具耗散项p-方程组的整体光滑解

该文考虑具耗散项的p-方程组初值问题的整体光滑解．我们在假设初值的振幅为任意给定，而其导数适当小时，得到了初值问题整体光滑解的存在性．     

Banach空间非线性混合型微分-积分方程整体解的存在性和唯一解

研究了Banach空间中非线性混合型微分-积分方程初值问题u′=f(t,u,Tu,Su),u(0)=x0的整体解,完全没有要求f的任何增性,利用Mnch不动点定理和比较结果得到了初值问题整体解的存在性和唯一解,并且给出了一致收敛于唯一解的迭代序列,改进推广和统一了已有的许多结果.     

单稳型二维格微分方程的整体解

通过解一个以-κ为初始时刻的初值问题序列,并且利用比较原理证明了单稳型二维格微分方程整体解的存在性和一些定性性质.     

具有弱阻尼项的广义IMBq方程初值问题解的整体存在性

证明具有弱阻尼项的广义IMBq方程乱u_(tt)-u_(xx)-u_(xxtt)+v_0u_t=f(u)_(xx),x∈R,t0的初值问题在C~2([0,∞);H~s(R))(s2是一实数)中存在惟一整体广义解和在C~2([0,∞);H~s(R))(s2/7)中存在惟一整体古典解,并给出上述初值问题解爆破的充分条件.     

一类具非线性二阶导数项的Schr(o)dinger方程整体解存在的最佳条件

本文讨论一类具非线性二阶导数项的schr(o)dinger方程,它在物理上描述了上混合振荡传播.根据基态的变分特征,运用势井方法和凹方法,我们获得了其初值问题整体解存在的一个最佳条件,另外还证明了当初值多小时,初值问题的整体解存在.     

非线性Schr\"{o}dinger方程组解的整体存在与有限时刻爆破的两个门槛结果[英文]

本文研究一类薛定谔方程的初值问题. 我们建立解的整体存在与有限时刻爆破的两个门槛结果并讨论了驻波解的不稳定性.     

一类具非线性二阶导数项的Schrödinger方程整体解存在的最佳条件

本文讨论一类具非线性二阶导数项的schr(o)dinger方程,它在物理上描述了上混合振荡传播.根据基态的变分特征,运用势井方法和凹方法,我们获得了其初值问题整体解存在的一个最佳条件,另外还证明了当初值多小时,初值问题的整体解存在.     

浅水波方程的初边值问题

本文用Kato关于拟线性演化方程的初值问题的存在性定理证明了浅水波方程在半无界直线上初值问题局部解的存在性。用解的先估计证明了整体解的存在性或解的Blow-up性质，并给出了解关于x的渐近估计。     

带线性退化阻尼项的可压缩欧拉方程组的整体正规解

本文研究了理想气体的带线性退化阻尼项的可压缩欧拉方程组的真空初值问题.利用能量估计的方法,在适当的初始条件下,获得了初值问题的正无偏见解整体存在的结果.推广了可压缩等熵欧拉方程组的结果.     

高阶非线性抛物型偏微分方程组的初值问题

本文讨论一般自治型高阶非线性抛物型偏微分方程组初值问题整体解的存在性，得到了这类问题对小初值存在整体经典解的充分条件。     

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.     

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.