Search

A nonoscillation criterion for a second-order linear difference equation is established correcting a result in [1]. [Copyright &y& Elsevier]

This paper presents a scalable multigrid preconditioner targeting large-scale systems arising from discontinuous Petrov–Galerkin (DPG) discretizations of high-frequency wave operators. This work is built on previously developed multigrid preconditioning techniques of Petrides and Demkowicz (Comput. Math. Appl. 87 (2021) pp. 12–26) and extends the convergence results from O (10 7) degrees of freedom (DOFs) to O (10 9) DOFs using a new scalable parallel MPI/OpenMP implementation. Novel contributions of this paper include an alternative definition of coarse-grid systems based on restriction of fine-grid operators, yielding superior convergence results. In the uniform refinement setting, a detailed convergence study is provided, demonstrating h and p robust convergence and linear scaling with respect to the wave frequency. The paper concludes with numerical results on hp -adaptive simulations including a large-scale seismic modeling benchmark problem with high material contrast. [ABSTRACT FROM AUTHOR]

Abstract In this paper, a mathematical proof of the existence of a global minimum of Self-Optim (Self-Optimizing Inverse Analysis Method) cost functional is presented based upon weak-solution theory of partial differential equations. The Self-Optim provides single global minimum rather than having multiple global minima corresponding to unrealistic solutions of the inverse problem. Furthermore, discrete approximation of the inverse problem and computational methods for the cost functional are proposed and the proof is numerically verified. This paper provides a rigorous mathematical foundation for applications of the Self-Optim method to various inverse problems in mechanics. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we propose a viral infection model with multi-target cells on a heterogeneous environment. Then we use the semigroup theory and a variational characterization to compute the local reproduction number R (x) and the basic reproduction number R 0. Furthermore, the model exhibits a threshold dynamics: the virus-free steady state E 0 is globally asymptotically stable if R 0 < 1 ; otherwise, the endemic steady state E ∗ is globally asymptotically stable. Finally, we perform some numerical examples to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

Abstract An elliptic optimal control problem involving the L 1 norm of the control in the cost functional is considered in this paper. We use the full discretization and the variational discretization to approximate the control problem and the efficient and reliable a posteriori error estimates are obtained for the two cases. For the variational discretization, we also analyze the convergence of adaptive finite element methods. In the end, some examples are provided to validate our analysis. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we use the exp-function method to construct some new soliton solutions of the Benjamin–Bona–Mahony and modified Benjamin–Bona–Mahony equations. These equations have important and fundamental applications in mathematical physics and engineering sciences. The exp-function method is used to find the soliton solution of a wide class of nonlinear evolution equations with symbolic computation. This method provides the concise and straightforward solution in a very easier way. The results obtained in this paper can be viewed as a refinement and improvement of the previously known results. [Copyright &y& Elsevier]

Abstract: The paper deals with absolute summability factors for infinite series. The main result obtained in this paper generalizes a recent paper of Rhoades and Savas [B. Rhoades, E. Savas, A summability factor theorem for generalized absolute summability, Real Anal. Exchange 31 (2) (2005–2006) 355–363]. [Copyright &y& Elsevier]

Abstract: This paper presents a new method to construct explicit bounds for the solutions of second order linear differential equations of the type ,, , which complements the method described in recent papers of the authors. The method lies in the use of Beesack’s version of Opial’s inequality. Some results on asymptotics of the solution for the case are also included. [Copyright &y& Elsevier]

Abstract: This paper deals with the pseudo-isochronicity for a class of septic differential systems. In this paper, we transform infinity into the origin so that the properties of infinity can be investigated with the methods developed for finite critical points. By calculating the singular point quantities and period constants of the origin, the problem of infinity being a pseudo-isochronous center has been solved in this case. [Copyright &y& Elsevier]

Abstract: A paper by D.L. Reiner researched function sequences of binomial type and established many interesting theorems. But because of an oversight in a lemma, some theorems in his paper need to be revised. This paper will revise these theorems and establish some new results on sequences of binomial type. [Copyright &y& Elsevier]

Abstract: The purpose of this paper is to show how the problem of finding roots (or zeros) of the monic quaternionic quadratic polynomials (MQQP) can be solved by its equivalent real quadratic form. The real quadratic form matrices, firstly defined in this paper, are used to form a simple equivalent real quadratic form of MQQP. Some necessary and sufficient conditions for the existence of roots of MQQP are also presented. The main idea of the practical method proposed in this work can be summarized in two steps: translating MQQP into its equivalent real quadratic form, and giving directly the quaternionic roots of MQQP by solving its equivalent real quadratic form. [Copyright &y& Elsevier]

Abstract: In this article, we will show that (1) the results about the triple I method for fuzzy reasoning obtained in the paper “Computers and Mathematics with Applications 44 (2002) 1567–1579” are correct; (2) Example 2.1 in the paper “Notes on triple I method of fuzzy reasoning” presented by Hua-wen Liu is incorrect; (3) -triple I method presented by Liu is a generalization of -triple I method. [Copyright &y& Elsevier]

