Limit behavior of global attractors for the complex Ginzburg–Landau equation on infinite lattices

In this work, the authors first show the existence of global attractors for the following lattice complex Ginzburg–Landau equation:

and for the following lattice Schrödinger equation:

Then they prove that the solutions of the lattice complex Ginzburg–Landau equation converge to that of the lattice Schrödinger equation as ε→0+. Also they prove the upper semicontinuity of as ε→0+ in the sense that .     

A Chebyshev type inequality for fuzzy integrals

In this paper, we prove a Chebyshev type inequality for fuzzy integrals. More precisely, we show that:

where μ is the Lebesgue measure on and f,g:[0,1]→[0,∞) are two continuous and strictly monotone functions, both increasing or both decreasing. Also, some examples and applications are presented.     

Global existence and blow-up solutions and blow-up estimates for a non-local quasilinear degenerate parabolic system

This paper deals with p-Laplacian systems

with null Dirichlet boundary conditions in a smooth bounded domain ΩR^N, where p,q>1, , and a,b>0 are positive constants. We first get the non-existence result for a related elliptic systems of non-increasing positive solutions. Secondly by using this non-existence result, blow-up estimates for above p-Laplacian systems with the homogeneous Dirichlet boundary value conditions are obtained under Ω=B_R={xR^N:|x|<R}(R>0). Then under appropriate hypotheses, we establish local theory of the solutions and obtain that the solutions either exists globally or blow-up in finite time.     

Kamenev-type oscillation criteria for even order neutral differential equations with deviating arguments

Sufficient conditions are established for the oscillation of even order neutral differential equations of the form

where n  2 is even integer.     

Positive solutions of nonlinear fractional boundary value problems using Adomian decomposition method

We use Adomian decomposition method for solving the fractional nonlinear two-point boundary value problem

where D is Caputo fractional derivative, c is a constant, μ > 0, and F:[0,1]×[0,∞)→[0,∞) a continuous function. The fractional Bratu problem is solved as an illustrative example.     

On the stability and boundedness of solutions of a kind of third order delay differential equations

In this paper, we study Eq. (1.1) for asymptotic stability of the zero solution when and uniformly bounded and uniformly ultimate bounded of all solutions when      

Existence and global attractivity of a periodic solution for a prey–predator model with sex-structure

In this paper, we investigate the following periodic sex-structure model:

The sufficient and realistic conditions are obtained for the existence of positive periodic solution of above system. Further, by constructing a V functional and using the result of the existence of positive periodic solutions, the global attractivity of a positive periodic solution for above system is obtained.     

Numerical solution of Hammerstein integral equations by using combination of spline-collocation method and Lagrange interpolation

The numerical solutions to the nonlinear integral equations of the Hammerstein-type:

with using B-splines functions are investigated. An interpolation method based on B-splines functions combined with a new collocation method is presented. Finally, for showing efficiency of the method we give some numerical examples.     

A new sharpened version of the Neuberg–Pedoe inequality

In this work, we present a new sharpened version of the classical Neuberg–Pedoe inequality. As an application, the following improved Neuberg–Pedoe inequality is derived:

     

Space-efficient geometric divide-and-conquer algorithms

We develop a number of space-efficient tools including an approach to simulate divide-and-conquer space-efficiently, stably selecting and unselecting a subset from a sorted set, and computing the kth smallest element in one dimension from a multi-dimensional set that is sorted in another dimension. We then apply these tools to solve several geometric problems that have solutions using some form of divide-and-conquer. Specifically, we present a deterministic algorithm running in time using extra memory given inputs of size n for the closest pair problem and a randomized solution running in expected time and using extra space for the bichromatic closest pair problem. For the orthogonal line segment intersection problem, we solve the problem in time using extra space where n is the number of horizontal and vertical line segments and k is the number of intersections.     

On oscillatory solutions of certain first order ordinary differential equations

By constructing a class of solutions to the integral inequality for t  t₀ large enough, where 0<A₁a(τ)A₂<+∞ and λ>1, that tend to zero as t→+∞ we address an open problem in the theory of nonlinear oscillations.     

