Quasi-Stationarity of Discrete-Time Markov Chains with Drift to Infinity

We consider a discrete-time Markov chain on the non-negative integers with drift to infinity and study the limiting behavior of the state probabilities conditioned on not having left state 0 for the last time. Using a transformation, we obtain a dual Markov chain with an absorbing state such that absorption occurs with probability 1. We prove that the state probabilities of the original chain conditioned on not having left state 0 for the last time are equal to the state probabilities of its dual conditioned on non-absorption. This allows us to establish the simultaneous existence, and then equivalence, of their limiting conditional distributions. Although a limiting conditional distribution for the dual chain is always a quasi-stationary distribution in the usual sense, a similar statement is not possible for the original chain.     

Quantum Invariants for Solving the Time-Dependent Schrödinger Equation in One Dimension

Extending the work of Lewis and Leach on classical invariants for solving the classical equation of motion in one-dimensional system, the quantum invariants in polynomial form of momentum are obtained. The involved Hamiltonian is time-dependent and quadratic in momentum.     

Invariant Solutions of the Yang–Mills Field Equations Coupled to a Scalar Doublet

The Yang–Mills system of field equations which includes coupling to an SU(2) scalar matter doublet is developed. It is shown that an SU(2) current for a scalar matter doublet can be developed. The basic structure which fits the Yang–Mills system is somewhat different from the case of the scalar triplet. Using this form for the scalar current, it is possible to write down the Yang–Mills system which couples to the scalar matter doublet. It is shown that several sets of solutions to this system of equations can be obtained.     

A mixed explicit-implicit antidiffusive method of navier-stokes equations for supersonic and hypersonic separated flows

The supersonic and hypersonic.laminar and turbulent vi-scous separated flows over two and three-dimensional com-pression corners are solved by the antidissipative explicit-implicit difference scheme presented in this paper.The re-sults obtained show that a high accuracy has been achieved bythis method and the time needed for computation is greatlyreduced.     

Pascal's Theorem and Quantum Deformation

By a transfer principle, Pascal's Theorem is equivalent to a theorem about point pairs on the real line. It appears that Pascal's Theorem is equivalent to the vanishing of a common invariant of six quadratic forms. Using the q-deformed invariant theory of Leitenberger (J. Algebra 222 (1999), 82), we construct corresponding quantum invariants by a computer calculation.     

Invariant Logics

A moda logic Λ is called invariant if for all automorphisms α of NExt K , α(Λ) = Λ. An invariant ogic is therefore unique y determined by its surrounding in the attice. It wi be established among other that a extensions of K.alt ₁ S4.3 and G.3 are invariant ogics. Apart from the results that are being obtained, this work contributes to the understanding of the combinatorics of finite frames in genera, something wich has not been done except for transitive frames. Certain useful concepts will be established, such as the notion of a d‐homogeneous frame.     

On Conformal Invariants Built from Spinor Fields

By means of a conformal covariant differentiation process we construct generating systems for conformally invariant symmetric (r, s)–spinors in an arbitrary curved space–time. Extending this method to conformally invariant linear differential operators acting on symmetric spinor fields some classes of such operators are derived.     

Ridged Domains,Embedding Theorems and Poincaré Inequalities

We study the embeddings E : W(X(Ω), Y(Ω)) ↪ Z(Ω), where X(Ω), Y(Ω) and Z(Ω) are rearrangement–invariant Banach function spaces (BFS) defined on a generalized ridged domain Ω, and W denotes a first–order Sobolev–type space. We obtain two–sided estimates for the measure of non–compactness of E when Z(Ω) = X(Ω) and, in turn, necessary and sufficient conditions for a Poincaré–type inequality to be valid and also for E to be compact. The results are used to analyse the example of a trumpet–shaped domain Ω in Lorentz spaces. We consider the problem of determining the range of possible target spaces Z(Ω), in which case we prove that the problem is equivalent to an analogue on the generalized ridge Γ of Ω. The range of target spaces Z(Ω) is determined amongst a scale of (weighted) Lebesgue spaces for “rooms and passages” and trumpet–shaped domains.     

关于拟概率测度的收敛理论

本文研究了拟概率空间上收敛概念之间的关系这一问题.利用类比的方法,在拟概率空间上提出了一些新的关于拟-随机变量的收敛概念并讨论了这些收敛概念之间的关系,获得了模糊测度下的收敛理论,推广了关于经典测度的收敛概念.     

Approximate counting via random optimization

Let ℱ_n be a family of subsets of {1,…,n}. We propose a simple randomized algorithm to estimate the cardinality of ℱ_n from the maximum weight of a subset X∈ℱ_n in a random weighting of {1,…,n}. The examples include enumeration of perfect matchings in graphs, bases in matroids, and Hamiltonian cycles in graphs. © 1997 John Wiley & Sons, Inc. Random Struct. Alg., 11 , 187–198 (1997)