查看更多>>摘要：We present a novel approach to the study of singular components for the family of shock induced copulas which is of great importance in many applications. We concentrate on three most known families of these copulas, Marshall (also called Marshall-Olkin), reflected maxmin (RMM for short), and maxmin. Although it is generally believed that "all"shock model copulas are singular, both RMM and maxmin contain nontrivial cases of members that are absolutely continuous. It seems that for the latter family this is observed for the first time. (C) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：This paper deals with the application of fuzzy Mellin transform for fuzzy valued functions. It is an attempt to investigate fuzzy Mellin transform in fractional sense and is called fuzzy fractional Mellin transform. Some techniques are proposed for the solution of fuzzy fractional order differential equations by using left-sided Riemann-Liouville fractional derivative. Moreover, some illustrative examples are solved to show the capability and effectiveness of fuzzy Mellin transforms method by converting it into a general solution for an analogous equation with the left-sided Riemann-Liouville derivative and then presenting its explicit representation. (C) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：In this article we study intrusive uncertainty quantification schemes for systems of conservation laws with uncertainty. While intrusive methods inherit certain advantages such as adaptivity and an improved accuracy, they suffer from two key issues. First, intrusive methods tend to show oscillations, especially at shock structures and second, standard intrusive methods can lose hyperbolicity. The aim of this work is to tackle these challenges with the help of two different strategies. First, we combine filters with the multi-element approach for the hyperbolicity-preserving stochastic Galerkin (hSG) scheme. While the limiter used in the hSG scheme ensures hyperbolicity, the filter as well as the multi-element ansatz mitigate oscillations. Second, we derive a multi-element approach for the intrusive polynomial moment (IPM) method. Even though the IPM method is inherently hyperbolic, it suffers from oscillations while requiring the solution of an optimization problem in every spatial cell and every time step. The proposed multi-element IPM method leads to a decoupling of the optimization problem in every multi-element. Thus, we are able to significantly decrease computational costs while improving parallelizability. Both proposed strategies are extended to adaptivity, allowing to adapt the number of basis functions in each multi-element to the smoothness of the solution. We finally evaluate and compare both approaches on various numerical examples such as a NACA airfoil and a nozzle test case for the two-dimensional Euler equations. In our numerical experiments, we observe the mitigation of spurious artifacts. Furthermore, using the multi-element ansatz for IPM significantly reduces computational costs. (C) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：Many classical synchronization problems such as the assembly line crew scheduling problem (ALCS), some data association problems or multisensor tracking problems can be formulated as finding intra-column rearrangements for a single matrix repre-senting costs, distances, similarities or time requirements. In this paper, we consider an extension of these problems to the case of multiple matrices, reflecting various possible instances (scenarios). To approximate optimal rearrangements, we introduce the Block Swapping Algorithm (BSA) and a further customization of it that we call the customized Block Swapping Algorithm (Cust BSA). A numerical study shows that the two algorithms we propose - in particular Cust BSA - yield high-quality solutions and also deal efficiently with high-dimensional set-ups. (C) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：A new approach to the study of multidimensional singularly perturbed problems of nonlinear heat conduction is proposed, based on the further development and use of asymptotic analysis methods. We study the question of the existence of classical Lyapunov stable stationary solutions with boundary and internal transition layers (stationary thermal structures) of the nonlinear heat transfer equation. We suggest the efficient algorithm for constructing an asymptotic approximation to the localization surface of the transition layer. To justify the constructed formal asymptotics, we use the principle of comparison. We consider the application of the results of asymptotic analysis to solving inverse problem of reconstructing the temperature dependence of the thermal conductivity coefficient from a known position of the internal layer of thermal structure. (C) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：Optical properties of materials related to light absorption and scattering are explained by the excitation of electrons. The Bethe-Salpeter equation is the state-of-the-art approach to describe these processes from first principles (ab initio), i.e. without the need for empirical data in the model. To harness the predictive power of the equation, it is mapped to an eigenvalue problem via an appropriate discretization scheme. The eigenpairs of the resulting large, dense, structured matrix can be used to compute dielectric properties of the considered crystalline or molecular system. The matrix always shows a 2 x 2 block structure. Depending on exact circumstances and discretization schemes, one ends up with a matrix