On the description of overgroups of E(m,R)?E(n,R)

The subgroups E(m,R) ⊗ E(n,R) ≤ H ≤ G = GL(mn,R) are studied under the assumption that the ring R is commutative and m, n ≥ 3. The group GL _m ⊗GL _n is defined by equations, the normalizer of the group E(m,R) ⊗ E(n,R) is calculated, and with each intermediate subgroup H it is associated a uniquely determined lower level (A,B,C), where A,B,C are ideals in R such that mA,A ² ≤ B ≤ A and nA,A ² ≤ C ≤ A. The lower level specifies the largest elementary subgroup satisfying the condition E(m, n,R, A,B,C) ≤ H. The standard answer to this problem asserts that H is contained in the normalizer N _G (E(m,n,R, A,B,C)). Bibliography: 46 titles.     

Complete description of invariant Einstein metrics on the generalized flag manifold SO(2n)/U(p)?× U(n ? p)

We find the precise number of non-K?hler SO(2n)-invariant Einstein metrics on the generalized flag manifold M = SO(2n)/U(p)×U(n−p) with n ≥ 4 and 2 ≤ p ≤ n−2. We use an analysis on parametric systems of polynomial equations and we give some insight towards the study of such systems. We also examine the isometric problem for these Einstein metrics.     

On the Diophantine Equation G n ( x )?= G m ( P ( x ))

 Let K be a field of characteristic 0 and let p, q, G ₀ , G ₁ , P ∈K[x], deg P ⩾ 1. Further, let the sequence of polynomials (G _n (x)) _n=0 ^∞ be defined by the second order linear recurring sequence

On the Diophantine Equation G n ( x )?= G m ( P ( x ))

 Let K be a field of characteristic 0 and let p, q, G ₀ , G ₁ , P ∈K[x], deg P ⩾ 1. Further, let the sequence of polynomials (G _n (x)) _n=0 ^∞ be defined by the second order linear recurring sequence

On solutions of functional-differential equations f ′( x ) = a ( x ) f ( g ( x )) + b ( x ) f ( x ) + c ( x ) in the large

We consider solutions of functional-differential equations

On Finite Pseudorandom Binary Sequences, V.On (nα) and (n 2α) Sequences

 Let k be a positive integer and α be a real number, and for if the fractional part of is <1/2 and e _n =−1 if it is ≥1/2. The pseudorandom properties of the sequence are studied. As measures of pseudorandomness, the regularity of the distribution relative to arithmetic progressions and the correlation are used. Here the special cases k=1 and k=2 are studied (while the case k>2 will be studied in the sequel). (Received 23 April 1999)     

Connected subgroups of SO(2, n) acting irreducibly on ?2,n

We classify all connected subgroups of SO(2, n) that act irreducibly on ℝ^{2, n} . Apart from SO ₀(2, n) itself these are U(1, n/2), SU(1, n/2), if n even, S ¹ · SO(1, n/2) if n even and n ≥ 2, and SO ₀(1, 2) for n = 3. Our proof is based on the Karpelevich Theorem and uses the classification of totally geodesic submanifolds of complex hyperbolic space and of the Lie ball. As an application we obtain a list of possible irreducible holonomy groups of Lorentzian conformal structures, namely SO ₀(2, n), SU(1, n), and SO ₀(1, 2).     

On the space l P(β)

Let be a sequence of positive numbers and 1 ≤p < ∞. We consider the spacel ^P(β) of all power series such that . We give a necessary and sufficient condition for a polynomial to be cyclic inl ^P(β) and a point to be bounded point evaluation onl ^P(β).     

n维双曲空间和n维球面空间中的正弦定理及应用

本文研究了n维双曲空间和n维球面空间中单形的正弦定理和相关几何不等式. 应用距离几何的理论和方法, 给出了n维双曲空间和n维球面空间中一种新形式的正弦定理, 利用建立的正弦定理获得了Hadamard 型和Veljan-Korchmaros型不等式. 另外, 建立了涉及两个n维双曲单形和n维球面单形的"度量加"的一些几何不等式.     

