On the Degree of Approximation by Spherical Translations

The degree of approximation of spherical functions by the translations formed by a function defined on the unit sphere is dealt with. A kind of Jackson inequality is established under the condition that none of the L^2（S^q） norms of the orthogonal projection operators of the translated function are zeros. In the present paper we show that the spherical translations share the same degree of approximation as that of spherical harmonics.     

基于粗糙集的患者满意度评价模型及其实证分析

在文献阅读及实地调研的基础上,本文提出了患者满意度的定义,建立了影响患者满意度的指标体系,介绍了粗糙集的相关概念及利用粗糙集进行评价的步骤,提出了新的约简方法,构建了基于粗糙集的患者满意度评价模型并进行了实证分析,得出了影响患者满意度的关键指标,并计算了关键指标权重,对江西省十个医院进行了综合评价值的计算.     

数学是……

数学是一首悠扬的歌
　　直线成了五线谱
　　圆连成了音符
　　唱出了奇妙的快乐
　　数学是一幅清新的画
　　曲线成了浪花
　　线性规划调出了最佳
　　绘出了斑斓的色彩     

标准体系的使用期的模型与分析

本文提出了关于标准体系使用期的两个模型。首先定义了标准使用期,然后讨论了模型的合理性。通过模型讨论了标准使用期的性质,给出了数值示例。提出了需进一步研究的问题。     

绿色食品需求函数的一种求解方法

本分析了影响绿色食品消费的因素，建立了消费消费绿色食品及同类一般食品的效用最大化数学规划模型，给出了Kuhn-Tucker条件；引入了绿色食品置信度参数并建立了一个可计算的二次效用函数，导出了该二次效用函数对应的需求函数，并详细地表述了求解过程和方法，讨论了绿色食品需求函数的性质。     

分层教学的Bayes分析

对学校分层教学进行了初步探索 ,提出了分层分班的 Bayes决策 ,介绍了分层分班方法 ,获得了一些结论 ,并完成了对这些结论的证明 ,从理论上论述了分层教学是实施“因材施教”教育原则和素质教育的有效途径 ,给出了应用实例 .     

网络安全产品研究

本文在研究了网络安全的国内外有关情况后对网络安全技术进行了探讨 ,介绍了一种简单而实用的网络安全产品 ,添补了这方面的空白 ,而且本文介绍的产品已经应用到了许多部门 ,为网络安全做出了贡献     

一类积分型中值定理的再研究

对一类积分型中值定理做了进一步的研究,减弱了定理的条件并加强了定理的结论,得到了一个更加一般的结果,并对该定理"中间点"的渐进性做了讨论,推广了已有的成果.     

系统动力学在城市污水再生回用系统中的应用

用系统动力学方法研究了城市污水回用系统.首先分析了影响城市污水回用系统的诸多因素以及它们之间的相互关系,探讨了污水再生回用系统行为和结构的特点,确定了系统中因素之间的定量关系,建立了城市污水回用系统动力学(SD)模型,并介绍了模型的检验方法.同时给出了SD模型的具体应用实例,对西北地区的某一城市的污水回用进行了预测和分析,提出了符合该城市发展的污水回用方案.     

基于概率论的防空武器系统对集群敌机的服务效能研究

论述了防空武器系统服务效能的概念,提出了服务效能的评估指标,做出了符合防空作战一般规律的假设,据此,通过概率论的方法分析了对抗系统的各种状态,论证了系统统计平衡状态的存在,进而建立了数学解析模型,最后得出了对防空武器系统服务效能的定量评估指标.     

The smooth structure set of <Emphasis Type="Italic">S</Emphasis><Superscript><Emphasis Type="Italic">p</Emphasis></Superscript> × <Emphasis Type="Italic">S</Emphasis><Superscript><Emphasis Type="Italic">q</Emphasis></Superscript>

We calculate \({\mathcal{S}^{{\it Diff}}(S^p \times S^q)}\), the smooth structure set of S ^p × S ^q , for p, q ≥ 2 and p + q ≥ 5. As a consequence we show that in general \({\mathcal{S}^{Diff}(S^{4j-1}\times S^{4k})}\) cannot admit a group structure such that the smooth surgery exact sequence is a long exact sequence of groups. We also show that the image of the forgetful map \({\mathcal{S}^{Diff}(S^{4j}\times S^{4k}) \rightarrow \mathcal{S}^{Top}(S^{4j}\times S^{4k})}\) is not in general a subgroup of the topological structure set.     

Arithmetical properties of the number of t-core partitions

Let Λ={λ ₁≥⋅⋅⋅≥λ _s ≥1} be a partition of an integer n. Then the Ferrers-Young diagram of Λ is an array of nodes with λ _i nodes in the ith row. Let λ _j ′ denote the number of nodes in column j in the Ferrers-Young diagram of Λ. The hook number of the (i,j) node in the Ferrers-Young diagram of Λ is denoted by H(i,j):=λ _i +λ _j ′−i−j+1. A partition of n is called a t-core partition of n if none of the hook numbers is a multiple of t. The number of t-core partitions of n is denoted by a(t;n). In the present paper, some congruences and distribution properties of the number of 2 ^t -core partitions of n are obtained. A simple convolution identity for t-cores is also given.      

