The path player game

We give an explicit PDE characterization for the solution of the problemof maximizing the utility of both terminal wealth and intertemporal consumption undermodel uncertainty. The underlying market model consists of a risky asset, whosevolatility and long-term trend are driven by an external stochastic factor process. Therobust utility functional is defined in terms of a HARA utility function with risk aversionparameter 0 < α < 1 and a dynamically consistent coherent risk measure, whichallows for model uncertainty in the distributions of both the asset price dynamics andthe factor process. Ourmethod combines recent results by Wittmüß (Robust optimizationof consumption with random endowment, 2006) on the duality theory of robustoptimization of consumption with a stochastic control approach to the dual problemof determining a ‘worst-case martingale measure’.     

On the Existence and Stability of Solutions for a System of Elliptic Equations

We show, using a dual variational method developed in the paper, the existence of solutions for a system of Dirichlet problems for partial differential equations involving p– and q–Laplacian. The stability of solutions and the existence of positive solutions is considered in the superlinear case.      

Approximating the nondominated set of an MOLP by approximately solving its dual problem

The geometric duality theory of Heyde and Löhne (2006) defines a dual to a multiple objective linear programme (MOLP). In objective space, the primal problem can be solved by Benson’s outer approximation method (Benson 1998a,b) while the dual problem can be solved by a dual variant of Benson’s algorithm (Ehrgott et al. 2007). Duality theory then assures that it is possible to find the (weakly) nondominated set of the primal MOLP by solving its dual. In this paper, we propose an algorithm to solve the dual MOLP approximately but within specified tolerance. This approximate solution set can be used to calculate an approximation of the weakly nondominated set of the primal. We show that this set is a weakly ε-nondominated set of the original primal MOLP and provide numerical evidence that this approach can be faster than solving the primal MOLP approximately.     

A variational theory for monotone vector fields

Monotone vector fields were introduced almost 40 years ago as nonlinear extensions of positive definite linear operators, but also as natural extensions of gradients of convex potentials. These vector fields are not always derived from potentials in the classical sense, and as such they are not always amenable to the standard methods of the calculus of variations. We describe here how the selfdual variational calculus, developed recently by the author, provides a variational approach to PDEs and evolution equations driven by maximal monotone operators. To any such vector field T on a reflexive Banach space X, one can associate a convex selfdual Lagrangian L _T on the phase space X × X ^* that can be seen as a “potential” for T, in the sense that the problem of inverting T reduces to minimizing a convex energy functional derived from L _T . This variational approach to maximal monotone operators allows their theory to be analyzed with the full range of methods—computational or not—that are available for variational settings. Standard convex analysis (on phase space) can then be used to establish many old and new results concerned with the identification, superposition, and resolution of such vector fields. Dedicated to Felix Browder on his 80th birthday     

Global attracting sets for neutral-type BAM neural networks with time-varying and infinite distributed delays

In this paper, the asymptotic property of a class of neutral-type BAM neural networks with time-varying and infinite distributed delays is discussed. By developing a new integral inequality and applying the properties of nonnegative matrix, some sufficient conditions for the Lagrange stability and the existence of the global attracting set of the considering model are obtained. Meanwhile, the estimation of the global attractive set is also given out. The results derived here generalize and improve the earlier publications. Finally, two numerical examples are given and analyzed to demonstrate our results.     

Generalization of some hypergeometric functions

In this paper, we make use of the Lagrange interpolation to obtain some algebraic identities, involving one or two infinite sets of variables.     

Fejér processes in theory and practice: Recent results

In this paper we briefly survey the recent results of the theory of Fejér mappings and processes as applied to solving various mathematical problems, including structured systems of linear and convex inequalities, operator equations, as well as problems of linear and quadratic programming which are not necessarily solvable (improper ones).     

Numerical simulation of premixed combustion using an enriched finite element method

In this paper we present a novel discretization technique for the simulation of premixed combustion based on a locally enriched finite element method (FEM). Use is made of the G-function approach to premixed combustion in which the domain is divided into two parts, one part containing the burned and another containing the unburned gases. A level-set or G-function is used to define the flame interface separating burned from unburned gases. The eXtended finite element method (X-FEM) is employed, which allows for velocity and pressure fields that are discontinuous across the flame interface. Lagrange multipliers are used to enforce the correct essential interface conditions in the form of jump conditions across the embedded flame interface. A persisting problem with the use of Lagrange multipliers in X-FEM has been the discretization of the Lagrange multipliers. In this paper the distributed Lagrange multiplier technique is adopted. We will provide results from a spatial convergence analysis showing good convergence. However, a small modification of the interface is required to ensure a unique solution. Finally, results are presented from the application of the method to the problems of moving flame fronts, the Darrieus–Landau instability and a piloted Bunsen burner flame.     

恒模盲多用户检测算法研究

根据优化理论和L agrange神经网络基本原理,针对线性约束恒模算法(LCCM A),提出了一种恒模盲多用户检测算法,构建了L agrange罚函数,推导出迭代公式.通过仿真实验表明,该算法在误码率、信干比和信道跟踪能力方面均有所改善.