Majorana zero modes induced by skyrmion lattice

One-dimensional s-wave superconductor with spin-orbit coupling is a platform for the realization of Majorana zero modes. The spin-exchange with the magnetic skyrmion lattice can induce spin-orbit coupling in a s-wave superconductor system and the effects are different from the constant spin-orbit coupling. The strength of the effective spin-orbit coupling as well as the rich topoloigcal phase diagram are directly connected to the radius of the skyrmion lattice R. We obtain the rich topological phase diagram of this system with different skyrmion lattice radii by numerically evaluating the spectrum of the system under the periodic boundary condition, and we also find the Majorana zero modes under the open boundary condition to verify the bulk-edge correspondence.     

ENTROPIC CONTRIBUTION TO THE INTERACTION PARAMETER xIN THE POLYMER／OLIGOMER SYSTEM： A LATTICE CLUSTER THEORY CONSIDERATION

Entropic contribution to the interaction parameter xeff in the model incompressible polymer/oligomer system is calculated by the lattice cluster theory (LCT). It is found that in the oligomer solvent, there exists a wide concentration range that the non-combinatorial “entropic interaction” term xeff φ1φ2 perceptibly counteracts the mean field combinary entropy ΔSMF. With the increase of the solvent size, both xeff and the ratio xefc φ1φ2/ΔSMF first reach their maximum and finally become trivially to zero. It is worth noting that no any demixing was found in the current calculation. This makes the controversial idea “entropically driven demixing” even elusive. However, we propose that further work on compressible polymer solution with structured monomer will witness the demixing owning to an increased configurational correlation.     

几类特定边界值条件下的常微分方程特征值问题

在文献[1]的基础上,借助于图形分析方法,讨论了几类特定边界值条件下的特征值问题.同时,本文对文献[1]中的错误结论作出了更正.本文给出的方法对讨论非线性边值问题的可解性提供了一种新的途径.     

动脉中血液脉动流的一种分析方法

动脉中的血液流动被分解为平衡状态(相当于平均压定常流状态)和叠加在平衡状态上的周期脉动流,利用Fung的血管应变能密度函数分析血管壁在平衡状态下的应力-应变关系,确定相对于平衡状态血管作微小变形所对应的周向弹性模量和轴向弹性模量,并建立在脉动压力作用下相应的管壁运动方程,与线性化Navier-Stokes方程联立,求得血液流动速度和血管壁位移的分析表达式,详细讨论血管壁周向和轴向弹性性质差异对脉博波、血液脉动流特性以及血管壁运动的影响.     

The Zero Divisor Graphs of Commutative Local Rings of Order p 4 and p 5

To each commutative ring R we can associate a zero divisor graph whose vertices are the zero divisors of R and such that two vertices are adjacent if their product is zero. Detecting isomorphisms among zero divisor graphs can be reduced to the problem of computing the classes of R under a suitable semigroup congruence. Presently, we introduce a strategy for computing this quotient for local rings using knowledge about a generating set for the maximal ideal. As an example, we then compute Γ(R) for several classes of rings; with the results in [4 Bloomfield , N. , Wickham , C. ( 2010 ). Local rings with genus 2 zero divisor graph . Comm. Alg. 38 ( 8 ): 2965 – 2980 .[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]] these classes include all local rings of order p ⁴ and p ⁵ for prime p.     

Stochastic calculus for Markov processes associated with non-symmetric Dirichlet forms

Nakao’s stochastic integrals for continuous additive functionals of zero energy are extended from the symmetric Dirichlet forms setting to the non-symmetric Dirichlet forms setting.It? ’s formula in terms of the extended stochastic integrals is obtained.     

The Qualitative Study of Space Quadratic Systems with a First Integral

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Classification of Homomorphisms from C (X) to Simple C*-Algebras of Real Rank Zero

Abstract Let A be a unital simple C*-algebra of real zero, stable rank one, with weakly unperforated K ₀₍ A) and unique normalized quasi-trace τ, and let X be a compact metric space. We show that two monomorphisms φ, ψ : C(X)→A are approximately unitarily equivalent if and only if φ and ψ induce the same element in KL(C(X), A) and the two lineal functionals τ∘φ and τ∘ψ are equal. We also show that, with an injectivity condition, an almost multiplicative morphism from C(X) into A with vanishing KK-obstacle is close to a homomorphism. Research partially supported by NSF Grants DMS 93-01082 (H.L) and DMS-9401515(G.G). This work was reported by the first named author at West Coast Operator Algebras Seminar (Sept. 1995, Eugene, Oregon)