限定Borel点的亚纯函数

设E是任意一个非空的闭实数集(mod 2π),ρ(θ)是E上一个上半连续的有界正值函数(0<ρ(θ)相似文献   

单位圆内亚纯函数的奇异点

本文对单位圆内零级亚纯函数得到了一个较为广泛的与正规定则相应的奇异点的存在性,并由此得到如下结果：若单位圆|z|＜1内的亚纯函数满足则存在点eiθ0（≤θ0＜2π）使得对任意正数ε＞0任意正整数。n≥1,恒有limr→l-0n（r,θ0,ε;flfm=a）=＋∞对每一有穷非零复数a成立．     

Fourier-Laplace级数的强逼近

设f是Rn(n≥3)中单位球面∑n-1上的可积函数,Sθ(f)是步长为θ∈R的平移算子.σδN(f)是Fourier-Laplace级数的δ阶Ceaaro平均.如果∫π0 |Sθ(f)-f|p/θ2dθ∈ L∞ (∑n- 1 ),则∑∞k=0 |σλk(f)-f|p∈L∞(∑n-1)且∑∞k=0(f)-f|p∈L∞(∑n-1 ),其中Eλk(f)为Cesaro平均σλk的等收敛算子.     

几类不具有捏制轨道系列完整性的单峰函数族

本文证明，存在着由单峰函数构成的Ｃｏ－函数族｛ｆλ），｛ｇλ｝及具有下列性质：（ｉ）各ｆλ均是分段线性的单峰平顶函数，各ｇλ及均是Ｃ∞－单峰平顶函数．但族｛ｆλ｝，｛ｇλ｝及均非一致平顶；（ｉｉ）族｛ｆλ｝及｛ｇλ｝均满足一致的Ｌｉｐｓｃｈｉｔｚ条件，但在峰顶处均非一致地可微；（ｉｉｉ）族在峰顶处一致地可微，但不满足一致的Ｌｉｐｓｃｈｉｔｚ条件；（ｉｖ）当０≤λ≤７／８时捏制序列Ｋ（ｆλ），Ｋ（ｇλ）及以均不大于ＲＬＣ，当７／８＜λ－≤１时Ｋ（ｆλ），Ｋ（ｇλ）及Ｋ均不小于ＲＬＬ（ＲＬＲ）∞，因而族｛ｆλ｝，｛ｇλ｝及均不具有捏制轨道系列的完整性．本文的结果解答了文［５］中提出的两个猜测．     

关于亚纯代数体函数奇异方向的存在性

本文证明了如下结果:对于有穷正级亚纯代数体函数,一定存在一条奇异方向L∶arg z=θ0(0≤θ0＜2π),使得对于任意δ∈(0,π/2),在角域Δ(θ0,δ)内,对任意复数a,对任意ε＞0,有∑i1|zi(a;Δ(θ0,δ))|σ=∞(σ等于ρ或ρ-ε)至多有2v个例外a值.     

关于整函数的Borel方向的分布

设超越整函数 f(■)的级为λ,下级为μ,ρ为非负实数,满足ρ≤λ.f(z)的全体级>ρ的Borel 方向与单位圆 F(0,2π;1)的交集为 E=I_j,这里 I为 E 的连通分支,其中ω_i为Ω的连通分支.记ω=min{measω_■},I=max{meas I_j},则当λ>π/ω时有(1)I≥min{π/μ,ω}当ρ≤μ时,(2)I■min{π/ρ,ω}当ρ>μ时.     

关于整函数的Borel方向的分布

设超越整函数f(z)的级为λ,下级为μ,ρ为非负实数,满足ρ≤λ.f(z)的全体级>ρ的Borel方向与单位圆F(0,2π;1)的交集为E=(?)I_j,这里I_j为E的连通分支, Ω=Γ(0,2π;1)\E=(?)ω_i, 其中ω_i为Ω的连通分支。记 ω=(?){meas ω_1},I=(?){meas I_(?)}, 则当λ>π/ω时有 (1)I≥min{π/μ,ω}当ρ≤μ时, (2)I≥min{π/ρ,ω}当ρ>μ时。     

