A GENERALIZATION OF SIMPSON'S RULE

Let TA(f)=integral form n= to 1/2(P_~n(x) + P_b^n(x))dx and let TM(f)=integral form n= to P_((+b)/2)^(n+1)(x)dx, where P_c^n denotes the Taylor polynomial to f at c of order n, where n is even. TA and TM are reach generalizations of the Trapezoidal rule and the midpoint rule, respectively. and are each exact for all polynomial of degree ≤n+1. We let L(f) = αTM(f) + (1-α)TA(f), where α =(2^(n+1)(n+1))/(2^(n+1)(n+1)+1), to obtain a numerical integration rule L which is exact for all polynomials of degree≤n+3 (see Theorem l). The case n = 0 is just the classicol Simpson's rule. We analyze in some detail the case n=2, where our formulae appear to be new. By replacing P_(+b)/2)^(n+1)(x) by the Hermite cabic interpolant at a and b. we obtain some known formulae by a different ap- proach (see [1] and [2]). Finally we discuss some nonlinear numerical integration rules obtained by taking piecewise polynomials of odd degree, each piece being the Taylor polynomial off at a and b. respectively. Of course all of our formulae can be compounded over subintervals of [a, b].

Combining the Rule of Law with the Rule of Morality——General Secretary Xi Jinping's Important Discourse on the Relationship Between the Rule of Law and Rule by Virtue

Key points:Throughout the ages,rule of law has been an indispensable means of governing a state.However,as General Secretary Xi Jinping has pointed out,it is not enough to govern a state by the rule of law

SYSTEM FOR AUTOMATIC GENERALIZATION OF TOPOGRAPHIC MAPS

With the construction of spatial data infi＇astructure, automated topographic map generalization becomes an indispensable component in the community of cartography and geographic information science. This paper describes a topographic map generalization system recently developed by the authors. The system has the following characteristics： 1） taking advantage of three levels of automation, i.e. fully automated generalization, batch generalization, and interactive generalization, to undertake two types of processes, i.e. intelligent inference process and repetitive operation process in generalization; 2） making use of two kinds of sources for generalizing rule library, i.e. written specifications and cartographers＇ experiences, to define a six-element structure to describe the rules; 3） employing a hierarchical structure for map databases, logically and physically; 4） employing a grid indexing technique and undo/redo operation to improve database retrieval and object generalization efficiency. Two examples of topographic map generalization are given to demonstrate the system. It reveals that the system works well. In fact, this system has been used for a number of projects and it has been found that a great improvement in efficiency compared with traditional map general- ization process can be achieved.

气象观测场在汽车试验场中的应用研究

汽车试验场作为汽车开展道路测试的重要场所,用于验证汽车产品的品质以及可靠性。除了场地道路外,气象条件作为汽车道路测试的重要一环,在《GB/T12534-1990汽车道路试验方法通则》中也有明确要求,如:试验时应是无雨无雾天气,相对湿度小于95%,气温0-40℃,风速不大于3m/s。同时气象条件也作为试验场道路管控的重要依据,实时风速、雨量、能见度等信息为场地管理者发布限速、限行、封场等通知提供必要参考依据,直接影响道路测试安全管控的及时性。因此,文章从气象观测场的建设、气象服务、异常天气道路管控等方面开展气象观测场在汽车试验场中的应用研究。

Approximate analytical solutions and mean energies of stationary Schrodinger equation for general molecular potential

The Schrodinger equation is solved with general molecular potential via the improved quantization rule.Expression for bound state energy eigenvalues,radial eigenfunctions,mean kinetic energy,and potential energy are obtained in compact form.In modeling the centrifugal term of the effective potential,a Pekeris-like approximation scheme is applied.Also,we use the Hellmann–Feynman theorem to derive the relation for expectation values.Bound state energy eigenvalues,wave functions and meanenergies of Woods–Saxon potential,Morse potential,Mobius squared and Tietz–Hua oscillators are deduced from the general molecular potential.In addition,we use our equations to compute the bound state energy eigenvalues and expectation values for four diatomic molecules viz.H_(2),CO,HF,and O_(2).Results obtained are in perfect agreement with the data available from the literature for the potentials and molecules.Studies also show that as the vibrational quantum number increases,the mean kinetic energy for the system in a Tietz–Hua potential increases slowly to a threshold value and then decreases.But in a Morse potential,the mean kinetic energy increases linearly with vibrational quantum number increasing.

