A boundary value problem for hypermonogenic functions in Clifford analysis

This paper deals with a boundary value problem for hypermonogenic functions in Clifford analysis. Firstly we discuss integrals of quasi-Cauchy's type and get the Plemelj formula for hypermonogenic functions in Clifford analysis, and then we address Riemman boundary value problem for hypermonogenic functions.     

Riemann boundary value problems for some K-regular functions in clifford analysis

In this paper, we study the R_m (m > 0) Riemann boundary value problems for regular functions, harmonic functions and bi-harmonic functions with values in a universal clifford algebra C(V_n,n). By using Plemelj formula, we get the solutions of R_m (m > 0) Riemann boundary value problems for regular functions. Then transforming the Riemann boundary value problems for harmonic functions and bi-harmonic functions into the Riemann boundary value problems for regular functions, we obtain the solutions of R_m (m > 0) Riemann boundary value problems for harmonic functions and bi-harmonic functions.     

A boundary value problem for hypermonogenic functions in Clifford analysis

This paper deals with a boundary value problem for hypermonogenic functions in Clifford analysis. Firstly we discuss integrals of quasi-Cauchy’s type and get the Plemelj formula for hypermonogenic functions in Clifford analysis, and then we address Riemman boundary value problem for hypermonogenic functions.

     

Clifford分析中广义超正则函数的一个非线性边值问题

讨论了Cliffrd分析中广义超正则函数的一个非线性边值问题.首先将广义超正则函数分解为两个奇异积分算子,然后给出了广义超正则函数的Plemelj公式及相关奇异积分算子的性质,最后利用Schauder不动点原理证明了广义超正则函数的一个非线性边值问题的解的存在性及积分表达式.     

BSDES IN GAMES,COUPLED WITH THE VALUE FUNCTIONS. ASSOCIATED NONLOCAL BELLMAN-ISAACS EQUATIONS

We establish a new type of backward stochastic differential equations(BSDEs)connected with stochastic differential games(SDGs), namely, BSDEs strongly coupled with the lower and the upper value functions of SDGs, where the lower and the upper value functions are defined through this BSDE. The existence and the uniqueness theorem and comparison theorem are proved for such equations with the help of an iteration method. We also show that the lower and the upper value functions satisfy the dynamic programming principle. Moreover, we study the associated Hamilton-Jacobi-Bellman-Isaacs(HJB-Isaacs)equations, which are nonlocal, and strongly coupled with the lower and the upper value functions. Using a new method, we characterize the pair(W, U) consisting of the lower and the upper value functions as the unique viscosity solution of our nonlocal HJB-Isaacs equation. Furthermore, the game has a value under the Isaacs' condition.     

Generalization of the weighted voting method using penalty functions constructed via faithful restricted dissimilarity functions

In this paper we present a generalization of the weighted voting method used in the exploitation phase of decision making problems represented by preference relations. For each row of the preference relation we take the aggregation function (from a given set) that provides the value which is the least dissimilar with all the elements in that row. Such a value is obtained by means of the selected penalty function. The relation between the concepts of penalty function and dissimilarity has prompted us to study a construction method for penalty functions from the well-known restricted dissimilarity functions. The development of this method has led us to consider under which conditions restricted dissimilarity functions are faithful. We present a characterization theorem of such functions using automorphisms. Finally, we also consider under which conditions we can build penalty functions from Kolmogoroff and Nagumo aggregation functions. In this setting, we propose a new generalization of the weighted voting method in terms of one single variable functions. We conclude with a real, illustrative medical case, conclusions and future research lines.     

Optimal value functions of generalized semi-infinite min-max programming on a noncompact set

In this paper, we study optimal value functions of generalized semi-infinite min-max programming problems on a noncompact set. Directional derivatives and subd-ifferential characterizations of optimal value functions are given. Using these properties, we establish first order optimality conditions for unconstrained generalized semi-infinite programming problems.     

Externality and Hamilton-Jacobi equations

The relationship between optimal control problems and Hamilton-Jacobi-Bellman equations is well known [9]. In fact the value function, defined as the infimum of the cost functional, satisfies in the viscosity sense an appropriate Hamilton-Jacobi-Bellman equation. In this paper we consider several control problems such that the cost functional associated to each problem depends explicitly on the value functions of the other problems. This leads to a system of Hamilton-Jacobi-Bellman equations. This is known, in economic context [14] cap XI, as an externality problem. In these problems may occur a lack of uniqueness of the value functions. We give conditions to ensure existence, uniqueness of the value functions and an implicit integral representation formula. Moreover, under uniqueness assumption, we prove that the variational solutions of the associated Hamilton-Jacobi system converge asymptotically to the value functions. We prove also an uniqueness theorem in the case of viscosity solutions of Hamilton-Jacobi-Bellman system.     

Properties of game options

A game option is an American option with the added feature that not only the option holder, but also the option writer, can exercise the option at any time. We characterize the value of a perpetual game option in terms of excessive functions, and we use the connection between excessive functions and concave functions to explicitly determine the value in some examples. Moreover, a condition on the two contract functions is provided under which the value is convex in the underlying diffusion value in the continuation region and increasing in the diffusion coefficient.Mathematics Subject Classification (2000) Primary 91A15, Secondary 60G40, 91B28     

The RH boundary value problem of the k-monogenic functions

In this paper we study the Riemann and Hilbert problems of k-monogenic functions. By using Euler operator, we transform the boundary value problem of k-monogenic functions into the boundary value problems of monogenic functions. Then by the Almansi-type theorem of k-monogenic functions, we get the solutions of these problems.     

