Solution Transformations and Their Effects on the Systems with Open Boundary Conditions

The solution transformations and properties of the R-matrices for two-component systems under these transformations are analyzed in details.Not all transformed R-matrices can be put into the Skalyanin‘s formalism.For those R-matrices with all required properties,the effects of solution transformations to the six-and eight-vertex systems with open boundary conditions are discussed.these effects can be one of the following types:the Hamiltonian is invariant or transposition-invariant or made in a similarity transformation,or its coupling coefficients are multiplied by an overall factor,or the spin of the system is rotated around the z axis or/and reflected with respect to some plane.In these cases,the transformed systems remain to be integrable.     

Indecomposable involutive set-theoretic solutions of the Yang–Baxter equation

We describe the indecomposable involutive non-degenerate set-theoretic solutions of the Yang–Baxter equation as dynamical extensions of non-degenerate left cycle sets. Moreover we characterize the indecomposable dynamical extensions and we produce several examples. As an application we construct a family of finite indecomposable solutions whose structure groups have not the unique product property.     

利用杨辉三角形对称性推导高阶运动微分方程

利用Mathematica数学软件计算函数r=r(q(t),t)各变量之间偏导和高阶导数的关系，发现具有杨辉三角形对称性.结合杨辉三角形的对称性规律和牛顿第二定律推导出了高阶运动微分方程，并讨论了理想约束系统下的高阶运动微分方程. 关键词： 杨辉三角形 牛顿第二定律 高阶运动微分方程 高阶力变率 高阶速度能量 理想约束     

Inverse Scattering Problem for the Schrödinger Operator with External Yang–Mills Potentials in Two Dimensions at Fixed Energy

ABSTRACT

We consider the Schrödinger equation in ?², with external Yang–Mills potentials that decay exponentially as |x| → ∞. We prove that the scattering amplitude at fixed positive energy determines the potentials uniquely modulo a gauge transformation, assuming that potentials are small.     

Yang index of the deleted product

For any a -dimensional polyhedron is constructed such that the Yang index of its deleted product equals . This answers a question of Izydorek and Jaworowski (1995). For any a -dimensional closed manifold with involution is constructed such that , but can be mapped into a -dimensional polyhedron without antipodal coincidence.

     

Evolutions of Yang Phase Under Cyclic Condition and Adiabatic Condition

There are three non-integrable phases in literatures： Berry phase, Aharonov-Anandan phase, and Yang phase. This article discusses the evolutions of Yang phase under the cyclic condition and the adiabatic condition for the general time-dependent harmonic oscillator, thus reveals the intimate relations between these three non-integrable phases.     

杨乐不等式的推广及加强

本文首先利用凸函数基本不等式和平均值不等式推广并加强了杨乐不等式 ,然后利用 Jensen不等式给出了两个更为广泛的结果 .     

Molecular mechanics-assisted crystal engineering of solid state photoreactions: application to the Yang photocyclization of α-1-norbornylacetophenone derivatives

Based on molecular mechanics, Yang photocyclization of α-1-norbornylacetophenone derivatives in the crystalline state was engineered through methylation adjacent to the carbonyl group, thus changing the conformation in the crystal and leading to enhanced diastereo- and enantioselectivity.     

规范场和爱因斯坦

文章讨论的主题是现代非亚贝尔规范场的理论思想．文章说明了这个理论思想是承传、推广和拓展了爱因斯坦的物理思想、目标和原则．规范场理论把爱因斯坦后半生努力奋斗而未能达到的目标提到现实，更加迫近和部分地圆了爱因斯坦的梦想。     

“碰撞-辐射”模型在Z箍缩等离子体K壳层线辐射谱分析中的应用

介绍了由K壳层谱线强度比估算等离子体状态参数的"碰撞-辐射"模型的基本原理.详细描述了自行研制的基于该模型的Z箍缩等离子体K壳层线辐射谱分析程序——ZSPEC的基本情况.给出了氖等离子体的计算结果,包括不同电离态离子的相对含量随电子温度的变化曲线和K壳层谱线强度比在"电子密度-电子温度"平面内的等高线分布图.该程序已在"阳"加速器Z箍缩实验结果分析中得到应用,将椭圆晶体谱仪测得的氖等离子体K壳层谱线强度比与ZSPEC程序计算结果相比较,得出在该发实验 关键词： 碰撞-辐射模型 K壳层线辐射谱')" href="#">K壳层线辐射谱 氖气喷气Z箍缩 阳加速器