关于亚纯函数微分多项式的值分布

运用Nevanlinna的亚纯函数理论方法，研究了亚纯函数微分多项式的值的分布理论，获得了若f（z）是超越亚纯函数,φ是关于f的微分多项式，满足条件N（r,f）＋N（r,1/f）=S（r,f）,关于φ零点的几个结果，改进并推广了YangCC和仪洪勋等人的有关结果．     

关于值分布论中一个著名猜测的推广

运用Nevanlinna的亚纯函数理论方法，研究了超越亚纯函数的值分布理论，获得了如下的结论：设f为超越亚纯函数，c为f的不恒等于0的的小函数，则当n≥3时，f^n f’-c有无穷多个零点；若附加条件厂只有有限多个级≤2的零点，则对一切正整数n，f^n f’-c都有无穷多个零点．因而对Chiang Y M的问题作出了部分回答．     

电离真空计的误差分析

本从影响电离真空计示值误差的7个方面，推导出电离真空计“误差 函数”y=f(x)和其表达式，并着重强调了误差函数的“与门”特性，进一步讨论了电离真空计误差函数f(x)中，自变量因子影响函数的方式和计算思路。     

拉伸速率对PP/GB复合材料力学性能的影响

应用Instron材料试验机考察了室温下拉伸速率对玻璃微珠填充聚丙烯复合材料的弹性模量和屈服强度的影响，结果表明，随着微珠含量的增加，试样的弹性模量（Ec）增大，且与拉伸应变速率呈近乎幂律函数关系，而屈服强度（бyc）则随着微珠体积分数（Φf）的增加呈线性函数形式下降，并随着拉伸应变速率的增加呈幂律函数形式提高，此外，讨论了Ec、Φf与бyc三者之间的关系。     

密度函数递归核估计的Bootstrap逼近

设X1，X2，…xn是从分布密度函数为f（x）的总体中抽取的独立同分布的样本，f（x）的递归核估计fn（x），本文讨论了fn（x）的渐近正态性以及Bootstrap逼近问题．     

一类具有线性分母的有理插值样条的逼近问题

对被插函数f(t)∈c^3[t0,tm]，讨论了一类具有线性分母的有理插值函数的逼近性质，证明了插值误差系数的有界性和其对参数的双重对称性。     

二次插值样条函数的积分性质

已知区间[a,b]的一个分划△:a=x_0相似文献   

神经网络对φ-有界变差函数的逼近

研究了以有界的sigmoidal函数σ为激活函数的单隐层神经网络对于在[a,b]上φ-有界变差函数f的逼近,得到的逼近偏差为‖σ‖φ-1{Vφ(fn)[a,b]/n}.倘若激活函数是Heaviside函数时,则逼近偏差为φ-1{Vφ(f)[a,b]/2n}.此外,在第3节中,我们还将上述结果扩充到了全实轴上.     

动态测试的数据处理(七)

动态测试数据的数学模型与成分分离在第一讲已述及,动态测试数据一般由表现为确定性函数有时兼为随机函数的被测变量,表现为确定性函数的系统误差和表现为随机函数的随机误差所组成。可见,动态测试数据 y(t)一般均含有确定性成分 f(t)和随机性成分 X(t)。为了便于分离 y(t)中被测变量的测量结果与系统误差和随机误差,对 f(t)与 X(t)还应予细分。如 f(t)可分为非周期     

亚纯函数族一个结果的研究

设F是区域D上的一亚纯函数族,k是一个正整数,H(f,f1,……f(k))是一个微分多项式,且(Γ/γ)H<(k+1)。如果对于任意的f(z)∈F,f(z)的零点重数≥k+1,极点重级至少为2,且f(k)(z)+H(f,f1,……f(k)≠1),则F在区域D上是正规的。     

Noise-Enhanced Measurement of Weak Doublet Spectra with a Fourier-Transform Spectrometer and a 1-Bit Analog-to-Digital Converter

