Showing papers in "Journal of Applied Mathematics and Computing in 2012"

Multiplicity of high energy solutions for superlinear Kirchhoff equations

Abstract: In this paper, we study the existence of infinitely many high energy solutions for the nonlinear Kirchhoff equations $$\left\{\everymath{\displaystyle}\begin{array}{l@{\quad}l}- \biggl(a+b\int_{R^3} | abla u|^2 dx\biggr)\Delta u + V(x)u=f(x,u),&x\in \mathbb {R}^3,\\[9pt]u\in H^1 (\mathbb {R}^3),\end{array}\right.$$ where a,b>0 are constants, V:ℝ3→ℝ is continuous and has a positive infimum. f is a subcritical nonlinearity which needs not to satisfy the usual Ambrosetti-Rabinowitz-type growth conditions.

Existence and global exponential stability of pseudo almost periodic solution for SICNNs with mixed delays

Abstract: Shunting Inhibitory Artificial Neural Networks are biologically inspired networks in which the synaptic interactions are mediated via a nonlinear mechanism called shunting inhibition, which allows neurons to operate as adaptive nonlinear filters. This paper considers the problem of existence and exponential stability of the pseudo almost periodic solution for shunting inhibitory cellular neural networks with mixed delays. The Banach fixed point theorem and the variant of a certain integral inequality with explicit estimate are used to establish the results. The results of this paper are new and they complement previously known results.

A generalization of the Leggett-Williams fixed point theorem and its application

Abstract: A generalization of the Leggett-Williams fixed point theorem is established. As an application, the existence of multiple nondecreasing positive solutions for a class of third-order m-point boundary value problems is obtained.

Existence and uniqueness of positive solutions for three-point boundary value problem with fractional q -differences

Abstract: In this paper, we consider the following nonlinear q-fractional three-point boundary value problem $$\begin{array}{l}(D_{q}^{\alpha}u)(t) + f(t,u(t))=0, \quad 0 < t < 1, 2 < \alpha< 3,\\ [2pt]u(0) = (D_qu)(0) = 0, \quad(D_qu)(1) = \beta(D_qu)(\eta),\end{array}$$ where 0<βη α-2<1. By using a fixed-point theorem in partially ordered sets, we obtain sufficient conditions for the existence and uniqueness of positive and nondecreasing solutions to the above boundary value problem.

The spectral method for solving systems of Volterra integral equations

Abstract: This paper presents a high accurate and stable Legendre-collocation method for solving systems of Volterra integral equations (SVIEs) of the second kind. The method transforms the linear SVIEs into the associated matrix equation. In the nonlinear case, after applying our method we solve a system of nonlinear algebraic equations. Also, sufficient conditions for the existence and uniqueness of the Linear SVIEs, in which the coefficient of the main term is a singular (or nonsingular) matrix, have been formulated. Several examples are included to illustrate the efficiency and accuracy of the proposed technique and also the results are compared with the different methods. All of the numerical computations have been performed on a PC using several programs written in MAPLE 13.

Boundary value problems for fractional differential equations involving caputo derivative in banach spaces

Abstract: In this paper, we study boundary value problems for fractional differential equations involving Caputo derivative in Banach spaces. A generalized singular type Gronwall inequality is given to obtain an important priori bounds. Some sufficient conditions for the existence of solutions are established by virtue of fractional calculus and fixed point method under some mild conditions. Two examples are given to illustrate the results.

Implicit peer methods for large stiff ODE systems

Abstract: Implicit two-step peer methods are introduced for the solution of large stiff systems. Although these methods compute s-stage approximations in each time step one-by-one like diagonally-implicit Runge-Kutta methods the order of all stages is the same due to the two-step structure. The nonlinear stage equations are solved by an inexact Newton method using the Krylov solver FOM (Arnoldi’s method). The methods are zero-stable for arbitrary step size sequences. We construct different methods having order p=s in the multi-implicit case and order p=s−1 in the singly-implicit case with arbitrary step sizes and s≤5. Numerical tests in Matlab for several semi-discretized partial differential equations show the efficiency of the methods compared to other Krylov codes.

