一元二次方程的根的判别式的应用

一元二次方程的根的判别式是初中代数的重要内容之一 ,它在中学数学中有着广泛的应用 ,成为近几年全国各地中考的热点问题 .为了帮助读者更好地掌握好这部分知识内容 ,现对它在初中数学中的应用进行归纳 ,以餮读者 .应用一 :判断一元二次方程 (或二元二次方程组 )的根的情况 ;或已知根的情况 ,求方程 (或组 )中的待定系数的取值范围 .一元二次方程ａｘ2 +ｂｘ +ｃ =0 (ａ≠ 0 )的根的判别式为△ =ｂ2 - 4ａｃ,它与这个方程的根有着十分密切的关系 :( 1)△ >0 方程有两个不等的实数根 ;( 2 )△ =0 方程有两个相等的实数根 .( 3)△ <0 方程…     

纯正的群的正则带的构造

本文研究纯正的群的正则带.在给出这类半群的若干特征后,建立了纯正的群的正则带的构造定理.作为应用,同时给出了纯正的群的右拟正规带的构造定理.     

图的邻域复形的同调群的不变性

本文研究了图的邻域复形同调群的不变性质。设G是一个简单连通图,x是G的一个顶点,以G/x表示G中剔去点v及其关联边而得到的图,给出了G和G/x的邻域复形的同阶同调群同构的充要条件。     

乘方的指数与其幂的位数的关系

为了探究乘方的指数与其幂的位数的关系,定义了几个有关的新概念,并且证明了两个关于乘方以及进制进位的定理,由此建立起关于乘方以及进制进位的理论体系,其中包括进位理论中判定乘方的指数与其幂的位数是否存在周期规律的判别法,以及进位规律的求解法和四条相关的性质.     

多项式的根的一个性质的判定

文献[1]在讨论多项式型的函数迭代方程的局部解析解的存在性时涉及到了多项式的根的一个性质.本文给出了判定该性质是否成立的一个简洁的条件,证明了多项式λ_nzⁿ+…+λ₂z²+λ₁z+λ₀有一个根α满足inf{｜λ_nα^nm+…+λ₂a^2m+λ₁α^m+λ₀｜：m=2,3,…｝>0当且仅当如下两个条件之中至少有一个成立：(i)该多项式有一个根β满足｜β｜>1;(ii)该多项式有一个根β满足｜β｜<1,且λ₀≠0.     

中心对称的多边形的外接圆周上点的性质

笔者发现中心对称的多边形的外接圆周上的点具有性质：中心对称的多边形每组对边上关于它的外接圆心的对称点将各边分为成比例线段,则此圆周上任意点到各个对称点的距离的平方和为定值,即有如下命题。     

算术课的开始的组织

每堂课的开始的合理组织,使很多教师感到困难,而且不仅是初教书的教师而已.每堂课的开始是由下列因素组成的:1. 家庭作业的检查.2. 能达到各种目的的口算作业.3. 为准备学习新教材和巩固旧教材的复习提问.4. 为了检查独立完成家庭作业的简短书     

二面角的平面角的研究

<正>学习立体几何对培养同学们的逻辑思维能力和空间想象力有着不可替代的作用.然而在学习过程中,包括笔者在内的很多同学对二面角的平面角概念有些模糊,除了二面角的平面角唯一性之外,最值性也是它被用来度量二面角的重要原因.本文将使用数形结合的方法探讨二面角的平面角的最值性.我们在已知二面角的棱上取一点,过这一点在两个半平面上各引一条射线,它们的夹角     

Toeplitz算子的谱的某些子集的连续性

本文研究了Hilbert空间上有界线性算子的谱的某些子集的连续性,利用算子谱的精密结构的分析方法,给出了Hilbert空间H上有界线性算子T的谱σ(T)的某些子集如Φn(T),Φ(T),Φ+(T),Φ-(T),σ0p(T)等连续的充要条件.特别在Hardy空间H2(Γ)上,研究了Toeplitz算子Tφ的谱σ(Tφ)的某些子集的连续性.     

关于子空间的和的推广的注记

对向量空间的子空间的和的概念不能推广到无限多个子空间的情形进行了讨论.     

Systems of generalized quasivariational inclusions problems with applications to variational analysis and optimization problems

In this paper, we study an existence theorem of systems of generalized quasivariational inclusions problem. By this result, we establish the existence theorems of solutions of systems of generalized equations, systems of generalized vector quasiequilibrium problem, collective variational fixed point, systems of generalized quasiloose saddle point, systems of minimax theorem, mathematical program with systems of variational inclusions constraints, mathematical program with systems of equilibrium constraints and systems of bilevel problem and semi-infinite problem with systems of equilibrium problem constraints. This research was supported by the National Science Council of the Republic of China.     

