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).     

关于一类弱Berwald的(α,β)-度量

本文研究了一类重要的形如F=α +εβ +β arctan(β/α) (ε为常数)的弱Berwald (α, β)-度量.利用S-曲率公式,获得了这类度量为弱Berwald度量的充要条件.并且还证明了F为具有标量旗曲率的弱Berwald度量当且仅当它们为Berwald度量且旗曲率消失.     

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.     

Optimality Conditions and Duality for?Nondifferentiable Multiobjective Fractional Programming Problems with?(C,α,ρ,d)-convexity

The purpose of this paper is to consider a class of nondifferentiable multiobjective fractional programming problems in which every component of the objective function contains a term involving the support function of a compact convex set. Based on the (C,α,ρ,d)-convexity, sufficient optimality conditions and duality results for weakly efficient solutions of the nondifferentiable multiobjective fractional programming problem are established. The results extend and improve the corresponding results in the literature.     

(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.     

The interior operation in a ψ -density topology

We prove that for an arbitrary setA ⊂ ℝ its interior in aψ-density topology equalsA ∩ φ^β(B), whereB is a measurable kernel ofA andβ is some countable ordinal. Moreover, eachβ, 1≤β<Ω, realizes the interior ofA for someA εS.     

一类α次殆β型螺形映照的偏差上界估计

本文研究了复向量空间Cn中开单位球Bn,复Banach空间中单位球B和域?p1,···,pn上一类α次殆β型螺形映照的偏差估计问题.利用不等式、矩阵及α次殆β型螺形映照的增长定理等方法,获得了上述域上的一类α次殆β型螺形映照的偏差上界估计,所得结果推广了一些已知的结论.     

Equivalence of Minimal ?0- and ?p-Norm Solutions of Linear Equalities, Inequalities and Linear Programs for Sufficiently Small p

For a bounded system of linear equalities and inequalities, we show that the NP-hard ℓ ₀-norm minimization problem is completely equivalent to the concave ℓ _p -norm minimization problem, for a sufficiently small p. A local solution to the latter problem can be easily obtained by solving a provably finite number of linear programs. Computational results frequently leading to a global solution of the ℓ ₀-minimization problem and often producing sparser solutions than the corresponding ℓ ₁-solution are given. A similar approach applies to finding minimal ℓ ₀-solutions of linear programs.     

Sum of sequence spaces and matrix transformations mapping in s α 0 ((Δ ? λ I ) h ) + s β ( c ) ((Δ ? μ I ) l )

We deal with the sum of sequence spaces. Then we apply these results to characterize matrix transformations mapping between s ^h,l (λ, μ) = s _α ⁰((Δ − λI) ^h ) + s _β ^(c)((Δ − μI) ^l ) and s _γ . Among other things the aim of this paper is to reduce the set (s ^h,l (λ, μ), s _γ to a set of the form S _τ,γ .      

The generalized bisymmetric solutions of the matrix equation A 1 X 1 B 1 + A 2 X 2 B 2 + ? + A l X l B l = C and its optimal approximation

For fixed generalized reflection matrix P, i.e. P ^T  = P, P ² = I, then matrix X is said to be generalized bisymmetric, if X = X ^T  = PXP. In this paper, an iterative method is constructed to find the generalized bisymmetric solutions of the matrix equation A ₁ X ₁ B ₁ + A ₂ X ₂ B ₂ + ⋯ + A _l X _l B _l  = C where [X ₁,X ₂, ⋯ ,X _l ] is real matrices group. By this iterative method, the solvability of the matrix equation can be judged automatically. When the matrix equation is consistent, for any initial generalized bisymmetric matrix group , a generalized bisymmetric solution group can be obtained within finite iteration steps in the absence of roundoff errors, and the least norm generalized bisymmetric solution group can be obtained by choosing a special kind of initial generalized bisymmetric matrix group. In addition, the optimal approximation generalized bisymmetric solution group to a given generalized bisymmetric matrix group in Frobenius norm can be obtained by finding the least norm generalized bisymmetric solution group of the new matrix equation , where . Given numerical examples show that the algorithm is efficient. Research supported by: (1) the National Natural Science Foundation of China (10571047) and (10771058), (2) Natural Science Foundation of Hunan Province (06JJ2053), (3) Scientific Research Fund of Hunan Provincial Education Department(06A017).     

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     

Some projectively flat (α, β)-metrics

In this paper, we study a class of Finsler metrics in the form , where is a Riemannian metric, β = b _i y ⁱ is a 1-form, and ε and k ≠ 0 are constants. We obtain a sufficient and necessary condition for F to be locally projectively flat and give the non-trivial special solutions. Moreover, it is proved that such projectively flat Finsler metrics with the constant flag curvature must be locally Minkowskian.     

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).     

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.     

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.     

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 .     

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

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.     

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).