两类距离边界条件域的拟共不变性和Mius变换的两个拟不变量

研究了两类距离边界条件域KBc和jBc,得到了它们的若干性质及它们的关系,证明了在一定条件下KBc和jBc是拟共不变的以及距离K(x1,x2)和j(x1,x2)在Mobius变换下具有拟不变性.     

一类拟线性两点边值问题的存在唯一性

本文在f(t,x),f_x(t,x),η(t)连续,f_x(t,x)≥-η(t),η(t)≤π~2+A~2/4,η(t)π~2+A~2/4条件下,证明了拟线性两点边值问题 x″=Ax′+f(t,x),x(0)=α,x(1)=β, 对于任给实数A,α,β都有唯一解。     

拟幂零积分算子

本文讨论积分算子的拟幂零性,对 L~p 空间上的积分算子(If)(x)=∫_0~(φ(x))f(t)dt 和 L~2空间上具有非负核的积分算子(Tf)(x)=∫_0~1K(x,t)f(t)dt,分别得到了用积分上限φ和核 K 表述的、使算子 I 和 T 为拟幂零的充要条件.     

Bernstein-Durrmeyer算子拟中插式的逼近

最近,为了得到更快的逼近速度,人们引入了某些著名算子的拟中插式.我们研究了Bernstein-Durrmeyer算子的拟中插式Mn(2r-1)(f,x),用Ditzian-Totik模得到了它们的正、逆定理和等价定理.这里.     

Bernstein-Durrmeyer算子拟中插式的逼近

最近,为了得到更快的逼近速度,人们引入了某些著名算子的拟中插式.我们研究了Bernstein-Durrmeyer算子的拟中插式Mn(2r-1)(f,x),用Ditzian-Totik模得到了它们的正、逆定理和等价定理.这里.     

一致区域与拟双曲度量

设 D 是 R~n(n≥2)的真子区域.F.W.Gehving 与 B.G.Osgood 证明,D 是一致区域的充分必要条件是:存在常数 c 和 d,使得 k_D(x_1,x_2)≤cj_D(x_1,x_2)+d,(?)x_1,x_2∈D.本文证明,这个条件可减弱为:存在一常数 A,使得K_D(x_1,x_2)≤A·j_D(x_1,x_2),(?)x_1,x_2∈D.这里 K_D(x_1,x_2)为 D 中任意两点 x_1,x_2的拟双曲度量,j_D(x_1,x_2)=1/2log([|x_1-x_2|]/[d(x_1,(?)D)]+1)([|x_1-x_2|]/[d(x_2,(?)D)]+1),d(x,(?)D)为 x 到(?)D 的欧氏距离.     

距离边界条件域和H(o)lder域

主要利用了距离边界条件域和Holder域的定义,建立了当kD(x1,x2)和jD(x1,x2)满足一定的条件后,两类距离边界条件域和Holder域之间的四个充要条件和一个充分条件.     

拟-k-仿正规算子的一个注解

设T是复希尔伯特空间H上的有界线性算子,若对任意的x∈H,T满足||T~(k+2)x||||Tx||~k≥||T~2x||~(k+1),则称T为拟-k-仿正规算子,其中k为正整数.该文给出了拟-k-仿正规算子的一些性质,如拟-k-仿正规算子是极,作为此性质的应用,证明了拟-k-仿正规算子满足Weyl定理.     

关于拟线性抛物型方程b(u)u_t=[a(u)u_x]_x反问题拟解的存在性问题

本文在 [1 ]中“ut=[a(u) ux]x的一个反问题”的基础上 ,解决了 b(u) ut=[a(u) ux]x 反问题拟解的存在性问题     

拟双曲度量与John圆

设D是R~2中的Jordan域,本文证明了D是b-John圆当且仅当存在常数c≥1,对任意的x_1,x_2∈D,有k_D(x_1,x_2)≤cH_D(x_1,x_2),这里kD(x_1,x_2)表示D中x_1与x_2二点的拟双曲距离,H_D(x_1,x_2)=1/2log(1+(l(γ))/(d(x_1,■D)))(1+(l(γ))/(d(x_2,■D))),其中l(γ)为D中连结x_1与x_2二点的拟双曲测地线的欧几里德长度.     

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.     

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.     

Singularities of Solutions of One Class of Equations of Continuum Mechanics

We analyze one class of families of integral equations and describe the dependence of the singularities of solutions of integral equations on the dimensions of the families of kernels of equations. On the basis of these results, we propose procedures for the construction of approximate solutions for a small parameter.     

Determination of asymptotic solutions of problems of nonlinear theories of thermoviscoelasticity

It is shown that the asymptotic solution of a problem of the nonlinear theory of thermoviscoelasticity, if it exists, can be found directly from the solution of the asymptotic boundary-value problem without completely solving the starting problem.M. V. Lomonosov Moscow State University. Translated from Mekhanika Polimerov, No. 3, pp. 395–400, May–June, 1976.     

Emptiness of set of points of lower semicontinuity of Lyapunov exponents

We consider parametric families of differential systems with coefficients that are bounded and continuous on the half-line and uniformly in time continuously depend on a real parameter. For each Lyapunov exponent, we construct a family such that the Lyapunov exponent of its systems treated as a function of the parameter is not a lower semicontinuous function for any value of the parameter.     

图表示范畴的两个子范畴

引进图表示范畴的两个子范畴,研究它们的同调性质。