两个素数和一个素数平方和的丢番图逼近(英文)

We show that if λ1 , λ2 , λ3 are non-zero real numbers, not all of the same sign, η is real and λ1 /λ2 is irrational, then there are infinitely many ordered triples of primes (p1 , p2 , p3 ) for which |λ1 p1 + λ2 p2 + λ3 p2 3 + η| < (max pj )- 1/40 (log max pj ) 4 .     

Diophantine Inequality by Unlike Powers of Primes*

Suppose that λ₁, · · ·, λ₅ are nonzero real numbers, not all of the same sign,satisfying that λ₁/λ₂is irrational. Then for any given real number η and ε > 0, the inequality |λ₁p₁+ λ₂p₂~2+ λ₃p₃~3+ λ₄p₄~4+ λ₅p₅~5+ η| <(■)^-19/756+ε has infinitely many solutions in prime variables p₁, · · ·, p₅. This result co...     

ON THE MULTIPLICATIVE INVERSE EIGENVALUE PROBLEMS

We present new sufficient conditions on the solvability and numerical methods for the following multiplicative inverse eigenvalue problem: Given an n x n real matrix A and n real numbers λ1 , λ2,..., λn, find n real numbers c1, c2,..., cn such that the matrix diag(c1,c2,...,cn)A has eigenvalues λ1,λ2,..., λn.     

On the Non-Commutative Neutrix Product of the Distributions x＋^λ and x^＋μ

Let f and g be distributions and let gn = （g ＊ δn）（x）, where δn （x） is a certain converging to the Dirac delta function. The non-commutative neutrix product fog of f and g to be the limit of the sequence {fgn }, provided its limit h exists in the sense that sequence is defined N-lim n-∞（f（x）g,, （x）, φ（x）〉 = （h（x）, φ（x）},for all functions p in 2. It is proved that （x^λ＋1n^px＋）0（x^μ＋1n^qx＋）=x＋^λμ1n^p＋qx＋,（x^λ-1n^qx-）=x-^λ＋μ1n^p＋qx-,for λ＋μ〈-1; λ,μ, λ＋μ≠-1,-2…and p,q=0,1,2……     

STABILITY OF THE SOLUTION OF THE ITERATED EQUATION sum from i=1 to n λ_if(x)=F(x)

This note is a further work of discussion on the iterated equation λ_1f(x)+λ_2f~2(x)+…λ_nf~n(x)-P(x), following the author's conclusions of the existence and uniqueness of this equation. In this note we prove that the sufficient condition of the stability of the solution is the same one as the uniqueness of the solution (see [4]).     

COMPUTING THE NEAREST BISYMMETRIC POSITIVE SEMIDEFINITE MATRIX UNDER THE SPECTRAL RESTRICTION

Let A and C denote real n × n matrices. Given real n-vectors x1, ... ,xm, m ≤ n, and a set of numbers L = {λ1,λ2,... ,λm}. We describe (I) the set (?) of all real n × n bisymmetric positive seidefinite matrices A such that Axi is the "best" approximate to λixi, i = 1,2,...,m in Frobenius norm and (II) the Y in set (?) which minimize Frobenius norm of ||C - Y||.An existence theorem of the solutions for Problem I and Problem II is given and the general expression of solutions for Problem I is derived. Some sufficient conditions under which Problem I and Problem II have an explicit solution is provided. A numerical algorithm of the solution for Problem II has been presented.     

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.     

混合幂丢番图不等式（英文）

It is proved that if λ_1, λ_2, ···, λ_7are nonzero real numbers, not all of the same sign and not all in rational ratios, then for any given real numbers η and σ, 0 σ 1/16, the inequality |λ_1x~2_1+ λ_2x~2_2+∑7 i=3λ_ix~4_i+ η| ( max1≤i≤7|x_i|)~(-σ)has infinitely many solutions in positive integers x_1, x_2, ···, x_7. Similar result is proved for |λ_1x~2_1+ λ_2x~2_2+ λ_3x~2_3+ λ_4x~4_4+ λ_5x~4_5+ λ_6x~4_6+ η| ( max1≤i≤6|xi|)-σ.These results constitute an improvement upon those of Shi and Li.     

THE UNIFORM CONVERGENCE RATE OF KERNEL DENSITY ESTIMATE

In this paper,we study the uniform convergence rate of kernel density estimate f_nand get optimal uniform rate of convergence without the assumption of compact supportfor kernel function.It is proved that if the density function f satisfies λ-condition andthe kernel function K is λ-good(see section 1),then we havelimsup (n/(logn))~(λ/(1+2λ))丨_n(x)-f(x)丨≤const,a.s.     

