On the order of summability of the Fourier inversion formula

In this article we show that the order of the point value, in the sense of Łojasiewicz, of a tempered distribution and the order of summability of the pointwise Fourier inversion formula are closely related. Assuming that the order of the point values and certain order of growth at infinity are given for a tempered distribution, we estimate the order of summability of the Fourier inversion formula. For Fourier series, and in other cases, it is shown that if the distribution has a distributional point value of order k, then its Fourier series is e.v. Cesàro summable to the distributional point value of order k+1. Conversely, we also show that if the pointwise Fourier inversion formula is e.v. Cesàro summable of order k, then the distribution is the (k+1)-th derivative of a locally integrable function, and the distribution has a distributional point value of order k+2. We also establish connections between orders of summability and local behavior for other Fourier inversion problems.     

A NEW ROPER-SUFFRIDGE EXTENSION OPERATOR ON BOUNDED COMPLETE REINHARDT DOMAINS

In this paper, we construct a new Roper-Suffridge extension operator Φr n,β1,,βn(f)(z) = F(z) = ((rf(z1/r)/z1)β1z1,(rf(z1/r)/z1)β2z2,...,(rf(z1/r)/z1)βnzn)',where f is a normalized locally biholomorphic function on the unit disc D, r = sup{|z1| : z =(z1, ···, zn) ∈Ω}, β1∈ [0, 1], 0 ≤βk≤β1, k = 2, ···, n, then we prove it can preserve the property of spirallikeness of type β, almost starlikeness of order α and starlikeness of orderα on bounded complete Reinhardt domain Ω, respectively.     

Surface plasmon interference formed by tightly focused higher polarization order axially symmetric polarized beams

We numerically study the surface plasmon interference formed by tightly focused higher polarization order axially symmetric polarized beams (ASPBs) based on the vectorial diffraction theory. The definition of ASPBs is stated, and the optical setup for surface plasmon polariton (SPP) excitation and mathematical expressions for interfering SPP fields are proposed. The simulation results show that the interfering SPP fields present a multi-focal spot pattern. In addition, the number of spots is related to the polarization order of the incident beams P as 2×(P-1), indicating potential utilization in near-field multiple optical trapping and near-field imaging and sensing. The unique interfering phenomenon is also explained.     

SOME COMPARISONS BETWEEN GENERALIZED ORDER STATISTICS

Some stochastic comparisons of generalized order statistics under the right spread order,the location independent riskier order and the total time transform order are investigated in this paper.The underlying distributions and parameters on which generalized order statistics are based are also surveyed to obtain the conditions for increasing the expectations of spacings between the first two generalized order statistics and between the last two generalized order statistics.     

Reply to “Comment on ＇Focusing of high polarization order axially-symmetric polarized beams＇”[Chin.Opt.Lett.8,1110 （2010）]

This is a reply to the recent comment by Lifeng Li on the paper ＂Focusing of high polarization order axially-symmetric polarized beams [Chin.Opt.Lett.7,938 （2009）]＂.We analyze the errors pointed out by the comment,further perfect the mathematical expressions,and present a numerical simulation at last.     

Domination number in graphs with minimum degree two

A set D of vertices of a graph G = （V, E） is called a dominating set if every vertex of V not in D is adjacent to a vertex of D. In 1996, Reed proved that every graph of order n with minimum degree at least 3 has a dominating set of cardinality at most 3n/8. In this paper we generalize Reed＇s result. We show that every graph G of order n with minimum degree at least 2 has a dominating set of cardinality at most （3n ＋IV21）/8, where V2 denotes the set of vertices of degree 2 in G. As an application of the above result, we show that for k ≥ 1, the k-restricted domination number rk （G, γ） ≤ （3n＋5k）/8 for all graphs of order n with minimum degree at least 3.     

台湾眼镜蛇毒的NMR研究

随着核磁共振技术的不断创新及分子模拟计算的长足进步,用NMR结合电脑计算已成为研究蛋白质结构及功能的主要方法,本文以实际的范例,介绍台湾眼镜蛇毒的NMR研究成果,台湾NMR的研究工作正在蓬勃发展,目前最高磁场为600MHz,分别装置在中研院生物医学研究所(台北)及清华大学化学系(新竹)。     

Modal analysis of the Oth order nulled phase masks

A simple modal analysis （MA） method to explain the diffraction process of 0th order nulled phase mask is presented. In MA, multiple reflections of the grating modes at grating interfaces are considered by introducing equivalent Fresnel coefficients. Analytical expressions of the diffraction efficiencies and modal guidelines for the 0th order hulled phase grating design are also presented. The phase mask structure, which comprises a high-index contrast HfO2 grating and a fused-silica substrate, is optimized using rigorous coupled-wave analysis around the 800-nm wavelength, after which the modal guideline for cancellation of the 0th order in a phase mask is verified. The proposed MA method illustrates the inherent physical mechanism of multiple reflections of the grating modes in the diffraction process, which can help to analyze and design both low-contrast and high-contrast gratings.     

一类亚纯系数高阶线性微分方程解的增长性

In this paper, we investigate the growth of solutions of higher order linear differ-ential equations with meromorphic coefficients. Under certain conditions, we obtain precise estimation of growth order and hyper-order of solutions of the equation.     

《数学季刊》征稿简则

一、《数学季刊》是综合性数学专业期刊,国内外发行,本刊以推进数学研究,介绍国内外创造性研究成果,指导青年数学工作者进行数学研究为宗旨,登载具有创造性的研究论文、研究：简报和专题研究综述等三类文章。