Post's Problem for Reducibilities of Bounded Complexity

In this paper we consider the we known method by E. Post of solving the problem of construction of recursively enumerable sets that have a degree intermediate between the degrees of recursive and complete sets with respect to a given reducibility. Post considered reducibilities ≤_m, ≤_btt, ≤_tt and ≤_T and solved the problem for al of them except ≤_T. Here we extend Post's original method of construction of incomplete sets onto two wide classes of sub‐Turing reducibilities what were studying in [1, 2].     

LocalH-theorem for a kinetic variational theory

A localH-theorem is derived for a recently proposed extension of Enskog kinetic theory to a dense model fluid composed of particles with interactions extending beyond a hard core.On leave from: Katedra Fizyki, Uniwersytetu Szczecinskiego, 70-451 Szczecin, Poland.     

几类凝聚图的轮廓

设Ｇ是个图，｜Ｖ（Ｇ）＝ｎ｜对Ｇ上的任一个标号ｆ：Ｖ（Ｇ）→｛１，…，ｎ｝记，且当ｊ≠ｉ时，Ｇ中有边以ｆ（－１）（ｊ）及ｆ（－１）（ｉ）为两端点｝）．称Ｐ（Ｇ）＝ｍｉｎ｛Ｐ（ｆ）：ｆ是Ｇ上的标号｝为图Ｇ的轮廓．对以Ｗ表示Ｇ中Ｗ的边界．本文证明：ｉ）若Ｇ是凝聚图，ｆ及ｆ是Ｇ上一对互逆标号，则Ｐ（Ｇ）＝Ｐ（ｆ）的充要条件是ｆ为凝聚标号，且此时若Ｇ，Ｈ均是凝聚图，则存在阶梯标号。使得路、回、完全留之间的下列乘积图也是凝聚图，且其轮廓为     

On Direct Product of HX Groups

ＯｎＤｉｒｅｃｔＰｒｏｄｕｃｔｏｆＨＸＧｒｏｕｐｓＭｉＨｏｎｇｈａｉ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓａｎｄＰｈｙｓｉｃｓ，ＨｅｂｅｉＵｎｉｖｅｒｓｉｔｙｏｆＴｅｃｈｎｏｌｏｇｙ）ＺｅｎｇＷｅｎｙｉ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍ...     

关于算子方程AXB－X＝C的解─—纪念C．Apostol

本文给出了算子方程ＡＸＢ－Ｘ＝Ｃ可解的若干充要条件，其中（Ａ，Ｂ）为下列情形之一：Ａ或Ｂ有闭值域；Ａ（Ｂ＊）有闭值域并且是单射或者相似于一个协亚正规算子并且Ｂ（Ａ＊）是单侧移位；Ａ＋（Ｂ（＊＋））幂有界，其值域Ｒ（Ａ＋）　Ｒ（Ａ）（Ｒ（Ｂ）　Ｒ（Ｂ＋）并且Ｂ（Ａ＊）是单侧移位；Ａ＝Ｕ＊且Ｂ＝Ｕ是Ｈａｒｄｙ空间上重数为１的单侧移位．而且，给出了解的表达式．     

MgnLa(n=2-6)掺杂团簇的密度泛函研究

采用密度泛函(DFT)中的B3LYP方法,选择CEP-31g基组,优化并得到了MgnLa(n=2- 6)小团簇的基态平衡结构,计算出了掺杂团簇的基态结构的平均键长、对称性、费米能级、能级间隙、束缚能、总能的二阶差分．结果表明,随着团簇原子数的增加,La原子更容易趋于团簇表面位置. 与未掺杂Mg团簇相比,La原子多采用取代其稳定基态结构的一个Mg原子形成掺杂团簇的稳定结构. 从有限的结果看,其中 Mg3La和 Mg6La的结构更为稳定．     

Efficient algorithms for solving certain nonconvex programs dealing with the product of two affine fractional functions

Two algorithms for finding a global minimum of the product of two affine fractional functions over a compact convex set and solving linear fractional programs with an additional constraint defined by the product of two affine fractional functions are proposed. The algorithms are based on branch and bound techniques using an adaptive branching operation which takes place in one-dimensional intervals. Results from numerical experiments show that large scale problems can be efficiently solved by the proposed methods.     

On the zeros ofζ (1)(s) — a (on the zeros of a class of a generalized Dirichlet series — XVII)

Some very precise results (see Theorems 4 and 5) are proved about thea-values of thelth derivative of a class of generalized Dirichlet series, forl≥l _o =l _o(a) (l _o being a large constant). In particular for the precise results on the zeros ofζ ⁽¹⁾ (s) —a (a any complex constant andl≥l _o) see Theorems 1 and 2 of the introduction.