Aledo, Juan A.Barzanouni, AliMalekbala, GhazalehSharifan, Leila...
13页
查看更多>>摘要：In this paper, we study the classical problems associated with fixed points in generalized parallel and sequential dynamical systems which are induced by a minterm or a maxterm Boolean function. In particular, we give a characterization of such fixed points which allows us to solve the fixed-point existence problem. Furthermore, we provide a method for counting the exact number of fixed points in such systems by means of a special kind of dominating sets. We demonstrate the main results for the case of generalized parallel dynamical systems induced by a minterm, what assure the same results in the case induced by maxterm thanks to the duality principle. In this context, the results are also valid for the sequential case, since the fixed points of any sequential system are the same of its parallel counterpart. These results generalize those given for parallel dynamical systems induced by such Boolean functions and also for normal AND-NOT networks (resp. OR-NOT networks) which are a particular case of generalized parallel dynamical systems induced by the minterm NOR (resp. maxterm NAND). (C)& nbsp;2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：In the present study, a consistent and conservative Phase-Field method, including both the model and scheme, is developed for multiphase flows with an arbitrary number of immiscible and incompressible fluid phases. The consistency of mass conservation and the consistency of mass and momentum transport are implemented to address the issue of physically coupling the Phase-Field equation, which locates different phases, to the hydrodynamics. These two consistency conditions, as illustrated, provide the "optimal "coupling because (i) the new momentum equation resulting from them is Galilean invariant and implies the kinetic energy conservation, regardless of the details of the Phase-Field equation, and (ii) failures of satisfying the second law of thermodynamics or the consistency of reduction of the multiphase flow model only result from the same failures of the Phase-Field equation but are not due to the new momentum equation. Physical interpretation of the consistency conditions and their formulations are first provided, and general formulations that are obtained from the consistency conditions and independent of the interpretation of the velocity are summarized. Then, the present consistent and conservative multiphase flow model is completed by selecting a reduction consistent Phase-Field equation. Several novel techniques are developed to inherit the physical properties of the multiphase flows after discretization, including the gradient based phase selection procedure, the momentum conservative method for the surface force, and the general theorems to preserve the consistency conditions on the discrete level. Equipped with those novel techniques, a consistent and conservative scheme for the present multiphase flow model is developed and analyzed. The scheme satisfies the consistency conditions, conserves the mass and momentum, and assures the summation of the volume fractions to be unity, on the fully discrete level and for an arbitrary number of phases. All those properties are numerically validated. Numerical applications demonstrate that the present model and scheme are robust and effective in studying complicated multiphase dynamics, especially for those with large-density ratios. (c) 2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：A novel deficient complete quartic spline S having type II complete endpoint conditions S "(a) = f "(a) , S "(b) = f "(b) is constructed, with the expression given in the terms of the second derivative on the mesh nodes, and taking prescribed values on these grid nodes and at midpoints. The existence and uniqueness of this spline is proved, and the error estimates are provided. For less smooth interpolated functions, the interpolation error estimate is given in terms of the uniform modulus of continuity considering S "(a) = S "(b) = 0 as endpoint conditions. Two numerical examples illustrate the geometric properties of this deficient quartic spline interpolation operator. The error estimates are obtained for S, S', S ", and S "' showing an optimal order of convergence O(h(5)). (C) 2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：There are, currently, very few implementations to compute the hyperbolic cosine of a matrix. This work tries to fill this gap. To this end, we first introduce both a new rational-polynomial Hermite matrix expansion and a formula for the forward relative error of Hermite approximation in exact arithmetic with a sharp bound for the forward error. This matrix expansion allows obtaining a new accurate and efficient method for computing the hyperbolic matrix cosine. We present a MATLAB implementation, based on this method, which shows a superior efficiency and a better accuracy than other state -of-the-art methods. The algorithm developed on the basis of this method is also able to run on an NVIDIA GPU thanks to a MEX file that connects the MATLAB implementation to the CUDA code. (C)& nbsp;2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：We formulate a simple algorithm for computing global exact symmetries of closed discrete curves