与其导数具有公共值的代数体函数的唯一性定理

该文定义了代数体函数与其导数的公共值,并得到了几个关于代数体函数与其导数具有公共值的唯一性定理.

代数体函数与其导数的唯一性

通过研究代数体函数的分担值和分支点之间的关系,得到一个关于代数体函数与其导数具有公共值的唯一性定理,将Gundersen和Mues-Steinmetz关于亚纯函数与其导数的一个唯一性定理推广到代数体函数.

代数体函数可约性的一个判定定理

孙道椿与高宗升在研究代数体函数的四则运算时,把"代数体函数是由不可约方程确定出来的"这一要求去掉了,这使得可约性成为代数体函数的另一个特性.研究了代数体函数经过复合运算后所得函数的可约性与原代数体函数的可约性之间的关系,得到了判定二者可约性相同的一个定理.

关于多值函数的概念及其教学

多值函数在复交函数论中是一个极其重要的概念，对这一概念的处理在众多函数论教科书中各有不同，甚至出现了某些混乱现象，作者对多值函数各种不同的定义方式进行了分析对比，并在教学中相应作了改进。

奇异粗糙集理论及其研究现状

简要介绍Pawlak粗糙集概念,着重介绍奇异集合、奇异粗糙集的基本概念,奇异粗糙集的两种结构,奇异粗糙集与Pawlak粗糙集的关系,以及奇异粗糙集的研究现状。

A topology optimization method based on element independent nodal density

A methodology for topology optimization based on element independent nodal density(EIND) is developed.Nodal densities are implemented as the design variables and interpolated onto element space to determine the density of any point with Shepard interpolation function.The influence of the diameter of interpolation is discussed which shows good robustness.The new approach is demonstrated on the minimum volume problem subjected to a displacement constraint.The rational approximation for material properties(RAMP) method and a dual programming optimization algorithm are used to penalize the intermediate density point to achieve nearly 0-1 solutions.Solutions are shown to meet stability,mesh dependence or non-checkerboard patterns of topology optimization without additional constraints.Finally,the computational efficiency is greatly improved by multithread parallel computing with OpenMP.

An SDN/NFV Based Framework for Management and Deployment of Service Based 5G Core Network

The traffic explosion and the rising of diverse requirements lead to many challenges for traditional mobile network architecture on flexibility, scalability, and deployability. To meet new requirements in the 5 G era, service based architecture is introduced into mobile networks. The monolithic network elements(e.g., MME, PGW, etc.) are split into smaller network functions to provide customized services. However, the management and deployment of network functions in service based 5 G core network are still big challenges. In this paper, we propose a novel management architecture for 5 G service based core network based on NFV and SDN. Combined with SDN, NFV and edge computing, the proposed framework can provide distributed and on-demand deployment of network functions, service guaranteed network slicing, flexible orchestration of network functions and optimal workload allocation. Simulations are conducted to show that the proposed framework and algorithm are effective in terms of reducing network operating cost.

Projection Operator on Rational Noncommutative Orbifold T^2/Z_4

In this paper, we introduce the reduced matrix in kq representation and provide the reduced matrix elements of a projection operator P on the rational noncommutative orbifold T^2/Z_4.we give the closed form for the projector by Jacobi elliptical functions. Since projectors correspond to soliton solutions of the field theory on the noncommutative orbifold, we thus present a corresponding soliton solution.

CONSTRUCTIONOFACLASSOFPNSEQUENCESWITHPRIMENUMBERPERIODSOF4t＋1FORM

A class of new PN sequence with prime number periods of 4t +1 form (t is an integer)is constructed.The advantage of these PN sequencs over the m(M) sequence is their large number of alternative periods.They have good pseudo random characteristics demonstrated by the expression of periodic autocorrelation function found out in this paper.

Two-Component Description for Relativistic Fermions

We propose a two-component form to describe massive relativistic fermions in gauge theories. Relations between the Green＇s functions in this form and those in the conventional four-component form are derived. It is shown that the S-matrix elements in both forms are exactly the same. The description of the fermion in the new form simplifies significantly the γ-matrix algebra in the four-component form. In particular, in perturbative calculations the propagator of the fermion is a scalar function. As examples, we use this form to reproduce the relativistic spectrum of hydrodron atom, the S-matrix of e＋e-→μ＋μ- and QED one-loop vacuum polarization of photon.

Spectrality of planar self-affine measures with two-element digit set

The iterated function system with two element digit set is the simplest case and the most important case in the study of self affine measures.The one dimensional case corresponds to the Bernoulli convolution whose spectral property is understandable.The higher dimensional analogue is not known,for which two conjectures about the spectrality and the non spectrality remain open.In the present paper,we consider the spectrality and non spectrality of planar self affine measures with two element digit set.We give a method to deal with the two dimensional case,and clarify the spectrality and non spectrality of a class of planar self affine measures.The result here provides some supportive evidence to the two related conjectures.

Extrapolation methods to compute hypersingular integral in boundary element methods

The composite trapezoidal rule for the computation of Hadamard finite-part integrals in boundary element methods with the hypersingular kernel I/sin2（x- s） is discussed, and the main part of the asymptotic expansion of error function is obtained. Based on the main part of the asymptotic expansion, a series is constructed to approach the singular point. An extrapolation algorithm is presented and the convergence rate is proved. Some numerical results are also presented to confirm the theoretical results and show the efficiency of the algorithms.

Density Results in Sobolev Spaces Whose Elements Vanish on a Part of the Boundary

This paper is devoted to the study of the subspace of Wm＇＂ of functions that vanish on a part γ0 of the boundary. The author gives a crucial estimate of the Poincare constant in balls centered on the boundary of γ0. Then, the convolution-translation method, a variant of the standard mollifier technique, can be used to prove the density of smooth functions that vanish in a neighborhood of γ0, in this subspace. The result is first proved for m = 1, then generalized to the case where m 〉 1, in any dimension, in the framework of Lipschitz-continuous domain. However, as may be expected, it is needed to make additional assumptions on the boundary of γ0, namely that it is locally the graph of some Lipschitz-continuous function.

A new procedure for investigating three-dimensional stress fields in a thin plate with a through-the-thickness crack

In the paper, a new procedure is proposed to investigate three-dimensional fracture problems of a thin elastic plate with a long through-the-thickness crack under remote uniform tensile loading. The new procedure includes a new analytical method and high accurate finite element simulations. In the part of theoretical analysis, three-dimensional Maxwell stress functions are employed in order to derive three-dimensional crack tip fields. Based on the theoretical analysis, an equation which can describe the relationship among the three-dimensional J-integral J(z), the stress intensity factor K(z) and the tri-axial stress constraint level Tz(z) is derived first. In the part of finite element simulations, a fine mesh including 153360 elements is constructed to compute the stress field near the crack front, J(z) and Tz(z). Numerical results show that in the plane very close to the free surface, the K field solution is still valid for in-plane stresses. Comparison with the numerical results shows that the analytical results are valid.