On the spectral function of the Poisson–Voronoi cells

Denote by (t)=∑_n1e^−λ_nt, t>0, the spectral function related to the Dirichlet Laplacian for the typical cell of a standard Poisson–Voronoi tessellation in . We show that the expectation E(t), t>0, is a functional of the convex hull of a standard d-dimensional Brownian bridge. This enables us to study the asymptotic behaviour of E(t), when t→0⁺,+∞. In particular, we prove that the law of the first eigenvalue λ₁ of satisfies the asymptotic relation lnP{λ₁t}−2^dω_dj_(d−2)/2^d·t^−d/2 when t→0⁺, where ω_d and j_(d−2)/2 are respectively the Lebesgue measure of the unit ball in and the first zero of the Bessel function J_(d−2)/2.     

On L 1 Bounds for Asymptotic Normality of Some Weakly Dependent Random Variables

In the present paper, we consider L ₁ bounds for asymptotic normality for the sequence of r.v.’s X ₁,X ₂,… (not necessarily stationary) satisfying the ψ-mixing condition. The L ₁ bounds have been obtained in terms of Lyapunov fractions which, in a particular case, under finiteness of the third moments of summands and the finiteness of ∑ _r≥1 r ² ψ(r), are of order O(n ^−1/2), where the function ψ participates in the definition of the ψ-mixing condition.      

Superconvergence of Legendre projection methods for the eigenvalue problem of a compact integral operator

In this paper, we consider the Galerkin and collocation methods for the eigenvalue problem of a compact integral operator with a smooth kernel using the Legendre polynomials of degree ≤n. We prove that the error bounds for eigenvalues are of the order O(n^−2r) and the gap between the spectral subspaces are of the orders O(n^−r) in L₂-norm and O(n^1/2−r) in the infinity norm, where r denotes the smoothness of the kernel. By iterating the eigenvectors we show that the iterated eigenvectors converge with the orders of convergence O(n^−2r) in both L₂-norm and infinity norm. We illustrate our results with numerical examples.     

On the ε-entropy of classes of holomorphic functions

Suppose thatB _R ^d is a ball of radiusR in ℂ ^d and σ is the standard measure on the unit sphere in ℂ ^d . ForR>1, 1≤p≤∞, and for the natural numbersl, d, byH _R ⁰ (l, p, d) we denote the class of functionsf holomorphic inB _R ^d and such that in the homogeneous polynomial expansion of the firstl summands the zero and radial derivatives of orderl belong to the closed unit ball of the Hardy spaceH ^p (B _R ^d ). In this paper an asymptotic formula for the ε-entropy of the classH _R ⁰ (l, p, d) in the spacesL ^p (σ), 1≤p<∞, and is obtained. Translated fromMatematicheskie Zametki, Vol. 68, No. 2, pp. 286–293, August, 2000.     

When Some Complement of a Submodule Is a Summand

A module M is said to satisfy the C ₁₁ condition if every submodule of M has a (i.e., at least one) complement which is a direct summand. It is known that the C ₁ condition implies the C ₁₁ condition and that the class of C ₁₁-modules is closed under direct sums but not under direct summands. We show that if M = M ₁ ⊕ M ₂, where M has C ₁₁ and M ₁ is a fully invariant submodule of M, then both M ₁ and M ₂ are C ₁₁-modules. Moreover, the C ₁₁ condition is shown to be closed under formation of the ring of column finite matrices of size Γ, the ring of m-by-m upper triangular matrices and right essential overrings. For a module M, we also show that all essential extensions of M satisfying C ₁₁ are essential extensions of C ₁₁-modules constructed from M and certain subsets of idempotent elements of the ring of endomorphisms of the injective hull of M. Finally, we prove that if M is a C ₁₁-module, then so is its rational hull. Examples are provided to illustrate and delimit the theory.     

Interval Valued Intuitionistic （S, T）-fuzzy Hv-submodules

On the basis of the concept of the interval valued intuitionistic fuzzy sets introduced by K. Atanassov, the notion of interval valued intuitionistic fuzzy Hv-submodules of an Hv-module with respect to a t-norm T and an s-norm S is given and the characteristic properties are described. The homomorphic image and the inverse image are investigated. In particular, the connections between interval valued intuitionistic （S, T）-fuzzy Hv-submodules and interval valued intuitionistic （S, T）-fuzzy submodules are discussed.     

Coincidences of projections and linear n-valued maps of tori

We prove that the Nielsen fixed point number N(φ) of an n-valued map φ:X?X of a compact connected triangulated orientable q-manifold without boundary is equal to the Nielsen coincidence number of the projections of the graph of φ, a subset of X×X, to the two factors. For certain q×q integer matrices A, there exist “linear” n-valued maps Φn,A,σ:Tq?Tq of q-tori that generalize the single-valued maps fA:Tq→Tq induced by the linear transformations TA:Rq→Rq defined by TA(v)=Av. By calculating the Nielsen coincidence number of the projections of its graph, we calculate N(Φn,A,σ) for a large class of linear n-valued maps.