Interpolation Problems for Functions with Zero Integrals over Balls of Fixed Radius

Doklady Mathematics - Let $${{V}_{r}}({{\mathbb{R}}^{n}})$$, n ≥ 2, be the set of functions $$f \in {{L}_{{{\text{loc}}}}}({{\mathbb{R}}^{n}})$$ with zero integrals over all balls in...     

涉及多个函数的Hardy型积分不等式

利用权系数方法和Fubini定理,研究涉及多个函数的Hardy型积分不等式,得到若干新的结果．     

Smooth Wavelet Tight Frames with Zero Moments

This paper considers the design of wavelet tight frames based on iterated oversampled filter banks. The greater design freedom available makes possible the construction of wavelets with a high degree of smoothness, in comparison with orthonormal wavelet bases. In particular, this paper takes up the design of systems that are analogous to Daubechies orthonormal wavelets—that is, the design of minimal length wavelet filters satisfying certain polynomial properties, but now in the oversampled case. Gröbner bases are used to obtain the solutions to the nonlinear design equations. Following the dual-tree DWT of Kingsbury, one goal is to achieve near shift invariance while keeping the redundancy factor bounded by 2, instead of allowing it to grow as it does for the undecimated DWT (which is exactly shift invariant). Like the dual tree, the overcomplete DWT described in this paper is less shift-sensitive than an orthonormal wavelet basis. Like the examples of Chui and He, and Ron and Shen, the wavelets are much smoother than what is possible in the orthonormal case.     

Integral Moments of L-Functions

We give a new heuristic for all of the main terms in the integralmoments of various families of primitive L-functions. The resultsagree with previous conjectures for the leading order terms.Our conjectures also have an almost identical form to exactexpressions for the corresponding moments of the characteristicpolynomials of either unitary, orthogonal, or symplectic matrices,where the moments are defined by the appropriate group averages.This lends support to the idea that arithmetical L-functionshave a spectral interpretation, and that their value distributionscan be modelled using Random Matrix Theory. Numerical examplesshow good agreement with our conjectures. 2000 Mathematics SubjectClassification 11M26, 15A52.     

图的一般邻点可区别均匀边染色和均匀全染色

提出了一般邻点可区别均匀边染色和全染色的新概念,研究了路P_n、圈C_n、星S_n、扇F_n、轮W_n、完全二部图K_(m,n)、2维平面网格图P_m×P_n的一般邻点可区别均匀边染色和全染色,具体给出这些图的一般邻点可区别均匀边染色和全染色指标.     

浅析偏导数恒为零的二元函数的特征

本文分析了一定条件下一阶偏导数恒为零的二元函数的特征,同时给出了条件改变时结论不一定成立的例子.在此基础上又探讨了二阶偏导数恒为零的情形下二元函数的特征,并给出了相应的例子.     

Covering Planar Graphs with a Fixed Number of Balls

In this note we prove that there exists a constant ρ such that any planar graph G of diameter ≤ 2R can be covered with at most ρ balls of radius R, a result conjectured by Gavoille, Peleg, Raspaud, and Sopena in 2001.     

On the Bernstein Inequality for Rational Functions with a Prescribed Zero

We extend some results of Giroux and Rahman (Trans. Amer. Math. Soc.193(1974), 67–98) for Bernstein-type inequalities on the unit circle for polynomials with a prescribed zero atz=1 to those for rational functions. These results improve the Bernstein-type inequalities for rational functions. The sharpness of these inequalities is also established. Our approach makes use of the Malmquist–Walsh system of orthogonal rational functions on the unit circle associated with the Lebesgue measure.     

一个积分算子的正不动点

本文给出了一个ｕ０—凹算子具有唯一正不动点的一个充分条件．     

On the Distribution of Zero Sets of Holomorphic Functions

Let M be a subharmonic function with Riesz measure ν _M in a domain D in the n-dimensional complex Euclidean space ? _n , and let f be a nonzero function that is holomorphic in D, vanishes on a set Z ? D, and satisfies |f| ? expM on D. Then restrictions on the growth of ν _M near the boundary of D imply certain restrictions on the dimensions or the area/volume of Z. We give a quantitative study of this phenomenon in the subharmonic framework.     

On Essential Sets of Fixed Points for Functions

This article studies essential stabilities of fixed points under the dual perturbations of functions and domains using uniform topology. We show that each fixed point for most functions has the ability to resist these dual perturbations. The existence result of minimal essential sets of fixed points is established, and the connectedness of minimal essential sets is proved under some conditions. These generalize some corresponding results in references.     

关于二元分式线性齐次复合函数的积分

通过把二重积分转化成曲线积分,得到二元分式线性齐次复合函数积分的两个定理及其若干推论,并构造一些比较典型的用一般方法难以计算的例子说明结论的应用.     

On the Bohr Radius for Two Classes of Holomorphic Functions

Using some multidimensional analogs of the inequalities of E. Landau and F. Wiener for the Taylor coefficients of special classes of holomorphic functions on Reinhardt domains we obtain some estimates for the Bohr radius.     

Integral Formula of Isotonic Functions over Unbounded Domain in Clifford Analysis

In this paper we mainly study the so-called isotonic Dirac system over more general types of unbounded domains in Euclidean space of even dimension. In such systems different Dirac operators in the half dimension act from the left and from the right on the functions considered. We obtain the integral representation of isotonic functions satisfying the decay condition over the unbounded domains, and show that the integral representation formula over the unbounded domains for holomorphic functions of several complex variables and for Hermitean monogenic functions may be derived from it.     

On Auslander-Reiten Components and Height Zero Lattices for Integral Group Rings

Let ?? G be the group ring of a finite group G over a complete discrete valuation ring ??. Then certain ?? G-lattices of height zero lie at the ends of their Auslander-Reiten components of tree class A _∞.     

On Approximation by Neural Networks with Optimized Activation Functions and Fixed Weights

Recently, Li [16] introduced three kinds of single-hidden layer feed-forward neural networks with optimized piecewise linear activation functions and fixed weights, and obtained the upper and lower bound estimations on the approximation accuracy of the FNNs, for continuous function defined on bounded intervals. In the present paper, we point out that there are some errors both in the definitions of the FNNs and in the proof of the upper estimations in [16]. By using new methods, we also give right approximation rate estimations of the approximation by Li’s neural networks.     

Moments for Hawkes Processes with Gamma Decay Kernel Functions

Methodology and Computing in Applied Probability - Hawkes processes have been widely studied, but their many probability properties are still difficult to obtain, including their moments. In the...