The Maximal Closed Classes of Unary Functions in p-Valued Logic

In many-valued logic the decision of functional completeness is a basic and important problem, and the thorough solution to this problem depends on determining all maximal closed sets in the set of many-valued logic functions. It includes three famous problems, i.e., to determine all maximal closed sets in the set of the total, of the partial and of the unary many-valued logic functions, respectively. The first two problems have been completely solved ([1], [2], [8]), and the solution to the third problem boils down to determining all maximal subgroups in the k-degree symmetric group S_k, which is an open problem in the finite group theory. In this paper, all maximal closed sets in the set of unary p-valued logic functions are determined, where p is a prime. Mathematics Subject Classification: 03B50, 20B35.     

小比距离密闭空腔爆炸爆后气体温度和压力测量技术研究

为实现空腔爆炸温度、压力变化趋势的准确测量,基于铠装K型热电偶和压力变送器,建立密闭空腔爆后气体温度、压力测量系统。设计密封隔热防护装置,将传感器的敏感端与信号调理模块分别安装在两个密封腔内,有效提高了传感器在大当量爆炸冲击条件下的存活率。在0.86m/kg^1/3比距离密闭空腔大当量爆炸条件下,对传感器及防护装置的性能进行考核验证,爆后测量采集到了有效的气体温度及压力变化历程,且传感器状态能够最终恢复至正常状态。测试结果表明,使用密封隔热安装的K型热电偶和压力变送器可以满足小比距离密闭空腔爆后气体静态温度、压力测量需求。     

经典轨道的封闭性和径向Schr?dinger方程的因式分解

研究表明,保证经典轨道具有封闭性的Bertrand定理可以进一步推广,在适当的角动量下,仍存在着非椭圆的闭合轨道．对于屏蔽Coulomb场,可获得广义Runge-Lenz矢量．这种轨道封闭性与径向Schr?dinger方程因式分解相对应．     

Gödel Kink Spacetime

A 2+1 version of a rotating perfect fluid spacetime of Gödel type is examined to see whether it has a Finkelstein-Misner kink. It is shown, by three different methods, that the kink number is one.     

Closed Curves in E 2 and S 2 Whose Total Squared Curvatures and Almost Minimal

The total squared curvature of a closed plane curve is minimized by a covering of a circle, if the rotation number of the curve is not zero. We measure the closeness of a closed plane curve to a circle by the difference of its total squared curvature from the minimum. A similar result is obtained for a simple closed curve in the 2-sphere.     

Homotopy Theories of Algebras over Operads

Homotopy theories of algebras over operads, including operads over “little n-cubes,” are defined. Spectral sequences are constructed and the corresponding homotopy groups are calculated.__________Translated from Matematicheskie Zametki, vol. 78, no. 2, 2005, pp. 278–285.Original Russian Text Copyright © 2005 by V. A. Smirnov.     

On the approximation to solutions of operator equations by the least squares method

We consider the equation Au = f, where A is a linear operator with compact inverse A ^–1 in a separable Hilbert space . For the approximate solution u _n of this equation by the least squares method in a coordinate system {e _k } _k that is an orthonormal basis of eigenvectors of a self-adjoint operator B similar to A ( (B) = (A)), we give a priori estimates for the asymptotic behavior of the expressions r _n = u _n – u and R _n = Au _n – f as n . A relationship between the order of smallness of these expressions and the degree of smoothness of u with respect to the operator B is established.__________Translated from Funktsional nyi Analiz i Ego Prilozheniya, Vol. 39, No. 1, pp. 85–90, 2005Original Russian Text Copyright © by M. L. GorbachukSupported by CRDF and Ukrainian Government Joint Grant UM1-2567-OD03.Translated by V. M. Volosov     

Extension closure of k-torsionfree modules

Let Λ be a left and right Noetherian ring. For a positive integer k, we give an equivalent condition that flat dimensions of the first k terms in the minimal injective resolution of Λ are less than or equal to k. In this case we show that the subcategory consisting of k-torsionfree modules is extension closed. Moreover we prove that for a Noetherian algebra every subcategory consisting of i-torsionfree modules is extension closed for any 1 ≤ i ≤ k if and only if every subcategory consisting of i-th syzygy modules is extension closed for any 1 ≤ i ≤ k. Our results generalize the main results in Auslander and Reiten [4].     

闭模糊n级正关联理想

引入闭模糊n级正关联理想 ，刻划其结构和性质。