几类半线性椭圆共振问题

设Ω∪→R^n是一个有界正则区域，{λk}是－△在H0（Ω）上的一列特征值。假定对某个给定的k，λk是单重的，φ为其相应的特征函数，∫φ^2=1，固定h∈H^-1使∫hφ=0。对于方程（P1）{－△u-λu g（x，u）=tφ h，u=0。σΩ本文利用连通技巧和闭联集理论，推广了文[1]、[3]、[4]中的一些结果。我们获得定理1 假设g:R^*→R满足（g1）g是具有周期原函数的连续周期函数，λk（k≥）简单。如果对任意s ∈R，有（H′4{λk-1≤λ g′（s）≤λk 1k＞1。const≤λ g′（s）≤λ2。则任意h∈H^1,E←τ1,τ2∈R。τ1≤0≤τ2使（i）（P1）有解当且仅当t∈[τ1,τ2]。(ii)如果t∈[τ1,τ2]－{0}，则（P1）至少有两个不同的解。定理2 假设（H′4）成立，λk简单，g满足（H2）任意s，g按x在Ω上可测；g∈C^1对a.e.x∈Ω。（H5）g有界limsg(x,s)=μ＞0。|s|→∞则任意h∈H′0, E←τ1,τ2∈R，τ1＜0＜τ2使（i）（P1）有解当且仅当t∈[τ1,τ2]。（ii）若t∈[τ1,τ2]－{0}，则（Pt）至少有两个不同的解。定理3 [3,prop.2.4]中的条件q＜v（-△-λkI）换成q≤v（-△-λkI）结论仍然成立。     

半平面上的无限级随机Dirichlet级数的值分布

本文通过 Dirichlet级数增长性研究结果改进 ,以及对独立随机变量列 { Zn} ,在条件 EZn=0 , 正数α>0 ,使得 ,0 相似文献   

单位圆内代数体函数的充满圆及Borel半径

研究了单位圆内具有有限个分支点的代数体函数,并用覆盖曲面的几何方定义了他们的级和Borel半径,得到了在单位圆内大于1的有穷级代数体函数必存在充满圆及Borel半径.     

涉及分担值的亚纯函数族的几个正规定则

设(ぁ)为区域D上的一族亚纯函数,a,b为互相判虽的两个复数.若对(ぁ)中任意函数f,f在D内的极点重数至少为2,且当f(z)=a时,f'(z)=a;f(z)=b时f'(z)=b,则(ぁ)在D内正规.     

Decompositions of positive self-dual boolean functions

A coterie, which is used to realize mutual exclusion in distributed systems, is a family C of subsets such that any pair of subsets in C has at least one element in common, and such that no subset in C contains any other subset in C. Associate with a family of subsets C a positive Boolean function f_c such that f_c(x) = 1 if the Boolean vector x is equal to or greater than the characteristic vector of some subset in C, and 0 otherwise. It is known that C is a coterie if and only if f_c is dual-minor, and is a non-dominated (ND) coterie if and only if f_c is self-dual. We study in this paper the decomposition of a positive self-dual function into smaller positive self-dual functions, as it explains how to represent and how to construct the corresponding ND coterie. A key step is how to decompose a positive dual-minor function f into a conjunction of positive self-dual functions f₁,f₂,…, f_k. In addition to the general condition for this decomposition, we clarify the condition for the decomposition into two functions f₁, and f₂, and introduce the concept of canonical decomposition. Then we present an algorithm that determines a minimal canonical decomposition, and a very simple algorithm that usually gives a decomposition close to minimal. The decomposition of a general self-dual function is also discussed.     

Correlation-Immune and Resilient Functions Over a Finite Alphabet and Their Applications in Cryptography

We extend the notions of correlation-immune functions and resilient functions to functions over any finite alphabet. A previous result due to Gopalakrishnan and Stinson is generalized as we give an orthogonal array characterization, a Fourier transform and a matrix characterization for correlation-immune and resilient functions over any finite alphabet endowed with the structure of an Abelian group. We then point out the existence of a tradeoff between the degree of the algebraic normal form and the correlation-immunity order of any function defined on a finite field and we construct some infinite families of t-resilient functions with optimal nonlinearity which are particularly well-suited for combining linear feedback shift registers. We also point out the link between correlation-immune functions and some cryptographic objects as perfect local randomizers and multipermutations.     