in the plane. The method is based on a suitable trigonometric interpolation of vertices of the given polyline and consequent computation of the symmetry group of the obtained trigonometric curve. The algorithm exploits the fact that the introduced unique assignment of the trigonometric curve to each closed discrete curve commutes with isometries. For understandable reasons, an essential part of the paper is devoted to determining rotational and axial symmetries of trigonometric curves. We also show that the formulated approach can be easily applied on unorganized clouds of points. A functionality of the designed detection method is presented on several examples. (C)& nbsp;2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：The Newton-Raphson (N-R) method is one of the most ubiquitous approaches with several applications in numerous areas to find the optimization solution. It has long been known that in practice to apply the N-R method, it is customarily required to be obtained the second derivative of the objective function. Nevertheless, it is difficult or impossible to find the second derivative of the target function in many situations, leading to the impossibility to obtain the optimization solutions. This paper conducts a numerical method, develops an algorithm, and provides the R code so that one will be able to obtain the optimization solutions when our proposed approach is used. This study investigates numerous simulation studies and a factual data set. Based on the findings in this work, it can be firmly concluded that the N-R method with the numerical method for the second derivative of the objective function is found to be a robust and trustworthy approach. (C)& nbsp;2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：In this work, we first establish a general Marsden's identity for Unified and Extended B-splines (UE B-splines or Omega B-splines for short). Then, by using this result, we construct univariate omega spline quasi-interpolants on a bounded interval and we study their approximation errors. For particular values of omega, we refind some already developed quasi-interpolants. As a practical side of these operators, we give some applications to numerical analysis especially quadrature formulas, differentiation and numerical solutions of linear Fredholm integral equations, which are illustrated by some numerical examples. (C)& nbsp;2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：In this paper, we propose a generalized interval type-2 fuzzy random variable based algorithm under mean chance value at risk criterion. First, we introduce the interval type-2 fuzzy random variable and then we propose a scalar expected value of the interval type-2 fuzzy random variables. Also the new concepts of mean chance value at risk and mean chance conditional value at risk are discussed. An application to the inverse 1 median location problem on tree network with uncertain costs proves that this algorithm solves this problem in O(n(2) log n) time. (C)& nbsp;2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：In many studies in applied sciences and engineering one should find outer pseudo inverse of a matrix. In this paper, we propose a new efficient algorithm for computing the outer pseudo-inverse of a matrix. We study the convergence analysis of the new algorithm. Finally, test problems and simulation results support the theoretical approach. (C)& nbsp;2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：In this paper we extend the Residual Arnoldi method for calculating an extreme eigenvalue (e.g. largest real part, dominant, etc.) to the case where the matrices depend on parameters. The difference between this Arnoldi method and the classical Arnoldi algorithm is that in the former the residual is added to the subspace. We develop a Tensor-Krylov method that can be interpreted as an application of the Residual Arnoldi algorithm to a set of matrices obtained by evaluating a parameter-dependent matrix in parameter values on a grid. The subspace contains an approximate Krylov space for all these points. Instead of adding the residuals for all parameter values to the subspace we create a low-rank approximation of the matrix consisting of these residuals and add only the column space to the subspace. In order to keep the computations efficient, it is needed to limit the dimension of the subspace and to restart once the subspace has reached the prescribed maximal dimension. The novelty of this approach is twofold. Firstly, we observed that a large error in the low-rank approximations is allowed without slowing down the convergence, which implies that we can do more iterations before restarting. Secondly, we pay particular attention to the way the subspace is restarted, since classical restarting techniques give a too large subspace in our case. We motivate why it is good enough to just keep the approximation of the searched eigenvector. At the end of the paper we extend this algorithm to shift-and-invert Residual Arnoldi method to calculate the eigenvalue close to a shift & USigma; for a specific parameter dependency. We provide theoretical results and report numerical experiments. The Matlab code is publicly available. (C)& nbsp;2021 Published by Elsevier B.V.
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