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})).     

On nonexistence of Kneser solutions of third-order neutral delay differential equations

The aim of this paper is to complement existing oscillation results for third-order neutral delay differential equations by establishing sufficient conditions for nonexistence of so-called Kneser solutions. Combining newly obtained results with existing ones, we attain oscillation of all solutions of the studied equations.     

Influence of saddle-splay deformation on lyotropic chromonic liquid crystals confined between two coaxial cylinders

ABSTRACT

A striking feature of lyotropic chromonic liquid crystals confined in cylinder model exhibit double-twist director configurations. Evidence suggests that saddle-splay deformation is among the most important factors for the distortions of director. Previous researches limit the director to distort at a fixed plane (r-? plane) by using specific boundary conditions such as degenerate planar anchoring condition. In this work, we consider lyotropic chromonic liquid crystals confined between two coaxial cylinders with free-surface boundary conditions and Rapini-Papoular-type anchoring conditions. By using finite-difference iterative method to solve the numerical solution of Euler equation, we find that saddle-splay deformation leads to double-twist director configurations under free-surface boundary conditions, which consist of the result under degenerate planar anchoring conditions. Furthermore, at Rapini-Papoular-type anchoring conditions, saddle-splay deformation has a great influence on the director in the radial direction (r direction) and the director distorts in three-dimensional space. Remarkably, our method provides a more accurate theory basis for the measured values of saddle-splay elastic constant K_24。     

Comparative structural analysis of a histone-like protein from Spiroplasma melliferum in the crystalline state and in solution

A solution of a histone-like protein from Spiroplasma melliferum (HUSpm) was examined by small-angle X-ray scattering (SAXS). The experimental SAXS curve was compared with those calculated for the HUSpm structures from the PDB databank obtained by both X-ray diffraction analysis and nuclear magnetic resonance spectroscopy. The model of the HUSpm structure in solution, which best agrees with the experimental SAXS data, has a shorter distance between the centers of mass of the HUSpm monomers compared to the crystal structure, indicating that the HUSpm monomers can be located closer to each other in solution than in the crystalline state.     

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.     

Oscillation theorems for symplectic difference systems

We consider symplectic difference systems involving a spectral parameter, together with the Dirichlet boundary conditions. The main result of the paper is a discrete version of the so-called oscillation theorem which relates the number of finite eigenvalues less than a given number to the number of focal points of the principal solution of the symplectic system. In two recent papers the same problem was treated and an essential ingredient was to establish the concept of the multiplicity of a focal point. But there was still a rather restrictive condition needed, which is eliminated here by using the concept of finite eigenvalues (or zeros) from the theory of matrix pencils.     

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.     

周期系数线性系统的稳定性

利用柯西矩阵的性质,讨论了周期系数线性矩阵的稳定性问题.将矩阵稳定的条件减弱为拟稳定,利用矩阵的不等式运算性质,得到了各种周期系统平凡解稳定的判据,所得结论,推广了现有文献的结论.最后,利用Matlab模拟仿真,验证了所得结果的可行性.