We demonstrate an efficient noise dithering procedure for measuring the power spectrum of a weak spectral doublet with a Fourier-transform spectrometer in which the subthreshold interferogram is measured by a 1-bit analog-to-digital converter without oversampling. In the absence of noise, no information is obtained regarding the doublet spectrum because the modulation term s(x) of its interferogram is below the instrumental detection limit B, i.e., |s(x)| < B, for all path difference x values. Extensive numerical experiments are carried out concerning the recovery of the doublet power spectrum that is represented by s(x) = (s(0)/2)exp(-pi(2)x(2)/beta)[cos(2pif(1)x) + cos(2pif(2)x)], where s(0) is a constant, beta is the linewidth factor, and ?f? = (f(1) + f(2))/2. Different values of ?f?, s(0), and beta are considered to evaluate thoroughly the accuracy of the procedure to determine the unknown values of f(1) and f(2), the spectral linewidth, and the peak values of the spectral profiles. Our experiments show that, even for short observation times, the resonant frequencies of s(x) could be located with high accuracy over a wide range of ?f? and beta values. Signal-to-noise ratios as high as 50 are also gained for the recovered power spectra. The performance of the procedure is also analyzed with respect to another method that recovers the amplitude values of s(x) directly.     

混合Hermite-Lagrange插值之同时逼近

对于(-1,1)中的结点组{X_k}_(k=1)~n,记l_k(x)为相应的Lagrange插值基本多项式,又记A_n=‖∑(2-x~2-x_k~2)(1-x_k~2)~-1丨l_k(x)‖。对于f∈C_([-1,1)~q与r=[q+2/2],本文证明满足条件H_n(f,x_k)=f(x_k)(k=1,2,…,n),H_n~(s)(f,±1)=f~(s)(±1)(s=0,1,…,n-1)的n+2r-1次代数多项式H_n(f,x)有逼近性质H_n~(s)(f,x)-f~(s)(x)=(?)其中δ_n(x)=n~(-1)(1-x~2)~(1/2),△_n(x)=δ_n(x)+n~(-2).作为证明的重要工具,本文还对n次代数多项式P_n(x),建立了另一形式的Bernstein不等武:若 P_n(x)=O(1)δ_n~q(x)ω(δ_n(x)),则p_n~(S)(X)=O(1)δ_n~(q-2S)(X)ω(δ_n(X))△_n~s(X)。     

Sub-actions for weakly hyperbolic one-dimensional systems

Let f be an expanding map of degree 2 in the unitary interval [0,1], with an indifferent fixed point at x = 0 (i. e. (0) = 1), increasing, surjective and C 1 in each injective branch [0, c ] and ( c ,1], with inf{ f ' ( x ) | x ] [ g , 1)\{ c }} > 1 for all g > 0. Let A : [0,1] M be a function f -Hölder in each injective branch, monotone in a small neighbourhood of the origin, with A (0)< m and A (1)< m, where m is the maximum value of Z A d w over all invariant probability measures of f. Our main result is to prove that there exists a f -Hölder function S : [0,1] M , which satisfies the subcohomology equation Using S we prove that, if A admits a unique measure which maximizes Z , then this measure is uniquely ergodic. If A =log f ' , we are analysing the measure of maximal Lyapunov exponent. We also use the function f to define a bidimensional bijective function B in the unitary square [0,1) 2 [0,1), which is a modification of the Baker's Map, having an indifferent fixed point at the origin. If A : [0,1) 2     

关于一类插值多项式的最高收敛阶

以第一类Tchebyshev多项式的零点作为插值节点，推广了伯恩斯坦提出的一个问题，构造了插值多项式算子Gn,b(f;x)，它不仅对f(x)∈C^a[-1,1](p≤a≤b-1，其中b为自然数）一致收敛，而且收剑阶达到了最佳。对算子Gn,b(f;x)，最高收敛阶不会超过1/n^6，这是对伯恩斯坦所提出问题的一个圆满的回答。     

人工神经网络的单调序列逼近

设Nn,Ф是以Ф为激活函数的具有n+1个神经元的前向单隐层人工神经网络的全体.主要证明了,若f∈C[0,1],则对于任意的ε>0,存在两个神经网络序列{Pn,Ф}和{Qn,Ф},使得在[0,1]上Qn,Ф(x)≤Qn+1,Ф(x)≤f(x)≤Pn+1,Ф(x)≤Pn,Ф(x),而且Pn,Ф(x)-Qn,Ф(x)≤(6+4(2~(1/2)))En,Ф(f),这里的En,Ф(f)为Nn,Ф中的元对f的最佳逼近.     

