航空器供油问题中完全逆序类中的多项式时间可解类

航空器供油问题是一类非线性组合优化问题,其目标函数为分式形式,该问题目前不存在多项式时间算法,也未被证明是NP完全问题。一般可以用置换来刻画n架飞机的一个供油顺序。该问题中有一类实例被称为“完全逆序类”,“完全逆序类”用动态规划算法求解计算时间为O(n2ⁿ),具有指数时间复杂度。本文通过对该“完全逆序类”问题做进一步分析,发现在“完全逆序类”中也存在着多项式时间可解的情况。定理1研究一类一次可解的情况,若问题满足定理1的条件,则求解一次即可找到其最优解;定理2研究一类多项式时间可解的情况,当问题满足定理2的条件时,其最优解可在多项式时间内获得。     

Hilbert algebras as implicative partial semilattices

The infimum of elements a and b of a Hilbert algebra are said to be the compatible meet of a and b, if the elements a and b are compatible in a certain strict sense. The subject of the paper will be Hilbert algebras equipped with the compatible meet operation, which normally is partial. A partial lower semilattice is shown to be a reduct of such an expanded Hilbert algebra i ?both algebras have the same ?lters.An expanded Hilbert algebra is actually an implicative partial semilattice (i.e., a relative subalgebra of an implicative semilattice),and conversely.The implication in an implicative partial semilattice is characterised in terms of ?lters of the underlying partial semilattice.     

<Emphasis Type="Italic">L</Emphasis><Superscript><Emphasis Type="Italic">p</Emphasis></Superscript> estimates and asymptotic behavior of extremal function to Hardy-Sobolev type inequality on the H-type group*

This paper is devoted to discuss the regularity of the weak solution to a class of non-linear equations corresponding to Hardy-Sobolev type inequality on the H-type group. Combining the Serrin's idea and the Moser's iteration, L^p estimates of the weak solution are obtained, which generalize the results of Garofalo and Vassilev in [6, 14]. As an application, asymptotic behavior of the weak solution has been discussed. Finally, doubling property and unique continuation of the weak solution are given. *This material is based upon work funded by Zhejiang Provincial Natural Science Foundation of China under Grant No. Y606144.     

Structures and Chromaticity of Extremal 3-Colourable Sparse Graphs

 Assume that G is a 3-colourable connected graph with e(G) = 2v(G) −k, where k≥ 4. It has been shown that s ₃(G) ≥ 2 ^{k −3}, where s _r (G) = P(G,r)/r! for any positive integer r and P(G, λ) is the chromatic polynomial of G. In this paper, we prove that if G is 2-connected and s ₃(G) < 2 ^{k −2}, then G contains at most v(G) −k triangles; and the upper bound is attained only if G is a graph obtained by replacing each edge in the k-cycle C _k by a 2-tree. By using this result, we settle the problem of determining if W(n, s) is χ-unique, where W(n, s) is the graph obtained from the wheel W _n by deleting all but s consecutive spokes. Received: January 29, 1999 Final version received: April 8, 2000     

On a Boolean-valued Model of the Strict Implication System(Continuous)

The reference [4] proved the consistency of S1 and S2 among Lewis' five strict implication systems in the modal logic by using the method of the Boolean-valued model. But, in this method, the consistency of S3, S4 and S5 in Lewis' five strict implication systems is not decided. This paper makes use of the properties: (1) the equivalence of the modal systems S3 and P3, S4 and P4; (2) the modal systems P3 and P4 all contained the modal axiom T(□p → p); (3) the modal axiom T is correspondence to the reflexive property in VB. Hence, the paper proves: (a) ‖As31‖ = 1; (b) ‖AS41‖ = 1; (c) ‖AS5l‖ = 1 in the model (where B is a complete Boolean algebra, R is reflexive property in VB). Therefore, the paper finally proves that the Boolean-valued model VB of the ZFC axiom system in set theory is also a Boolean-valued model of Lewis' the strict implication system S3, S4 and S5.     

On the Product and Factorization of Lattice Implication Algebras

In this paper,the concepts of product and factorization of lattice implication algebra areproposed,the relation between lattice implication product algebra and its factors and some properties oflattice implication product algebras are discussed.     

连续时间马尔可夫决策过程的折扣模型

本文考虑的是转移速率族任意且费用率函数可能无界的连续时间马尔可夫决策过程的折扣模型．放弃了传统的要求相应于每个策略的　Ｑ　－过程唯一等条件,而首次考虑相应每个策略的　Ｑ　－过程不一定唯一,　转移速率族也不一定保守,　费用率函数可能无界,　且允许行动空间非空任意的情形．　本文首次用"α－折扣费用最优不等式"更新了传统的α－折扣费用最优方程,并用"最优不等式"和新的方法,不仅证明了传统的主要结果即最优平稳策略的存在性,　而且还进一步探讨了（　∈＞０　　）－最优平稳策略,具有单调性质的最优平稳策略,　以及（∈≥０）　－最优决策过程的存在性,　得到了一些有意义的新结果．　最后,　提供了一个迁移率受控的生灭系统例子,　它满足本文的所有条件,　而传统的假设（见文献［１－１４］）均不成立．     

唯一分解整半群上的Mobius函数及其反演公式

陈兆斗首先在文献[1]中定义出了有单位元并满足消去律的唯一分解交换半群上的Mbius函数.本文我们首先证明了Mbius函数作为半群(M1,*)上的元素是常值函数ζ(·)的逆函数.其后获得了该Mbius函数的一些相关结果并给出了三个Mbius反演公式.     

允许卖空的资本市场中存在非负均衡价格向量的充要条件

For the capital market satisfying standard assumptions that are widely adopted in the equilibrium analysis,a necessary and sufficient condition for the existence and uniqueness of a nonnegative equilibrium price vector that clears the mean-variance capital market with short sale allowed is derived. Moreover, the given explicit formula for the equilibrium price shows clearly the relationship between prices of assets and statistical properties of the rate of return on assets, the desired rates of return of individual investors as well as other economic quantities.The economic implication of the derived condition is briefly discussed. These results improve the available results about the equilibrium analysis of the mean-variance market.