Strength of convergence in the orbit space of a groupoid

Let G be a second-countable locally-compact Hausdorff groupoid with a Haar system, and let {xn} be a sequence in the unit space G(0) of G. We show that the notions of strength of convergence of {xn} in the orbit space G(0)/G and measure-theoretic accumulation along the orbits are equivalent ways of realising multiplicity numbers associated to a sequence of induced representation of the groupoid C^?-algebra.     

Existence of partial transposition means representability in cylindric algebras

We show that the representability of cylindric algebras by relativized set algebras depends on the scope of the operation transposition which can be defined on the algebra. The existence of “partial transposition” assures this kind of representability of the cylindric algebra (while the existence of transposition assures polyadic representation). Further we characterize those cylindric algebras in which the operator transposition can be introduced (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

An Analog of the Fubini–Studi Form for Two-Dimensional Toric Varieties

For two-dimensional toric varieties X, an analog of the Fubini–Studi form ₀ is constructed together with the canonical form ₀ that is the kernel of an integral representation for holomorphic functions in d-circular domains in C ^d connected with two-dimensional toric varieties X. This kernel is shown to be a closed differential form in C ^d defining the associated positive form ₀ on X.     

Solving the Simple Plant Location Problem using a Data Correcting Approach

The Data Correcting Algorithm is a branch and bound type algorithm in which the data of a given problem instance is `corrected' at each branching in such a way that the new instance will be as close as possible to a polynomially solvable instance and the result satisfies an acceptable accuracy (the difference between optimal and current solution). In this paper the data correcting algorithm is applied to determining exact and approximate optimal solutions to the simple plant location problem. Implementations of the algorithm are based on a pseudo-Boolean representation of the goal function of this problem, and a new reduction rule. We study the efficiency of the data correcting approach using two different bounds, the Khachaturov-Minoux bound and the Erlenkotter bound. We present computational results on several benchmark instances, which confirm the efficiency of the data-correcting approach.     

(-*)b-方程的Cs+ap,q-形式解及其Lsp,q估计

In this paper, by using holomorphic support function of strictly pseudoconvex domain on Stein manifolds and the kernel defined by DEMAILY J P and Laurent Thiebaut, we construct two integral operators Tq and Sq which are both belong to Cs+αp,q-1((**)D) and obtain integral representation of the solution of (p,q)-form (**)b-equation on the boundary of pseudoconvex domain in Stein manifolds and the Lsp,q extimates for the solution.     

Martingales and stochastic integrals in the theory of continuous trading

This paper develops a general stochastic model of a frictionless security market with continuous trading. The vector price process is given by a semimartingale of a certain class, and the general stochastic integral is used to represent capital gains. Within the framework of this model, we discuss the modern theory of contingent claim valuation, including the celebrated option pricing formula of Black and Scholes. It is shown that the security market is complete if and only if its vector price process has a certain martingale representation property. A multidimensional generalization of the Black-Scholes model is examined in some detail, and some other examples are discussed briefly.     

The general scheme for higher-order decompositions of zero-curvature equations associated with 337-1337-1337-1(2)

Within the framework of zero-curvature representation theory, the decompositions of each equation in a hierarchy of zero-curvature equations associated with loop algebra by means of higher-order constraints on potential are given a unified treatment, and the general scheme and uniform formulas for the decompositions are proposed. This provides a method of separation of variables to solve a hierarchy of (1+1)-dimensional integrable systems. To illustrate the general scheme, new higher-order decompositions of two hierarchies of zero-curvature equations are presented.This project is supported by the National Basic Research Project Nonlinear Science.     

The construction of orthodox super rpp semigroups

We define orthodox super rpp semigroups and study their semilattice decompositions. Standard representation theorem of orthodox super rpp semigroups whose sub-band of idempotents is in the varieties of bands described by an identity with at most three variables are obtained.     

Quiver-graded Richardson orbits

In Lie theory, a dense orbit in the nilpotent radical of a parabolic group under the operation of the parabolic is called a Richardson orbit. We define a quiver-graded version of Richardson orbits generalizing the classical definition in the case of the general linear group. We define a quasi-hereditary algebra called the nilpotent quiver algebra whose isomorphism classes of Δ-filtered modules correspond to orbits in our generalized setting. We translate the existence of a Richardson orbit into the existence of a rigid Δ-filtered module of a given dimension vector. We study an idempotent recollement of this algebra whose associated intermediate extension functor can be used to produce Richardson orbits in some situations. This can be explicitly calculated in examples. We also give examples where no Richardson orbit exists.     

Riesz and Poisson-Jensen Representation Formulas for a Class of Ultraparabolic Operators on Lie Groups

The aim of this paper is to give some representation formulas of Riesz and Poisson-Jensen type for super-solutions to a class of hypoelliptic ultraparabolic operators on a homogeneous Lie group . Our results complete the ones obtained in Cinti (Math Scand 100:1–21, 2007). We also provide a suitable theory for -Green functions and for -Green potentials of Radon measures. The proofs mostly rely on the use of appropriate techniques relevant to the Potential Theory for . Investigation supported by University of Bologna. Funds for selected research topics.