Integrable symplectic maps associated with discrete Korteweg‐de Vries‐type equations

In this paper, we present novel integrable symplectic maps, associated with ordinary difference equations, and show how they determine, in a remarkably diverse manner, the integrability, including Lax pairs and the explicit solutions, for integrable partial difference equations which are the discrete counterparts of integrable partial differential equations of Korteweg‐de Vries‐type (KdV‐type). As a consequence it is demonstrated that several distinct Hamiltonian systems lead to one and the same difference equation by means of the Liouville integrability framework. Thus, these integrable symplectic maps may provide an efficient tool for characterizing, and determining the integrability of, partial difference equations.     

Backward transfer influences from quadratic functions instruction on students’ prior ways of covariational reasoning about linear functions

The study reported in this article examined the ways in which new mathematics learning influences students’ prior ways of reasoning. We conceptualize this kind of influence as a form of transfer of learning called backward transfer. The focus of our study was on students’ covariational reasoning about linear functions before and after they participated in a multi-lesson instructional unit on quadratic functions. The subjects were 57 students from two authentic algebra classrooms at two local high schools. Qualitative analysis suggested that quadratic functions instruction did influence students’ covariational reasoning in terms of the number of quantities and the level of covariational reasoning they reasoned with. These results further the field’s understanding of backward transfer and could inform how to better support students’ abilities to engage in covariational reasoning.     

A new result on irreducible NFSRs with respect to cascade connection

Nonlinear feedback shift registers (NFSRs) are widely used in stream cipher design as building blocks. The cascade connection of NFSRs, known as an important architecture, has been adopted in Grain family of stream ciphers. In this paper, a new sufficient condition under which an NFSR cannot be decomposed into the cascade connection of two smaller NFSRs is presented, which is easy to be verified from the algebraic normal form (ANF) of the characteristic function. In fact, our results are also applicable to nonsingular Boolean functions, which actually improve a previous research of Rhodes [6] where the characteristic functions of NFSRs cannot be contained.     

Thermodynamics of substituted coumarin VII: Potentiometric and spectrophotometric studies of 1-acetyl-2-(coumarin-iminecarboxamide-3-yl) hydrazine transition metal complexes

The dissociation constant of l-acetyl-2-(coumariniminecarboxamide-3-yl) hydrazine (ACCH) has been determined potentiometrically in 0.1 M KC1 and 40% (v/v) ethanol-water mixture. The stepwise stability constants of the formed complexes of Mn²⁺, Co²⁺, Ni²⁺, Cu²⁺, Zn²⁺ and UO₂ ²⁺ with ACCH have been determined. The stability constants were found to UO₂ ²⁺ > Cu²⁺> Zn²⁺ > Ni²⁺ < CO²⁺ < Mn²⁺. The effect of temperature on the dissociation of ACCH and the stability of its formed complexes were studied. The corresponding thermodynamic functions were also determined and discussed. The spectral data of ACCH were investigated in pure organic solvents as well as in Britton Robinson buffer solutions of varying pH values. The dissociation constant pK^H ₁ of ACCH and the overall stability constants logβ of their complexes were determined in 20% (v/v) ethanol-water mixture at 298K.     

The thermodynamic functions and the regions of (P,T)-states of dense carbon and boron nitride modifications

Abstract

For the first time the thermodynamic functions for boron nitride and carbon were defined in the temperature range 300 to 4000K by a computational procedure which was impossible in the previous empirical approach. This involved the application of the theoretical functions from Refs. 1, 2, and 3. There the temperature dependence of the heat capacity is characterized by a sum of two Debye functions that reflect the contribution of vibration modes of different characteristic temperature to the heat capacity. The above-mentioned theoretical functions make it possible to calculate the thermodynamic function without allowing for the anharmonic effect in the temperature range rather wider th-an the one wherein the initial experiments were conducted. It is sufficient for their computation to define Debye characteristic temperatures. One of the procedures of their calculation using experimental enthalpy data is described in Ref. 4. Besides, this work contains the majority of known experimental and theoretical data which enable various methods of the thermodynamic function characterizations for carbon and boron nitride to be compared.     

全球治理困境与国家“再现”的最终逻辑

在全球治理危机频现和大国战略竞争加剧的背景下,“国家中心主义”回归引发了人们对经济全球化走势的担忧。本轮国家中心主义回归的逻辑是：此前自由主义全球化的过度发展导致国家功能隐退;而当全球治理状况恶化时,国家的重要性再度凸现,成为各国社会谋求自我体系安全的唯一“阀门”,民族主义、保护主义思潮亦大行其道。从中期看,未来的全球体系重建过程将充满国家中心主义与自由主义两种理性的持续角力,国家与市场的作用都将在“拉锯战”相互影响与重塑。从远期看,新型全球化将是国家与市场关系再平衡的产物,国家仍是兼具服务本民族发展及其外部性的主要工具。国家处理内外发展与治理多重挑战的“灵活度”即为评判其核心竞争力的最终标准。     

平面八节点四边形理性元

推导平面八节点四边形理性有限元列式,采用具有直到四次多项式的平面问题的微分方程的解作为插值函数,算例结果表明平面八节点四边形理性有限元的有效性.     

函数列的黎曼积分极限定理的应用

利用函数列的极限理论方法,研究函数列积分极限中积分和极限可交换次序的问题.对一致收敛的可积函数列给出积分的极限定理,对一致有界局部一致收敛函数列给出积分控制收敛定理,通过大量实例表明该理论的意义所在.     

由正交表变换得到的2阶平衡的相关免疫函数

本本文给出了一种运用正交表变换来得到2阶相关免疫函数的特征矩阵的新方法,构造出10个不同的(8,4,2,2)特征矩阵,得到了几个相关结论。