复杂系统的一般数学框架(Ⅰ)

复杂系统的基本和最简单的结构就是网络.根据这一思想,本系列论文拟发展一套处理复杂系统的新数学框架.本文详细论述了系统的概念、一般描述方法:系统=(硬部,软部,环境)和局整关系,包括子系统、元素与系统的关系和系统与系统的关系;给出了系统运算的基本法则;简要论述了系统的软、硬部之间的诱导转化.     

A unified theory for coherent systems in reliability part III: Two special cases for multinary systems—binary-type coherence and homogeneous coherence

As shown in a companion-paper,¹ binary and multinary coherent systems can be studied with unified arguments, through monotone binary coherent systems. These are binary coherent systems submitted to some monotone constraint and generalize the classic theory of free binary coherent systems. By considering the unified point of view thus obtained, this paper gives what is perhaps the most suggestive representation for multinary coherent systems, since this extends the definition of binary coherent systems in terms of series-parallel (parallel-series) structures. Then, this paper examines the special case of multinary systems that can be studied directly with the classic theory of free binary coherent systems. It thus enlarges and complements, in a shorter unified manner, the particular cases considered in earlier studies.     

Sensitivity of non-autonomous discrete dynamical systems

In this paper, the sensitivity for non-autonomous discrete systems is investigated. First of all, two sufficient conditions of sensitivity for general non-autonomous dynamical systems are presented. At the same time, one stronger form of sensitivity, that is, cofinite sensitivity, is introduced for non-autonomous systems. Two sufficient conditions of cofinite sensitivity for general non-autonomous dynamical systems are presented. We generalized the result of sensitivity and strong sensitivity for autonomous discrete systems to general non-autonomous discrete systems, and the conditions in this paper are weaker than the correlated conditions of autonomous discrete systems.     

Nonsymmetric systems on nonsmooth planar domains

We study boundary value problems, in the sense of Dahlberg, for second order constant coefficient strongly elliptic systems. In this class are systems without a variational formulation, viz. the nonsymmetric systems. Various similarities and differences between this subclass and the symmetrizable systems are examined in nonsmooth domains.

     

Linear stationary control systems over a Boolean semiring: Geometric properties and the isomorphism problem

In the present paper, we consider linear stationary dynamical systems over a Boolean semiring B. We analyze the complete observability, identifiability, reachability, and controllability of such systems. We define the notion of a “graph of modules” of completely controllable, completely reachable Boolean linear stationary systems by analogy with the spaces of modules in the case of systems over fields. We give a graph-theoretic interpretation of systems of this class. We solve the isomorphism problem in this class of systems.     

复杂系统的泛系聚类方法

本文利用半等价算子ε_i和相等化算子δ_i研究了复杂系统的聚类问题;阐述了分析运筹复杂系统的δ(1,3)解耦原理、对偶转化原理和大系统分解原理;详细讨论了复杂系统的连通性与解耦性并提供了有关定理.最后,利用泛系聚类方法讨论了复杂系统的层次分析.     

若干类时滞切换系统的稳定性问题

主要研究了镇定切换系统的鲁棒稳定性问题.用切换lyapunov函数方法,通过定义指标函数,讨论了基于切换lyapunov函数的若干类时滞切换系统的稳定性问题,用矩阵不等式研究了时滞,时滞摄动和不确定时滞的切换系统的鲁棒稳定性.     

Distribution semigroups and control systems

We introduce the new concept of a distributional control system. This class of systems is the natural generalization of distribution semigroups to input/state/output systems. We showthat, under the Laplace transform, this new class of systems is equivalent to the class of distributional resolvent linear systems which we introduced in an earlier article. There we showed that this latter class of systems is the correct abstract setting in which to study many non-well-posed control systems such as the heat equation with Dirichlet control and Neumann observation. In this article we further show that any holomorphic function defined and polynomially bounded on some right half-plane can be realized as the transfer function of some exponentially bounded distributional resolvent linear system.     

A theory for synchronization of dynamical systems

In this paper, a theory for synchronization of multiple dynamical systems under specific constraints is developed from a theory of discontinuous dynamical systems. The concepts on synchronization of two or more dynamical systems to specific constraints are presented. The synchronization, desynchronization and penetration of multiple dynamical systems to multiple specified constraints are discussed, and the necessary and sufficient conditions for such synchronicity are developed. The synchronicity of two dynamical systems to a single specific constraint and to multiple specific constraints is investigated. Finally, the synchronization and the corresponding complexity for multiple slave systems with multiple master systems are discussed briefly. The meaning of synchronization for dynamical systems with constraints is extended as a generalized, universal concept. The theory presented in this paper may be as a universal theory for dynamical systems. The paper provides a theoretic frame work in order to control slave systems which can be synchronized with master systems through specific constraints in a general sense.