感应电压叠加器模块对方波脉冲的响应

为了解感应电压叠加器(IVA)对馈入脉冲的响应特性,尤其对上升前沿、平顶的影响,从理论和实验两个方面对IVA模块进行了研究。介绍了IVA的工作原理,利用集总参数方法建立了相应的电路模型,通过拉普拉斯变换分析了感应电压叠加器对方波脉冲上升前沿和平顶的响应,并在一个特定的IVA模块上进行了实验研究。选择输出阻抗约1.2Ω、脉宽约1μs的脉冲形成网络作为馈源,在匹配负载上得到的波形与输入波形在幅值、上升前沿方面达到了很好的吻合,平顶出现略微的顶降,与理论预期相一致。     

低温金属抗磁演示实验

基于电磁感应定律,设计了金属跳环抗磁演示实验装置,实验可演示铜、铝、不锈钢、塑料等材料的圆环在变化螺线管磁场中因电磁感应电流而上跳的实验现象,且结合液氮低温环境演示低温下金属环的环跳,可比对两种条件下的环跳高度,拓展了电磁感应实验内容,现象直观、明显。     

Decay of correlations for the Rauzy-Veech-Zorich induction map on the space of interval exchange transformations and the central limit theorem for the Teichmüller flow on the moduli space of Abelian differentials

The aim of this paper is to prove a stretched-exponential bound for the decay of correlations for the Rauzy-Veech-Zorich induction map on the space of interval exchange transformations. A corollary is the Central Limit Theorem for the Teichmüller flow on the moduli space of abelian differentials with prescribed singularities.

     

Analytical Solutions of Electromagnetic Fields from Current Dipole Moment on Spherical Conductor in a Low-Frequency Approximation

We analytically derive the solutions for electromagnetic fields of electric current dipole moment, which is placed in the exterior of the spherical homogeneous conductor, and is pointed along the radial direction. The dipole moment is driven in the low frequency f = 1 kHz and high frequency f = 1 GHz regimes. The electrical properties of the conductor are appropriately chosen in each frequency. Electromagnetic fields are rigorously formulated at an arbitrary point in a spherical geometry, in which the magnetic vector potential is straightforwardly given by the Biot- Savart formula, and the scalar potential is expanded with the Legendre polynomials, taking into account the appropriate boundary conditions at the spherical surface of the conductor. The induced electric fields are numerically calculated along the several paths in the low and high frequeny excitation. The self-consistent solutions obtained in this work will be of much importance in a wide region of electromagnetic induction problems.     

Small data solutions of 2-D quasilinear wave equations under null conditions

2 Abstract For the 2-D quasilinear wave equation(?_t~2-?_x)u+2∑ij=0g~(ij)(?u)?_(ij)u = 0 satisfying i,j=0 null condition or both null conditions, a blowup or global existence result has been shown by Alinhac. In this paper, we consider a more general 2-D quasilinear wave equation(?_t~2-?_x)_u+2∑ij=0g~(ij)(?u)?_(ij)u = 0 satisfying null conditions with small initial data and the coefficients i,j=0 depending simultaneously on u and ?u. Through construction of an approximate solution,combined with weighted energy integral method, a quasi-global or global existence solution are established by continuous induction.     

Blow-up of solutions to a parabolic system with nonlocal source

This paper deals with a parabolic system with different diffusion coefficients and coupled nonlocal sources, subject to homogeneous Dirichlet boundary conditions. The conditions on global existence, simultaneous or non-simultaneous blow-up, blow-up set, uniform blow-up profiles and boundary layer are got using comparison principle and asymptotic analysis methods.     

Quasi-linear PDEs and forward–backward stochastic differential equations: Weak solutions

In this paper, we study the existence, uniqueness and the probabilistic representation of the weak solutions of quasi-linear parabolic and elliptic partial differential equations (PDEs) in the Sobolev space $H_{\rho }^1({\mathbb{R}}^d)$. For this, we study first the solutions of forward–backward stochastic differential equations (FBSDEs) with smooth coefficients, regularity of solutions and their connection with classical solutions of quasi-linear parabolic PDEs. Then using the approximation procedure, we establish their convergence in the Sobolev space to the solutions of the FBSDES in the space $L_{\rho }^2({\mathbb{R}}^d;{\mathbb{R}}^d)?L_{\rho }^2({\mathbb{R}}^d;{\mathbb{R}}^k)?L_{\rho }^2({\mathbb{R}}^d;{\mathbb{R}}^{k\times d})$. This gives a connection with the weak solutions of quasi-linear parabolic PDEs. Finally, we study the unique weak solutions of quasi-linear elliptic PDEs using the solutions of the FBSDEs on infinite horizon.     

Extremal graphs for the k‐flower

The Turán number of a graph H, , is the maximum number of edges in any graph of order n that does not contain an H as a subgraph. A graph on vertices consisting of k triangles that intersect in exactly one common vertex is called a k‐fan, and a graph consisting of k cycles that intersect in exactly one common vertex is called a k‐flower. In this article, we determine the Turán number of any k‐flower containing at least one odd cycle and characterize all extremal graphs provided n is sufficiently large. Erdős, Füredi, Gould, and Gunderson determined the Turán number for the k‐fan. Our result is a generalization of their result. The addition aim of this article is to draw attention to a powerful tool, the so‐called progressive induction lemma of Simonovits.     

Some Mixed Problems for Semilinear Parabolic type Equation

In this paper, some mixed problem with third type boundary value for a semilinear parabolic equation is investigated. Here the solvability theorems for considered problem and the uniqueness theorem for a model case of the problem are showed.     

Existence of Solutions for a Parabolic System Modelling Chemotaxis with Memory Term

In this paper, we come up with a parabolic system modelling chemotaxis with memory term, and establish the local existence and uniqueness of weak solutions. The main methods we use are the fixed point theorem and semigroup theory.