Existence and exponential stability of almost periodic solution for shunting inhibitory cellular neural networks with impulses

In this paper, by using the contraction principle and Gronwall–Bellman’s inequality, some sufficient conditions are obtained for checking the existence and exponential stability of almost periodic solution for shunting inhibitory cellular neural networks (SICNNs) with impulse. Our results are essentially new. It is the first time that the existence of almost periodic solutions for the impulsive neural networks are obtained.     

生物转化体系中R-肾上腺素光学纯度的测定

以羟丙基-β-环糊精(HP-β-CD)为手性选择剂,采用高效毛细管电泳技术,对肾上腺素对映体拆分进行了研究。以55mmol/LTris-磷酸(含30g/LHP-β-CD,pH2.5)为运行缓冲液,分离电压23kV,柱温22℃,采用压力正极进样(3kPa×4s),肾上腺素对映体于13min内获得良好分离(RS=2.12)。在波长214nm处进行紫外检测,迁移时间和峰面积的相对标准偏差≤3.7%,峰面积与S-肾上腺素含量在0.3～130μg/L范围内呈良好的线性关系(相关系数为0.9951),回收率在97.5%～102.5%之间,肾上腺素对映体检出限(S/N=3)可达0.1μg/L,将其应用于手性生物转化样品分析,可很好地检测出R-肾上腺素的光学纯度。本研究为该类药物的生物不对称转化提供了很好的分析方法。     

k-Regular partitions and overpartitions with bounded part differences

Recently, partitions with fixed or bounded difference between largest and smallest parts have attracted a lot of attention. In this paper, we provide both analytic and combinatorial proofs of the generating function for k-regular partitions with bounded difference kt between largest and smallest parts. Inspired by Franklin’s result, we further find a new proof of the generating function for overpartitions with bounded part differences by using Dousse and Kim’s results on (q, z)-overGaussian polynomials.

     

Design of Biosolvents Through Hydroxyl Functionalization of Compounds with High Dielectric Constant

We proposed basic principles for biosolvent design on the viewpoint of ionization. Two classes of biosolvents, based on cyclic carbonate moiety and amide moiety, were designed through hydroxyl functionalization of highly dielectric compound. The newly designed compounds, glycerol carbonate (GC) and N-hydroxymethyl formamide (HOF), were synthesized for the development of soluble enzymatic systems and characterized by ¹³C NMR and ¹H NMR. All the characterization data were consistent with the expected structures. Using conductance measurements, the pK _a values of trichloroacetic acid in GC and HOF were determined as 0.80 and 0.85 at 25.0 °C, which was very close to that in water (pK _a = 0.70), suggesting that the ionizing and dissociating abilities of GC and HOF are similar to those of water. The effects of various reaction parameters on activity and stability of Candida antarctica lipase B and lipase from Pseudomonas cepacia were investigated using the transesterification of ethyl butyrate with n-butanol as a model reaction. The activities of lipases in GC and HOF were comparable to those in water, indicating that the newly designed compounds were biocompactible. Biosolvent design is a promising and versatile method for developing new biosolvents.     

Light-extraction efficiency and forward voltage in GaN-based light-emitting diodes with different patterns of V-shaped pits

We present a new method of making a textured V-pit surface for improving the light extraction efficiency in GaN- based light-emitting diodes and compare it with the usual low-temperature method for p-GaN V-pits. Three types of GaNbased light-emitting diodes （LEDs） with surface V-pits in different densities and regions were grown by metal-organic chemical vapor deposition. We achieved the highest output power and lowest forward voltage values with the p-InGaN V-pit LED. The V-pits enhanced the light output power values by 1.45 times the values of the conventional LED owing to an enhancement of the light scattering probability and an effective reduction of Mg-acceptor activation energy. Moreover, this new technique effectively solved the higher forward voltage problem of the usual V-pit LED.     

具有线性脉冲的周期捕食系统的持久性

研究具有HollingIV功能性反应和脉冲的周期捕食食饵系统．找到了影响该系统动力学行为的阈值Ro．证明了当Ro〈1时,该系统的食饵灭绝周期解是局部渐近稳定的;当R0〉1时,该系统的食饵灭绝周期解变得不稳定且食饵将一致持久．     

随机度量空间及其应用

首先证明取值于度量空间(可分或不可分)的随机元可构成随机度量空间;取值于赋范空间的随机元可嵌入到随机赋范空间中.接着给出这些结论对随机算子的应用.最后统一给出赋范空间上几乎处处有界的随机线性泛函的表示.     

On two unimodal descent polynomials

The descent polynomials of separable permutations and derangements are both demonstrated to be unimodal. Moreover, we prove that the $\gamma$-coefficients of the first are positive with an interpretation parallel to the classical Eulerian polynomial, while the second is spiral, a property stronger than unimodality. Furthermore, we conjecture that they are both real-rooted.     

Random walks and the effective resistance sum rules

In this paper, using the intimate relations between random walks and electrical networks, we first prove the following effective resistance local sum rules:

     

Bäcklund transformation,infinite conservation laws and periodic wave solutions to a generalized (2+1)-dimensional Boussinesq equation

Under investigation in this paper is a generalized (2+1)-dimensional Boussinesq equation, which can be used to describe the water wave interaction. By using Bell polynomials, a lucid and systematic approach is proposed to systematically study the integrability of the equation, including its bilinear representation, soliton solutions, periodic wave solutions, Bäcklund transformation and Lax pairs, respectively. Furthermore, by virtue of its Lax equations, the infinite conservation laws of the equation are also derived with the recursion formulas. Finally, the asymptotic behavior of periodic wave solutions is shown with a limiting procedure.