LP(X)中MP归结推理

首先讨论格值命题逻辑系统LP(X)中子句的规则型范式以及极简规则型子句集的形式,然后定义MP归结式以及(A,α)-归结演绎、α-逻辑推理以及α-不可满足,讨论了它们的一系列逻辑性质,最后证明了MP归结推理的可靠性以及弱完备性.     

格值命题逻辑系统LP(X)的闭包算子

In this paper, closure operators of lattice-valued propositional logic LP(X) are studied. A family of classical closure operators are defined and the relation between them and closure operators of LP(X) is investigated. At the same time, a tool for checking compactness of LP(X) is given.     

(α,β)-fuzzy Subalgebras of Q-algebras

In this note by two relations belonging to (∈) and quasi-coincidence (q) between fuzzy points and fuzzy sets,the notion of (α,β)-fuzzy Q-algebras,the level Q-subalgebra is introduced where α,β are any two of {∈,q,∈∨q,∈∧q} with α≠∈∧q.Then we state and prove some theorems which determine the relationship between these notions and Q-subalgebras.The images and inverse images of (α,β)-fuzzy Q-subalgebras are defined,and how the homomorphic images and inverse images of (α,β)-fuzzy Q-subalgebra becomes (α,β)-fuzzy Q-algebras are studied.     

一类射影平坦的多项式(α，β)度量

讨论了一类具有如下形式的Finsler度量F=α+εβ+kβ~2/α+k~2β~4/3α~3-k~3β~6/5α~5,其中α=(a_(ij)y~iy~j)~(1/2)是一个Riemann度量,β=b_iy~i是一个1-形式,ε和k≠0是常数,研究了这类度量的旗曲率性质,得到了F为局部射影平坦的充要条件.     

Characterization of $(c)$-Riordan Arrays, Gegenbauer-Humbert-Type Polynomial Sequences, and $(c)$-Bell Polynomials

Here presented are the definitions of(c)-Riordan arrays and(c)-Bell polynomials which are extensions of the classical Riordan arrays and Bell polynomials.The characterization of(c)-Riordan arrays by means of the A-and Z-sequences is given,which corresponds to a horizontal construction of a(c)-Riordan array rather than its definition approach through column generating functions.There exists a one-to-one correspondence between GegenbauerHumbert-type polynomial sequences and the set of(c)-Riordan arrays,which generates the sequence characterization of Gegenbauer-Humbert-type polynomial sequences.The sequence characterization is applied to construct readily a(c)-Riordan array.In addition,subgrouping of(c)-Riordan arrays by using the characterizations is discussed.The(c)-Bell polynomials and its identities by means of convolution families are also studied.Finally,the characterization of(c)-Riordan arrays in terms of the convolution families and(c)-Bell polynomials is presented.     

A Concentration Theorem of (R,p)-anders on Hadamard Manifolds

In this note, we prove a concentration theorem of (R, p)-anders. As a simple corollary, one can prove that (X, p)-anders do not admit coarse embeddings into Hadamard manifolds with bounded sectional curvatures.     

A Theorem for Generalized Extension ofOperators and Some Applications

In this note it is shown that every bounded linear operator T Э B(Y,Z)defined on a closed subspace Y of a Banach space X admits a generalized extension T Э B(X, V). Some examples of the applications are given; especially, a characterization of H.I. spaces is obtained.     

局部β-凸空间L~β(μ,X)(0＜β≤1)的共轭锥的次表示定理

对于0β≤1,有限测度空间(Ω,Σ,μ)与Hilbert空间X,本文研究向量值局部β-凸函数空间L~β(μ,X)的共轭锥[L~β(μ,X)]_β~*的表示问题.在赋范锥(X_β~*,‖-‖)对μ满足Randon-Nikodym性质的条件下,证明次表示定理[L~β(μ,X)]_β~*(?)L~∞(μ,X_β~*).     

On the Dirichlet form of three-dimensional Brownian motion conditioned to hit the origin

Our concern in this paper is the energy form induced by an eigenfunction of a self-adjoint extension of the restriction of the Laplace operator to C_c~∞(R~3\{0}).We will prove that this energy form is a regular Dirichlet form with core C_c~∞(R~3).The associated diffusion X behaves like a 3-dimensional Brownian motion with a mild radial drift when far from 0,subject to an ever-stronger push toward 0 near that point.In particular,{0}is not a polar set with respect to X.The diffusion X is rotation invariant,and admits a skew-product representation before hitting{0}:its radial part is a diffusion on(0,∞)and its angular part is a time-changed Brownian motion on the sphere S~2.The radial part of X is a"reflected"extension of the radial part of X~0(the part process of X before hitting{0}).Moreover,X is the unique reflecting extension of X~0,but X is not a semi-martingale.     

