Tunneling of Spinor Bose-Einstein Condensates in Optical Lattice

In this letter, we have studied the tunneling effects and fluctuations of spinor Bose-Einstein condensates in optical lattice. It is found that there exist tunneling effects and fluctuations between lattices l and l ＋ 1, l and l - 1, respectively. In particular, when the optical lattice is infinitely long and the spin excitations are in the long-wavelength limit, tunneling effects disappear between lattices I and l＋ 1, and I and l - 1. In this case the fluctuations are a constant, and the magnetic soliton appears.     

多孔微结构光纤中飞秒激光脉冲超连续谱的产生

报道了利用800nm飞秒激光脉冲在多孔微结构光纤中产生超连续谱展宽的现象，连续谱展宽范围为440—890nm.基于标量波近似理论对微结构光纤包层的有效折射率和基模的有效面积以及光纤的色散特性进行了计算，发现微结构光纤具有特殊的控制色散和波导特性的能力，对超连续谱展宽的机理进行了初步解释.本文的理论分析和实验结果有较好的一致性，认为即使包层由无序填充气线组成的多孔微结构光纤也可以出现超连续谱展宽效应. 关键词： 多孔微结构光纤 超连续谱 有效折射率 色散     

Total absolute curvature and tightness of noncompact manifolds

In the first part we prove an extension of the Chern-Lashof inequality for noncompact immersed manifolds with finitely many ends. For this we give a lower bound of the total absolute curvature in terms of topological invariants of the manifold. In the second part we discuss tightness properties for such immersions. Finally, we give an upper bound for the substantial codimension.

     

Proper efficiency and duality for a class of constrained multiobjective fractional optimal control problems containing arbitrary norms

We establish necessary and sufficient conditions for properly efficient solutions of a class of nonsmooth nonconvex optimal control problems with multiple fractional objective functions, linear dynamics, and nonlinear inequality constraints on both the state and control variables. Subsequently, we utilize these proper efficiency criteria to construct two multiobjective dual problems and prove appropriate duality theorems. Also, we specialize and discuss these results for a particular case of our principal problem which contains square roots of positivesemidefinite quadratic forms. As special cases of the main proper efficiency and duality results, this paper also contains similar results for control problems with multiple, fractional, and ordinary objective functions.     

Realization of fixed point sets

Letf:XX be a selfmap of a compact connected polyhedron, andA a nonempty closed subset ofX. In this paper, we shall deal with the question whether or not there is a mapg:XX homotopic tof such that the fixed point set Fixg ofg equalsA. We introduce a necessary condition for the existence of such a mapg. It is shown that this condition is easy to check, and hence some sufficient conditions are obtained.Partially supported by the Natural Science Foundation of Liaoning University.     

成组加工中的加工全程和延误工件数问题

本文在同组工件连续加工的条件下考虑了单机加工中的二个排序问题,其目标函数分别为极小加工全程和延误工件数。文中在不同的条件下对它们给出了多项式时间算法。     

幂向量,复合向量数及其函数理论

本文提出向量为其幂向量和向量幂级数．向量幂级数由一实数和某一向量联合组成的“复合向量数”及其函数有重要涵义．这数也有运算法则．从复合向量数的函数理论分析知其函数有导数和解析函数的必要和充分条件．这些条件构成了“双曲型”方程的特征以及函数的积分性质等．     

关于模q的原根中D.H.Lehmer数的分布

设奇数ｑ≥３存在原根，本文研究模ｑ的原根中Ｄ．Ｈ．Ｌｅｈｍｅｒ数的分布性质，并给出一个较强的渐近公式。     

ON THE TOTAL COLORING OF GRAPH G ∨H

ＯＮＴＨＥＴＯＴＡＬＣＯＬＯＲＩＮＧＯＦＧＲＡＰＨＧ∨Ｈ￥ＸｕＢａｏｇａｎｇ（许宝刚）（Ｍａｔｈ．ｏｆＤｅｐｔ．，ＳｈａｎｄｏｎｇＵｎｉｖｅｒｓｉｔｙ，Ｊｉｎａｎ２５０１００，Ｃｈｉｎａ．）Ａｂｓｔｒａｃｔ：Ｔｈｅｔｏｔａｌｃｈｒｏｍａｔｉｃｎｕｍｂ...     

Geometric indices and the Alexander polynomial of a knot

It is well-known that any Laurent polynomial satisfying and is the Alexander polynomial of a knot in . We show that can be realized by a knot which has the following properties simultaneously: (i) tunnel number 1; (ii) bridge index 3; and (iii) unknotting number 1.