本刊英文版Vol.20(2004),No.2论文摘要

<正> Some Arithmetic on tlie Hardy Sums s_2(h, k) and s_3(h, k) Mümün CANAbstract In this work, Rademacher's two questions about Dedekind sums are applied tothe Hardy sums s_2(h, k) and s_3(h, k). Some relations between these sums are obtained and someinequalities are given.     

SCORE LISTS IN （h, k）-BIPARTITE HYPERTOURNAMENTS

Given non-negative integers m,n,h and k with m ≥ h ＞ 1 and n ≥ k ＞ 1, an (h, k)-bipartite hypertournament on m n vertices is a triple (U, V, A), where U and V are two sets of vertices with |U| = m and |V| = n, and A is a set of (h k)-tuples of vertices,called arcs, with at most h vertices from U and at most k vertices from V, such that for any h k subsets U1 ∪ V1 of U ∪ V, A contains exactly one of the (h k)! (h k)-tuples whose entries belong to U1 ∪ V1. Necessary and sufficient conditions for a pair of non-decreasing sequences of non-negative integers to be the losing score lists or score lists of some(h, k)-bipartite hypertournament are obtained.     

（r, s）-STABILITY OF UNFOLDING OFF-EQUIVARIANT BIFURCATION PROBLEM

In this paper,the F-equivariant (s,t)-equivalence relation and F-equivariant infinitesimally (r,s)-stability of F-equivariant bifurcation problem are defined. The criterion for F-equivariant infinitesimally (r, s)-stability is proven when F is a compact finite Lie group . Transversality condition is used to characterize the stability.     

I THE （μ＋ κ）oORBITS OF ESSENTIALLY NORMAL OPERATORS AND THEIR STRONG IRREDUCIBILITY

The authors characterize the (μ +κ)-orblts of a class essmntially normal operators and provethat some essentially normal operators with connected spectrum are strongly irreducible aftera small compact perturbation. This partially answers a question of Domigo A. Herrero.     

格点偏序集的一些组合恒等式（英）

This paper is devoted to the counting of j-chains of lattice-point poset. The incidence function and two basic enumerators associated with it are introduced and evaluated. Our results contain a lot of combinatorial sums.     

DOMAIN OF THE DOUBLE SEQUENTIAL BAND MATRIX B（r,s） ON SOME MADDOX＇S SPACES

The domain of generalized difference matrix B(r, s) in the classical spaces l∞,c, and c0 was recently studied by Kirisci and Bassar in [16]. The main goal of this article is to introduce the paranormed sequence spaces l∞( B, p), c( B, p), and c0( B, p), which are more general and comprehensive than the corresponding consequences of the matrix domain of B(r, s), as well as other studies in literature. Besides this, the alpha-, beta-, and gamma-duals of the spaces l∞( B, p), c( B, p), and c0( B, p) are computed and the bases of the spaces c( B, p)and c0( B, p) are constructed. The final section of this article is devoted to the characterization of the classes(λ( B, p) :) and( : λ( B, p)), where λ∈ {c, c0, l∞}and is any given sequence space. Additionally, the characterization of some other classes which are related to the space of almost convergent sequences is obtained by means of a given lemma.     

On Approximation of Function Classes in Lorentz Spaces with Anisotropic Norm

In this paper, Lorentz space of functions of several variables and Besov＇s class are considered. We establish an exact approximation order of Besov＇s class by partial sums of Fourier＇s series for multiple trigonometric system.     

EXISTENCE OF SOLUTIONS OF A FAMILY OF NONLINEAR BOUNDARY VALUE PROBLEMS IN L^2-SPACES

By using the perturbation results of sums of ranges of accretive mappings of Calvert and Gupta (1978),the abstract results on the existence of solutions of a family of nonlinear boundary value problems in L^2 (Ω) are studied. The equation discussed in this paper and the methods used here are extension and complement to the corresponding results of Wei Li and He Zhen‘s previous papers. Especially,some new techniques are used in this paper.     

Some Limit Theorems for Sequences of Pairwise NQD Random Variables

In this article, the authors study some limit properties for sequences of pairwise NQD random variables, which are not necessarily identically distributed. They obtain Baum and Katz complete convergence and the strong stability of Jamison＇s weighted sums for pairwise NQD random variables, which may have different distributions. Some wellknown results are improved and extended.     

Readjustment of the Paper [J.Kaur and S.S.Bhatia,Integrability and L~1-Convergence of Double Cosine Trigonometric Series,Anal.Theory Appl.,27(1)(2011),pp.32–39.]

In this paper, we show that new modified double cosine trigonometric sums introduced in [1] are inappropriate, the class of double sequences Jd introduced there is unusable for such sums and consequently the results obtained in it are completely incorrect. We here introduce appropriate modified double cosine trigonometric sums making the class Jd usable considering a particular double cosine trigonometric series.     

Some estimations for the least degree of identities of subspaces M1(m,k) (F) of the matrix superalgebra M(m,k)(F)

We estimate the least degree of identities of subspaces M ₁^(m,k) (F) of the matrix superalgebra M ^(m,k)(F) over the field F for arbitrary m and k. For subspaces M ₁^(m,1) (F) (m≥1) and M ₁^(2,2) (F) we obtain concrete minimal identities.     