Isometries on the Quasi-Banach Spaces Lp （0〈p〈1）

We study the extension of isometries between the unit spheres of quasi-Banach spaces Lp for 0〈p〈1. We give some sufficient conditions such that an isometric mapping from the the unit sphere of Lp（μ） into that of another LP（ν） can be extended to be a linear isometry defined on the whole space.     

An improved approximation algorithm for the partial Latin square extension problem

Previous work on the partial Latin square extension (PLSE) problem resulted in a 2-approximation algorithm based on the LP relaxation of a three-dimensional assignment IP formulation. We present an e/(e−1)-approximation algorithm that is based on the LP relaxation of a packing IP formulation of the PLSE problem.     

Markov decision processes for infinite horizon problems solved with the cosine simplex method

This article presents a new method of linear programming (LP) for solving Markov decision processes (MDPs) based on the simplex method (SM). SM has shown to be the most efficient method in many practical problems; unfortunately, classical SM has an exponential complexity. Therefore, new SMs have emerged for obtaining optimal solutions in the most efficient way. The cosine simplex method (CSM) is one of them. CSM is based on the Karush Kuhn Tucker conditions, and is able to efficiently solve general LP problems. This work presents a new method named the Markov Cosine Simplex Method (MCSM) for solving MDP problems, which is an extension of CSM. In this article, the efficiency of MCSM is compared to the traditional revised simplex method (RSM); experimental results show that MCSM is far more efficient than RSM.     

A dynamic programming extension to the steady state refinery-LP

Standard LPs, widely used for planning in the processing industry, are powerful tools for making economic decisions, but do not cover time relationships inside the planning timeframe. To include sequence-dependent issues within the optimization process, an algorithmic extension to the LP was developed. DPX (Dynamic Programming Extension) is used to solve a whole class of problems that are dynamic in time.     

A bilevel programming approach to the travelling salesman problem

We show that the travelling salesman problem is polynomially reducible to a bilevel toll optimization program. Based on natural bilevel programming techniques, we recover the lifted Miller-Tucker-Zemlin constraints. Next, we derive an O(n²) multi-commodity extension whose LP relaxation is comparable to the exponential formulation of Dantzig, Fulkerson and Johnson.     

Linear programming formulation of MDPs in countable state space: The multichain case

We present an Linear Programming formulation of MDPs with countable state and action spaces and no unichain assumption. This is an extension of the Hordijk and Kallenberg (1979) formulation in finite state and action spaces. We provide sufficient conditions for both existence of optimal solutions to the primal LP program and absence of duality gap. Then, existence of a (possibly randomized) average optimal policy is also guaranteed. Existence of a stationary average optimal deterministic policy is also investigated.     

Total Valuation Rings of Ore Extensions

We consider extensions of a total valuation ring V of a skew field K to the Ore extension K(X;σ, δ) for an endomorphism σ of K and a σ-derivation δ. It is shown that there exists an extension R of V with X ∈ R, such that ${\overline X}$ is transcendental over V/J(V) if and only if (σ,δ) is compatible with V, where ${\overline X} = X + J(R^(1))$ . In the case V is invariant, it is established that there is an invariant extension R of V in K(X;σ,δ) such that ${\overline X}$ is transcendental if and only if σ(a)V = aV and δ(a) ∈ aV for all a ∈ K.     

格值命题逻辑系统中基于滤子的MP归结演绎

给出了格值命题逻辑系统中子句的极简规则型范式,定义了MP归结.结合格蕴涵代数中滤子的性质,对格值命题逻辑系统中基于滤予的MP归结演绎及其语义与语法性质进行了研究,证明了归结演绎的可靠性与完备性定理.为进一步研究格值逻辑的自动归结推理奠定了理论基础.     

一类集值映射的周期点与混沌

设X为完备的紧致度量空间,k(X)为X的所有非空紧子集赋予Hausdorff度量所得的空间,■为f到k(X)的自然扩张.本文研究了动力系统(k(X),■)与动力系统(X,f)的周期点之间的相互关系.利用所得结论,彻底解决了Fedeli和廖公夫等人提出的一些公开问题.