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

Topological hochschild homology of extensions of ?/p? by polynomials, and of ?[x]/(xn) and ?[x]/(xn?1)

Topological Hochschild homology is calculated for the rings /p[x]/(f(x)) (where p is prime and f(x) /p[x] any polynomial), [x]/(x ⁿ) and [x]/(x ⁿ–1). A spectral sequence argument is used for calculating the homology of the topological Hochschild homology spectrum, from which its stable homotopy structure can be read off since the spectrum is known for a priori reasons to be a restricted product of Eilenberg-MacLane spectra.     

The Lindel?f number of Cp(X)×Cp(X) for strongly zero-dimensional X

We prove that if X is a strongly zero-dimensional space, then for every locally compact second-countable space M, C _p (X, M) is a continuous image of a closed subspace of C _p (X). It follows in particular, that for strongly zero-dimensional spaces X, the Lindel?f number of C _p (X)×C _p (X) coincides with the Lindel?f number of C _p (X). We also prove that l(C _p (X ⁿ )^κ) ≤ l(C _p (X)^κ) whenever κ is an infinite cardinal and X is a strongly zero-dimensional union of at most κcompact subspaces.     

Pairwise ?-independence of the sets TiA for a mixing transformation T

If an ergodic automorphism T of a probability space is not partially rigid, then for any numbers a ∈ (0, 1) and ɛ > 0 there exists a set A such that all sets T ⁱ A, i > 0, are pairwise ɛ-independent. __________ Translated from Funktsional’nyi Analiz i Ego Prilozheniya, Vol. 43, No. 2, pp. 88–91, 2009 Original Russian Text Copyright ? by V. V. Ryzhikov This research was carried out under the Program for Support of Leading Scientific Schools in the Russian Federation (grant no. 6849.2006.1).     

On the subspace L((x ∧ y)m) of Sm(∧2?4)

We take the exterior power ℝ⁴ ∧ ℝ⁴ of the space ℝ⁴, its mth symmetric power V = S ^m (∧²ℝ⁴) = (ℝ⁴ ∧ ℝ⁴) ∨ (ℝ⁴ ∧ ℝ⁴) ∨ ... ∨(ℝ⁴ ∧ ℝ⁴), and put V ₀ = L((x ∧ y)∨ ... ∨(x ∧ y): x, y ∈ ℝ⁴). We find the dimension of V ₀ and an algorithm for distinguishing a basis for V ₀ efficiently. This problem arose in vector tomography for the purpose of reconstructing the solenoidal part of a symmetric tensor field. Original Russian Text Copyright ? 2009 Gubarev V. Yu. The author was supported by the State Maintenance Program for the Leading Scientific Schools of the Russian Federation (Grant NSh-344.2008.1). __________ Novosibirsk. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 50, No. 3, pp. 503–514, May–June, 2009.     

KO?i groups of G3(?n), n odd

We use the work of Karoubi and Mudrinski on the real Grothendieck's groups of certain complex projective bundles to show that the torsion of the KO ^–i groups of G ₃( ⁿ ), n odd, are related to the known torsion of the KO ^–i groups of G₂( ⁿ ).     

关于矩阵方程X+A*X-αA+B*X-βB=I的正定解

本文研究了矩阵方程X+A*X-αA+B*X-βB=I在α,β∈(0,1]时的正定解.利用单调有界极限存在准则,构造三种迭代算法,获得了方程的正定解,拓宽了此类方程的求解方法.数值算例说明算法的可行性.     

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 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.     

Embedding of Hpω in the class eL

We obtain the necessary conditions for the embedding H _p ^ω ⊂ e ^L (1≤p∞) with convex modulus of continuity ω in terms of this modulus. In the case p=1 these conditions are also sufficient.     

