Symmetry Classification of Partial Differential Equations Based on Wu's Method

Lie algorithm combined with differential form Wu's method is used to complete the symmetry classification of partial differential equations(PDEs)containing arbitrary parameter.This process can be reduced to solve a large system of determining equations,which seems rather difficult to solve,then the differential form Wu's method is used to decompose the determining equations into a series of equations,which are easy to solve.To illustrate the usefulness of this method,we apply it to some test problems,and the results show the performance of the present work.

Self-evident Automated Proving Based on Point Geometry from the Perspective of Wu's Method Identity

The algebraic methods represented by Wu's method have made signi?cant breakthroughs in the ?eld of geometric theorem proving. Algebraic proofs usually involve large amounts of calculations, thus making it diffcult to understand intuitively. However, if the authors look at Wu's method from the perspective of identity, Wu's method can be understood easily and can be used to generate new geometric propositions. To make geometric reasoning simpler, more expressive, and richer in geometric meaning, the authors establish a geometric algebraic system(point geometry built on nearly 20 basic properties/formulas about operations on points) while maintaining the advantages of the coordinate method, vector method, and particle geometry method and avoiding their disadvantages. Geometric relations in the propositions and conclusions of a geometric problem are expressed as identical equations of vector polynomials according to point geometry. Thereafter, a proof method that maintains the essence of Wu's method is introduced to ?nd the relationships between these equations. A test on more than 400 geometry statements shows that the proposed proof method, which is based on identical equations of vector polynomials, is simple and e?ective. Furthermore, when solving the original problem, this proof method can also help the authors recognize the relationship between the propositions of the problem and help the authors generate new geometric propositions.

Significance of activation energy and Wu's slip features in Cross nanofluid with motile microorganisms

The current article investigates the impact of the bioconvection in an unsteady flow of magnetized Cross nanofluid with gyrotactic microorganisms and activation energy over a linearly stretched configuration.The analysis has been performed by utilizing the realistic Wu's slip boundary and zero mass flux conditions.The effects of nonlinear thermal radiation and the activation energy are also addressed.The governing flow equations are deduced to a dimensionless form by considering suitable transformations which are numerically targeted via a shooting algorithm.The physical visualization of each physical parameter governing the flow problem has been displayed graphically for distribution of velocity,temperature,concentration and motile microorganisms.The numerical treatment for the variation of skin friction coefficient,local Nusselt number,local Sherwood number and motile density number is performed in tabular forms.

Solving SAT by Algorithm Transform of Wu's Method

Recently algorithms for solving propositional satisfiability problem,or SAT, have aroused great illterest, and more attention has been paid to trans-formation problem solving. The commonly used transformation is representationtransform, but since its ifltermediate computing procedure is a black box from theviewpoint of the original problem, this aPproach has many limitations. In this paper, a new approach called algorithm transform is proposed and applied to solvingSAT by Wu's method, a general algorithm for solving polynomial equations. By es-tablishing the correspondellce between the primitive operation in Wu's method andclause resolution in SAT, it is shown that Wu's method, when used for solving SAT,is primarily a restricted clause resolution procedure. While Wu's method illtroduceselltirely new concepts, e.g. characteristic set of clauses, to resolution procedure, thecomplexity result of resolution procedure suggests an exponential lower bound toWu's method for solving general polynomial equations. Moreover, this algorithmtransform can help achieve a more efficiellt imp1ementation of Wu's method since itcan avoid the complex manipulation of polynomials and can make the best use ofdomain specific knowledge.

Applications of interval arithmetic in solving polynomial equations by Wu's elimination method

Wu's elimination method is an important method for solving multivariate polynomial equations. In this paper, we apply interval arithmetic to Wu's method and convert the problem of solving polynomial equations into that of solving interval polynomial equations. Parallel results such as zero-decomposition theorem are obtained for interval polynomial equations. The advantages of the new approach are two-folds: First, the problem of the numerical instability arisen from floating-point arithmetic is largely overcome. Second,the low efficiency of the algorithm caused by large intermediate coefficients introduced by exact compaction is dramatically improved. Some examples are provided to illustrate the effectiveness of the proposed algorithm.

