半线性抛物型方程组解的Blow—up现象

本文研究某一类半线性抛物方程组解的Ｂｌｏｗ－ｕｐ存在性及Ｂｌｏｗ－ｕｐ点集的性质，并证明在一定条件下单点Ｂｌｏｗ－ｕｐ。     

关于一类拟线性抛物方程解的Blow—up问题

本文利用Ｆｏｕｒｉｅｒ空间的比较原理研究一类拟线性抛物方程解的Ｂｌｏｗ－ｕｐ问题，并给出了其解在有限时刻Ｂｌｏｗ－ｕｐ的条件。     

一类非线性反应扩散方程解的Blow—up问题

本文得用极大值原理研究一类非线性反应扩散方程在各种边界条件下解的Ｂｌｏｗ－ｕｐ问题，给出了整体解不存在的一系列定理，并得到了Ｂｌｏｗ－ｕｐ时间Ｔ的上界。     

关于一类拟线性拟抛物方程解的Blow─up问题

本文利用Ｆｏｕｒｉｅｒ空间的比较原理研究一类拟线性拟抛物方程解的Ｂｌｏｗ－ｕｐ问题，并给出了其解在有限时刻Ｂｌｏｗ－ｕｐ的条件。     

关于具有非线性边界条件的非线性抛物型方程Blow－up现象

本文讨论下列具有非线性边界条件的初边值问题的整体解和Ｂｌｏｗ－ｕｐ现象．该于如此现象我们已经得到一些结果，这里我们的目的是放松边界函数ｆ（ｕ）的假设，得到类似结果．     

一个反应扩散过程的门槛结果

本文讨论反应扩散方程Ｃａｕｃｈｙ问题（ｕｔ－△ｕ＝ｕ＾ｐ－ｕ＾ｐ－ｕ，Ｘ∈Ｒ＾ｎ，ｔ∈（０，Ｔ），ｕ（ｘ，０）＝ｕ０（ｘ）≥０，Ｘ∈Ｒ＾ｎ，解的整体存在性，渐近性质和Ｂｌｏｗ－ｕｐ问题，其中１＜ｑ＜ｐ＜ｎ＋２／ｎ－２，ｎ≥３或者１＜ｑ＜ｐ＋∞，ｎ＝２．得到门槛结果。     

带有非线性边界条件抛物型方程组BLOW-UP和整体存在性问题

本文讨论带有非线性边界条件ｕｎ＝ｆ（ｕ，ｖ），ｖｎ＝ｇ（ｕ，ｖ）的抛物型方程组ｕｔ＝Δｕ，ｖｔ＝Δｖ解的存在性问题．如果ｆ（ｕ，ｖ），ｇ（ｕ，ｖ）关于其变量是非降的正的Ｃ１函数，或者只是正的Ｃ１函数满足ｆ（ｕ，ｖ）ｍｆ１（ｕ），ｇ（ｕ，ｖ）ｍｇ１（ｖ），ｍ是一个正常数，给出了解整体存在和Ｂｌｏｗ－ｕｐ的不同的充分条件．     

关于Fujita型反应扩散方程组的Cauchy问题

本文研究Ｆｕｊｉｔａ型反应扩散方程组ｕｔ－Δｕ＝α１｜ｕ｜ｑ１－１ｕ＋β１｜ｖ｜ｐ１－１ｖ，（ｘ∈ＲＮ，ｔ＞０），ｖｔ－Δｖ＝α２｜ｕ｜ｑ２－１ｕ＋β２｜ｖ｜ｐ２－１ｖ，ｕ（ｘ，０）＝ｕ０（ｘ）０，ｖ（ｘ，０）＝ｖ０（ｘ）０，（ｘ∈ＲＮ）Ｌｐ解的整体存在性和有限时间Ｂｌｏｗ ｕｐ问题．这里ｑｉ＞１，ｐｉ＞１（ｉ＝１，２），α１０，α２＞０，β１＞０，β２０，１ｐ＋∞．     

神经传播型方程解的blow－up

本文研究神经传播型非线性拟双曲方程Ｕｔｔ－△ｕｔ＝ｆ（ｕ）ｕｔ＋ｇ（ｕ）Ｏ）的初边值问题与初值问题解的ｂｌｏｗ－ｕｐ问题，不但研究了对任意非负初值解的ｂｌｏｗ－ｕｐ，而且利用一种改进了的特征函数法研究了对充分大初值解的ｂｌｏｗ－ｕｐ．     

守恒相场模型弱解的Blow—up

本文讨论一类守恒相场模型弱解的性态,证明当ａ２ｐ－１＜０及初始数据充分大时解在有限时刻Ｂｌｏｗ－ｕｐ     

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.     

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.