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。     

On concentration of solution to a Schrödinger logarithmic equation with deepening potential well

In this work, we prove the existence of positive solution for the following class of problems where λ>0 and is a potential satisfying some conditions. Using the variational method developed by Szulkin for functionals, which are the sum of a C¹ functional with a convex lower semicontinuous functional, we prove that for each large enough λ>0, there exists a positive solution for the problem, and that, as λ→+∞, such solutions converge to a positive solution of the limit problem defined on the domain Ω=int(V^?1({0})).     

基于网格自适应加密技术的 GPU 高效运行实现研究

针对传统解算器未能实现 GPU 上运行网格自适应加密过程，造成 GPU 与 CPU 之间繁琐的数据交换的问题，本文发展优化了一种 GPU 加速的基于非结构自适应加密网格的解算器 VA2DG。利用加密网格表的方式实现网格自适应加密过程在 GPU 上高速运行，并通过原子操作并行生成网格加密表，对废弃的网格及时回收，节约存储空间，加快运行速度。     

Preparation of 17β‐estradiol surface molecularly imprinted polymers and their application to the analysis of biological samples

17β‐Estradiol (E2) surface molecularly imprinted polymers have been prepared using functionalized monodispersed poly(glycidyl methacrylate‐co‐ethylene dimethacrylate) beads as a support. The resulting polymers were found to be uniform in size (5 μm), and the surfaces of the microspheres possessed large pore‐like structures. A chromatographic experiment demonstrated that the resulting microspheres exhibited high levels of recognition and selectivity toward the target molecule. The particles were employed as a novel sorbent in a molecularly imprinted SPE protocol. A method was then developed involving the combination of the pretreatment with HPLC to determine the levels of estrogen secreted from Michigan Cancer Foundation‐7 cells. The obtained results revealed that the extraction recoveries of E2 from real samples were in the range of 73.0–97.5% with RSDs of < 7.5% (n = 3). Calibration curves were established with R values > 0.9996 for concentrations in the range of 0.50–100.00 ng/mL. The LOD of this new method was 0.14 ng/mL. Compared with traditional C₁₈ SPE agents, the particles showed high selectivity and extraction efficiency for E2 in the pretreatment process. The particles could therefore be used to determine trace estrogen in biological samples with a UV detector only.     

分数阶中立型时滞微分方程解的存在性及指数估计

近年来,随着分数阶微分方程在众多领域的广泛应用,其理论研究也引起了国内外学者的关注.论文研究分数阶中立型时滞微分方程在解存在的前提下其解的指数估计.首先,由分步法讨论分数阶中立型时滞微分方程的解的存在唯一的条件;然后,在解存在的前提下,利用Gronwall不等式,给出分数阶中立型时滞微分方程解的指数估计.