Cocycle d'Euler etK2

In this paper we construct a canonical 2-cocycle on the groupP SL(2,k) with values in the Witt groupW(k) of the fieldk. This allows us to produce anatural homomorphism :H ₂(SL(2,k); Z)I ²(k), whereI ²(k) is the square of the fundamental ideal. We prove that this homomorphism is in fact a lift of Milnor's symbol.

     

On Generalized Hardy Sums <Emphasis Type="Italic">s</Emphasis><Subscript>5</Subscript>(<Emphasis Type="Italic">h,k</Emphasis>)

The aim of this paper is to study generalized Hardy sums s ₅(h, k). By using mediants and the adjacent difference of Farey fractions, we establish a relationship between s ₅(h, k) and Farey fractions. Using generalized Dedekind sums and a generalized periodic Bernoulli function, we define generalized Hardy sums s _5,p (h,k). A relationship between s _5,p (h, k) and the Hurwitz zeta function is established. By using the definitions of Lambert series and cotπz, we establish a relationship between s ₅(h,k) and Lambert series.__________Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 56, No. 10, pp. 1434–1440, October, 2004.     

Approximations from Subspaces of C0(X)

We show among other things that if B is a linear space of continuous real-valued functions vanishing at infinity on a locally compact Hausdorff space X, for which there is a continuous function h defined in a neighbourhood of 0 in the real line which is non-affine in every neighbourhood of 0 and satisfies |h(t)|k |t| for all t, such that hb is in B whenever b is in B and the composite function is defined, then every function in C₀(X) which can be approximated on every pair of points in X by functions in B can be approximated uniformly by functions in B.     

On the Function w( x)=|{1= s= k : x= a s (mod n s)}|

For a finite system of arithmetic sequences the covering function is w(x) = |{1 s k : x a_s (mod n_s)}|. Using equalities involving roots of unity we characterize those systems with a fixed covering function w(x). From the characterization we reveal some connections between a period n₀ of w(x) and the moduli n₁, . . . , n_k in such a system A. Here are three central results: (a) For each r=0,1, . . .,n_k/(n₀,n_k)–1 there exists a Jc{1, . . . , k–1} such that . (b) If n₁ ···n_k–l <n_k–l+1 =···=n_k (0 < l < k), then for any positive integer r < n_k/n_k–l with r 0 (mod n_k/(n₀,n_k)), the binomial coefficient can be written as the sum of some (not necessarily distinct) prime divisors of n_k. (c) max_(xw(x) can be written in the form where m₁, . . .,m_k are positive integers.The research is supported by the Teaching and Research Award Fund for Outstanding Young Teachers in Higher Education Institutions of MOE, and the National Natural Science Foundation of P. R. China.     

2-Summing operators on C([0, 1], lp) with values in l1

Let Ω be a compact Hausdorff space, X a Banach space, C(Ω, X) the Banach space of continuous X-valued functions on Ω under the uniform norm, U: C(Ω, X) → Y a bounded linear operator and U ^#, U _# two natural operators associated to U. For each 1 ≤ s < ∞, let the conditions (α) U ∈ Π _s (C(Ω, X), Y); (β)U ^# ∈ Π _s (C(Ω), Π _s (X, Y)); (γ) U _# ε Π _s (X, Π _s (C(Ω), Y)). A general result, [10, 13], asserts that (α) implies (β) and (γ). In this paper, in case s = 2, we give necessary and sufficient conditions that natural operators on C([0, 1], l _p ) with values in l ₁ satisfies (α), (β) and (γ), which show that the above implication is the best possible result.     

When isf(x1, x2, ..., xn) =u1(x1) +u2(x2) + ... +un(xn)?

We discuss subsetsS of ℝⁿ such that every real valued functionf onS is of the formf(x₁, x₂, ..., x_n) =u ₁(x₁) +u ₂(x₂) +...+u _n(x_n), and the related concepts and situations in analysis.     

On αrγs(k)-perfect graphs

For some integer k0 and two graph parameters π and τ, a graph G is called πτ(k)-perfect, if π(H)−τ(H)k for every induced subgraph H of G. For r1 let α_r and γ_r denote the r-(distance)-independence and r-(distance)-domination number, respectively. In (J. Graph Theory 32 (1999) 303–310), I. Zverovich gave an ingenious complete characterization of α₁γ₁(k)-perfect graphs in terms of forbidden induced subgraphs. In this paper we study α_rγ_s(k)-perfect graphs for r,s1. We prove several properties of minimal α_rγ_s(k)-imperfect graphs. Generalizing Zverovich's main result in (J. Graph Theory 32 (1999) 303–310), we completely characterize α_2r−1γ_r(k)-perfect graphs for r1. Furthermore, we characterize claw-free α₂γ₂(k)-perfect graphs.     

Universal embeddings for theD4(2) hexagon andJ2near-octagon

The universal embeddings overF₂ of the generalized hexagon for³D₄(2)and the near-octagon forJ₂are determined to be the 28-dimensional adjoint modules: for typeD₄in the first case, and in the second from the 14-dimensional adjointF₄-module forG₂(4)containingJ₂.