A discrete KdV equation hierarchy: continuous limit,diverse exact solutions and their asymptotic state analysis

In this paper, a discrete KdV equation that is related to the famous continuous KdV equation is studied. First, an integrable discrete KdV hierarchy is constructed, from which several new discrete KdV equations are obtained. Second, we correspond the first several discrete equations of this hierarchy to the continuous KdV equation through the continuous limit. Third, the generalized (m, 2N − m)-fold Darboux transformation of the discrete KdV equation is established based on its known Lax pair. Finally, the diverse exact solutions including soliton solutions, rational solutions and mixed solutions on non-zero seed background are obtained by applying the resulting Darboux transformation, and their asymptotic states and physical properties such as amplitude, velocity, phase and energy are analyzed. At the same time, some soliton solutions are numerically simulated to show their dynamic behaviors. The properties and results obtained in this paper may be helpful to understand some physical phenomena described by KdV equations.     

基于4，8-二氢二呋咱[3，}4-b，e]吡嗪高能材料的设计与筛选

为了寻找高能量密度的材料,本文设计了一系列基于4,8-二氢二呋咱[3,4-b,e]吡嗪的含能材料. 利用密度泛函理论研究了它们结构与性质之间的关系. 结果表明,这些设计化合物的性质受到含能基团和杂环取代基的影响. -N₃含能基团是提高设计化合物生成热的最有效取代官能团,而四唑环/-C(NO₂)₃基团对炸药的爆轰性能有较大贡献. 键解离能分析表明,引入-NHNH₂,-NHNO₂,-CH(NO₂)₃和-C(NO₂)₃基团会显著降低键解离能. 由于化合物A8,B8,C8,D8,E8和F8具有良好的爆轰性能和热稳定性,最终被筛选为潜在的高能密度材料. 此外,还计算了这些筛选化合物的电子结构.     

离子液体BMIMPF6修饰碳糊电极电化学测定维生素E

用疏水性离子液体1-丁基-3-甲基咪唑六氟磷酸([BMIM]PF6)作粘合剂制备了离子液体修饰碳糊电极(IL/CPE)。采用循环伏安法(CV)研究了维生素E(vitamin E,VE)的氧化产物生育酚红在IL/CPE和未修饰碳糊电极(CPE)上的电化学行为,结果表明生育酚红在IL/CPE上氧化过程更易于进行,峰电流响应ip也明显增加,表明IL/CPE对生育酚红的氧化还原反应具有良好的电催化作用。同时测定了电极过程的动力学参数:电荷转移系数α=0.8746,扩散系数D=1.65×10-3cm2/s,电极反应速率常数kf=6.64×10-2cm/s。采用方波伏安法(SWV)发现生育酚红氧化峰电流与其浓度在1.53×10-4mol/L～8.39×10-7mol/L范围内呈线性关系,检出限为1.58×10-8mol/L。该法可用于VE实际样品的分析测定。     

Guillain-Barré syndrome and anti-ganglioside antibodies: a clinician-scientist's journey

Guillain-Barré syndrome (GBS) is the most frequent cause of acute flaccid paralysis. Having seen my first GBS patient in 1989, I have since then dedicated my time in research towards understanding the pathogenesis of GBS. Along with several colleagues, we identified IgG autoantibodies against ganglioside GM1 in two patients with GBS subsequent to Campylobacter jejuni enteritis. We proceeded to demonstrate molecular mimicry between GM1 and bacterial lipo-oligosaccharide of C. jejuni isolated from a patient with GBS. Our group then established a disease model for GBS by sensitization with GM1 or GM1-like lipo-oligosaccharide. With this, a new paradigm that carbohydrate mimicry can cause autoimmune disorders was demonstrated, making GBS the first proof of molecular mimicry in autoimmune disease. Patients with Fisher syndrome, characterized by ophthalmoplegia and ataxia, can develop the disease after an infection by C. jejuni. We showed that the genetic polymorphism of C. jejuni sialyltransferase, an enzyme essential to the biosynthesis of ganglioside-like lipo-oligosaccharides determines whether patients develop GBS or Fisher syndrome. This introduces another paradigm that microbial genetic polymorphism can determine the clinical phenotype of human autoimmune diseases. Similarities between the clinical presentation of Fisher syndrome and Bickerstaff brainstem encephalitis have caused debate as to whether they are in fact the same disease. We demonstrated that IgG anti-GQ1b antibodies were common to both, suggesting that they are part of the same disease spectrum. We followed this work by clarifying the nosological relationship between the various clinical presentations within the anti-GQ1b antibody syndrome. In this review, I wanted to share my journey from being a clinician to a clinician-scientist in the hopes of inspiring younger clinicians to follow a similar path.(Communicated by Kunihiko SUZUKI, M.J.A.).     

Au_nAg_m~-(n+m=2～4)负离子团簇光脱附电子谱计算

利用密度泛函理论,通过几何优化和态密度计算了Au_nAg_m^-（n+m=2～4）团簇的光电子光谱,结果显示只有Au₂Ag₂^-团簇的第一个峰发生了0.5eV的红移,而其它团簇的峰位置符合的很好,因此理论计算给出的团簇结构是合理的.     

Dynamic inventory and pricing policy in a capacitated stochastic inventory system with fixed ordering cost

We study a dynamic inventory and pricing optimization problem in a periodic review inventory system with setup cost and finite ordering capacity in each period. We show that the optimal inventory control is characterized by an (s,s^′,p) policy in four regions of the starting inventory level.     

Iterative Algorithms for Equilibrium Problems

We consider equilibrium problems in the framework of the formulation proposed by Blum and Oettli, which includes variational inequalities, Nash equilibria in noncooperative games, and vector optimization problems, for instance, as particular cases. We show that such problems are particular instances of convex feasibility problems with infinitely many convex sets, but with additional structure, so that projection algorithms for convex feasibility can be modified in order to improve their convergence properties, mainly achieving global convergence without either compactness or coercivity assumptions. We present a sequential projections algorithm with an approximately most violated constraint control strategy, and two variants where exact orthogonal projections are replaced by approximate ones, using separating hyperplanes generated by subgradients. We include full convergence analysis of these algorithms.     

Degenerate first-order inverse problems in Banach spaces

We are concerned with an inverse problem for a degenerate linear evolution equation of first-order. Both hyperbolic and parabolic cases will be considered. We indicate sufficient conditions for the existence and uniqueness of a solution. All the results can be applied to inverse problems for equations from mathematical physics. As a possible application of the abstract theorems, some examples of partial differential equations are given.     

Similarity in soft set theory

We introduce and study the concept of similarity between soft sets, which is an extension of the equality for soft set theory. We also introduce the concepts of conjunction parameter (α∧β) and disjunction parameter (α∨β) of ordered pair parameter 〈α,β〉 for soft set theory, and we investigate modified operations of soft set theory in terms of ordered parameters.     

Conservation laws for some compacton equations using the multiplier approach

This paper is an application of the variational derivative method to the derivation of the conservation laws for partial differential equations. The conservation laws for (1+1) dimensional compacton k(2,2) and compacton k(3,3) equations are studied via multiplier approach. Also the conservation laws for (2+1) dimensional compacton Zk(2,2) equation are established by first computing the multipliers.