge datasets. Experimental results show that, compared with existing advanced approaches, the proposed method not only achieves competitive performance in terms of multiple objective metrics but also provides feasible guidance in multi-channel speech enhancement pipeline design. • This paper proposes to decouple the spatial and spectral processing inspired by Taylor's approximation theory. • Beamforming in spatial domain is reformulated into the adaptive weighting of beamed components in the beamspace domain. • Speech recovery is decomposed into the superimposition of the 0th-order non-derivative and high-order derivative terms. [ABSTRACT FROM AUTHOR]

An adaptive fuzzy sliding control (AFSMC) approach is adopted in this paper to address the problem of angular position control and vibration suppression of rotary flexible joint systems. AFSMC consists of fuzzy-based singleton control action and switching control law. By adjusting fuzzy parameters with the self-learning ability to discard system nonlinearities and uncertainties, singleton control based on fuzzy approximation theory can estimate the perfect control law of feedback linearization. To enhance robustness, an additional switching control law is incorporated to reduce the approximation error between the derived singleton control action and the perfect control law of feedback linearization. AFSMC's closed-loop stability will be demonstrated via sliding surface and Lyapunov function analysis of error function. In order to demonstrate the effectiveness of the AFSMC in tracking performance as well as its ability to respond to model uncertainties and external perturbations, simulations are carried out using Simulink and Matlab in order to demonstrate how well it adapts to these situations. Based on these results, it can be concluded that the AFSMC performs satisfactorily in terms of tracking. [ABSTRACT FROM AUTHOR]

In this paper we study a C 1 Virtual Element Method (VEM) on polyhedral meshes for bi-harmonic eigenvalue problems in three dimensions. Optimal order error estimates for the eigenfunctions and a double order for the eigenvalues are obtained by using the approximation theory of compact self-adjoint operators. Finally, a set of tests will numerically prove the theoretical result of the proposed scheme. [ABSTRACT FROM AUTHOR]

In this paper, circuit implementation and anti-synchronization are studied in coupled nonidentical fractional-order chaotic systems where a fractance module is introduced to approximate the fractional derivative. Based on the open-plus-closed-loop control, a nonlinear coupling strategy is designed to realize the anti-synchronization in the fractional-order Rucklidge chaotic systems and proved by the stability theory of fractional-order differential equations. In addition, using the frequency-domain approximation and circuit theory in the Laplace domain, the corresponding electronic circuit experiments are performed for both uncoupled and coupled fractional-order Rucklidge systems. Finally, our circuit implementation including the fractance module may provide an effective method for generating chaotic encrypted signals, which could be applied to secure communication and data encryption. [ABSTRACT FROM AUTHOR]