Strongly almost convergent generalized difference sequences associated with multiplier sequences

Let Λ = (λ _k ) be a sequence of non-zero complex numbers. In this paper we introduce the strongly almost convergent generalized difference sequence spaces associated with multiplier sequences i.e. w ₀[A,Δ ^m ,Λ,p], w ₁[A,Λ ^m ,Λ,p], w _∞[A,Δ ^m ,Λ,p] and study their different properties. We also introduce Δ _Λ ^m -statistically convergent sequences and give some inclusion relations between w ₁[Δ ^m ,λ,p] convergence and Δ _Λ ^m -statistical convergence. Communicated by Pavel Kostyrko     

Strongly almost (<Emphasis Type="Italic">ω, λ, q</Emphasis>)-summable sequences

The purpose of this paper is to introduce the spaces of sequences that are strongly almost (ω, λ, q)-summable with respect to a modulus function. We give some relations related to these sequence spaces. It is also shown that if a sequence is strongly (ω, λ, q)-summable with respect to a modulus function, then it is S(λ _q )-statistically convergent.     

On generalized statistical convergence of double sequences via ideals

The concept of statistical convergence is one of the most active area of research in the field of summability. Most of the new summability methods have relation with this popular method. In this paper we generalize the notions of statistical convergence, (λ, μ)-statistical convergence, (V, λ, μ) summability and (C, 1, 1) summability for a double sequence x = (x _jk ) via ideals. We also establish the relation between our new methods.     

The continuity of superposition operators on some sequence spaces defined by moduli

Let λ and μ be solid sequence spaces. For a sequence of modulus functions Φ = (ϕ k) let λ(Φ) = {x = (x _k ): (ϕk(|x _k |)) ∈ λ}. Given another sequence of modulus functions Ψ = (ψ_k), we characterize the continuity of the superposition operators P _f from λ(Φ) into μ (Ψ) for some Banach sequence spaces λ and μ under the assumptions that the moduli ϕk (k ∈ ℕ) are unbounded and the topologies on the sequence spaces λ(Φ) and μ(Ψ) are given by certain F-norms. As applications we consider superposition operators on some multiplier sequence spaces of Maddox type. This research was supported by Estonian Science Foundation Grant 5376.     

Small deviations of the maximal element of a sequence of weighted independent random variables

Consider a sequence {X _i } of independent copies of a nonnegative random variable X and let M = sup _{j ≥ 1}λ _j X _j , where {λ _j } is a nonincreasing sequence of positive numbers for which P(M < ∞) = 1. The asymptotic behavior of -logP(M < r) as r → 0 is studied.     

On some new generalized difference sequence spaces defined by a sequence of moduli

In this paper, we define the new generalized difference sequence spaces [V, λ, F, p, q]₀(Δ _v ^m ), [V, λ, F, p, q]₁(Δ _v ^m ) and [V, λ, F, p, q]_∞(Δ _v ^m ). We also study some inclusion relations between these spaces.     

Almost lacunary statistical and strongly almost lacunary convergence of sequences of fuzzy numbers

The purpose of this paper is to introduce the concepts of almost lacunary statistical convergence and strongly almost lacunary convergence of sequences of fuzzy numbers. We give some relations related to these concepts. We establish some connections between strongly almost lacunary convergence and almost lacunary statistical convergence of sequences of fuzzy numbers. It is also shown that if a sequence of fuzzy numbers is strongly almost lacunary convergent with respect to an Orlicz function then it is almost lacunary statistical convergent.     

Almost <Emphasis Type="Italic">C</Emphasis>(λ)-manifolds

In this paper, we study almost C(λ)-manifolds. We obtain necessary and sufficient conditions for an almost contact metric manifold to be an almost C(λ)-manifold. We prove that contact analogs of A. Gray’s second and third curvature identities on almost C(λ)-manifolds hold, while a contact analog of A. Gray’s first identity holds if and only if the manifold is cosymplectic. It is proved that a conformally flat, almost C(λ)-manifold is a manifold of constant curvature λ.     

New double sequence spaces of fuzzy numbers

Abstract

In this paper we introduce some new double sequence spaces of fuzzy numbers using Orlicz function and also we examine that if a sequence of fuzzy numbers is double strongly convergent with respect to an Orlicz function then it is double statistical convergent.     

On some generalized difference paranormed sequence spaces associated with multiplier sequence defined by modulus function

In this article we introduce the paranormed sequence spaces(f,Λ,△m,p),c0(f,Λ,△m,p) and ■∞(f,Λ,△m,p),associated with the multiplier sequence Λ =(λk),defined by a modulus function f.We study their different properties like solidness,symmetricity,completeness etc.and prove some inclusion results.     

Inverse problem for zeros of certain koebe-related functions

If w₁,…,w _N is a finite sequence of nonzero points in the unit disk, then there are distinct points λ₁,…, λ_N on the unit circle and positive numbers Μ₁,…,Μ _N such that is the zero sequence of the function 1 — . The points λ₁,…, λ_N and numbers Μ₁,…,Μ_N are unique (except for reorderings).     