Asymptotic analysis of a perturbation problem

An asymptotic expansion is constructed for the solution of the initial-value problem

when t is restricted to the interval [0,T/ε], where T is any given number. Our analysis is mathematically rigorous; that is, we show that the difference between the true solution u(t,x;ε) and the Nth partial sum of the asymptotic series is bounded by ε^N+1 multiplied by a constant depending on T but not on x and t.     

Minimum weight pseudo-triangulations

We consider the problem of computing a minimum weight pseudo-triangulation of a set of n points in the plane. We first present an -time algorithm that produces a pseudo-triangulation of weight which is shown to be asymptotically worst-case optimal, i.e., there exists a point set for which every pseudo-triangulation has weight , where is the weight of a minimum weight spanning tree of . We also present a constant factor approximation algorithm running in cubic time. In the process we give an algorithm that produces a minimum weight pseudo-triangulation of a simple polygon.     

The oscillation of higher-ordernonlinear difference equations

The authors discuss the relation of the oscillation of the following two difference equations,

where m ≥ 2, τ : N → N, N isthe set of integers, |n − τ(n)| ≤ Mfor n N₀, M is a positive integer, is nondecreasing in x, xf(n, x)> 0, as x ≠ 0. Wewill show some relations of the oscillation of the above two equations. Especially, for m to be even, we establish the equivalenceof the oscillation of the above two difference equations.     

The number of translates of a closed nowhere dense set required to cover a Polish group

For a Polish group let be the minimal number of translates of a fixed closed nowhere dense subset of required to cover . For many locally compact this cardinal is known to be consistently larger than which is the smallest cardinality of a covering of the real line by meagre sets. It is shown that for several non-locally compact groups . For example the equality holds for the group of permutations of the integers, the additive group of a separable Banach space with an unconditional basis and the group of homeomorphisms of various compact spaces.     

Global stability of a rational difference equation

In this paper, we study the global stability of the difference equation , where the parameters a,a_i(0,∞) for i=0,…,k, x_-k,…, x_-1[0,∞) and x₀(0,∞). We prove that the unique positive equilibrium is globally asymptotically stable if and only if it is locally asymptotically. Also we provide sufficient condition for it to be globally asymptotically stable and our results solve the open problem proposed by Kulenović and Ladas (Dynamics of Second Order Rational Difference Equations with Open Problems and Conjectures, Chapman & Hall/CRC, Boca Raton, 2002).     

Metabolic control analysis of trio enzymes system

For practical purposes the calculation of rate constants is not particularly valuable, since their physical significance is not clear. Of greater practical use are metabolic control coefficients and elasticities. Given the definition of the flux control coefficients , concentration control coefficient and elasticity . We can calculate symbolic formulae for these using computer algebra techniques. These are then functions of V_max, K_m, K_i enzyme and concentrations. Having derived estimates of V_max, K_m, K_i using the fitting method we can then calculate values of the control coefficients and elasticities. Furthermore we can calculate the metabolic control parameters using symbolic values for the conventional kinetic parameters. Using these we have verified the summation and connectivity theorems. This is a useful cross check on the reliability of the calculations.     

Limit shape of convex lattice polygons with minimal perimeter

Let n be a positive integer and · any norm in . Denote by B the unit ball of · and the class of convex lattice polygons with n vertices and least ·-perimeter. We prove that after suitable normalization, all members of tend to a fixed convex body, as n→∞.     

Uniform asymptotic expansions of the Pollaczek polynomials

Two uniform asymptotic expansions are obtained for the Pollaczek polynomials P_n(cosθ;a,b). One is for , , in terms of elementary functions and in descending powers of . The other is for , in terms of a special function closely related to the modified parabolic cylinder functions, in descending powers of n. This interval contains a turning point and all possible zeros of P_n(cosθ) in θ(0,π/2].     

Augmenting the connectivity of geometric graphs

Let G be a connected plane geometric graph with n vertices. In this paper, we study bounds on the number of edges required to be added to G to obtain 2-vertex or 2-edge connected plane geometric graphs. In particular, we show that for G to become 2-edge connected, additional edges are required in some cases and that additional edges are always sufficient. For the special case of plane geometric trees, these bounds decrease to and , respectively.