附加广义函数的几个导数

作者证明了广义函数（ｘ±ｉ０）^λｌｎ^k（ｘ±ｉ０）的表示定理,给出了附加广义函数的导数：（ｌｎ^kｘ_±）＇,（ｘ^λ_±ｌｎ^kｘ_±）＇,（ｘ^-n_±ｌｎ^k＇ｘ_±）＇,（ｄ／ｄｘ）｛（ｘ±ｉ０）^λｌｎ^k（ｘ±ｉ０     

直径为5的整树新类

本文通过更广泛的二次不定方程ｄ_１ｘ^２－ｄ₂ｙ^２＝１的解，构造出了更多的直径为５的整树     

重分形Hausdorff测度的有限测度子集

设μ为 Ｒ^d上 Ｂｏｒｅｌ概率测度,ｑ,ｔ∈Ｒ,记 Ｈ_μ^q,t为 Ｏｌｓｅｎ定义的重分形 Ｈａｕｓｄｏｒｆｆ测度,证明了当μ为测度时,Ｈ_μ^q,t的有限测度子集存在．     

局部域上的局部Hardy空间

文献［１］，［２］，［３］中讨论了Ｒ^ｎ上的局部Ｈａｒｄｙ空间，并利用乘子定理证明了ｈ_ｐ（Ｒ^ｎ）＝Ｆ_p.2⁰（Ｒ^ｎ）．本文利用Ｃｈｅｂｙｓｈｅｖ等式及正则函数的性质证明了在局部域上有类似的结果ｈ_ｐ（Ｒ^ｎ）＝Ｆ_p.2⁰（Ｒ^ｎ），从而建立起函数空间之间的关系，并由此给出一个乘子定理．     

关于一类微分方程周期解的存在性的注记

本文主要探讨下列周期系数微分方程dy/dt=(A₁(t)y+A₂(t)y²+A₃(t)y³)/(a₀(t)+a₁(t)y+a₂(t)y²)(**)的周期解个数问题，利用方程（**）解的差率法得到了方程（**）周期解的个数定理．本文仅在Ａ_i（ｔ），ａ_j（ｔ）（ｉ＝１，２，３，ｊ＝０，１，２）是连续周期函数的条件下得到这一结论，从而减弱了文［２］中相应定理的条件，即Ａ_i（ｔ），ａ_j（ｔ）均是连续可微的周期函数．     

关于Buchsbaum环的注记

本文证明了下述结论，设Ａ是一个级数为ｄ的Ｂｕｃｈｓｂａｕｍ环，（ａ₁，ａ₂，…，ａ_n）是Ａ的一个参数系统，则任何正整数ｎ，Ａ／（ａ₁，ａ₂，…，ａ_k）ⁿ（１≤ｋ≤ｄ）仍是ｄ－ｋ维的Ｂｕｃｈｓｂａｕｍ环．     

一类超临界椭圆方程正解的存在性

本文讨论了球上半线性椭圆Ｄｉｒｉｃｈｌｅｔ问题Δｕ＋λｕ^ｑ＋ｕ^p＝０正解的存在性,其中,λ∈Ｒ,０〈ｑ〈１,ｐ〉ｐ_ｃ≡(Ｎ＋２)/(Ｎ－２)（Ｎ〉２）．在条件Ｎ≤６或Ｎ〉６,ｐ〈ｐ_Ｎ≡（Ｎ＋１－(２Ｎ－３)^1/2）／（Ｎ－３－(２Ｎ－３)^1/2）下,证明了存在唯一的λ₀,λ₀〉０,当λ＝λ₀时,有唯一的径向奇异解及无穷多个正解。     

简单对角BL时间序列模型的参数的矩估计及其渐近分布

本文研究简单对角ＢＬ模型ｘ_ｔ＝ｅ_ｔ＋ｂｘ_ｔ－１ｅ_ｔ-1参数ｂ和σ_t^２的估计问题，其中｛ｅ_ｔ｝是白噪声，Ｅ（ｅ_ｔ）＝０，ｅ（ｅ_ｔ）＜＋∞证明了矩估计b和σ_t^２的渐近正态性．     

Dirac定理的局部化与Hamilton图

设Ｇ为一个ｎ阶２－连通图，ｎ≥３．若｜Ｄ_ｎ／２（Ｋ_１，３）｜≥２且满足下述条件之一：ｉ）｜Ｄ_ｎ／２（Ｋ_１，３＋ｅ）｜≥２，ii）若Ｋ_１，３＋ｅ→Ｇ，ｘｙ(?)Ｅ（Ｋ_１，３＋ｅ），则ｍａｘ｛ｄＧ（ｘ），ｄＧ（ｙ）｝≥ｎ／２，则Ｇ是一个Ｈａｍｉｌｔｏｎｉａｎ图或其闭包为ｓＰ|⊕Ｈ，这里ｓＰ⊕Ｈ是一类极小２－边连通图．     

α型β级Bazilevic函数的Fekete-Szeg?问题

设Ｂ（α，β）（α＞０，０≤β＜１）表示在单位圆盘内定义的规范化的α型β级Ｂａｚｉｌｅｖｉｃ函数类．本文对Ｂ（α，β）中函数ｆ（ｚ）＝ｚ＋∑from∞to(ｎ＝２)ａ_ｎｚ^ｎ得到｜ａ３－λａ₂²｜（０≤λ≤１）的准确估计．     

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.     

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.     

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.