This work is concerned with the asymptotic behavior of systems of parabolic equations arising from null-recurrent switching diffusions, which are diffusion processes modulated by continuous-time Markov chains. A sufficient condition for null recurrence is presented. Moreover, convergence rate of the solutions of systems of homogeneous parabolic equations under suitable conditions is established. Then a case study on verifying one of the conditions proposed is provided with the use of a two-state Markov chain. To verify the condition, boundary value problems (BVPs) for parabolic systems are treated, which are not the usual two-point BVP type. An extra condition in the interior is needed resulting in jump discontinuity of the derivative of the corresponding solution.
In this paper we establish the existence, uniqueness and iterative approximation of solutions for two classes of functional equations arising in dynamic programming of multistage decision processes. The results presented here extend, and unify the corresponding results due to Bellman, Bhakta and Choudhury, Bhakta and Mitra, Liu and others.
In order to describe a solid which deforms smoothly in some region, but non smoothly in some other region, many multiscale methods have been recently proposed that aim at coupling an atomistic model (discrete mechanics) with a macroscopic model (continuum mechanics). We provide here a theoretical basis for such a coupling in a one-dimensional setting, in the case of convex energy.
In this paper, we discuss a large number of sets of global parametric sufficient optimality conditions under various generalized (η, ρ)-invexity assumptions for a semi-infinite minmax fractional programming problem.
In this paper, we present a random graph model with spatial reuse for a mobile ad hoc network (MANET) based on the dynamic source routing protocol. Many important performance parameters of the MANET are obtained, such as the average flooding distance (AFD), the probability generating function of the flooding distance, and the probability of a flooding route to be symmetric. Compared with the random graph model without spatial reuse, this model is much more effective because it has a smaller value of AFD and a larger probability for finding a symmetric valid route.
Empirical likelihood is discussed by using the blockwise technique for strongly stationary, positively associated random variables. Our results show that the statistics is asymptotically chi-square distributed and the corresponding confidence interval can be constructed.
For a coupled system of multiplayer dynamics of fluids in porous media, the characteristic finite element domain decomposition procedures applicable to parallel arithmetic are put forward. Techniques such as calculus of variations, domain decomposition, characteristic method, negative norm estimate, energy method and the theory of prior estimates are adopted. Optimal order estimates in L2 norm are derived for the error in the approximate solution.
An efficient method based on the projection theorem, the generalized singular value decomposition and the canonical correlation decomposition is presented to find the least-squares solution with the minimumnorm for the matrix equation ATXB+BTXTA = D. Analytical solution to the matrix equation is also derived. Furthermore, we apply this result to determine the least-squares symmetric and sub-antisymmetric solution of the matrix equation CTXC = D with minimum-norm. Finally, some numerical results are reported to support the theories established in this paper.
In this paper, we will establish several strong convergence theorems for the approximation of common fixed points of r?strictly asymptotically pseudocontractive mappings in uniformly convex Banach spaces using the modiied implicit iteration sequence with errors, and prove the necessary and sufficient conditions for the convergence of the sequence. Our results generalize, extend and improve the recent work, in this topic.
This paper is devoted to the study ofthe existence of single and multiple positive solutions for the first order boundary value problem x′ = f(t, x), x(0) = x(T), where f ∈ C([0, T] × R) . In addition, we apply our existence theorems to a class of nonlinear periodic boundary value problems with a singularity at the origin. Our proofs are based on a fixed point theorem in cones. Our results improve some recent results in the literatures.
In this paper, we use Daubechies scaling functions as test functions for the Galerkin method, and discuss Wavelet-Galerkin solutions for the Hamilton-Jacobi equations. It can be proved that the schemes are TVD schemes. Numerical tests indicate that the schemes are suitable for the Hamilton-Jacobi equations. Furthermore, they have high-order accuracy in smooth regions and good resolution of singularities.
In this paper, we investigate a class of Hamiltonian systems arising in nonlinear composite media. By detailed analysis and computation we obtain a decaying estimates on the semigroup and prove the orbital instability of two families of explicit solitary wave solutions (slow family in anisotropic case and solitary waves in isotropic case), which theoretically verify the related guess and numerical results.
In this paper, we study Henig efficiency in vector optimization with nearly cone-subconvexlike set-valued function. The existence of Henig efficient point is proved and characterization of Henig efficiency is established using the method of Lagrangian multiplier. As an interesting application of the results in this paper, we establish a Lagrange multiplier theorem for super efficiency in vector optimization with nearly conesubconvexlike set-valued function.
In this paper we propose a modification of the Landweber iteration termed frozen Landweber iteration for nonlinear ill-posed problems. A convergence analysis for this iteration is presented. The numerical performance of this frozen Landweber iteration for a nonlinear Hammerstein integral equation is compared with that of the Landweber iteration. We obtain a shorter running time of the frozen Landweber iteration based on the same convergence accuracy.