Nonexistence of [n, 5, d]q Codes Attaining the Griesmer Bound for q4 ?2q2 ?2q+1 ≤ d≤ q4?2q2 ?q

We prove that there does not exist a [q⁴+q³−q²−3q−1, 5, q⁴−2q²−2q+1]_q code over the finite field for q≥ 5. Using this, we prove that there does not exist a [g_q(5, d), 5, d]_q code with q⁴ −2q² −2q +1 ≤ d ≤ q⁴ −2q² −q for q≥ 5, where g_q(k,d) denotes the Griesmer bound.MSC 2000: 94B65, 94B05, 51E20, 05B25     

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.     

Sharp estimates for the convergence rate of double Fourier series in terms of orthogonal polynomials in the space L2((a, b) × (c, d); p(x)q(y))

Sharp estimates are obtained for the convergence rate of double Fourier series in terms of general orthogonal polynomials in some classes of functions and for the Kolmogorov N-widths of these classes. These results find applications in numerical analysis. Original Russian Text ? V.A. Abilov, M.K. Kerimov, 2009, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2009, Vol. 49, No. 8, pp. 1364–1368.     

Weyl’s theorem for algebraically wF(p, r, q) operators with p, r?>?0 and q?≥?1

If T (or T*) is an algebraically wF(p, r, q) operator with p, r > 0 and q ≥ 1 acting in an infinite-dimensional separable Hilbert space, then we prove that Weyl’s theorem holds for f(T) for any f ∈ Hol(σ(T)), where Hol(σ(T)) is the set of all analytic functions in an open neighborhood of σ(T). Moreover, if T* is a wF(p, r, q) operator with p, r > 0 and q ≥ 1, then the a-Weyl’s theorem holds for f(T). In addition, if T (or T*) is an algebraically wF(p, r, q) operator with p, r > 0 and q ≥ 1, then we establish the spectral mapping theorems for the Weyl spectrum and for the essential approximate point spectrum of T for any f ∈ Hol(σ(T)), respectively. Finally, we examine the stability of Weyl’s theorem and the a-Weyl’s theorem under commutative perturbations by finite-rank operators.     

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 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.     

The classical 1-system of Q?(7, q) and two-character sets

We will show that associated with the classical 1-system of the elliptic quadric Q ⁻(7, q) are certain infinite families of two-character sets with respect to hyperplanes, and partial ovoids of Q ⁺(15, q).     

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).     

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

Subexponential ultracontractivity and L p ? L q functional calculus

 We prove that if a symmetric submarkovian semigroup (T _t ) _t>0 satisfies an estimate of the form

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

漫谈曲线x~(2/3) y~(2/3)=a~(2/3)的构成

曲线总是作为符合某种条件的动点的集合(轨迹)。方程x~(2/3) y~(2/3)=a~(2/3)所表示的是一种特殊的曲线。它是符合什么条件的动点的集合呢?一般都是采用圆的一种内摆线形成方法而得出方程。有的书上就直接就方程进行讨论,从而指出这个方程所表示的曲线通常称为星形线。     

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.     

方程x''(t)=ax(t)+bx(3[(t+1)/3])的数值稳定性分析

本文研究了分段连续型微分方程x''(t)=ax(t)+bx(3[(t+1)/3]) Euler-Maclaurin方法的数值稳定性问题.利用特征分析的方法,获得了数值解稳定的充分条件,进而证明了Euler-Maclaurin方法保持了精确解的稳定性.最后给出了一些数值例子.     

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.     

旗传递5-(v,k,2)设计的分类

本文研究了5-(v,k,2)设计的分类问题.利用典型群PSL(2,q)的子群作用于投影线的轨道定理,证明了旗传递5-(v,k,2)设计的自同构群的基柱不能与PSL(2,3n)同构.从而证明了不存在旗传递的5-(v,k,2)设计.     

Involutions on surfaces with pg?=?q?=?0 and K2?=?3

We study surfaces of general type S with p _g  = 0 and K ² = 3 having an involution i such that the bicanonical map of S is not composed with i. It is shown that, if S/i is not rational, then S/i is birational to an Enriques surface or it has Kodaira dimension 1 and the possibilities for the ramification divisor of the covering map S → S/i are described. We also show that these two cases do occur, providing an example. In this example S has a hyperelliptic fibration of genus 3 and the bicanonical map of S is of degree 2 onto a rational surface.     

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

(α,β)-γ开集与(α,β)-γ-Ti空间

本文首先给出(α,β)-γ开集定义,获得了(α,β)-γ开集性质;然后引入了(α,β)-γ-T_i空间和(α,β)-γ-T_i^*空间概念(i=0,1/2,1,2,5/2),并得到它们更广泛的拓扑性质.     

Surfaces with pg?=?q?=?1, K2?=?8 and nonbirational bicanonical map

We prove that if the bicanonical map of a minimal surface of general type S with p _g  = q = 1 and K_S²=8{K_{S}^2=8} is nonbirational, then it is a double cover onto a rational surface. An application of this theorem is the complete classification of minimal surfaces of general type with p_g=q=1, K_S²=8{p_{g}=q=1, K_{S}^2=8} and nonbirational bicanonical map.