关于两个多元多项式互素问题

给出了两个二元多项式互素的充要条件 ,然后利用这个充要条件推出二元多项式互素的性质 ,最后给出一般的 n元多项式互素的充要条件 .     

关于两个多元多项式互素问题

给出了两个二元多项式互素的充要条件，然后利用这个充要条件推出二元多项式互素的性质，最后给出一般的n元多项式互素的充要条件。     

一类两圆锥曲线有三个公共点的充要条件

一类两圆锥曲线有三个公共点的充要条件胡望杰（浙江永康一中）笔者在文［１］中证明了一类两圆锥曲线有唯一公共点的充要条件，得出了五个定理及二个推论．本文旨在证明一类两圆锥曲线有三个公共点的充要条件，并举例说明本文的定理及推论的应用．定理１抛物线ｙ２＝２ｐ...     

简议充要条件命题的证明

<正>一个用充要条件叙述的命题,实际上包含着两个互逆的命题,即p是q(p、q也可以分别为两个命题)的充要条件相当于"若p则q"和"若q则p"这两个命题的总和.因此,要证明一个充要条件的命题,必须采取双向证明的方法,即既要证充分性,又要证明必要性.     

关于幂等阵的相似与线性组合

证明了数域上两个同阶幂等阵相似的充要条件是它们有相同的秩;给出了幂等阵的相似标准型;讨论了两个幂等阵的线性组合仍是幂等阵的充要条件.     

宽平稳序列均方遍历性的两个充要条件(英文)

本文研究了宽平稳序列具有均方遍历性的充要条件问题.利用施瓦兹不等式,获得了复宽平稳序列均方遍历性的两个充要条件和一个易于验证的充分条件.     

集合范畴上超滤函子的余代数

定义了集合范畴上的超滤函子F_u(-),并研究了相关性质.包括函子F_u(-)在有限集上保拉回,一个集合的子集成为F_u-子余代数的充要条件,以及两个余代数之间的态射是F_u-余代数同态的充要条件,子集成为子余代数的充要条件,最后以拓扑空间作为F_u-余代数的具体实例,研究了拓扑空间的连续映射与超滤函子的余代数同态之间的关系.     

线性模型中不可估参数的线性估计的可容许性

对一般线性模型在平方损失函数下，得到了一维不可估参数函数的线性估计为可容许估计的充要条件，以及模型中参数向量（非线性可估）的线性估计为可容许估计的两个充要条件，并得到了多维参数函数（可估或不可估）的线性估计为可容许估计的一个充分条件以及特殊情况下的一个充要条件．     

LR-C半群的半直积

给出了两个半群的半直积是LR-C半群的充要条件.     

双二次Bezier曲面的正性与凸性

本文利用Ｓｔｕｒｍ序列及若干个关于根的判别式给出了四次多项式在区间〔０，＋∞）上为正及非负的充要条件，进而得到了双二次Ｂｅｚｉｅｒ曲面正性与凸性的充要条件，最后还给出了几个图形示例。     

Depth notions for orthogonal regression

Global depth, tangent depth and simplicial depths for classical and orthogonal regression are compared in examples, and properties that are useful for calculations are derived. The robustness of the maximum simplicial depth estimates is shown in examples. Algorithms for the calculation of depths for orthogonal regression are proposed, and tests for multiple regression are transferred to orthogonal regression. These tests are distribution free in the case of bivariate observations. For a particular test problem, the powers of tests that are based on simplicial depth and tangent depth are compared by simulations.     

具有双裂纹的弹性复合材料板承受剪切冲击时的动应力强度因子

本文研究了两个材半限弹性的接合面附近存在与接合面平行的双裂纹，并承受剪切冲击时的瞬态应力，运用付里叶（Ｆｏｕｒｉｅｒ）和拉普拉斯（Ｌａｐｌａｃｅ）变换，将问题归结为求解二元积分方程，求解时将裂纹所在面上，下的位移差展成级数，并让其自动满足裂纹面外的位移差为零的条件，利用裂纹面上的边界条件和施密特（Ｓｃｈｍｉｄｔ）方法求解级数中的待定系数，在拉普拉斯像空间中，求得动应力强度因子，并将其数值地逆变换至     

The systems approach and fuzzy set theory bridging the gap between mathematical and language-oriented economists

Ideas are presented to show how fuzzy mathematics can be applied in macro-economics in combination with the systems approach in order to bridge the gap between mathematical and language-oriented economists.Two reasons are given.From a mathematical point of view, fuzzy sets, fuzzy relations and fuzzy logic are not fuzzy at all. They are all well defined, but tend to be more complicated than traditional, mathematical concepts used in economics.From a language-oriented economist's point of view, fuzzy sets, etc. are used to express mathematically the type of concepts which are typical in language and most valuable in dealing with complex systems like an economy.The paper deals with economics in general terms, but examples are provided to illustrate the ideas.     