Vector subdivision schemes in (Lp(?s))r(1?p?∞) spaces

The purpose of this paper is to investigate the refinement equations of the form

Hypersurfaces in the Lorentz-Minkowski space satisfying Lkψ?=?Aψ?+?b

We study hypersurfaces in the Lorentz-Minkowski space \mathbbLⁿ⁺¹{\mathbb{L}^{n+1}} whose position vector ψ satisfies the condition L _k ψ = Aψ + b, where L _k is the linearized operator of the (k + 1)th mean curvature of the hypersurface for a fixed k = 0, . . . , n − 1, A ? \mathbbR^(n+1)×(n+1){A\in\mathbb{R}^{(n+1)\times(n+1)}} is a constant matrix and b ? \mathbbLⁿ⁺¹{b\in\mathbb{L}^{n+1}} is a constant vector. For every k, we prove that the only hypersurfaces satisfying that condition are hypersurfaces with zero (k + 1)th mean curvature, open pieces of totally umbilical hypersurfaces \mathbbSⁿ₁(r){\mathbb{S}^n_1(r)} or \mathbbHⁿ(-r){\mathbb{H}^n(-r)}, and open pieces of generalized cylinders \mathbbS^m₁(r)×\mathbbR^n-m{\mathbb{S}^m_1(r)\times\mathbb{R}^{n-m}}, \mathbbH^m(-r)×\mathbbR^n-m{\mathbb{H}^m(-r)\times\mathbb{R}^{n-m}}, with k + 1 ≤ m ≤ n − 1, or \mathbbL^m×\mathbbS^n-m(r){\mathbb{L}^m\times\mathbb{S}^{n-m}(r)}, with k + 1 ≤ n − m ≤ n − 1. This completely extends to the Lorentz-Minkowski space a previous classification for hypersurfaces in \mathbbRⁿ⁺¹{\mathbb{R}^{n+1}} given by Alías and Gürbüz (Geom. Dedicata 121:113–127, 2006).     

环Fpm[u]/<ua>上一类常循环码

本文研究有限链环上一类λ-常循环码.利用x~n-1在R_a[x]上可唯一分解为两两互素的首一基本不可约多项式乘积,刻画了R_a中长为p~sn的所有λ-常循环码,推广了开晓山等人在文献[4]中的结果.     

Asymptotics of the Best Polynomial Approximation of?|x|p and?of?the Best Laurent Polynomial Approximation of sgn(x) on Two Symmetric Intervals

We present a new method that allows us to get a direct proof of the classical Bernstein asymptotics for the error of the best uniform polynomial approximation of |x| ^p on two symmetric intervals. Note that, in addition, we get asymptotics for the polynomials themselves under a certain renormalization. Also, we solve a problem on asymptotics of the best approximation of sgn(x) on [−1,−a]∪[a,1] by Laurent polynomials.      

Gaussian Estimates of Order α and L p -Spectral Independence of Generators of C 0-Semigroups

We prove L^p-spectral independence for generators of C₀-semigroups estimated by the positive C₀-semigroup . In the preliminary process of the proof, we obtain the asymptotic expansion formula for the integral kernel of the C₀-semigroup .     

Poisson boundary of GLd(?)

We construct the Poisson boundary for a random walk supported by the general linear group on the rational numbers as the product of flag manifolds over the p-adic fields. For this purpose, we prove a law of large numbers using Oseledets’ multiplicative ergodic theorem. The only assumption we need is some moment condition on the measure governing the jumps of the random walk, but no irreducibility hypothesis is made.     

关于f+a(f(k))n值分布的一个注记

本文研究亚纯函数的值分布问题.利用值分布理论,获得了一个带精简密指量的模分布的不等式,改进了Xu和Yang等人的结果.     

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

Quasirecognition by prime graph of F4(q) where q?=?2n?>?2

The prime graph of a finite group G is denoted by Γ(G). In this paper as the main result, we show that if G is a finite group such that Γ(G) = Γ(F ₄(q)), where q = 2 ⁿ  > 2, then G has a unique nonabelian composition factor isomorphic to F ₄(q). We also show that if G is a finite group satisfying |G| = |F ₄(q)| and Γ(G) = Γ(F ₄(q)), where q = 2 ⁿ  > 2, then G @ F₄(q){G \cong F_4(q)}. As a consequence of our result we give a new proof for a conjecture of Shi and Bi for F ₄(q) where q = 2 ⁿ  > 2.