A query on the year of King Wu's conquest over King Zhou determined by the Xia-Shang-Zhou Chronology Project -Materials finding and astronomical methods for chronological studies of China

This paper reviews the studies on the event that King Wu of the Western Zhou Dynasty defeated King Zhou of the late Shang Dynasty, an important historical event in Chinese history, and questions on the year in which this event took place determined by researchers of the Xia-Shang-Zhou Chronology Project of China in 2000. This paper also discusses on how to obtain primordial materials and how to use astronomical methods in the chronological studies of Chinese history. With both the new astronomical methods (the Moon Age Calendar Method and the Direct Solving Method) and the calculation based on the confirmed real-time materials, especially scriptures on oracle bones and bronze vessels, this paper obtains a more accurate and reliable result, putting the event at BC 1040 to BC 1030.

Fast Theorem-Proving and Wu's Method

In this paper, the possibility of fast algorithm is discussed for me-chanical theorem proving, where the degeneracy condition are considered in designingof these algorithms. It is found that all of the methods depend seriously on some prin-ciples appearing in Wu's Method. In other words, some principles in Wu's Methodare the instinctive properties in these new fast algorithms of theorem proving.

PSEUDO-DIVISION ALGORITHM FOR MATRIX MULTIVARIABLE POLYNOMIAL AND ITS APPLICATION

Pseudo-division algorithm for matrix multivariable polynomial are given, thereby with the view of differential algebra, the sufficient and necessary conditions for transforming a class of partial differential equations into infinite dimensional Hamiltonianian system and its concrete form are obtained. Then by combining this method with Wu's method, a new method of constructing general solution of a class of mechanical equations is got, which several examples show very effective.

ON A COLLISION PROBLEM

Traffic control is necessary for traffic safety in driving cars. To avoid collision of cars in crossroads is an important practical problem. We study in this paper the collision problem of two cars in elliptical forms which move with uniform speed on two crossroads orthogonal to each other. In applying Wb Wen-tsun's method of mathexnatics-mechanization we find conditions such that collision will not occur. We have also determined in the possible colliding case the time and place of first collision.

Decomposing the Radicals of Polynomial Ideals by Rational Univariate Representations

In this paper,the notion of rational univariate representations with variables is introduced.Consequently,the ideals,created by given rational univariate representations with variables,are defined.One merit of these created ideals is that some of their algebraic properties can be easily decided.With the aid of the theory of valuations,some related results are established.Based on these results,a new approach is presented for decomposing the radical of a polynomial ideal into an intersection of prime ideals.

On the Mechanization of Straightedge and Compass Constructions

The geometric constructions obtained with only straightedge and compass are famous and play a special role in the development of geometry. On the one hand, the constructibility of ?gures is a key ingredient in Euclid geometry and, on the other hand, unconstructibility gave birth to famous open problems of the ancient Greece which were unlocked only in the nineteenth century using discoveries in algebra. This paper discusses the mechanization of straightedge and compass constructions. It focuses on the algebraic approaches and presents two methods which are implemented; one is due to Lebesgue and the other one was jointly designed by Gao and Chou. Some links between the algebraic approach of constructions and synthetic geometry are described.

WELL-BEHAVED BASIS AND LR ARRAYS

In this paper, we will use Wu's method to study two-dimensional linear recurring arrays,investigate the relation between well-behaved basis and linear recurring arrays.

Object-Oriented Analysis of ELIMINO

ELIMINO is a mathematical research system developed for theimplementation of Wu's method, a powerful method for polynomial equation systemsolving and geometric theorem proving. The aim of ELIMINO is to provide usera programmable interpreting environment to use Wu's method in scientific researchand engineering computation. In this paper, the development of ELIMINo systemis outlined and the techniques adopted are discussed, then some details about theobject-oriented analysis of ELIMINO are presented.

吴舟桥:Wu’s Model,医匠底色

吴舟桥迎来了学医的第十一个年头。他曾不止一次地面对这样的调侃——你都学医了你还不后悔？或是这样的疑问——花了这么长的时间值不值？在北医三院外科楼一间休息室里,吴舟桥再次回忆起这些问题。他说,他喜欢学医,这件事毫无疑问。当天,吴舟桥的白大褂里面,是一件黑色衬衫。配上他的棕色尖头皮鞋,蓝色格纹长裤,这一身在欧洲留学期间置办来的打扮,

ORDERING IN AUTOMATED THEOREMPROVING OF DIFFERENTIAL GEOMETRY

A new ordering method is proposed for automated theorem proving of differential geometry,by which Cartan's moving frame method can be combined with Wu's elimination principle.