The ascending chain condition for real ideas

If A is a ring satisfying the ascending chain condition for real ideals, then this condition is also satisfied by the polynomial ring A[X]. However, an example is given to illustrate that the condition need not to hold in the power series ring A[[X]]. It is also shown that if every real prime ideal is the real ideal generated by finitely many elements, then the ring satisfies the ascending chain condition for real ideals. So, the analogues of Hilbert basis theorem and Cohen's theorem hold for real ideals.     

Continuous optimization problems and a polynomial hierarchy of real functions

The close connection between the maximization operation and nondeterministic computation has been observed in many different forms. We examine this relationship on real functions and give a characterization of NP-time computable real functions by the maximization operation. A natural extension of NP-time computable real functions to a polynomial hierarchy of real functions has a characterization by alternating operations of maximization and minimization. Although syntactically this hierarchy of real functions can be treated as a polynomial hierarchy of operators, the well-known Baker-Gill-Solovay separation result does not apply to this hierarchy. This phenomenon is explained by the inherent structural properties of real functions, and is compared with recent studies on positive relativization.     

Closure and connected component of a planar global semianalytic set defined by analytic functions definable in o-minimal structure

We consider a global semianalytic set defined by real analytic functions definable in an o-minimal structure. When the o-minimal structure is polynomially bounded, we show that the closure of this set is a global semianalytic set defined by definable real analytic functions. We also demonstrate that a connected component of a planar global semianalytic set defined by real analytic functions definable in a substructure of the restricted analytic field is a global semianalytic set defined by definable real analytic functions.     

实循环矩阵与实对角矩阵相似问题

本文中我们证明了与实对角矩阵相似的每一个实循环矩阵都是对称的．并给出了一个正交变换，使得任意的ｎ×ｎ实循环对称矩阵通过该变换与实对角矩阵相似．     

关于实Hilbert环

通过引进“强实Hilbert环”这一概念,本文证明了,一个环A是强实Hilbert环,当且仅当多项式环A[X]是实Hilbert环,当且仅当A[X]的每个实极大理想在A上的局限是实极大的,从而文献[1]中两个主要结果被否定.此外,本文还研究了所谓的“严格的实Hilbert环”,这类环对于半代数零点定理等方面的探讨更具应用意义.     

Complexification of real cycles and the Lawson suspension theorem

The space of totally real r-cycles of a totally real projectivevariety is embedded into the space of complex r-cycles by complexification.The holomorphic taffy argument in the proof of Lawson's suspensiontheorem is proved by using Chow forms, and this proof givesan analogous result for totally real cycle spaces. The Sturmtheorem is used to derive a criterion for a real polynomialsof degree d to have d distinct real roots, and this criterionis used to prove the openness of some subsets of real divisors.This enables us to prove that the suspension map induces a weakhomotopy equivalence between two enlarged spaces of totallyreal cycle spaces.     

面向需求的房地产市场投机度界定及诱因辨析

基于理性范式,遵循消费者均衡条件,根据我国面临的局部经济过热背景,推定了房地产投机的实质是需求结构扭曲,而且经济周期影响需求结构的途径是收入和替代效应,据此并借助空间几何方向余弦概念具体界定了房地产市场投机度,进而求解了收入效应和替代效应催生地产泡沫的诱因变量,确定了引发投机度波动的诱因变量变动域,即:货币的边际效用降低率越小,投机度越高;收入增长对投机度影响具有不确定性;缩小包括房地产在内的商品价格的上升幅度、增加非地产投资收益率并稳定地产投资收益率可抑制房地产泡沫.     

A sufficient condition that a matrix have eigenvalues with non-zero real parts

If A is a complex matrix let à be the real matrix obtained by replacing the diagonal elements of A by the moduli of their real parts and by replacing the off-diagonal elements by the negative of their moduli. Then we show that if à is an M-matrix the eigenvalues of A have nonzero real parts and, moreover, the moduli of the real parts are bounded below by the minimum of the real parts of the eigenvalues of Ã.     

康托尔实数的局限性

康托尔为我们建立了集合论，并且证明了实数的不可数性，但是其中留下了很多疑点． 1．—个实数能在每—个集合论模型中出现的充分必要条件是它是可以被集合论来定义的．那些在集合论模型中不出现的实数，我们可以把他们叫做看不见的实数． 2．在实数的十进位无穷小数表示法中有些是我们能确切地知道它的第几位是什么，但是对另外的一些实数我们对它们就只能有模糊的认识，也就是说它的第几位是什么我们不可能全部知道．我们可以把他们叫做写不出的实数． 3．由于Cantor关于实数是不可数的证明不是构造性的证明，而是用所谓的归谬证法．它们中有很多是看不见写不出的实数．因此说它们是虚拟的实数． 4．虚拟实数就像银行中的虚拟货币，你可用它来买东西，它可从—个户头转拨到另—个户头，但是钱的实体是不存在的。这个现象也让我们对某些数学工具的合法性挺出质疑．我们用对角线法来证明实数的基数比自然数的基数大。但是我们并没有真正有效的地构造出那么多的实数．因此我们没有办法来确切地定义它们．也可以说它们中的绝大多数是不可以定义的．在一般的情况下虚拟实数是不可以个别地使用的．     

人民币实际有效汇率变动对我国机电产品进出口影响的实证分析

从实证的角度,采用协整分析方法研究了1985~2004年人民币实际有效汇率变动对我国机电产品进出口的影响.实证研究结果表明,人民币实际有效汇率对我国机电产品进出口均有显著影响,但是对进口的影响作用更大;相比汇率弹性,我国机电产品的出口对国外实际收入变化的敏感性要强,而其进口对人民币实际有效汇率变化的敏感性要强于对国内实际收入变化的敏感性.     

