THE GLOBAL APPROXIMATION BY LEFT-BERNSTEIN-DURRMEYER QUASI-INTERPOLANTS IN Lp[0, 1]

In this paper,we will use the 2r-th Ditzian-Totik modulus of smoothness wp^2r(f,t)p to discuss the direct and inverse theorem of approximation by Left-Bernstein-Durrmeyer quasi-interpolants Mn^[2r-1]f for functions of the space Lp[0,1](1≤p≤ ∞)。     

Average B-width and infinite dimensional G-width of some smooth function classes on the line

In this paper, we get the exact values of average σ-B width and infinite dimensional σ-G width of Sobolev class B^r _p(R) in the metric L_p(R) (1≤p≤∞) and obtain the exact (σ∈N) and strong asymptotic (σ>1) results of infinite dimensional σ-G widths of Sobolev-Wiener class W^r _pq (R) in the metric L_q(R) and its dual case W^r _p(R) in the metric L_qp(R) (1≤q≤p≤∞). Supported by the National Natural Science Foundation of China (No. 19671012) and by the Doctoral Programme Foundation of Institution of Higher Education of National Education Committee of China.     

SOLVING SYMMETRIC MONOTONE LINEAR VARIATIONAL INEQUALITIES BY SOME MODIFIED LEVITIN-POLYAK PROJECTION METHODS

Some modified Levitin-Polyak projection methods are proposed in this paper for solving monotone linear variational inequality x∈Ω，（x′-x)^T(Hx c)≤0，for any x′∈Ω.It is pointed out that there are similar methods for solving a general linear variational inequality.     

Discrete characterization of the Paley-Wiener space with several variables

In this paper, we obtain a characterization of the Paley-Wiener space with several variables, which is denoted byB _{π, p} (R ⁿ ), 1≤p<∞, i.e., for 1<p<∞,B _{π, p} (R ⁿ ) is isomorphic tol _p (Z ⁿ ), and forp=1,B _{π, 1} (R ⁿ ) is isomorphic to the discrete Hardy space with several variables, which is denoted byH(Z ⁿ ). This project is supported by the National Natural Science Foundation of China (19671012) and Doctoral Programme Institution of Higher Education Foundation of Chinese Educational Committee and supported by Youth Foundation of Sichuan.     

On a problem of D.H. Lehmer and pseudorandom binary sequences

Let p be an odd prime, and f(x), g(x) ∈ [x]. Define

Existence of positive solutions for a singular <Emphasis Type="Italic">p</Emphasis>-Laplacian differential equation

In this paper, we are concerned with the existence of positive solutions for a singular p-Laplacian differential equation
（φp（u＇））＇＋β/r φp（u＇）-γ ｜u＇｜^p/u ＋ g（r）=0,0〈r〈1,
subject to the Dirichlet boundary conditions： u（0） = u（1） =0, where φp（s） = ｜sl^P-2s,p 〉 2,β 〉0, γ〉（p-1）/p （β ＋ 1）, and g（r） ∈ C^1 [0, 1] with g（r） 〉 0 for all τ ∈ [0, 1]. We use the method of elliptic regularization, by carrying out two limit processes, to get a positive solution.     

A rough hypersingular integral operator with an oscillating factor on function space

The singular integral operator Tα,βf(x) = p.v.∫Rnei|y|-βΩ(y') /|y|n αf(x-y)dy,defined for all test functions f is studied, where Ω(y') is a distribution on the unit sphere Sn-1 satisfying certain cancellation condition. It is proved that Tα,β is a bounded operator from the Triebel-Lizorkin space Fs,qp to the Triebel-Lizorkin space Fs γ,qp, provided that Ω(y') is a distribution in the Hardy space Hr(Sn-1) with r = (n - 1)/(n - 1 γ).     

ESTIMATE FOR DISTANCE-COEFFICIENT OF MATRICES

ＥＳＴＩＭＡＴＥＦＯＲＤＩＳＴＡＮＣＥ┐ＣＯＥＦＦＩＣＩＥＮＴＯＦＭＡＴＲＩＣＥＳＬＵＦＡＮＧＹＡＮＡｂｓｔｒａｃｔ．ＭｏｔｉｖａｔｉｏｎｏｆｔｈｉｓｐａｐｅｒｉｓａｎｏｐｅｎｐｒｏｂｌｅｍｅｘｐｏｓｅｄｂｙＢ．Ｂｅａｕｚａｍｙ［１］．ＬｅｔＭｂｅａ...     

Separation properties forMW-fractals

Corresponding to the irreducible 0–1 matrix (a _ij ) _n×n , take similitude contraction mappingsϕ _ij for eacha _ij =1, ina _ij =1, in R ^d with ratio 0<r _ij <1. There are unique nonempty compact setsF ₁,…,F _n satisfying for each1≤i≤n, F _i. We prove that open set condition holds if and only ifF _i is ans-set for some1≤i≤n, wheres is such that the spectral radius of matrix (r _ij ³ ) _{n x n} is 1. Partly supported by Natural Science Foundation of China, and partly by Natural Science Foundation of Hubei Province     

BOUNDARY VALUE PROBLEMS FOR SECOND ORDER MIXED-TYPE FUNCTIONAL DIFFERENTIAL EQUATIONS

We use the topological degree method to deal with the generalized Sturm-Liouville boundary value problem (BVP) for second order mixed-type functional differential equation x(t)=f(t,xt,xt), 0≤t≤T. Existence principle and theorem for solutions of the BVP are obtained.     

