一类分数阶差分方程边值问题多重正解的存在性

考虑一类高阶分数阶差分方程边值问题.构造相关的格林函数,利用不等式技巧,分析格林函数的特征性质.运用不动点指数理论,获得了该分数阶差分方程边值问题存在多重正解的充分条件,举例说明了所获理论的有效性.     

一维对流扩散方程解的逐点衰减估计

本文研究一维空间对流扩散方程柯西问题.利用格林函数,频谱分解,傅立叶变换等方法,得到了方程解的逐点估计.结果显示解沿特征线作传播.     

几何对称法在求取某些区域格林函数中的应用

格林函数法是数学物理方程中一种常用的方法,适用于求解狄利克雷问题.针对几种特殊区域上的上狄利克雷问题,采用几何对称法求取这些区域对应的格林函数,该方法对于该区域上格林函数的求解是有效的.     

含有积分、反周期和带P-Laplacian算子的分数阶微分方程边值问题解的存在性

利用格林函数的性质和Banach压缩映射原理讨论了含P-Laplacian算子反周期边值问题的解.首先,求出与该边值问题相关的格林函数并给出了格林函数的性质;然后将边值问题转化为与其等价的积分方程,利用格林函数的性质及Banach压缩映射原理得到边值问题解的唯一性;最后给出实例验证结果的合理性.     

关于Couette问题解的计算与修正

Couette问题的解已被前人利用格林函数方法推导出来,但是这个结果不够严格,在此按照同样的方法进行计算与修正,对所求的解进行验证,并将结果推广到一般的线性问题.     

G·格林与位势理论

格林(G·Green,1793~1841年)是19世纪前期英国数学家,他继承了前人的成果,引入了位势概念,建立了“格林函数”,提出“格林定理”和 n 维空间概念.直到今天,学过高等数学和大学物理的人都知道“格林公式”、“格林函数”、“格林算子”、“格林空间”和“格林测度”等.1　移植思维出成果格林创立位势理论运用的是移植思维方法.大家知道,数学抽象性这一特点,具有促成不同学科领域相互模拟、相互移植的功能.以二阶常微分方程为例d2ydx2 pdydx Qy = f(x)在力学中可表示为强迫振动方程,在电学中可表示为电阻、电感、电容串联电路方程,在…     

非线性积分方程与格林函数方法——粒子-空穴相互作用的无规位相(RPA)自屏蔽I

本文强调了非线性积分方程在格林函数理论中的应用及其物理含意。此外,文中提出了一个浅明的方法,应用这方法可将一类三时格林函数满足的线性积分方程转化为只含二时格林函数的线性积分方程。作为举例,文中对粒子-空穴格林函数建立了一组非线性积分方程,并且证明了其解包括粒子-空穴相互作用的所有各级无规位相(RPA)自屏蔽。     

一类分数阶p-Laplacian差分方程边值问题正解的存在性北大核心CSCD

研究一类带p-Laplacian算子的分数阶差分方程边值问题.利用格林函数的特征性质、压缩映射原理及锥上的不动点定理等非线性方法,获得了该分数阶pLaplacian差分方程边值问题解的唯一性及正解的存在性条件,举例说明了所得结论的正确性.     

一类分数阶p-Laplacian差分方程边值问题正解的存在性

研究一类带p-Laplacian算子的分数阶差分方程边值问题.利用格林函数的特征性质、压缩映射原理及锥上的不动点定理等非线性方法,获得了该分数阶pLaplacian差分方程边值问题解的唯一性及正解的存在性条件,举例说明了所得结论的正确性.     

凯莱-海森堡群上的格林函数

本文研究凯莱-海森保群上的格林函数.利用凯莱-海森堡群上热核的解析表达式,导出了一阶凯莱-海森堡群上的格林函数的有理分式表示的公式.     

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.     

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...     

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．     

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.