Dielectric and structural properties of A-cation-deficient perovskites, tetragonal tungsten bronzes and their composites in the K2Sr4(Mgx Nb10-x) Li3xO30 system

In the K2Sr4(MgxNb10-x) Li3xO30 system (0x1.33), two phases, one having a tetragonal tungsten bronze (TTB) structure and the other having a perovskite-type structure, are observed after calcination and sintering. The synthesis of single-phase samples, having either of these structure types, has allowed for the determination of their respective contribution to the system's dielectric properties, specifically r=f (T ) and tg=f (T) over the temperature range –60 to 150 °C. Using X-ray and electron diffraction techniques, scanning electron microscope observations and energy dispersive spectroscopy analysis, various A-cation-deficient perovskite phases were characterized, in particular Sr0.8(Mg0.2Nb0.8)O3. The compositional ability of the TTB structure in this system is also correlated to the r=f (T ) curves, which exhibit a broad maximum. © 1998 Kluwer Academic Publishers     

On the construction of irreducible self-reciprocal polynomials over finite fields

The transformationf(x)f ^Q x^deg(f) f(x + 1/x) for f(x) is studied. Simple criteria are given for the case that the irreducibility off is inherited by the self-reciprocal polynomialf ^Q . Infinite sequences of irreducible self-reciprocal polynomials are constructed by iteration of thisQ-transformation.     

Random and deterministic perturbation of a class of skew-product systems

Abstract. This paper is concerned with the stability properties of skew-products T (x,y) = (f(x), g(x,y)) in which (f,X,mu) is an ergodic map of a compact metric space X and g: Xx Rn Rn is continuous. We assume that the skew-product has a negative maximal Lyapunov exponent in the fibre. We study the orbit stability and stability of mixing of T(x,y) = (f(x), g(x,y)) under deterministic and random perturbation of g. We show that such systems are stable in the sense that for any > 0 there is a pairing of orbits of the perturbed and unperturbed system such that paired orbits stay within a distance of each other except for a fraction of the time. Furthermore, we show that the invariant measure for the perturbed system is continuous (in the Hutchinson metric) as a function of the size of the perturbation to g (Lipschitz topology) and the noise distribution. Our results have applications to the stability of Iterated Function Systems which 'contract on average'.     

Disordering of the Ni3Si intermetallic compound by mechanical milling

The ordered f c c intermetallic compound Ni₃Si was mechanically milled in a high-energy ball mill. The severe plastic deformation produced by milling induced transformations with increasing milling time as follows: ordered f c c disordered f c c nanocrystalline f c c. The structural and microstructural evolution with milling time was followed by X-ray diffraction, TEM, hardness tests, and differential scanning calorimetry (DSC). Complete disordering occurred at milling times of 2 h and kept the saturated H of the DSC peak in the range of estimated enthalpy even after 60 h milling. The structural development during milling of the f c c solid solution for Ni₃Si was presumably dominated by the formation and refinement of a dislocation cell structure into microcrystallites which eventually reached nanometre dimensions.     

Phase composition,crystal structure,and microwave dielectric properties of 0.8Mg2SiO4–0.2Ca0.9Sm0.2/3Al4x/3Ti1−xO3 ceramics

Journal of Materials Science: Materials in Electronics - 0.8Mg2SiO4–0.2Ca0.9Sm0.2/3Al4x/3Ti1?xO3 (x?=?0, 0.05, 0.1, 0.15, 0.2, and 0.25) ceramics with zero τf and high...