General Information

In this paper, we propose and analyze an SQP-type method for solving linearly constrained convex minimization problems where the objective functions are too complex to be evaluated exactly. Some basic results for global convergence and local superlinear convergence are obtained according to the properties of the approximation sequence. We illustrate the applicability of our approach by proposing a new method for solving two-stage stochastic programs with fixed recourse.     

Structure of Regular Solutions of the Three-Body Schrödinger Equation near the Pair Impact Point

We investigate the six-dimensional Schrödinger equation for a three-body system with central pair interactions of a more general form than Coulomb interactions. Regular general and special physical solutions of this equation are represented by infinite asymptotic series in integer powers of the distance between two particles and in the sought functions of the other three-body coordinates. Constructing such functions in angular bases composed of spherical and bispherical harmonics or symmetrized Wigner D-functions is reduced to solving simple recursive algebraic equations. For projections of physical solutions on the angular bases functions, we derive boundary conditions at the pair impact point.     

On the Similarity between Volterra Operators and Transformation Operators for Integro-Differential Operators of Fractional Order

We establish the similarity between certain Volterra integral operators and the Riemann--Liouville fractional integration operator as well as the existence of a triangular transformation operator for integro-differential equations of fractional order. The results obtained are consistent with similar results for the case of integer order.     

On Global Optimality Conditions and Cutting Plane Algorithms

We discuss global optimality conditions and cutting plane algorithms for DC optimization. The discussion is motivated by certain incorrect results that have appeared recently in the literature on these topics. Incidentally, we investigate the relation of the Tikhonov reciprocity theorem to the optimality conditions for general nonconvex global optimization problems and show how the outer-approximation scheme developed earlier for DC programming can be used to solve a wider class of problems.     

On a Construction of Fast Direct Solvers

Fast direct solvers for the Poisson equation with homogeneous Dirichlet and Neumann boundary conditions on special triangles and tetrahedra are constructed. The domain given is extended by symmetrization or skew symmetrization onto a rectangle or a rectangular parallelepiped and a fast direct solver is used there. All extendable domains are found. Eigenproblems are also considered.     

On the Global Stability of Solutions of Moment Systems in Nonequilibrium Thermodynamics

In this paper, we study the linearization of the Cauchy problem and the mixed problem for the system of Grad--Hermite moments in nonequilibrium thermodynamics in the neighborhood of the equilibrium state. Stability conditions for solutions of the Cauchy problem are proved as a generalization of the classical Hermite--Biller theorem on stable polynomials. For the mixed problem, we prove an analog of the Vishik--Lyusternik theorem on small singular perturbations of general elliptic problems. The last observation allows us to introduce the Shapiro--Lopatinskii condition, which implies the well-posedness of the mixed problem.     

On Solvability of a Boundary Value Problem for Singular Integral Equations

This paper deals with the solvability of boundary value problems for singular integral equations of the form (i)-(ii).By an algebraic method we reduce the problem (i)-(ii) to a system of linear algebraic equations which gives all solutions in a closed form.AMS Subject Classification: 47G05, 45GO5, 45E05     

Degenerate nonlinear hyperbolic conservation laws: Non classical geometrical theory

Kinetic selection principles have been shown to be useful and physically reasonable in nonlinear hyperbolic problems with large amplitude phase transitions. We refer to Abeyaratne and Knowles, [A-K], for discussion on the subject. They also have been used for degenerate nonlinear problems, where the genuine nonlinearity property of Lax is violated. This is the framework of Liu, [Li], in the kinetic situation of Hayes and Le Floch, [H-L], where their so-called non classical shocks may be seen as small amplitude phase transitions. Here, we describe the local geometry generated by the generic non genuinely nonlinear assumption. A geometric kinetic criterion can be used to select indeterminate simple waves and obtain the well-posedness of the local Riemann problem. A particular case is the entropic kinetic criterion of Hayes and Le Floch.

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Sunto Principi di selezione cinetica sono stati mostrati utili e fisicamente ragionevoli in problemi iperbolici con transizioni di fase di grande ampiezza. Ci riferiamo ad Abeyaratne e Knowles, [A-K], per discussioni sull'argomento. Detti principi sono stati usati per problemi nonlineari degeneri, dove la proprietà di genuina nonlinearità di Lax è violata. Questo è la prospettiva di Liu, [Li], nella situazione cinetica di Hayes e Le Floch, [H-L], dove i loro così detti urti non classici possono essere considerati come transizioni di fase di piccola ampiezza. Qui, descriviamo la geometria locale generata dall'ipotesi generica genuinamente nonlineare. Un criterio di geometria cinetica può essere usato per selezionare onde semplici indeterminate ed ottenere la buona posizione per il problema locale di Riemann. Un caso particolare è il criterio di entropia cinetico di Hayes e Le Floc.

     

Stability Conditions of the MMAP [ K ]/ G [ K ]/1/ LCFS Preemptive Repeat Queue

In this paper, we study the stability conditions of the MMAP[K]/G[K]/1/LCFS preemptive repeat queue. We introduce an embedded Markov chain of matrix M/G/1 type with a tree structure and identify conditions for the Markov chain to be ergodic. First, we present three conventional methods for the stability problem of the queueing system of interest. These methods are either computationally demanding or do not provide accurate information for system stability. Then we introduce a novel approach that develops two linear programs whose solutions provide sufficient conditions for stability or instability of the queueing system. The new approach is numerically efficient. The advantages and disadvantages of the methods introduced in this paper are analyzed both theoretically and numerically.     

THE BOUNDARY VALUE PROBLEMS OF A CLASS OF ELLIPTIC EQUATION WITH A CURVE OF TURNING POINT

The boundary value problems of a class of elliptic equation with a curveof turning point are considered. Using the method of multiple scales and thecomparison theorem, the asymptotic behavior of solution for the boundary valueproblem is studied.