Abstract: The aim of this paper is to correct the results about triple I method for fuzzy reasoning obtained in paper [S. Song, C. Feng, E.S. Lee, Triple I method of fuzzy reasoning, Computers and Mathematics with Applications 44 (2002) 1567–1579]. [Copyright &y& Elsevier]

Abstract: Molodtsov introduced the theory of soft sets, which can be seen as a new mathematical approach to vagueness. In this paper, we first point out that several assertions (Proposition 2.3 (iv)–(vi), Proposition 2.4 and Proposition 2.6 (iii), (iv)) in a previous paper by Maji et al. [P.K. Maji, R. Biswas, A.R. Roy, Soft set theory, Comput. Math. Appl. 45 (2003) 555–562] are not true in general, by counterexamples. Furthermore, based on the analysis of several operations on soft sets introduced in the same paper, we give some new notions such as the restricted intersection, the restricted union, the restricted difference and the extended intersection of two soft sets. Moreover, we improve the notion of complement of a soft set, and prove that certain De Morgan’s laws hold in soft set theory with respect to these new definitions. [Copyright &y& Elsevier]

Abstract: This paper deals with the existence of positive solutions for the fourth-order nonlinear ordinary differential equation subject to the boundary conditions: where are constants such that , and . By means of a fixed-point theorem due to Krasnaselskii, some new existence results of positive solutions for the above multi-point boundary value problem are obtained, which improve the main results of Graef et al. [J.R. Graef, C. Qian, B. Yang, A three-point boundary value problem for nonlinear fourth-order differential equations, J. Math. Anal. Appl. 287 (2003) 217–233]. An example is given to demonstrate the main results of this paper. [Copyright &y& Elsevier]

In this paper, we present a Newton-type method for a class of mathematical programs with complementarity constraints. Under the MPEC-LICQ, we use the definition of B-stationary point to construct a constrained equations model, and apply the Newton method to solve the problem. At the end of this paper, numerical results are reported to show our method's validity. [Copyright &y& Elsevier]

Abstract: This paper deals with a class of real-valued random-walk processes, observed over random epochs of time, that forms a delayed renewal process. The present model does not restrict this class to a merely monotone random walk, which is easier to analyze and find explicit form functional. The objective is to find the first passage of the process exiting a rectangular set and registering the value of the process at this time, thus generalizing past models where either the observed process was monotone or the first passage time reduced to the moment of the first drop. The joint transformation of the named random characteristics of the process are derived in a closed form. The paper concludes with examples, including numerical examples, demonstrating the use of the results as well as practical applications to finance. [Copyright &y& Elsevier]

Abstract: This paper is concerned with a Lotka-Volterra cooperation-diffusion model with a saturating interaction term for one species. The goal of the paper is to investigate the asymptotic behavior of the time- dependent solution in relation to the corresponding steady-state solutions under homogeneous Neumann boundary condition. Some simple and easily verifiable conditions are given to the rate constants so that for every nontrivial nonnegative initial function the corresponding time-dependent solution converges to one of the nonnegative constant steady-state solutions as time tends to infinity. This convergence result leads to the existence and uniqueness of a positive (or nonnegative) steady-state solution and the global asymptotic stability of a given nonnegative constant steady-state solution. In terms of ecological dynamics, it also gives some coexistence, permanence and extinction results for the model. [Copyright &y& Elsevier]

Abstract: Discrete models and continuous control systems are considered in regard to optimality of their trajectories. Some aspects of the principle of optimality [1, p. 83] are analyzed, and it is shown to imply total optimality, that is, the optimality of every part of an optimal trajectory. Certain autonomous systems with free admissible variations possess this property. Nonautonomous optimal systems are not, in general, totally optimal, in which case the principle of optimality is not valid. A modification is proposed for the derivation of the main functional equation to demonstrate that dynamic programming and its functional equations are valid also in the case of nonoptimal remaining trajectories under a certain contiguity condition that is defined and analyzed in the paper. Control systems with incomplete information or structural limitations on controls do not, in general, satisfy the contiguity condition. Control problems for such systems may have optimal solutions which, however, cannot be obtained by dynamic programming. This fact is shown in an example of a widely used engineering system for which an optimal trajectory has all its remaining parts nonoptimal and noncontiguous to the optimal trajectory. The paper presents theoretical justification of dynamic programming for contiguous systems that do not conform to the principle of optimality. Examples are presented to illustrate the results which open new avenues in modeling and optimization of general (not totally optimal) control systems. [Copyright &y& Elsevier]

Abstract: This paper presents results of research into the use of the Bellman-Zadeh approach to decision making in a fuzzy environment for solving multiobjective optimization problems. Its application conforms to the principle of guaranteed result and provides constructive lines in obtaining harmonious solutions on the basis of analyzing associated maxmin problems. The use of the Bellman-Zadeh approach has served as a basis for solving a problem of multiobjective allocation of resources (or their shortages) and developing a corresponding adaptive interactive decision-making system (AIDMS1). Its calculating kernel permits one to solve maxmin problems using an algorithm based on a nonlocal search (modification of the Gelfand''s and Tsetlin''s “long valley” method). The AIDMS1 includes procedures for considering linguistic variables to reflect conditions that are difficult to formalize as well as procedures for constructing and correcting vectors of importance factors for goals. The use of these procedures permits one to realize an adaptive approach to processing information of a decision maker to provide successive improving of the solution quality. C++ windows of the AIDMS1 are presented for input, output, and special possibilities related to considering linguistic variables and constructing and correcting vectors of importance factors. The results of the paper are universally applicable and are already being used to solve power engineering problems. [Copyright &y& Elsevier]

