由偏序关系的可达阵导出Hasse图的有效算法——兼谈其在认知诊断中的作用

假设0-1矩阵Q的行表示属性,对矩阵Q采用行逐对比较方法导出表示属性层级关系的Hasse图.然而,这个Hasse图和由可达矩阵R导出的Hasse图可能不一致.证明了包含R的Q阵的行逐对比较的方法与R导出的Hasse图是一致的,由此得出由偏序关系的可达矩阵导出Hasse图的一个有效算法,并讨论其在认知诊断中的应用.     

On the validity of planar, thick curved beam models derived with respect to centroidal and neutral axes

Most dynamic analyses of planar curved beams found in the literature are carried out based on a curved beam model which assumes that the neutral axis coincides with the centroidal axis of the curved beam. This assumption leads to governing equations of motion which are relatively simple with analysis results that have acceptable accuracy for shallow curved beams. However, when a curved beam is not shallow and/or its cross section is not doubly symmetric, the offset distance between the neutral and centroidal axes may be large enough to influence the in-plane dynamics of the curved beam even for small motion. In this paper, the validity of this underlying assumption for modeling a linear curved beam is examined. To this end, two sets of equations of motion governing the in-plane dynamics of a planar curved beam are derived, in a consistent manner for comparison, based on the linear strain-displacement relations and Hamilton’s principle. The first set of equations is derived from the displacement components measured with reference to the neutral axis of the curved beam while the second set is derived with respect to the centroidal axis of the cross section. The curved beam is considered extensional and the effects of rotary inertia and radial shear deformation are included. In addition to the curvature parameter that characterizes the wave motion for both curved beam models, an eccentricity parameter is introduced in the first model to account for the offset between the neutral and centroidal axes. The dynamic behavior predicted by each curved beam model is compared in terms of the dispersion relations, frequency spectra, cutoff frequencies, natural frequencies and modeshapes, and frequency responses. In order to ensure that the comparison is accurate, the wave propagation technique is applied to obtain exact wave solutions. It is shown that, when the curvature parameter is not small, the underlying assumption has a substantial impact on the accuracy of the linear dynamic analysis of a curved beam.     

SHEAR-HORIZONTAL WAVES IN A ROTATED Y-CUT QUARTZ PLATE WITH AN ISOTROPIC ELASTIC LAYER OF FINITE THICKNESS

We study shear-horizontal (SH) waves in a rotated Y-cut quartz plate carrying an isotropic elastic layer of finite thickness.The three-dimensional theories of anisotropic elasticity and isotropic elast...     

Sign or root of unity ambiguities of certain Gauss sums

Gauss sums play an important role in number theory and arithmetic geometry. The main objects of study in this paper are Gauss sums over the finite field with q elements. Recently, the problem of explicit evaluation of Gauss sums in the small index case has been studied in several papers. In the process of the evaluation, it is realized that a sign (or a root of unity) ambiguity unavoidably occurs. These papers determined the ambiguities by the congruences modulo L, where L is certain divisor of the order of Gauss sum. However, such method is unavailable in some situations. This paper presents a new method to determine the sign (root of unity) ambiguities of Gauss sums in the index 2 case and index 4 case, which is not only suitable for all the situations with q being odd, but also comparatively more efficient and uniform than the previous method.     

Fluctuation relations for heat exchange in the generalized Gibbs ensemble

In this work, we investigate the heat exchange between two quantum systems whose initial equilibrium states are described by the generalized Gibbs ensemble. First, we generalize the fluctuation relations for heat exchange discovered by Jarzynski and Wójcik to quantum systems prepared in the equilibrium states described by the generalized Gibbs ensemble at various generalized temperatures. Secondly, we extend the connections between heat exchange and the Rényi divergences to quantum systems under generic initial conditions. These relations are applicable for quantum systems with conserved quantities and universally valid for quantum systems in the integrable and chaotic regimes.     

Solution of Spin and Pseudo-Spin Symmetric Dirac Equation in (1+1) Space-Time Using Tridiagonal Representation Approach

The aim of this work is to find exact solutions of the Dirac equation in(1+1) space-time beyond the already known class.We consider exact spin(and pseudo-spin) symmetric Dirac equations where the scalar potential is equal to plus(and minus) the vector potential.We also include pseudo-scalar potentials in the interaction.The spinor wavefunction is written as a bounded sum in a complete set of square integrable basis,which is chosen such that the matrix representation of the Dirac wave operator is tridiagonal and symmetric.This makes the matrix wave equation a symmetric three-term recursion relation for the expansion coefficients of the wavefunction.We solve the recursion relation exactly in terms of orthogonal polynomials and obtain the state functions and corresponding relativistic energy spectrum and phase shift.     

On the Generalized Heisenberg Supermagnetic Model

In this paper, we construct the generalized Heisenberg supermagnetic models with two different constraints and investigate the integrability of the super integrable systems. By virtue of the gauge transformation, their corresponding gauge equivalent counterparts are derived, i.e., the super and fermionic mixed derivative nonlinear Schrödinger equations, respectively.     

构性理论:对设计的建构

 对设计科学的讨论首先应当探究设计的本质。本文以构性理论为基础探索设计,认为构性理论的提出是由于事物本身存在的方式,提出了构性理论的基本概念,并基于此对设计中的相关概念进行了重新定义;探究了设计本质,建立了设计驱动-设计蕴含-设计匹配的设计过程模型（AIM模型）,即通过设计驱动获得需求、问题、目的3种形式的构性关系来源,通过设计蕴含得到构性关系模式,通过设计匹配得到具体的构性关系,再通过子AIM模型进一步完善。最后通过空轨列车逃生问题设计事例验证了构性理论的有效性,从而奠定了构性理论的思想和概念基础,建立了设计过程模型,为设计本质和设计科学的探究提供了新的观点和思路。     

四色猜想的解析论证及其在地图绘制中的应用

依据欧拉定理,研究了边数差和着色数计算公式,对四色猜想进行了研究．借助四面体顶点数与面积数相等的原则、多面体边数不变的原则和多余理论,用边数差数学计算方法论证了四色猜想．用简单的数学公式和几何作图方法说明了四色猜想的合理性,为其提供了可靠的理论依据．用“三色包点”和“以面切体”的几何作图法,证明多面体和平面地图的着色数恒为4;非三色包点的图形,可以通过“以面切体”的方法转换成三色包点的图形;使用多余国家、多余边数的数学技巧代替计算机使用的不可避免性、可约性是合适的．理论分析及实例论证表明该方法简单可行．