On the Seneta Sequences

In this paper, we prove some properties of the Seneta sequences and functions, and in particular we prove a representation theorem in the Karamata sense for the sequences from the Seneta class SOc.     

SL(n+1,R)/S(GL(1,R)×GL(n,R))上线丛的一个超几何方程

本文研究了伪黎曼对称空间SL（n+1,R）/S（GL（1,R）×GL（n,R））线丛上的微分方程.利用李代数方法,即Casimir算子得到这个微分算子.这个微分算子是一个超几何方程,这个结论推广了文献[1,3,5]中的微分方程.     

关于m-HPK(n1,n2,n3,n4)-残差图

本文研究了3-维超平面完备残差图以及m 重3-维超平面完备残差图. 利用容斥原理以及集合的运算性质等方法, 分别获得了3-维超平面完备残差图和m 重3-维超平面完备残差图的最下阶以及二者的唯一极图, 将文献[1] 中定义的残差图从平面推广到超平面上.     

观察时间服从Erlang(n)分布的对偶模型红利支付

本文研究了观察时间服从Erlang（n）分布的对偶模型红利支付问题.在收益额的拉普拉斯变换是有理拉普拉斯变换的情况下,获得了破产之前总贴现红利V（u;b）的求解方法.该结果推广了文献[8]的相应结论.     

On a Class of Vector-Valued Sequences Associated with Multiplier Sequences

In this article we introduce the vector valued sequence space m(E_k,φ,∧),associated with themultiplier sequence ∧=(λ_k) of non-zero complex numbers,and the terms of the sequence are chosen from theseminormed spaces E_k,seminormed by f_k for all k∈N.This generalizes the sequence space m(φ) introducedand studied by Sargent.We study some of its properties like solidity,completeness,and obtain some inclusionresults.We also characterize the multiplier problem and obtain the corresponding spaces dual to m(E_k,φ,∧).We prove some general results too.     

唯一g(x)-clean环

本文研究了唯一g(x)-clean环的性质与结构.利用g(x)-clean环的方法,得到了唯一g(x)-clean环与g(x)-clean环的关系,唯一g(x)-clean环与一类特殊的生成环的等价条件,以及斜Hurwitz级数环的g(x)-clean性,推广了g(x)-clean环的研究结果.     

Spherical Harmonic Analysis on Buildings of Type ? n

 To any locally finite thick building of type there is naturally associated a commutative algebra of operators. When is constructed from a local field F with local ring , and , then is isomorphic to the convolution algebra of compactly supported bi-K-invariant functions on PGL(n+1,F). We give a proof, valid for any , that the multiplicative functionals on may all be expressed in terms of Hall–Littlewood polynomials. Regarding as a subalgebra of the C ^*-algebra of bounded operators on the space of square summable functions on the vertex set of , we find the spectrum of the C ^*-algebra , the closure of . This generalizes results obtained in [3] when n = 1 and in [5] when n = 2.     

Lie Symmetries of the Equation ut(x, t)?+?g(u)ux(x, t) = 0

In this paper the invariance criterion is applied for the nonlinear equation

Asymptotic stability for the Navier–Stokes equations in L n

Considering the Navier–Stokes equations in W ì \mathbbRⁿ\Omega \subset {\mathbb{R}}^n, we prove the asymptotic stability for weak solutions in the marginal class u ∈ C _B (0, ∞; L ⁿ ) with arbitrary initial and external perturbations.     

Cauchy problem F(t, x(t), x′(t)) = 0, x(0) = 0: solvability and asymptotics of solutions

For the singular Cauchy problem, the authors find some sufficient conditions for the existence of continuously differentiable solutions x: (0, ρ] → ℝ (ρ > 0 is sufficiently small) of the form