M/G/1 queue with single working vacation

Abstract: In this paper, an M/G/1 queue with single working vacation is analyzed. Using the method of supplementary variable and the matrix-analytic method, we obtain the queue length distribution and service status at the arbitrary epoch under steady state conditions. Further, we derive expected busy period and expected busy cycle. Finally, server special cases are presented.

On the computation of fixed points in Boolean networks

Abstract: In this paper we study the problem of finding fixed points of AND-NOT Boolean networks and relate it to the problem of finding maximal independent sets of a graph. Furthermore, we provide a sharp upper bound for the number of fixed points of normal AND-NOT Boolean networks. We also show that any AND-NOT Boolean network can be transformed into a normal AND-NOT Boolean network.

On the stability in a discrete two-species competition system

Abstract: The paper discusses a two-species discrete competition system. The local stability of positive equilibrium is obtained. Further, a sufficient condition for the global asymptotic stability of positive equilibrium is established by using an iteration scheme and the comparison principle of difference equations.

Existence results for fractional functional differential equations with impulses

Abstract: In this paper, we discuss some existence results for a class of multi-point boundary value problem for impulsive fractional functional differential equations. Some sufficient conditions are obtained by using suitable fixed point theorems. Examples are also given to illustrate our results.

BL-general fuzzy automata and accept behavior

Abstract: In this note, we focus on behavior of BL-general fuzzy automata (for simplicity BL-GFA) and we obtain the free realization for a given behavior, that is, a BL-general fuzzy automaton whose behavior is given behavior. Then we find the realization with the minimum number of states. The minimization takes two steps: at first discard all superfluous states, and then we merge all pairs of states which have the same behavior. Moreover we prove some theorems. In particular, we show that the minimal reduction of the reachable part of an BL-GFA is the minimal realization of the behavior it. Finally we give some examples to clarify these notions.

On the existence of solutions for fractional differential inclusions with anti-periodic boundary conditions

Abstract: The existence of solutions of an anti-periodic boundary value problem for fractional differential inclusions of order α∈(2,3] is investigated. Several results are obtained by using suitable fixed point theorems when the right hand side has convex or non convex values.

Remarks on the concepts of t -designs

Abstract: We define the concept of t-design for real hyperbolic space ℍ n , as an analogue of the definition of Euclidean t-design. Then, we discuss the similarities between the concept of t-design on ℍ n or ℝ n , and the concept of relative t-design defined for association schemes by Delsarte: Pairs of vectors in the space of an association scheme (1977).

Existence and uniqueness of positive solutions to m-point boundary value problem for nonlinear fractional differential equation

Abstract: In this paper, we consider the following nonlinear fractional m-point boundary value problem Open image in new window where \(D_{0+}^{\alpha}\) is the standard Riemann-Liouville fractional derivative. By the properties of the Green function, the lower and upper solution method and fixed-point theorem in partially ordered sets, some new existence and uniqueness of positive solutions to the above boundary value problem are established. As applications, examples are presented to illustrate the main results.

B-convergence of split-step one-leg theta methods for stochastic differential equations

Abstract: For stochastic differential equations (SDEs) with a superlinearly growing and globally one-sided Lipschitz continuous drift coefficient, the explicit schemes fail to converge strongly to the exact solution (see, Hutzenthaler, Jentzen and Kloeden in Proc. R. Soc. A, rspa.2010.0348v1–rspa.2010.0348, 2010). In this article a class of implicit methods, called split-step one-leg theta methods (SSOLTM), are introduced and are shown to be mean-square convergent for such SDEs if the method parameter satisfies $\frac{1}{2}\leq\theta \leq1$ . This result gives an extension of B-convergence from the theta method for deterministic ordinary differential equations (ODEs) to SSOLTM for SDEs. Furthermore, the optimal rate of convergence can be recovered if the drift coefficient behaves like a polynomial. Finally, numerical experiments are included to support our assertions.

