奇异半线性椭圆问题解的存在与不存在性(英文)

本文研究了奇异半线性椭圆问题.利用上下解方法,获得了该问题解的一个存在性和不存在性结果.     

一类非线性积-微分方程极值解的存在性定理

本文讨论非线性积-微分方程初值问题的极值解的存在性。其中利用单调迭代法和上、下解方法,得到了最小解和最大解的存在性定理。     

一类带有扩散与时滞的流行性传染病模型的行波解

讨论了一类带有扩散与时滞的流行性传染病模型的行波解的存在性.首先,将系统的行波解的存在性问题转化为一个二阶常微分方程组的单调解的存在性问题;应用单调方法和不动点方法,进一步地将问题转化为方程组的上下解的构造问题;应用所建立的引理与定理,通过构造适合的上下解,证明了系统单调行波解的存在性.     

一类非线性积－微分方程极值解的存在性定理

本文讨论非线性积－微分方程初值问题的极值解的存在性．其中“利用单调迭代法和上、下解方法，得到了最小解和最大解的存在性定理．     

具有时滞的非线性微分方程的概周期解的存在性及唯一性

本文研究了一类具有时滞的非线性微分方程的有界解及概周期解的存在性及唯一性问题。利用变量替换和不动点方法及逼近法,我们得到了此类方程有界解和概周期解的存在性及唯一性的一些有趣的新结果。我们的结果大大改进和推广了文［２］的主要结果。     

带Hardy位势的双调和椭圆方程的正负解及变号解

本文讨论带Hardy位势的四阶渐近线性椭圆方程,应用变分方法,我们得到了正负解及变号解的存在性.     

时滞脉冲微分方程三点边值问题解的存在性和唯一性

研究一类时滞与脉冲共存的微分方程三点边值问题,利用上下解与单调迭代方法获得了边值问题解的存在性定理和唯一性定理,给出求解该类问题解析近似解的迭代方法,得出了新的结论.     

非线性三阶常微分方程的非线性三点边值问题解的存在性

基于上下解方法,在一定条件下,得到了一类带有非线性混合边界条件的三阶常微分方程的非线性三点边值问题解的存在性,作为上述存在性结果的应用,在推论中给出了一类三阶非线性微分方程三点边值问题解的存在性.     

空间中的时滞积分微分方程数值方法及其牛顿迭代解的存在唯一性

该文分析了扩展的一般线性方法关于Banach 空间中一类时滞积分微分方程数值解的可解性, 给出了其方法的解的存在唯一性判据, 并探讨了其Newton迭代解的性态. 所获结果可应用于扩展的Runge-Kutta方法和扩展的线性多步方法等.     

解椭圆型问题的无限元方法

本文给了一个求解变系数椭圆型方程的无限元方法。在解具有奇性时可获得很准确的奇性数值解,而且计算量小,不需要事先知道方程解的奇性阶及特解的解析表达式。最后给了一个数值例子,将它与有限元方法做了比较。     

Estimates of stability of characterization of additive types of distributions

An estimate of stability of characterization of distribution types is obtained for the case of additive types. Under some conditions, the estimate has the order ε^1/3L(ε), where L(ε) is a slowly varying function. Proceedings of the Seminar on Stability Problems for Stochastic Models, Moscow, Russia, 1996, Part I.     

一类完全正则半群簇子簇格的性质

本文研究了完全正则半群簇的子簇格［Ｖ＋∩ＰＶ，Ｖ＋∩ＰＶ］的某些格运算性质，我们证明了簇Ｖ＋∩ＰＶ可分解为Ｖ与Ｖ＋∩ＰＶ的并；对任意完全正则半群簇Ｗ，有Ｗ∩（Ｖ∨Ｖ＋∩ＰＶ）＝（Ｗ∩Ｖ）∨（Ｗ∩Ｖ＋∩ＰＶ）．特别地，我们得到了等式Ｖ＋∩ＰＶ＝Ｖ成立的若干条件．     

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...     

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.     

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.     

Preservation of equivalence of derivations under reduction of depth of formulas

In this paper we consider derivations in the (&, )-fragment of the intuitionistic propositional calculus. As is known, replacement of any occurrence of a formula [F] in a sequent S by an occurrence of the formula [p], where p is a new propositional variable, with the simultaneous addition to the antecedent of the formula F p or p F depending on the sign of the occurrence of F in S, leaves the derivability unchanged. We give a proof of the fact that the natural extension of this transformation to derivations preserves the relation of equivalence of derivations, i.e., transformed derivations are equivalent if and only if the originals are equivalent. (Derivations are considered equivalent if certain of their normal forms coincide, or, what is the same, if their deductive terms coincide.) It is proved that by the iteration of this transformation, each derivation of an arbitrary sequent S can be transformed into a derivation of a sequent S, depending only on S, whose succedent is a variable, and in the antecedent there occur only formulas of the form a,a & b, a b,,(a b) c, a & b c, a (b & c), wherea, b, c are variables. Here if S is balanced, then S is also balanced. (A sequent is called balanced if each variable occurs in it no more than twice.) The familiar correspondence between certain concepts of the theory of categories and concepts of the theory of proofs allows one to assert that there has been constructed a univalent functor, mapping a free Cartesian closed category into itself.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 88, pp. 197–207, 1979.     

Estimate of growth of Lebesgue functions of linear methods of summation

Sufficient conditions are obtained in terms of matrix elements for the boundedness of Lebesgue functions of linear methods of summation of expansions in orthogonal systems of polynomial type.Translated from Matematicheskie Zametki, Vol. 6, No. 3, pp. 277–286, September, 1969.     

Birational aspects of the geometry of Varieties of Sums of Powers

Varieties of Sums of Powers describe the additive decompositions of a homogeneous polynomial into powers of linear forms. The study of these varieties dates back to Sylvester and Hilbert, but only few of them, for special degrees and number of variables, are concretely identified. In this paper we aim to understand a general birational behavior of VSP. To do this we birationally embed these varieties into Grassmannians and prove the rational connectedness of many VSP in arbitrary degrees and number of variables.