γ-variable first-order logic of uniform attachment random graphs

We study logical limit laws for uniform attachment random graphs. In this random graph model, vertices and edges are introduced recursively: at time $n+1$, the vertex $n+1$ is introduced together with m edges joining the new vertex with m different vertices chosen uniformly at random from $1,\dots ,n$. We prove that this random graph obeys convergence law for first-order sentences with at most $m?2$ variables.     

安培环路定理的拓扑学描述

近年来拓扑学在量子力学中得到了广泛的运用.本文将安培环路定理积分式重新表达为一矢量场在轮胎参数面上的第一类陈数积分.数值模拟展示了该积分值为一整数即第一陈数,其代表矢量场的整体性质:当经历连续变换时,矢量场的局部数值发生改变但整体积分值即陈数仍保持不变;若陈数发生改变,则表明矢量场变换的连续性条件发生破坏,矢量场出现奇点.进一步通过高斯映射将该矢量场从参数轮胎面映射到单位球面上,并给出了第一陈数的直观几何意义.理论和数值结果揭示了安培环路定理的拓扑学本质,表明拓扑概念在经典物理学中也会有广泛应用.     

Sliding mode control for a diffuse interface tumor growth model coupling a Cahn–Hilliard equation with a reaction–diffusion equation

We consider the sliding mode control (SMC) problem for a diffuse interface tumor growth model coupling a Cahn–Hilliard equation with a reaction–diffusion equation perturbed by a maximal monotone nonlinearity. We prove existence and regularity of strong solutions and, under further assumptions, a uniqueness result. Then, we show that the chosen SMC law forces the system to reach within finite time a sliding manifold that we chose in order that the tumor phase remains constant in time.     

Linearized filtering of affine processes using stochastic Riccati equations

We consider an affine process $X$ which is only observed up to an additive white noise, and we ask for the law of $X_t$, for some $t>0$, conditional on all observations up to time $t$. This is a general, possibly high dimensional filtering problem which is not even locally approximately Gaussian, whence essentially only particle filtering methods remain as solution techniques. In this work we present an efficient numerical solution by introducing an approximate filter for which conditional characteristic functions can be calculated by solving a system of generalized Riccati differential equations depending on the observation and the process characteristics of $X$. The quality of the approximation can be controlled by easily observable quantities in terms of a macro location of the signal in state space. Asymptotic techniques as well as maximization techniques can be directly applied to the solutions of the Riccati equations leading to novel very tractable filtering formulas. The efficiency of the method is illustrated with numerical experiments for Cox–Ingersoll–Ross and Wishart processes, for which Gaussian approximations usually fail.     

Gauge functions and Galilean invariance of Lagrangians

A novel method to make Lagrangians Galilean invariant is developed. The method, based on null Lagrangians and their gauge functions, is used to demonstrate the Galilean invariance of the Lagrangian for Newton's law of inertia. It is suggested that this new solution of an old physics problem may have implications and potential applications to all gauge-based theories of physics.     

白色荧光粉CaF2∶Yb3+/Eu3+/La3+的制备及其上转换发光特性

采用改进的两步高温固相熔融法制备了Yb^3+、Eu^3+、La^3+共掺杂CaF 2的上转换荧光粉。基于荧光猝灭原理,通过改变La^3+掺杂浓度来调节CaF 2∶Yb^3+/Eu^3+材料的发光性能,并在980 nm近红外光激发下,获得了该材料的白色上转换发光(UCL)。在该发光体系中,Yb^3+不仅起到了敏化Eu^3+的作用,同时,Yb^3+二聚体(Yb^3+-dimer)自身合作发出波长范围480~540 nm的绿色荧光。而白光三基色中的绿光正是来自Yb^3+二聚体的合作发光。Eu^3+则作为激活剂,同时发出红色和蓝色荧光。荧光寿命测试结果表明Yb^3+-dimer与Eu^3+之间存在有效的能量传递。值得注意的是,在980 nm激光激发下,1%La^3+掺杂的样品表现出最佳的红、绿、蓝三基色光比列,实现了材料的上转换白光发射,其色度坐标为(0.311,0.340)。     

PN结物理特性的开放式测量实验方法研究

开放式、综合性量测实验的设计与应用,在巩固基础理论知识的同时,能够有效培养学生的动手实践能力、数据处理及分析能力,一定程度代表着大学物理实验课程的教学模式改革方向。以PN结物理特性的测量实验为例,基于通用型仪器与元器件的积木式组合,设计出简单、适用的实验电路;t=17.95℃时所采集的原始实验数据经三种模式回归分析,比较验证了PN结扩散电流与电压间遵循的玻尔兹曼分布律;计算出的玻尔兹曼常数与FD-PN-4测定仪的量测值相比,其结果说明了开放式测量实验方法的有效性。     

Analysis of a Cahn–Hilliard–Brinkman model for tumour growth with chemotaxis

Phase field models recently gained a lot of interest in the context of tumour growth models. Typically Darcy-type flow models are coupled to Cahn–Hilliard equations. However, often Stokes or Brinkman flows are more appropriate flow models. We introduce and mathematically analyse a new Cahn–Hilliard–Brinkman model for tumour growth allowing for chemotaxis. Outflow boundary conditions are considered in order not to influence tumour growth by artificial boundary conditions. Existence of global-in-time weak solutions is shown in a very general setting.     

Controlling the Length of Cooperative Supramolecular Polymers with Chain Cappers

The design and the characterization of supramolecular additives to control the chain length of benzene-1,3,5-tricarboxamide (BTA) cooperative supramolecular polymers under thermodynamic equilibrium is unraveled. These additives act as chain cappers of supramolecular polymers and feature one face as reactive as the BTA discotic to interact strongly with the polymer end, whereas the other face is nonreactive and therefore impedes further polymerization. Such a design requires fine tuning of the conformational preorganization of the amides and the steric hindrance of the motif. The chain cappers studied are monotopic derivatives of BTA, modified by partial N-methylation of the amides or by positioning of a bulky cyclotriveratrylene cage on one face of the BTA unit. This study not only clarifies the interplay between structural variations and supramolecular interactions, but it also highlights the necessity to combine orthogonal characterization methods, spectroscopy and light scattering, to elucidate the structures and compositions of supramolecular systems.