A Note on the Mean Value of Numbersof the Solutions of x^α≡ 1（modn）

Let T = T(p, q, α) be the number of solutions of the congruence x^α ≡ 1 (mod p^ηq^θ). Let A and B be sets of primes satisfying x₁ < p ≤ x₂ and y₁ < q ≤ y₂, respectively. A mean value estimation of is given. Supported by National Natural Science Foundation of China (No. 19971024) and Zhejiang Provincial Natural Science Foundation of China (No. 199047)     

On Hua-Tuan’s conjecture

Let G be a finite group and |G| = pn, p be a prime. For 0 m n, sm(G) denotes the number of subgroups of of order pm of G. Loo-Keng Hua and Hsio-Fu Tuan have ever conjectured: for an arbitrary finite p-group G, if p > 2, then sm(G) ≡ 1, 1 + p, 1 + p + p2 or 1 + p + 2p2 (mod p3). In this paper, we investigate the conjecture, and give some p-groups in which the conjecture holds and some examples in which the conjecture does not hold.     

Some results on distance two labelling of outerplanar graphs

Let G be an outerplanar graph with maximum degree △. Let χ（G^2） and A（G） denote the chromatic number of the square and the L（2, 1）-labelling number of G, respectively. In this paper we prove the following results： （1） χ（G^2） = 7 if △= 6; （2） λ（G） ≤ △ ＋5 if △ ≥ 4, and ）,（G）≤ 7 if △ = 3; and （3） there is an outerplanar graph G with △ = 4 such that ）λ（G） = 7. These improve some known results on the distance two labelling of outerplanar graphs.     

The cobordism classification of involution on DOLD manifoldP(1,2l)

Supposing the smooth involution of the DOLD manifoldP(1,2l) satisfies the following condition: the fiberation π:P(1,2l)× _T×(−1)S^∞→RP(∞) is totally nonhomologous to zero (cf. [1, p373]), this paper determines the classification of smooth involution on the DOLD manifoldP(1,2l) totally. Supported by the Foundation of Tian Yuan and the Natural Science Foundation of Hebei province.     

Multiple Solutions and Its Morse Index for One-Dimensional Nonlinear Problem

The multiple solutions for one-dimensional cubic nonlinear problem u" u~3=0,u(0)=u(π)=0are computed,on the basis of the eigenpairs of-φ"_k=λ_(kφk),k=1,2,3....There exist two nonzero solutions±u_k corresponding to each k,and their Morse index MI(k) for 1(?)k(?)20 is to be exactly determined.It isshown by the numerical results that MI(k)(?)k.     

Almost everywhere convergence of Riesz means on noncompact symmetric spaceSL(3,H)/Sp(3)

LetG/K be the noncompact Riemannian symmetric spaceSL(3,H)/Sp(3). We shall prove in this paper that forf∈L ^p(SL(3,H)/Sp(3)), 1≤p≤2, the Riesz means of orderz off with respect to the eigenfunctions expansion of Laplace operator almost everywhere converge tof for Rez >δ(n,p). The critical index δ(n,p) is the same as in the classical Stein's result for Euclidean space, and as in the noncompact symmetric spaces of rank one and of complex type. Partially supported by National Natural Science Foundation of China     

A parallel algorithm for generating multiple ordering spanning trees in undirected weighted graphs

1.IntroductionLetG=(V,E,W)beaconnected,weightedandundirectedgraph,VeEE,w(e)(相似文献   

Some Elements of Finite Order in K2Q

Let K2 be the Milnor functor and let Фn （x）∈ Q[X] be the n-th cyclotomic polynomial. Let Gn（Q） denote a subset consisting of elements of the form {a, Фn（a）}, where a ∈ Q^＊ and {, } denotes the Steinberg symbol in K2Q. J. Browkin proved that Gn（Q） is a subgroup of K2Q if n = 1,2, 3, 4 or 6 and conjectured that Gn（Q） is not a group for any other values of n. This conjecture was confirmed for n =2^T 3S or n = p^r, where p ≥ 5 is a prime number such that h（Q（ζp）） is not divisible by p. In this paper we confirm the conjecture for some n, where n is not of the above forms, more precisely, for n = 15, 21,33, 35, 60 or 105.     

The Dissipative Quasi-geostrophic Equation in Weak Morrey Spaces

The author studies the Cauchy problem of the dissipative quasi-geostrophic equation in weak Morrey spaces. The global well-posedness is established for any small initial data in the weak space Mp^＊,γ（R^n）, with 1〈p〈∞and A = n-（2α-1）p, and for a small external force in a time-weighted weak Morrey space.     

Potential space estimates in local Hardy spaces for Green potentials in convex domains

Let Ω be a bounded co.nvex domain in Rn(n≥3) and G(x,y) be the Green function of the Laplace operator -△ on Ω. Let hrp(Ω) = {f ∈ D'(Ω) :(E)F∈hp(Rn), s.t. F|Ω = f}, by the atom characterization of Local Hardy spaces in a bounded Lipschitz domain, the bound of f→(△)2(Gf) for every f ∈ hrp(Ω) is obtained, where n/(n 1)＜p≤1.