Abstract: In this paper we deal with sensitivity analysis in multiobjective differential programs with equality constraints. We analyze the quantitative behavior of the optimal solutions according to changes of right-hand side values included in the original optimization problem. One of the difficulties lies in the fact that the efficient solution in multiobjective optimization in general becomes a set. If the preference of the decision maker is represented by a scalar utility which transforms optimal solutions in optima, we may apply existing methods of sensitivity analysis. However, when dealing with a subset of optimal points, the existence of a Fréchet differentiable selection of such a set-valued map is usually assumed. The aim of the paper is to investigate the derivative of certain set-valued maps of efficient points. We show that the sensitivity depends on a set-valued map associated to the T-Lagrange multipliers and a projection of its sensitivity. [Copyright &y& Elsevier]

Abstract: n this paper, the M/G/1 processor-sharing queue with disasters is given a detailed analysis by means of extending the supplementary variable method. The transient and steady-state distributions of the queue length are expressed as a simple and computable form, the Laplace-Stieltjes transform of the sojourn time is derived, and the Laplace transform of the busy period and its mean are obtained. Also, the approach developed in this paper is shown to be able to study more complicated M/G/1 processor-sharing models. [Copyright &y& Elsevier]

Abstract: In this paper, the exponential periodicity and stability of neural networks with Lipschitz continuous activation functions are investigated, without assuming the boundedness of the activation functions and the differentiability of time-varying delays, as needed in most other papers. The neural networks contain reaction-diffusion terms and both variable and unbounded delays. Some sufficient conditions ensuring the existence and uniqueness of periodic solution and stability of neural networks with reaction-diffusion terms and both variable and unbounded delays are obtained by analytic methods and inequality technique. Furthermore, the exponential converging index is also estimated. The methods, which does not make use of Lyapunov functional, is simple and valid for the periodicity and stability analysis of neural networks with variable and/or unbounded delays. The results extend some previous results. Two examples are given to show the effectiveness of the obtained results. [Copyright &y& Elsevier]

This paper deals with a new existence theory for positive periodic solutions to a kind of nonautonomous functional differential equation by employing the fixed-point theorem in cones. Applying the general theorems established to several biomathematical models, the paper improves some previous results and obtains some new results. [Copyright &y& Elsevier]

We prove that the equation x2 − kxy + y2 + x = 0 with k ∊ N+ has an infinite number of positive integer solutions x and y if and only if k = 3. For k = 3 the quotient SHAPE="SOL" ALIGN="C" STYLE="S">xy is asymptotically equal to (3 + √5)/2 or (3 − √5)/2. Results of the paper are based on data obtained via Computer Algebra System (derive 5). Some derive procedures presented in the paper made it possible to discover interesting regularities concerning simple continued fractions of certain numbers. [Copyright &y& Elsevier]

In this paper, the following inverse heat conduction problem: ut = uxx, x≥0, t≥0, u(x,0) = 0, x≥0 u(1,t) = g(t), t≥0, u&z.sfnc;x→∞ is bounded, is considered again. This problem is severely ill-posed: its solution (if it exists) does not depend continuously on the data; a small perturbation in the data may cause a dramatically large error in the solution for 0 < x < 1. In this paper, a new wavelet regularization method for this problem is given. Moreover, we can easily find the regularization parameter J such that some sharp stable estimates between the exact solution and the approximate one in Hr(R)-norm meaning is given. [Copyright &y& Elsevier]

In a recent paper [1] a number of numerical schemes for the shallow water equations based on a conservative linearization are analyzed. In particular, it is established that the schemes are related through the use of a source term. In this paper this technique is applied to the Euler equations, and further analysis suggests a new formulation of an existing scheme having the same key properties. [Copyright &y& Elsevier]

In this paper, we propose and analyse a modified projection-type dynamical system associated with variational inequalities by using the technique of updating the solution. We prove that the globally asymptotic stability of this dynamical system requires only the pseudomonotonicity of the underlying operator, which is a weaker condition than monotonicity. The results obtained in this paper represent a significant improvement of the previously known results. [Copyright &y& Elsevier]

Abstract In this paper, we consider the following nonlinear waveequation with variable exponents: u t t − div (| ∇ u | r (⋅) − 2 ∇ u) + | u t | m (⋅) − 2 u t = 0. By using a lemma by Komornik, we prove the decay estimates for the solution under suitable assumptions on the variable exponents m , r and the initial data. We also give two numerical applications to illustrate our theoretical results. [ABSTRACT FROM AUTHOR]