Geo/Geo/1 retrial queue with working vacations and vacation interruption

Abstract: Consider a Geo/Geo/1 retrial queue with working vacations and vacation interruption, and assume requests in the orbit try to get service from the server with a constant retrial rate. During the working vacation period, customers can be served at a lower rate. If there are customers in the system after a service completion instant, the vacation will be interrupted and the server comes back to the normal working level. We use a quasi birth and death process to describe the considered system and derive a condition for the stability of the model. Using the matrix-analytic method, we obtain the stationary probability distribution and some performance measures. Furthermore, we prove the conditional stochastic decomposition for the queue length in the orbit. Finally, some numerical examples are presented.

Error estimates for series solutions to a class of nonlinear integral equations of mixed type

Abstract: In this paper, we prove that the accelerated Adomian polynomials formula suggested by Adomian (Nonlinear Stochastic Systems: Theory and Applications to Physics, Kluwer, Dordrecht, 1989) and the accelerated formula suggested by El-Kalla (Int. J. Differ. Equs. Appl. 10(2):225–234, 2005; Appl. Math. E-Notes 7:214–221, 2007) are identically the same. The Kalla-iterates exhibit the same faster convergence exhibited by Adomian’s accelerated iterates with the additional advantage of absence of any derivative terms in the recursion, thereby allowing for ease of computation. Moreover, the formula of El-Kalla is used directly to prove the convergence of the series solution to a class of nonlinear two dimensional integral equations. Convergence analysis is reliable enough to estimate the maximum absolute truncated error of the Adomian series solution.

A two-strain epidemic model with mutant strain and vaccination

Abstract: In this paper, it is assumed that the spread of a pathogen can mutate in the host to create a second, cocirculating, mutant strain. Vaccinated individuals perhaps becomes infected after being in contact with individuals infected with mutant strain. A two-strain epidemic model with vaccination is firstly investigated. The existence and stability properties of equilibria in this model are examined. By analyzing the characteristic equation and constructing Lyapunov functions, the conditions for local and global stability of the infection-free, boundary and endemic equilibria are established. The existence of Hopf bifurcation from the endemic equilibrium is also examined as this equilibrium loses its stability. Our theoretical results are confirmed by numerical simulations.

Mean-square exponential stability of stochastic theta methods for nonlinear stochastic delay integro-differential equations

Abstract: This paper deals with the mean-square exponential stability of stochastic theta methods for nonlinear stochastic delay integro-differential equations. It is shown that the stochastic theta methods inherit the mean-square exponential stability property of the underlying system. Moreover, the backward Euler method is mean-square exponentially stable with less restrictions on the step size. In addition, numerical experiments are presented to confirm the theoretical results.

Markov measures and extended zeta functions

Abstract: In this paper we study a family of representations of the Cuntz algebras Op where p is a prime. These algebras are built on generators and relations. They are C∗-algebras and their representations are a part of non-commutative harmonic analysis. Starting with specific generators and relations we pass to an ambient C∗-algebra, for example in one of the Cuntz-algebras. Our representations are motivated by the study of frequency bands in signal processing: We construct induced measures attached to those representations which turned out to be related to a class of zeta functions. For a particular case those measures give rise to a class of Markov measures and q-Bernoulli polynomials. Our approach is amenable to applications in problems from dynamics and mathematical physics: We introduce a deformation parameter q, and an associated family of q-relations where the number q is a “quantum-deformation,” and also a parameter in a scale of (Riemann-Ruelle) zeta functions. Our representations are used in turn in a derivation of formulas for this q-zeta function.

Existence and uniqueness of solutions for a nonlinear fractional differential equation

Abstract: In this paper we prove the existence and uniqueness of solutions for a class of the nonlinear fractional differential equation with initial condition and investigate the dependence of the solution on the order of the differential equation and on the initial condition. Then we give an example to demonstrate the main results.

Oscillation of second order quasilinear neutral delay differential equations

Abstract: In this paper, by employing Riccati transformation technique, some new sufficient conditions for the oscillation criteria are given for the second order quasilinear neutral delay differential equations with delayed argument in the form $$\bigl(r(t)\bigl|z'(t)\bigr|^{\alpha-1}z'(t)\bigr)'+q(t)f\bigl(x\bigl(\sigma(t)\bigr)\bigr)=0,\quad t\geq t_0,$$ where z(t)=x(t)−p(t)x(τ(t)), 0≤p(t)≤p 0, α>0. Two examples are considered to illustrate the main results.

