On the Relative Twist Formula of l-adic Sheaves

We propose a conjecture on the relative twist formula of l-adic sheaves, which can be viewed as a generalization of Kato—Saito's conjecture. We verify this conjecture under some transversal assumptions. We also define a relative cohomological characteristic class and prove that its formation is compatible with proper push-forward. A conjectural relation is also given between the relative twist formula and the relative cohomological characteristic class.     

On the Brauer p-dimension of Henselian discrete valued fields of residual characteristic p > 0

Let $(K,v)$ be a Henselian discrete valued field with residue field $\stackrel{?}{K}$ of characteristic $p>0$, and ${\text{Brd}}_p(K)$ be the Brauer p-dimension of K. This paper shows that ${\text{Brd}}_p(K)\ge n$ if $[\stackrel{?}{K}:{\stackrel{?}{K}}^p]=p^n$, for some $n\in \mathbb{N}$. It proves that ${\text{Brd}}_p(K)=\infty$ if and only if $[\stackrel{?}{K}:{\stackrel{?}{K}}^p]=\infty$.     

3d过渡金属掺杂M_2@Si_(20)(M=Sc-Zn)团簇的密度泛函理论研究

利用密度泛函理论(DFT)研究3d过渡金属掺杂硅团簇的几何结构和稳定性,计算了绝热电子亲和能和垂直电离能,内嵌双金属间距,自旋磁矩等.结果表明内嵌的Sc、Ti、V、Mn金属二聚体和十二面体硅笼构成了稳定的富勒烯结构,随着d电子数目的增加其内嵌的富勒烯构型有部分畸变,总体而言Si_(20)团簇掺杂双金属后稳定性得到了提高.     

Potts models with magnetic field: Arithmetic,geometry, and computation

We give a sheaf theoretic interpretation of Potts models with external magnetic field, in terms of constructible sheaves and their Euler characteristics. We show that the polynomial countability question for the hypersurfaces defined by the vanishing of the partition function is affected by changes in the magnetic field: elementary examples suffice to see non-polynomially countable cases that become polynomially countable after a perturbation of the magnetic field. The same recursive formula for the Grothendieck classes, under edge-doubling operations, holds as in the case without magnetic field, but the closed formulae for specific examples like banana graphs differ in the presence of magnetic field. We give examples of computation of the Euler characteristic with compact support, for the set of real zeros, and find a similar exponential growth with the size of the graph. This can be viewed as a measure of topological and algorithmic complexity. We also consider the computational complexity question for evaluations of the polynomial, and show both tractable and NP-hard examples, using dynamic programming.     

Invariant discrete flows

In this paper, we investigate the evolution of joint invariants under invariant geometric flows using the theory of equivariant moving frames and the induced invariant discrete variational complex. For certain arc length preserving planar curve flows invariant under the special Euclidean group , the special linear group , and the semidirect group , we find that the induced evolution of the discrete curvature satisfies the differential‐difference mKdV, KdV, and Burgers' equations, respectively. These three equations are completely integrable, and we show that a recursion operator can be constructed by precomposing the characteristic operator of the curvature by a certain invariant difference operator. Finally, we derive the constraint for the integrability of the discrete curvature evolution to lift to the evolution of the discrete curve itself.     

A survey of surface tension,molar volume and density for Sn–Ag–Cu–Bi–Sb quinary alloys as lead-free solders

ABSTRACT

By applying the geometric models and the theoretical equation, the surface tension, the molar volume and the density were studied. The empirical calculations were carried out in temperature range 623?K?≤?T?≤?1123?K. Only few thermophysical properties were estimated for eight quinary alloys: Sn3.55Ag0.5Cu3Bi3Sb, Sn3.48Ag0.5Cu3Bi5Sb, Sn3.48 Ag0.5Cu5Bi3Sb, Sn3.40 Ag0.5Cu5Bi5Sb, Sn3.53Ag1Cu3Bi3Sb, Sn3.46Ag1Cu3Bi5Sb, Sn3.46Ag1Cu5Bi3Sb, Sn3.38Ag1Cu5Bi5Sb. The results show that surface tension and density have a linear appearance for all temperatures. We have also studied the influence of the composition and temperature in the studied alloys. The obtained theoretical results are compared with the experimental ones and with the conventional Pb–Sn welds.     

n-In0.35Ga0.65N/p-Si异质结的制备及其电学性能研究

采用双光路双靶材脉冲激光沉积(PLD)系统在p-Si衬底上外延生长InGaN薄膜,研究了InGaN薄膜的显微组织结构和n-InGaN/p-Si异质结的电学性能。研究表明,InGaN薄膜为单晶结构,沿[0001]方向择优生长,薄膜表面光滑致密,In的原子含量为35%。霍尔(Hall)效应测试表明In_0.35Ga_0.65N薄膜呈n型半导体特性,具有高的载流子浓度和迁移率及低的电阻率。I-V曲线分析表明In_0.35Ga_0.65N/p-Si异质结具有良好的整流特性,在±4 V时的整流比为25,开路电压为1.32 V。In_0.35Ga_0.65N/p-Si异质结中存在热辅助载流子隧穿和复合隧穿两种电流传输机制。经拟合,得到异质结的反向饱和电流为1.05×10^-8 A,势垒高度为0.86 eV,理想因子为6.87。     

基于图像的二维剪纸自动生成方法

中国剪纸的设计极具挑战性, 要求画面简洁、直观, 还需要表达特定的文化内涵, 且整张剪纸须整体连通。提出了一种基于图像的二维剪纸自动生成方法, 能够将任意数码照片自动转化为剪纸图形。首先，利用图像分割方法建立区域连接图; 接着, 基于该连接图对颜色、边界对比度和区域连通性进行数学建模, 并获得优化目标函数; 最后, 通过模拟退火算法求解目标方程, 自动生成保持图像内容的剪纸图形。还开发了连通性后处理和区域指定等用户交互工具, 允许用户在自动生成的剪纸图形中方便地加入个人设计。实验表明, 所生成的剪纸图形画面简洁、整体连通。 本方法在降低剪纸设计难度的同时还可满足个性化的设计需求, 有助于传播和传承我国的民间剪纸艺术。