二阶曲线间的射影映射

平面上的射影变换,将二阶曲线变为另一二阶曲线,这个射影变换也可以称为这两个二阶曲线间的射影映射.若两个二阶曲线相切,则存在以切点为射影中心的两个二阶曲线间的射影映射;若两个二阶曲线相离,则存在以两个二阶曲线公切线交点为射影中心的射影映射;若两个二阶曲线相交,则存在以其中一交点为射影中心的两个二阶曲线间的射影映射.     

二阶导数的几何意义

对一元函数二阶导数的几何意义进行阐释,认为一元函数的二阶导数是描述函数对应曲线的曲率的一个重要指标:二阶导数的绝对值与曲线曲率成正比;在驻点处,二阶导数的绝对值与曲率相等.     

集值优化Benson真有效元的二阶刻画

引进了一种新的二阶组合切锥, 利用它引进了一种新的二阶组合切导数, 称为二阶组合径向切导数, 并讨论了它的性质及它与二阶组合切导数的关系, 借助二阶径向组合切导数, 分别建立了集值优化取得Benson真有效元的最优性充分和必要条件.     

集值向量优化的二阶最优性必要条件

在赋范空间中给出了集值映射的二阶切集的概念,利用二阶切集,定义了集值映射的二阶切导数。然后,获得了集值向量优化问题弱极小元的两个二阶最优性必要条件。     

抛物型方程基于POD方法的时间二阶中心差的时间二阶精度简化有限元格式

本文将特征正交分解(Proper Orthogonal Decomposition,简记为POD)方法应用于抛物型方程通常时间二阶中心差的时间二阶精度有限元格式(简称为通常格式),简化其为一个自由度极少但具有时间二阶精度的有限元格式,并给出简化的时间二阶中心差的时间二阶精度有限元格式(简称为简化格式)解的误差分析.数值...     

均衡约束为二阶锥约束广义方程的数学规划问题的二阶充分条件(英)

本文考虑一类均衡约束为二阶锥约束广义方程的数学规划问题. 我们通过一个非光滑映射的方向导数, 给出了临界锥的定义, 并建立它在可行点处的等价形式. 基于此临界锥, 我们提出了均衡约束为二阶锥约束广义方程的数学规划问题的二阶充分性条件, 并且验证了在适当的条件下, M-稳定点处的二阶充分性条件是二阶增长条件成立的充分条件.     

关于非退化的二阶曲线的分类研究

从抛物线的一种判定方法出发,借助于欧氏平面上非退化的二阶曲线的度量性质,通过对欧氏平面上非退化二阶曲线类型的研究,探究出确定非退化二阶曲线类型的若干定理。     

二阶直接控制系统绝对稳定性的充分必要条件

二阶直接控制系统的绝对稳定性,目前尚未见到充分必要条件。本文给出了二阶直接控制系统的绝对稳定性的充分必要条件,并且解决了各种临界情况的绝对稳定性,从而完全解决了二阶直接控制系统的绝对稳定性问题。研究二阶直接控制系统     

广义二阶导数和二阶混合偏导数之间的关系

给出并证明了函数在一点处广义二阶可导的一个充分条件,分析了二元函数在一点的广义二阶导数和二阶混合偏导数之间的关系.     

一类二阶变系数线性微分方程及其解的构造方法

利用构造法构造二阶变系数线性齐次微分方程及其解,根据这种方法也能求得某些二阶变系数线性齐次微分方程的非零解,并给出了二阶变系数线性齐次微分方程存在非零解的充要条件.     

Study of the blow-up of solutions of systems of equations of hydrodynamic type

Mathematical Notes - We study the initial boundary-value problem for three-dimensional systems of equations of pseudoparabolic type. The system is similar to the Oskolkov system, but differs from...     

Distribution of types of symmetry of tensors of high degree

The asymptotic distribution of tensors of degree N in symmetry types is studied in this paper.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 155, pp. 181–186, 1986.     

Characterization of types of asymptotic discernibility of families of hypotheses

We give a characterization of the types of asymptotic discernibility of families of hypotheses in the case of hypothetical measures that are not, in general, mutually absolutely continuous. The case when the logarithm of the likelihood ratio admits an asymptotic expansion of the type of an expansion with local asymptotic normality is examined in detail. Examples are studied.Translated fromTeoriya Sluchainykh Protsessov, Vol. 15, pp. 64–71, 1987.     

Axiomatizability of reducts of algebras of relations

In this paper, we prove that any subreduct of the class of representable relation algebras whose similarity type includes intersection, relation composition and converse is a non-finitely axiomatizable quasivariety and that its equational theory is not finitely based. We show the same result for subreducts of the class of representable cylindric algebras of dimension at least three whose similarity types include intersection and cylindrifications. A similar result is proved for subreducts of the class of representable sequential algebras. Received October 7, 1998; accepted in final form September 10, 1999.     

Lengths of periods of continued fractions of square roots of integers

Empirical study of the period’s length T of the continued fractions of $\sqrt{Q}$ (for growing integers Q) shows several strange asymptotical results, for instance, $T\leq C\sqrt{Q}\ln{Q}$ . These results show important differences between the statistics of the elements of the continued fractions of random real numbers and of square roots of random integers.