SOLVING COLORED YANG-BAXTER EQUATION BY WU’S METHOD

In this article, we discuss nonsymmetric solutions of the colored Yang-Baxter equation dependent on spectral as well as colored parameters and give all seven-vertex solutions by Wu＇s method. It is also proved that the solutions are composed of six groups of basic solutions up to five solution transformations. Moreover, al l solutions can be classified into two categories called Baxter type and free-fermion type.

On resolution to Wu's conjecture on Cauchy function's exterior singularities

This is a series of studies on Wu＇s conjecture and on its resolution to be presented herein. Both are devoted to expound all the comprehensive properties of Cauchy＇s function f（z） （z = x ＋ iy） and its integral J[f（z）]≡（2πi）-∮cf（t）（t-z）-1dt taken along the unit circle as contour C,inside which（the open domain D＋） f（z） is regular but has singularities distributed in open domain Doutside C. Resolution is given to the inverse problem that the singularities of f（z） can be determined in analytical form in terms of the values f（t） of f（z） numerically prescribed on C（｜t｜ = 1） ,as so enunciated by Wu＇s conjecture. The case of a single singularity is solved using complex algebra and analysis to acquire the solution structure for a standard reference. Multiple singularities are resolved by reducing them to a single one by elimination in principle,for which purpose a general asymptotic method is developed here for resolution to the conjecture by induction,and essential singularities are treated with employing the generalized Hilbert transforms. These new methods are applicable to relevant problems in mathematics,engineering and technology in analogy with resolving the inverse problem presented here.

The Study of Wu Ningkun＇s Chinese versions of The Great Gatsby from the Perspective of Skopos Theory

Skopos theory has provoked a lot of research interest among scholars since it was introduced in the 1970s, Skopos theory has formed a new perspective of translation practice and research by breaking the traditional idea of translation equivalence so to some extent it is an important supplement to translation theories. In Skopos theory, translation is considered to be a purposeful communicative action, and the specific translation purpose determines the whole translational action. Functionally adequate means that the translation should be adequate to the requirements of the translation and it works as the criterion of translation. Skopos theory enables translators to select appropriate translation strategies according to their own purposes, so as to effectively solve the dilemma in the translation process whether faithfully display the form of source text or flexibly retain the sense of the source text. The Great Gatsby is the masterpiece of the American writer Fitzgerald, F. S.. He not only depicted the intoxicating atmosphere of the unprecedented prosperity in American history after the First World War with vivid images and cheerful rhythms but also described the sorrows about the disillusionment of the ＂American Dream＂ after the war. This paper takes the Skopos of German functionalism as a point to analyze The Great Gatsby translated by Wu Ningkun from the perspective of skopos theory. Through the analysis of the specific translation of the selected paragraphs, I conclude Wu＇s translation strategies from lexical aspect, syntactic aspect and discourse aspect. In Wu＇s version he kept the styles, rhythms, and American thoughts of the source text by foreignization. His skopos is to offer an opportunity to broaden the horizon of readers who are hunger for new ideas and knowledge at that time therefor it is rather necessary to absorb the ＂exotic elements＂ in the his translations.

Algorithms for computing the global infimum and minimum of a polynomial function

By catching the so-called strictly critical points,this paper presents an effective algorithm for computing the global infimum of a polynomial function.For a multivariate real polynomial f ,the algorithm in this paper is able to decide whether or not the global infimum of f is finite.In the case of f having a finite infimum,the global infimum of f can be accurately coded in the Interval Representation.Another usage of our algorithm to decide whether or not the infimum of f is attained when the global infimum of f is finite.In the design of our algorithm,Wu’s well-known method plays an important role.

A MAPLE PACKAGE OF AUTOMATED DERIVATION OF HOMOTOPY ANALYSIS SOLUTION FOR PERIODIC NONLINEAR OSCILLATIONS

Based on the homotopy analysis method, a general analytic technique for strongly nonlinear problems, a Maple package of automated derivation （ADHO） for periodic nonlinear oscillation systems is presented. This Maple package is valid for periodic oscillation systems in rather general, and can automatically deliver the accurate approximations of the frequency co and the mean of motion δof a nonlinear periodic oscillator. Based on the homotopy analysis method which is valid even for highly nonlinear problems, this Maple package can give accurate approximate expressions even for nonlinear oscillation systems with strong nonlinearity. Besides, the package is user-friendly： One just needs to input a governing equation and initial conditions, and then gets satisfied analytic approximations in few seconds. Several different types of examples are given in this paper to illustrate the validity of this Maple package. Such kind of package provides us a helpful and easy-to-use tool in science and engineering to analyze periodic of this Maple package from the is published publicly. nonlinear oscillations. And it is free address http：//numericaltank.sjtu to download the electronic version edu.cn/sjliao.htm once the paper

Determination of the limits for multivariate rational functions

The purpose of this paper is to solve the problem of determining the limits of multivariate rational functions.It is essential to decide whether or not limxˉ→0f g=0 for two non-zero polynomials f,g∈R[x1,...,xn]with f(0,...,0)=g(0,...,0)=0.For two such polynomials f and g,we establish two necessary and sufcient conditions for the rational functionf g to have its limit 0 at the origin.Based on these theoretic results,we present an algorithm for deciding whether or not lim(x1,...,xn)→(0,...,0)f g=0,where f,g∈R[x1,...,xn]are two non-zero polynomials.The design of our algorithm involves two existing algorithms:one for computing the rational univariate representations of a complete chain of polynomials,another for catching strictly critical points in a real algebraic variety.The two algorithms are based on the well-known Wu’s method.With the aid of the computer algebraic system Maple,our algorithm has been made into a general program.In the final section of this paper,several examples are given to illustrate the efectiveness of our algorithm.

Exact Computation of the Topology and Geometric Invariants of the Voronoi Diagram of Spheres in 3D

In this paper, we are addressing the exact the Voronoi diagram of spheres using Wu＇s algorithm. computation of the Delaunay graph （or quasi-triangulation） and Our main contributions are first a methodology for automated derivation of invariants of the Delaunay empty circumsphere predicate for spheres and the Voronoi vertex of four spheres, then the application of this methodology to get all geometrical invariants that intervene in this problem and the exact computation of the Delaunay graph and the Voronoi diagram of spheres. To the best of our knowledge, there does not exist a comprehensive treatment of the exact computation with geometrical invariants of the Delaunay graph and the Voronoi diagram of spheres. Starting from the system of equations defining the zero-dimensional algebraic set of the problem, we are applying Wu＇s algorithm to transform the initial system into an equivalent Wu characteristic （triangular） set. In the corresponding system of algebraic equations, in each polynomial （except the first one）, the variable with higher order from the preceding polynomial has been eliminated （by pseudo-remainder computations） and the last polynomial we obtain is a polynomial of a single variable. By regrouping all the formal coefficients for each monomial in each polynomial, we get polynomials that are invariants for the given problem. We rewrite the original system by replacing the invariant polynomials by new formal coefficients. We repeat the process until all the algebraic relationships （syzygies） between the invariants have been found by applying Wu＇s algorithm on the invariants. Finally, we present an incremental algorithm for the construction of Voronoi diagrams and Delaunay graphs of spheres in 3D and its application to Geodesy.