Finiteness of circulant weighing matrices of fixed weight

Let n be a fixed positive integer. Every circulant weighing matrix of weight n arises from what we call an irreducible orthogonal family of weight n. We show that the number of irreducible orthogonal families of weight n is finite and thus obtain a finite algorithm for classifying all circulant weighing matrices of weight n. We also show that, for every odd prime power q, there are at most finitely many proper circulant weighing matrices of weight q.     

Multiple limit cycle bifurcations of the FitzHugh–Nagumo neuronal model

In this paper, we complete the global qualitative analysis of the well-known FitzHugh–Nagumo neuronal model. In particular, studying global limit cycle bifurcations and applying the Wintner–Perko termination principle for multiple limit cycles, we prove that the corresponding dynamical system has at most two limit cycles.     

Optimal estimates of the field enhancement in presence of a bow-tie structure of perfectly conducting inclusions in two dimensions

This paper deals with the field enhancement due to insertion of a bow-tie structure of perfectly conducting inclusions into the two-dimensional space with a given field. The field enhancement is represented by the gradient blow-up of a solution to the conductivity problem. The bow-tie structure consists of two disjoint bounded domains which have corners with possibly different aperture angles. The domains are parts of cones near the vertices which are nearly touching to each other. We construct functions explicitly which characterize the field enhancement. As consequences, we derive optimal estimates of the gradient in terms of the distance between two inclusions and aperture angles of the corners. The estimates show in quantitatively precise way that the field is enhanced beyond the corner singularities due to the interaction between two inclusions, and the blow-up rate is much higher than the one for the case of inclusions with smooth boundaries.     

Singular Functions and Characterizations of Field Concentrations: a Survey

In the presence of closely located inclusions of the extreme material property, the physical fields, such as the electric field and the stress tensor, may be concentrated and arbitrarily large in the narrow region between two inclusions. Recently there has been significant progress on the quantitative characterization of the field concentration in the contexts of electrostatics(Laplace equation), linear elasticity(Lamé system), and viscous flow(Stokes system). This paper is to review such progress in a coherent way.     

Vibrational Spectra of Ethylenediamine Salts. I. Tentative Assignments of Infrared and Far Infrared Spectra

Abstract

We wish to report on some hitherto partly unnoticed and unexplained features in the infrared spectra of hydrogen halides of ethylenediamine. We have prepared normal, C-, N-, and perdeuterated ethylenediammonium chlorides and bromides and measured their infrared spectra in the range 4000–10 cm^?1.     

基于LMS自适应时延估计和FPGA的超声波测风系统研究

利用超声波传感器进行风速测量时,温度对超声波传播有很大影响,时延估计对超声波测风系统的精度起到很大的作用。本超声波测风系统为避免温度对风速测量中的影响,采用了基于时差法的测量原理,为了提高时延估计值的精度,提出了基于最小均方(LMS)自适应时延估计的测量方法,研制了以单片机Atmega128和现场可编程门阵列(FPGA)为核心的硬件系统。仿真和实际测试的结果表明,该超声波测风系统的时延估计值精确度较高,具有很高的应用价值。     

On the influence of local fluctuations in volume fraction of constituents on the effective properties of nonlinear composites. Application to porous materials

Composite materials often exhibit local fluctuations in the volume fraction of their individual constituents. This paper studies the influence of such small fluctuations on the effective properties of composites. A general asymptotic expansion of these properties in terms of powers of the amplitude of the fluctuations is given first. Then, this general result is applied to porous materials.As is well-known, the effective yield surface of ductile voided materials is accurately described by Gurson's criterion. Suitable extensions for viscoplastic solids have also been proposed. The question addressed in the present study pertains to nonuniform distributions of voids in a typical volume element or in other words to the presence of matrix-rich and pore-rich zones in the material. It is shown numerically and analytically that such deviations from a uniform distribution result in a weakening of the macroscopic carrying capacity of the material.     

Partial Orderings in the Category of Matrices over the Quaternion Field

ＰａｒｔｉａｌＯｒｄｅｒｉｎｇｓｉｎｔｈｅＣａｔｅｇｏｒｙｏｆＭａｔｒｉｃｅｓｏｖｅｒｔｈｅＱｕａｔｅｒｎｉｏｎＦｉｅｌｄＺｈｕａｎｇＷａｊｉｎ（庄瓦金）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＺｈａｎｇＮｏｒｍａｌＣｏｌｌｅｇｅ，Ｆｕｊｉ...     

MODAL ANALYSIS OF A SLOTTED WAVEGUIDE: COMPARISON BETWEEN ANALYTIC SOLUTION AND COMPUTER SIMULATIONS

Because of the complicated geometry of the slotted structure, analytical theories of such structures are inevitably developed on the basis of simplifying assumptions. On the other hand, the accuracy of the theory is of importance to the design of microwave interaction structures. In this study, modes of the slotted waveguide are investigated analytically and simulated with the HFSS code. It is shown that, in spite of the approximations made, the dispersion relation and field patterns of the standard analytical theory are in excellent agreement with the HFSS simulations over the complete range of the slot depth. Modes not built into the theory will also be noted.     

非圆截面环流器FY-1实验(Ⅰ)——被动运行部分

本文简略地描述了FY-1装置结构、等离子体基本参数的测量和等离子体位形的调试,初步考察了硬X射线产额与工作气压的关系。实验分析表明,FY-1装置已形成的等离子体环流放电属于逃逸放电。在场成形线圈作被动运行时,通过改变其回路连接方式和外串电感值,可适当调节等离子体平衡位置和位形。MHD平衡计算与实验测量拟合结果表明,等离子体截面可调节为不同截面积和拉长比(k=1.1—1.4)的椭圆。