structure such as [AB] H-1 = [(-B) (A) (-A) (B)] is an element of C-2nx2n, A=A(H), B = B-H, or H-2 = [(-BH) (A) (-AT) (B)] is an element of C-2nx2n or R-2nx2n, A = A(H), B = B-T. H-1 can be acquired for crystalline systems (see Sander et al. (2015)), H-2 is a more general form found e.g. in Shao et al. (2016) and Penke et al. (2020), which can for example be used to study molecules. Additionally, certain definiteness properties may hold. In this work, we compile theoretical results characterizing the structure of H-1 and H-2 in the language of non-standard scalar products. These results enable us to develop a generalized perspective on the currently used direct solution approach for matrices of form H-1. This new viewpoint is used to develop two alternative methods for solving the eigenvalue problem. Both have advantages over the method currently in use and are well suited for high performance environments and only rely on basic numerical linear algebra building blocks. The results are extended to hold even without the mentioned definiteness property, showing the usefulness of our new perspective. (C) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：In this work, we consider multidimensional diffusion-reaction equations with time fractional partial derivatives of the Caputo type and orders of differentiation in (0, 1). The models are extensions of various well-known equations from mathematical physics, biology, and chemistry. In the present manuscript, we will impose initial-boundary data on a closed and bounded spatial multidimensional domain. Single-term and multi term fractional systems are considered in this work. In the first stage, we show that the fractional models possess energy-like functionals which are dissipated in L-2(Omega) with respect to time. The systems are investigated rigorously from the analytical point of view, and dissipative numerical models to approximate their solutions are proposed and rigorously analyzed. Our discretizations will make use of the uniform L1 approximation scheme to estimate the time-fractional derivatives, and the usual central difference operators to approximate the spatial Laplacian. To that end, various results of the literature will be crucial, including some useful discrete forms of Paley-Wiener inequalities. Some numerical examples are included to show the asymptotic behavior of the numerical methods and, ultimately, their dissipative character. (C) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：Several generalizations of Shannon entropy have been introduced in the literature. One of such a measure is the cumulative residual Tsallis entropy (CRTE) which can be viewed as an alternative dispersion measure. In this paper, we obtain some further results for such a measure, in relation with the cumulative residual Tsallis entropy and with the variance of random variables. Specifically, we present new equivalent expressions, bounds, normalized CRTE, connection to the differential entropy and excess wealth transform and stochastic comparisons involving such measures. Besides, the dynamic version of such under consideration measure is elaborated and some monotonicity results are also given. Finally, we consider the problem of estimating the CRTE by means of the empirical CRTE. In this regard, we use two different empirical estimators of cumulative distribution function to estimate CRTE. Then, we study practical results of the second estimator in blind image quality assessment. (C) 2021 Published by Elsevier B.V.
查看更多>>摘要：In this paper, we study the stability of a numerical boundary treatment of high order compact finite difference methods for parabolic equations. The compact finite difference schemes could achieve very high order accuracy with relatively small stencils. To match the convergence order of the compact schemes in the interior domain, we take the simplified inverse Lax-Wendroff (SILW) procedure (Tan et al., 2012; Li et al., 2017) as our numerical boundary treatment. The third order total variation diminishing (TVD) Runge-Kutta method (Shu and Osher, 1988) is taken as our time-stepping method in the fully-discrete case. Two analysis techniques are adopted to check the algorithm's stability, one is based on the Godunov-Ryabenkii theory, and the other is the eigenvalue spectrum visualization method (Vilar and Shu, 2015). Both the semi-discrete and fully-discrete cases are investigated, and these two different analysis techniques yield consistent results. Several numerical experimental results are shown to validate the theoretical results. (C) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：A class of high order extended boundary value methods (HEBVMs) suitable for the numerical approximation of stiff systems of ordinary differential equations (ODEs) is constructed. This class of BVMs is based on the second derivative class of linear multistep formulas (LMF) and it provides a set of very highly stable methods that can produce considerably accurate solutions to stiff systems whose Jacobians have some large eigenvalues lying close to the imaginary axis. The class of BVMs derived herein is of high order, small error constants and large region of absolute stability. Specifically, it is O-k1,O- k2-stable, A(k1, k2)-stable with (k(1), k(2))-boundary conditions and order p = k + 4 for values of the step length k >= 1. The numerical results obtained from standard linear and non-linear stiff systems indicate that this scheme is highly competitive with existing methods. (C) 2021 Elsevier B.V. All rights reserved.
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