The Ehrenfest urn is a model for the diffusion of gases between two chambers. Classic research deals with this system as a Markovian model with a fixed number of balls, and derives the steady-state behavior as a binomial distribution (which can be approximated by a normal distribution). We study the gradual change for an urn containing n (a very large number) balls from the initial condition to...

Solving large scale convex semidefinite programming (SDP) problems has long been a challenging task numerically. Fortunately, several powerful solvers including SDPNAL, SDPNAL+ and QSDPNAL have recently been developed to solve linear and convex quadratic SDP problems to high accuracy successfully. These solvers are based on the augmented Lagrangian method (ALM) applied to the dual problems with...

Superlinear dose dependence of thermoluminescence (TL) and optically stimulated luminescence (OSL) has been reported for many materials. The theoretical explanation has been ascribed to competition of either traps or recombination centers, during the excitation stage or during the read-out phase. There has been an account in the literature on superlinearity of OSL associated with merely one tra...

Interior point method (IPM) defines a search direction at each interior point of a region. These search directions form a direction field which in turn gives rise to a system of ordinary differential equations (ODEs). The solutions of the system of ODEs can be viewed as underlying paths in the interior of the region. In [31], these off-central paths are shown to be well-defined analytic curves ...

An interior point method (IPM) defines a search direction at each interior point of a region. These search directions form a direction field which in turn gives rise to a system of ordinary differential equations (ODEs). The solutions of the system of ODEs can be viewed as underlying paths in the interior of the region. In [C.-K. Sim and G. Zhao, Math. Program. Ser. A, 110 (2007), pp. 475–499],...

In this article the problem of solving a system of singular nonlinear equations will be discussed. The theory of local and Q-superlinear converegence for the nonlinear operators is developed.

— We give some multiplicity results on existence of nontrivial solutions for superlinear elliptic equations with a saddle structure near 0. We make use of a combination of bifurcation theory and minimax methods.

A modified BFGS method is proposed for unconstrained optimization. The global convergence and the superlinear convergence of the convex functions are established under suitable assumptions. Numerical results show that this method is interesting.

In this paper we present a novel variational approach to the question of existence and multiplicity of positive solutions to semipositone problems in a bounded smooth domain of RN . We consider both the sublinear and superlinear cases.

By constructing a special cone and using fixed point index theory, this paper investigates the existence of positive solutions of singular superlinear coupled integral boundary value problems for differential systems