Stable real invariant semidefinite subspaces and stable factorizations of symmetric rational matrix functions

Stability of certain classes of invariant subspaces of a real matrix which is selfadjoint in a real indefinite inner product, is studied. The study is motivated by, and subsequently applied to, the problem of stability for minimal factorizations of real symmetric rational matrix functions.     

实分片代数曲线的某些研究

分片代数曲线作为二元样条函数的零点集合是经典代数曲线的推广. 利用代数的基本知识, 本文对实分片代数曲线的基本性质进行了初步讨论, 并且将实分片代数曲线与相应的二元样条分类进行讨论. 最后, 对实分片代数曲线上的孤立点进行了研究.     

Error bounds in the gap metric for dissipative balanced approximations

We derive an error bound in the gap metric for positive real balanced truncation and positive real singular perturbation approximation. We prove these results by working in the context of dissipative driving-variable systems, as in behavioral and state/signal systems theory. In such a framework no prior distinction is made between inputs and outputs. Dissipativity preserving balanced truncation of dissipative driving-variable systems is addressed and a gap metric error bound is obtained. Bounded real and positive real input–state–output systems are manifestations of a dissipative driving-variable system through particular decompositions of the signal space. Under such decompositions the existing bounded real and positive real balanced truncation schemes can be seen as special cases of dissipative balanced truncation and the new positive real error bounds follow.     

基于投机价格模型的房地产发展态势研究

近年来我国房地产业发展迅速,但同时房地产业也面临较为严峻的问题和挑战.基于投机价格衡量法,建立房地产行业发展稳定度模型,并且通过SPSS软件对相关数据进行回归分析,测算出全国房地产市场的发展稳定度,结果表明我国房地产行业发展态势基本处于警戒区域,最后提出促进我国房地产市场健康稳定发展的对策.     

An Improved Upper Complexity Bound for the Topology Computation of a Real Algebraic Plane Curve

The computation of the topological shape of a real algebraic plane curve is usually driven by the study of the behavior of the curve around its critical points (which includes also the singular points). In this paper we present a new algorithm computing the topological shape of a real algebraic plane curve whose complexity is better than the best algorithms known. This is due to the avoiding, through a sufficiently good change of coordinates, of real root computations on polynomials with coefficients in a simple real algebraic extension of to deal with the critical points of the considered curve. In fact, one of the main features of this algorithm is that its complexity is dominated by the characterization of the real roots of the discriminant of the polynomial defining the considered curve.     

On Real Closed Regular Rings

The aim of this paper is to investigate some properties of real closed regular rings, in particular, the role played by real place in a real closed regular ring.2000 Mathematics Subject Classification: 13J25This work was supported by NSF of Jiangxi Province, China.     

图灵机计算实数函数的稳定性

定义在全体实数上的可计算函数是一个很重要的概念．在这以前定义可计算的实数函数有两个途径．第一个途径是首先要定义可计算实数的指标．想要确定实数函数y=f（x）是不是可以计算就要看是否存在一个自然数的（部分）递归函数将可计算实数x的指标对应到可计算实数y的指标．这样一来对实数函数的研究依赖于对自然数函数的研究．第二个定义可计算的实数函数的途径是以逼近为基础的．一个实数函数是可以计算的如果它既是序列可计算的同时也是一致连续的．用这个途径来定义可计算实数函数使用的条件过强以至于很多有用的实数函数成为不可计算的实数函数．例如“〈”和“=”的命题函数就是不可以计算的因为它们是不连续的命题函数．本文讨论了图灵机的稳定性并且给出了一个基于稳定图灵机的可计算实数函数的定义．我们的定义不需要用到自然数的（部分）递归函数．根据我们的定义很多常用实数函数特别是一些不连续的常用实数函数都是可以计算的．用我们的定义来讨论可计算实数函数的性质比原来的定义要方便得多．     

超实数系统及其一致连续问题

基于模型论的观点与方法介绍超实数系统的构造及其公理体系,以说明非标准分析.由于超实数系统是普通实数系统的一个真扩张,所以,实数系统中的一致连续问题可推广至超实数系统.     

The Cauchy–Schwarz inequality and the induced metrics on real vector spaces mainly on the real line

It is very well known that the Cauchy–Schwarz inequality is an important property shared by all inner product spaces and the inner product induces a norm on the space. A proof of the Cauchy–Schwarz inequality for real inner product spaces exists, which does not employ the homogeneous property of the inner product. However, it is shown that a real vector space with a product satisfying properties of an inner product except the homogeneous property induces a metric but not a norm. It is remarkable to see that the metric induced on the real line by such a product has highly contrasting properties relative to the absolute value metric. In particular, such a product on the real line is given so that the induced metric is not complete and the set of rational numbers is not dense in the real line.     

Strongly real hilbert rings and the real jacobson semisimplicity

In this paper, several false results in reference [1] related to rela Hilbert rings and the ral Jacobson semisimplicity are negated by a counterexample. By introducing the notion of a strongly real Hilbert ring, we characterize those rings of which every finitely generated real extension is real jacobson semisimple. Moreover, the so-called strictly real Hilbert rings are considered.