Optimization problems of the third edge-connectivity of graphs

The third edge-connectivity λ3(G) of a graph G is defined as the minimum cardinality over all sets of edges, if any, whose deletion disconnects G and each component of the resulting graph has at least 3 vertices. An upper bound has been established for λ3(G) whenever λ3(G) is well-defined. This paper first introduces two combinatorial optimization concepts, that is, maximality and superiority, of λ3(G), and then proves the Ore type sufficient conditions for G to be maximally and super third edge-connected. These concepts and results are useful in network reliability analysis.     

Completeness of the system {z^λn} in L^2[B,α0]

Let B be an unbounded domain located outside an angle domain with vertex at the origin, A ={λn}（n = 1,2,...） be a sequence of complex numbers satisfying sup ｜ arg（λn）｜ 〈 α 〈 π/2 and denote by M（∧） = {z^λ, λ ∈ ∧} the corresponding system of functions z^λ（λ∈∧）. Let α0（z） be a weight function defined on B. We obtain a completeness theorem for the system M（∧） in the Hilbert space L^2 [B, α0].     

Two cardinal versions of diamond

Roughly speaking, ◇_K,λ asserts the existence of a sequence of size <κ sets that captures every subset ofλ on a stationary set. The paper is devoted to the study of ◇_K,λ and related principles, which are for instance obtained by considering sequences of larger sets, or by requesting the simultaneous capture of many subsets ofλ. Our main result is that ◇_K,λ holds in caseλ>2^<K .     

Suites de longueur minimale associees a un ensemble normal donne

For a given subsetA of the set of real numbers, we search a sequence Λ=(λ _n) of real numbers such that bothA is the normal setB(Λ) associated to Λ, and Λ takes its values in a bounded interval, with a minimal lengthM. A lower bound ofM is obtained, which gives some necessary conditions of existency of such a bounded sequence Λ. More details are given whenA is a subset of the set of integers. In this case, the problem is to find a polynomialQ of lowest degree such that the productP.Q has non-negative coefficients, for some special given polynomialP.      

Almost-all results on the p λ problem. II

Summary Suppose that 1/2 ≦ λ < 1. Balog and Harman proved that for any real θ there exist infinitely many primes p satisfying p^λ-θ < p^{-(1-λ)/2+ ε} (with an asymptotic result). In the present paper we establish that for almost all θ in the interval 0 ≦ θ < 1 there exist infinitely many primes p such that {p^λ-θ} < p^{-min{(2-λ)/6,(14-9λ)/32}+ε}. Thus we obtain a better result for almost all θ than for a single θ if λ>1/2.     

Small deviations of the maximal element of a sequence of independent variables with smooth weights

We study logarithmic small deviations of M = sup_{j \geqslant 1} l_jX_j M = \mathop {\sup }\limits_{j \geqslant 1} {\lambda_j}{X_j} , where {X _j } are i.i.d. nonnegative random variables and {λ _j } is a sequence of positive nonincreasing numbers that satisfies certain conditions of regularity. Bibliography: 3 titles.     

The asymptotic behavior of Chern-Simons Higgs model on a compact Riemann surface with boundary

We study the self-dual Chern-Simons Higgs equation on a compact Riemann surface with the Neumann boundary condition.In the previous paper,we show that the Chern-Simons Higgs equation with parameter λ0 has at least two solutions(uλ1,uλ2) for λ sufficiently large,which satisfy that uλ1→u0 almost everywhere as λ→∞,and that uλ2→∞ almost everywhere as λ→∞,where u 0 is a(negative) Green function on M.In this paper,we study the asymptotic behavior of the solutions as λ→∞,and prove that uλ2-uλ2 converges to a solution of the Kazdan-Warner equation if the geodesic curvature of the boundary M is negative,or the geodesic curvature is nonpositive and the Gauss curvature is negative where the geodesic curvature is zero.     

Electron scattering at the domain wall

We study the transmission and reflection coefficients for the Hamiltonian of a spin-polarized electron passing through the domain wall in a ferromagnetic quantum wire. We prove that total reflection occurs for energies λ ∈ (−α, α) (−α is the boundary of the essential spectrum) for both sufficiently small and sufficiently large λ, which agrees with the ballistic magnetoresistance effect in ferromagnetic nanocontacts. For energies λ > α, almost total reflection becomes almost total transmission, and both effects occur without a spin flip.     

一类无限矩阵拓扑代数

Let λ and μ be sequence spaces and have both the signed-weak gliding hump property, (λ,μ) the algebra of the infinite matrix operators which transform λ into μ. In this paper, it is proved that if λ and μ are β-spaces and λ^β and ,μ^β have also the signed-weak gliding hump property, then for any polar topology τ, ((λ,μ),τ) is always sequentially complete locally convex topological algebra.