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。     

借助数轴透析金属与盐溶液的反应进程

借助数轴透析“一种金属与溶液中多种盐反应”和“多种金属与溶液中一种盐反应”中溶质与滤渣的组成,直观地将反应进程和结果展现其中,建立思维模型,化难为易,有利于学生掌握与应用。     

High-temperature fluorescence of low- and high concentration aqueous ATP solution

Abstract

The results of an experimental study of luminescence of an aqueous solution of adenosine triphosphate (ATP) at room temperature are presented. High-temperature fluorescence of low- and high-concentrated solution was experimentally detected and analyzed. The shape of the fluorescence spectrum, the excited state lifetime and the temperature behavior of the emission intensity indicate the formation in the high-concentrated solution of rather stable dimer-like complexes, which can form excimer states.     

Multiple bright and dark soliton solutions in three component spinor Bose-Einstein condensates

We investigate a quasi one dimensional spin-1 Bose-Einstein Condensates (BEC) in the absence of an external confinement governed by a system of three coupled Gross-Pitaevskii (GP) equation. Based on the Lax-pair, we construct one soliton solution employing gauge transformation method. In addition, the multiple bright and dark soliton solutions are obtained by properly choosing amplitude dependent parameter in the Lax-pair. The results of the paper emphasizes the richness in the structure of soliton solutions admitted by the spin components, a phenomenon which has never been brought out to the fore. We have also extended the gauge transformation method to generate two soliton solutions.