A boundary Schwarz lemma for pluriharmonic mappings from the unit polydisk to the unit ball

In this article, we present a Schwarz lemma at the boundary for pluriharmonic mappings from the unit polydisk to the unit ball, which generalizes classical Schwarz lemma for bounded harmonic functions to higher dimensions. It is proved that if the pluriharmonic mapping f ∈ P(D~n, B~N) is C~(1+α) at z0 ∈ E_rD~n with f(0) = 0 and f(z_0) = ω_0∈B~N for any n,N ≥ 1, then there exist a nonnegative vector λ_f =(λ_1,0,…,λ_r,0,…,0)~T∈R~(2 n)satisfying λ_i≥1/(2~(2 n-1)) for 1 ≤ i ≤ r such that where z'_0 and w'_0 are real versions of z_0 and w_0, respectively.     

On a class of self-similar processes with stationary increments in higher order Wiener chaoses

We study a class of self-similar processes with stationary increments belonging to higher order Wiener chaoses which are similar to Hermite processes. We obtain an almost sure wavelet-like expansion of these processes. This allows us to compute the pointwise and local Hölder regularity of sample paths and to analyse their behaviour at infinity. We also provide some results on the Hausdorff dimension of the range and graphs of multidimensional anisotropic self-similar processes with stationary increments defined by multiple Wiener–Itô integrals.     

A REPRESENTATION FORMULA RELATED TO SCHR(O)DINGER OPERATORS

Schr(o)dinger operator is a central subject in the mathematical study of quantum mechanics.Consider the Schrodinger operator H = -△ V on R, where △ = d2/dx2 and the potential function V is real valued. In Fourier analysis, it is well-known that a square integrable function admits an expansion with exponentials as eigenfunctions of -△. A natural conjecture is that an L2 function admits a similar expansion in terms of "eigenfunctions" of H, a perturbation of the Laplacian (see [7], Ch. Ⅺ and the notes), under certain condition on V.     

On a class of Riemann surfaces

It is considered the class of Riemann surfaces with dimT1 = 0, where T1 is a subclass of exact harmonic forms which is one of the factors in the orthogonal decomposition of the spaceΩH of harmonic forms of the surface, namely The surfaces in the class OHD and the class of planar surfaces satisfy dimT1 = 0. A.Pfluger posed the question whether there might exist other surfaces outside those two classes. Here it is shown that in the case of finite genus g, we should look for a surface S with dimT1 = 0 among the surfaces of the form Sg\K , where Sg is a closed surface of genus g and K a compact set of positive harmonic measure with perfect components and very irregular boundary.     

CONTENTS OF VOLUME 30

正~~     

Instructions for contributions

正Applied Mathematics-A Journal of Chinese Universities,Series B(Appl.Math.J.Chinese Univ.,Ser.B)is a comprehensive applied mathematics journal jointly sponsored by Zhejiang University,China Society for Industrial and Applied Mathematics,and Springer-Verlag.It is a quarterly journal with     

Journal of Mathematical Research with Applications Guide for Authors

正Journal overview:Journal of Mathematical Research with Applications(JMRA),formerly Journal of Mathematical Research and Exposition(JMRE)created in 1981,one of the transactions of China Society for Industrial and Applied Mathematics,is a home for original research papers of the highest quality in all areas of mathematics with applications.The target audience comprises:pure and applied mathematicians,graduate students in broad fields of sciences and technology,scientists and engineers interested in mathematics.     

Staircase transportation problems with superadditive rewards and cumulative capacities

A cumulative-capacitated transportation problem is studied. The supply nodes and demand nodes are each chains. Shipments from a supply node to a demand node are possible only if the pair lies in a sublattice, or equivalently, in a staircase disjoint union of rectangles, of the product of the two chains. There are (lattice) superadditive upper bounds on the cumulative flows in all leading subrectangles of each rectangle. It is shown that there is a greatest cumulative flow formed by the natural generalization of the South-West Corner Rule that respects cumulative-flow capacities; it has maximum reward when the rewards are (lattice) superadditive; it is integer if the supplies, demands and capacities are integer; and it can be calculated myopically in linear time. The result is specialized to earlier work of Hoeffding (1940), Fréchet (1951), Lorentz (1953), Hoffman (1963) and Barnes and Hoffman (1985). Applications are given to extreme constrained bivariate distributions, optimal distribution with limited one-way product substitution and, generalizing results of Derman and Klein (1958), optimal sales with age-dependent rewards and capacities.To our friend, Philip Wolfe, with admiration and affection, on the occasion of his 65th birthday.Research was supported respectively by the IBM T.J. Watson and IBM Almaden Research Centers and is a minor revision of the IBM Research Report [6].