分担函数集的正规定则

本文将亚纯函数正规性与分担函数集相结合,探讨了亚纯函数族F正规与F中任意两个函数f与g分担函数的个数,f与其导数f'分担函数的个数及函数f的重值的个数三者之间的关系,给出了一个综合判定亚纯函数族正规的充分条件.     

Algebraic values of analytic functions

Given an analytic function of one complex variable f, we investigate the arithmetic nature of the values of f at algebraic points. A typical question is whether f() is a transcendental number for each algebraic number . Since there exist transcendental entire functions f such that for any t0 and any algebraic number , one needs to restrict the situation by adding hypotheses, either on the functions, or on the points, or else on the set of values.

Among the topics we discuss are recent results due to Andrea Surroca on the number of algebraic points where a transcendental analytic function takes algebraic values, new transcendence criteria by Daniel Delbos concerning entire functions of one or several complex variables, and Diophantine properties of special values of polylogarithms.     

Summation of Some Trigonometric and Schlömilch Series

In this paper we consider trigonometric series in terms of the Riemann zeta function and related functions of reciprocal powers. The obtained closed form formulas we apply to the evaluation of the Riemann zeta function and related functions of reciprocal powers. One can establish recursive relations for them and relations between any two of those functions. These closed formulas enable us also to find sums of some Schlömilch series. We give an example which shows how the convergence of a trigonometric series can be accelerated by applying Krylov's method and our formula (7).     

Algebraic and topological closure conditions for classes of pseudo-Boolean functions

We examine classes of real-valued functions of 0-1 variables closed under algebraic operations as well as topological convergence, and having a certain local characteristic (requiring that any function not in the class should have a k-variable minor not belonging to this class). It is shown that for k=2, the only 4 maximal classes with these properties are those of submodular, supermodular, monotone increasing and monotone decreasing functions. All the 13 locally defined closed classes are determined and shown to be intersections of the 4 maximal ones. All maximal classes for k≥3 are determined and characterized by the sign of higher order derivatives of the functions in the class.     

Pairs of Dual Wavelet Frames from Any Two Refinable Functions

Starting from any two compactly supported refinable functions in L₂(R) with dilation factor d,we show that it is always possible to construct 2d wavelet functions with compact support such that they generate a pair of dual d-wavelet frames in L₂(R). Moreover, the number of vanishing moments of each of these wavelet frames is equal to the approximation order of the dual MRA; this is the highest possible. In particular, when we consider symmetric refinable functions, the constructed dual wavelets are also symmetric or antisymmetric. As a consequence, for any compactly supported refinable function in L₂(R), it is possible to construct, explicitly and easily, wavelets that are finite linear combinations of translates (d · – k), and that generate a wavelet frame with an arbitrarily preassigned number of vanishing moments.We illustrate the general theory by examples of such pairs of dual wavelet frames derived from B-spline functions.     

Solving knapsack sharing problems with general tradeoff functions

A knapsack sharing problem is a maximin or minimax mathematical programming problem with one or more knapsack constraints (an inequality constraint with all non-negative coefficients). All knapsack sharing algorithms to date have assumed that the objective function is composed of single variable functions called tradeoff functions which are strictly increasing continuous functions. This paper develops optimality conditions and algorithms for knapsack sharing problems with any type of continuous tradeoff function including multiple-valued and staircase functions which can be increasing, decreasing, unimodal, bimodal, or even multi-modal. To do this, optimality conditions are developed for a special type of multiple-valued, nondecreasing tradeoff function called an ascending function. The optimal solution to any knapsack sharing problem can then be found by solving an equivalent problem where all the tradeoff functions have been transformed to ascending functions. Polynomial algorithms are developed for piecewise linear tradeoff functions with a fixed number of breakpoints. The techniques needed to construct efficient algorithms for any type of tradeoff function are discussed.     

A singular function with a non-zero finite derivative

This paper exhibits, for the first time in the literature, a continuous strictly increasing singular function with a derivative that takes non-zero finite values at some points. For all the known “classic” singular functions—Cantor’s, Hellinger’s, Minkowski’s, and the Riesz–Nágy one, including its generalizations and variants—the derivative, when it existed and was finite, had to be zero. As a result, there arose a strong suspicion (almost a conjecture) that this had to be the case for any singular function. We present here a singular function, constructed as a patchwork of known classic singular functions, with derivative 1 on a subset of the Cantor set.