存在水平差异化的多寡头双边平台企业竞争研究

构建了多寡头双边平台企业竞争的Salop双环模型,研究了双边平台企业在不同规模下均衡解的存在性以及均衡解的结构。研究发现:不论双边平台企业规模如何,双边平台企业的收益不仅受平台对买卖双方制定的价格总量的影响,而且还受价格结构的影响;多寡头双边平台企业在竞争中存在明显的买方市场时,买方并不能获得类似单边市场里的主动权,且若卖方存在竞争,则无论买方是否存在竞争,均不存在均衡解;无论是买方竞争还是卖方竞争,若存在均衡解,则对双边平台企业、买方和卖方均有利,出现三方多赢的局面。     

Some properties of complex matrix-variate generalized Dirichlet integrals

Dirichlet integrals and the associated Dirichlet statistical densities are widely used in various areas. Generalizations of Dirichlet integrals and Dirichlet models to matrix-variate cases, when the matrices are real symmetric positive definite or hermitian positive definite, are available [4]. Real scalar variables case of the Dirichlet models are generalized in various directions. One such generalization of the type-2 or inverted Dirichlet is looked into in this article. Matrix-variate analogue, when the matrices are hermitian positive definite, are worked out along with some properties which are mathematically and statistically interesting.     

An application of a boundary element method to natural convection

The direct boundary element method is applied to the numerical modelling of thermal fluid flow in a transient state. The Navier-Stokes equations are considered under the Boussinesq approximation and the viscous thermal flow equations are expressed in terms of stream function, vorticity, and temperature in two dimensions. Boundary integral equations are derived using logarithmic potential and time-dependent heat potential as fundamental solutions. Boundary unknowns are discretized by linear boundary elements and flow domains are divided into a series of triangular cells. Charged points are translated upstream in the numerical evaluation of convective terms. Unknown stream function, vorticity, and temperature are staggered in the computational scheme.

Simple iteration is found to converge to the quasi steady-state flow. Boundary solutions for two-dimensional examples at a Reynolds number 100 and Grashoff number 10⁷ are obtained.     

MTL代数的特征定理

对于逻辑系统代数结构的研究,是一个十分重要的研究课题.近期提出的BL代数,R_0代数,MTL代数就是这个方向具有代表性的研究成果.本文讨论MTL代数的性质与结构,给出这种代数的几个特征定理,澄清这种代数与其它代数结构的关系.鉴于单位区间中由左连续t-范数诱导的剩余蕴涵与MTL代数的紧密联系,本文还考察了这种模糊蕴涵的特征性质.     

The use of analysis of variance procedures in biological studies

The analysis of variance (ANOVA) is widely used in biological studies, yet there remains considerable confusion among researchers about the interpretation of hypotheses being tested. Ambiguities arise when statistical designs are unbalanced, and in particular when not all combinations of design factors are represented in the data. This paper clarifies the relationship among hypothesis testing, statistical modelling and computing procedures in ANOVA for unbalanced data. A simple two-factor fixed effects design is used to illustrate three common parametrizations for ANOVA models, and some associations among these parametrizations are developed. Biologically meaningful hypotheses for main effects and interactions are given in terms of each parametrization, and procedures for testing the hypotheses are described. The standard statistical computing procedures in ANOVA are given along with their corresponding hypotheses. Throughout the development unbalanced designs are assumed and attention is given to problems that arise with missing cells.     

Normal families of holomorphic functions and mappings on a Banach space

The authors lay the foundations for the study of normal families of holomorphic functions and mappings on an infinite-dimensional normed linear space. Characterizations of normal families, in terms of value distribution, spherical derivatives, and other geometric properties are derived. Montel-type theorems are established. A number of different topologies on spaces of holomorphic mappings are considered. Theorems about normal families are formulated and proved in the language of these various topologies. Normal functions are also introduced. Characterizations in terms of automorphisms and also in terms of invariant derivatives are presented.     

混合位置分布中分量参数的统计推断

对混合位置分布族,当混合比已知时,提出了关于分量参数的假设检验和区间估计方法,所提出的方法基于广义枢轴模型.在一定的条件下,检验的实际水平等于名义水平,且各置信域的实际覆盖率等于名义覆盖率.在更一般的场合,检验是相合的,并且各置信域的实际覆盖率趋于名义覆盖率.模拟显示所给的方法是令人满意的.