L p (p>1) solutions for one-dimensional BSDEs with linear-growth generators

Abstract: In this paper we study the existence and uniqueness of L p (p>1) solutions for one-dimensional backward stochastic differential equations (BSDEs in short) whose generator g and terminal condition ξ satisfy \(\mathbf{E}[|\xi|^{p}+(\int_{0}^{T} |g(t,0,0)|\, \mathrm {d}t)^{p}] 1) solutions of BSDEs is obtained in this paper.

Global optimization algorithm for a generalized linear multiplicative programming

Abstract: This article present a branch and bound algorithm for globally solving generalized linear multiplicative programming problems with coefficients. The main computation involve solving a sequence of linear relaxation programming problems, and the algorithm economizes the required computations by conducting the branch and bound search in R p , rather than in R n , where p is the number of rank and n is the dimension of decision variables. The proposed algorithm will be convergent to the global optimal solution by means of the subsequent solutions of the series of linear relaxation programming problems. Numerical results are given to show the feasibility and effectiveness of the proposed algorithm.

Fluid model driven by an M/M/1 queue with multiple vacations and N-policy

Abstract: This paper studies a fluid model driven by an M/M/1 queue with multiple exponential vacations and N-policy. The expression for the Laplace transform of the joint steady-state distribution of the fluid model is of a simple matrix power function form or matrix factorial form. Based on this fact, we introduce a new method of fluid model—modified matrix geometric solution method. The Laplace transform and Laplace-Stieltjes transform of the steady-state distribution of the buffer content are concisely expressed through the minimal positive solution to a crucial quadratic equation. Finally, we give concise expression for the performance measure—mean buffer content, which is useful in parameter design of fluid model and various practical applications.

A study of higher-order nonlinear ordinary differential equations with four-point nonlocal integral boundary conditions

Abstract: This paper investigates some new existence results for an nth-order nonlinear differential equation with four-point nonlocal integral boundary conditions (strip/slit like conditions). Our results are based on some standard fixed point theorems and Leray-Schauder degree theory.

Location for the right eigenvalues of quaternion matrices

Abstract: This paper aims to discuss the location for right eigenvalues of quaternion matrices. We will present some different Gerschgorin type theorems for right eigenvalues of quaternion matrices, based on the Gerschgorin type theorem for right eigenvalues of quaternion matrices (Zhang in Linear Algebra Appl. 424:139–153, 2007), which are used to locate the right eigenvalues of quaternion matrices. We shall conclude this paper with some easily computed regions which are guaranteed to include the right eigenvalues of quaternion matrices in 4D spaces.

Stability and convergence of fully discrete finite element schemes for the acoustic wave equation

Abstract: In this paper, we investigate the stability and convergence of some fully discrete finite element schemes for solving the acoustic wave equation where a discontinuous Galerkin discretization in space is used. We first review and compare conventional time-stepping methods for solving the acoustic wave equation. We identify their main properties and investigate their relationship. The study includes the Newmark algorithm which has been used extensively in applications. We present a rigorous stability analysis based on the energy method and derive sharp stability results covering some well-known CFL conditions. A convergence analysis is carried out and optimal a priori error estimates are obtained. For sufficiently smooth solutions, we demonstrate that the maximal error in the L2-norm error over a finite time interval converges optimally as O(hp+1+Δts), where p denotes the polynomial degree, s=1 or 2, h the mesh size, and Δt the time step.

Multiobjective fractional programming problems involving (p,r)−ρ−(η,θ)-invex function

Abstract: In this paper we move forward in the study of multiobjective fractional programming problem and established sufficient optimality conditions under the assumption of (p,r)−ρ−(η,θ)-invexity. Weak, strong and strict converse duality theorems are also derived for three type of dual models related to multiobjective fractional programming problem involving aforesaid invex function.