Optimality functions in stochastic programming

Optimality functions define stationarity in nonlinear programming, semi-infinite optimization, and optimal control in some sense. In this paper, we consider optimality functions for stochastic programs with nonlinear, possibly nonconvex, expected value objective and constraint functions. We show that an optimality function directly relates to the difference in function values at a candidate point and a local minimizer. We construct confidence intervals for the value of the optimality function at a candidate point and, hence, provide a quantitative measure of solution quality. Based on sample average approximations, we develop an algorithm for classes of stochastic programs that include CVaR-problems and utilize optimality functions to select sample sizes.     

Leafwise Brownian Motions and Some Function Theoretic Properties of Laminations

We discuss the value distribution of Borel measurable functions which are subharmonic or meromorphic along leaves on laminations. They are called leafwise subharmonic functions or meromorphic functions respectively. We consider cases that each leaf is a negatively curved Riemannian manifold or Kähler manifold. We first consider the case when leaves are Riemannian with a harmonic measure in L.Garnett sense. We show some Liouville type theorem holds for leafwise subharmonic functions in this case. In the case of laminations whose leaves are Kähler manifolds with some curvature condition we consider the value distribution of leafwise meromorphic functions. If a lamination has an ergodic harmonic measure, a variant of defect relation in Nevanlinna theory is obtained for almost all leaves. It gives a bound of the number of omitted points by those functions. Consequently we have a Picard type theorem for leafwise meromorphic functions.     

A Gilmore-Gomory construction of integer programming value functions

In this paper, we analyze how sequentially introducing decision variables into an integer program (IP) affects the value function and its level sets. We use a Gilmore-Gomory approach to find parametrized IP value functions over a restricted set of variables. We introduce the notion of maximal connected subsets of level sets - volumes in which changes to the constraint right-hand side have no effect on the value function - and relate these structures to IP value functions and optimal solutions.     

C~2空间中广义解析函数的一个带位移带共轭值的非线性边值问题

讨论C2空间中广义解析函数的一个带位移带共轭的非线性边值问题.首先讨论解的形式,然后用积分方程的理论和Schauder不动点定理证明了解的存在性.     

逐段单调函数的高度与拓扑共轭

迭代运算下,函数值可以交叉于不同的子区间,使得逐段单调函数的高度异常复杂.本文考虑一个非单调点的连续函数类.首先给出高度的充分必要条件,以此获得此类函数的一种划分.其次针对函数类的一个非空子集,给出判定拓扑共轭的充分必要条件和构造拓扑共轭的新方法.进一步地,我们阐明这样的事实:两个逐段单调函数拓扑共轭是其高度相等的充分不必要条件,最后举例说明.     

Data envelopment analysis with nonlinear virtual inputs and outputs

An underlying assumption in DEA is that the weights coupled with the ratio scales of the inputs and outputs imply linear value functions. In this paper, we present a general modeling approach to deal with outputs and/or inputs that are characterized by nonlinear value functions. To this end, we represent the nonlinear virtual outputs and/or inputs in a piece-wise linear fashion. We give the CCR model that can assess the efficiency of the units in the presence of nonlinear virtual inputs and outputs. Further, we extend the models with the assurance region approach to deal with concave output and convex input value functions. Actually, our formulations indicate a transformation of the original data set to an augmented data set where standard DEA models can then be applied, remaining thus in the grounds of the standard DEA methodology. To underline the usefulness of such a new development, we revisit a previous work of one of the authors dealing with the assessment of the human development index on the light of DEA.     

A Different Version of Flett＇s Mean Value Theorem and an Associated Functional Equation

In this paper we present a mean value theorem derived from Flett‘s mean value theorem. It turns out that cubic polynomials have the midpoint of the interval as their mean value point. To answer what class of functions have this property, we consider a functional equation associated with this mean value theorem. This equation is then solved in a general setting on abelian groups.     

Singular boundary integral equations of boundary value problems of the elasticity theory under supersonic transport loads

We consider a transport boundary value problem for an isotropic elastic medium bounded by a cylindrical surface of arbitrary cross-section and subjected to supersonic transport loads. We pose the corresponding hyperbolic boundary value problem and prove the uniqueness of the solution with regard to shock waves. To solve the problem, we use the method of generalized functions. In the space of generalized functions, we obtain the solution, perform its regularization, and construct a dynamic analog of the Somigliana formula and singular boundary equations solving the boundary value problem.     

Mixed boundary value problems with a shift for a pair of metaanalytic and analytic functions

In this article, we reconsider the mixed boundary value problem on the unit circle for a pair of metaanalytic and analytic functions as in Du and Wang (2008) [9]. By adopting appropriate transformations, we convert the problem into two independent boundary value problems for analytic functions. We then obtain expressions of solution and condition of solvability for the mixed boundary value problem. The forms of the solutions and the condition of solvability here are rather dissimilar to those in Du and Wang (2008) [9]. But the equivalence is established at the end of this article.     

Two-stage integer programs with stochastic right-hand sides: a superadditive dual approach

We consider two-stage pure integer programs with discretely distributed stochastic right-hand sides. We present an equivalent superadditive dual formulation that uses the value functions in both stages. We give two algorithms for finding the value functions. To solve the reformulation after obtaining the value functions, we develop a global branch-and-bound approach and a level-set approach to find an optimal tender. We show that our method can solve randomly generated instances whose extensive forms are several orders of magnitude larger than the extensive forms of those instances found in the literature. This work is supported by National Science Foundation grants DMI-0217190 and DMI-0355433.