A NEW SELF-ADAPTIVE ITERATIVE METHOD FOR GENERAL MIXED QUASI VARIATIONAL INEQUALITIES

The general mixed quasi variational inequality containing a nonlinear term φ is a useful and an important generalization of variational inequalities. The projection method can not be applied to solve this problem due to the presence of nonlinear term. It is well known that the variational inequalities involving the nonlinear term φ are equivalent to the fixed point problems and resolvent equations. In this article, the authors use these alternative equivalent formulations to suggest and analyze a new self-adaptive iterative method for solving general mixed quasi variational inequalities. Global convergence of the new method is proved. An example is given to illustrate the efficiency of the proposed method.

Generating Fuzzy Rule-based Systems from Examples Based on Robust Support Vector Machine

This paper firstly proposes a new support vector machine regression (SVR) with a robust loss function, and designs a gradient based algorithm for implementation of the SVR, then uses the SVR to extract fuzzy rules and designs fuzzy rule-based system. Simulations show that fuzzy rule-based system technique based on robust SVR achieves superior performance to the conventional fuzzy inference method, the proposed method provides satisfactory performance with excellent approximation and generalization property than the existing algorithm.

General Provisions of the Civil Law and Commercial Legislation: Consensus, Problems and Options——Taking Commercial Agency as an Example

In the context of the codification of China's Civil Code, the academic consensus has been to make commercial legislation systematic and establish commercial norms with proper legislative expression. Many direct and indirect commercial norms in General Provisions of the Civil Law provide evidence that civil law has been turned into commercial law. However, a general overview shows that the absence of related norms, including agency in duty, reveals that General Provisions of the Civil Law is lacking commercial law's characteristics. In addition to the Civil Code, using General Rules of Commercial Law is a relatively reasonable choice for commercial legislative arrangements, such as norms in relation to agency in duty. Taking commercial agency as an example, legislators should adopt problem-oriented and limited systematic patterns of "residue law" instead of unified patterns of codification.

From the General Provisions of Civil Law to the General Rules of Civil Law:A Historic Leap

The General Provisions of Civil Law(民法通则),formulated in the early days of reform and opening up,was a special law that set out the basic principles or rules of civil law,defining civil subjects,civil legal acts and the agency system,declaring the civil rights enjoyed by civil subjects,establishing a relatively complete system of civil liability system,and so on.It kindled awareness of civil rights among the mass of the population,ensured China’s rapid economic and social development,and laid down a basic framework and content for the civil code,so holds an important position in contemporary Chinese history.But with the development of the economy and society,civil law has had to change with the times.Civil law jurisprudence injects theoretical support into contemporary civil law legislation,and the blueprint for law based governance provides a powerful impetus to the historic leap forward of contemporary Chinese civil law,providing the necessary conditions for the codification of civil law.The completion of the General Rules of Civil Law(民法总则)answers the requirements of the economic,humanist and legal character of the times,demonstrates the humanist stance and spirit of the civil code,rises to the challenge of modern scientific and technological development,and ensures people’s enjoyment and control of their new-style rights and their objective forms.This signifies that the GPCL has accomplished its historical task and civil law in contemporary China has realized a historic leap forward,laying a foundation for the compilation of the Chinese civil code,including the specific provisions of the framework and the contents of its individual parts.

THE CONSTITUTIVE EQUATION RESEMBLANCE OF ELASTIC-PLASTIC MULTIPHASE SOLID

Based on composite materials, the equivalent elastic-plastic constitutive equations of multiphase solid are researched. According to the suggested definition of. constitutive equivalence it is demonstrated that the multiphase solid, composed of several kinds of homogeneous elastic-plastic media that conform to the generalized normality rule, has the same type of constitutive equations as its constituents have that also conform to the generalized normality rule.

Does Digitalization Matter for Grievance Redress Mechanism?An Analysis of the E-Government Procurement in the Local Government

Public procurement denotes the attainment of goods,works,or services required by governments through contracts.Public procurement is usually plagued with covert practices and exclusive forms of corruption in Bangladesh.The cost of development finance is much higher in public procurement than that of others in Bangladesh.There have been no unified rules or laws regarding government purchases since 2006.The Government of Bangladesh enacted its ever first act of public procurement,the Public Procurement Act,2006(PPA,2006),and the Public Procurement Rules,2008(PPR,2008).The procurement entity must disseminate procurement information through electronic medium i.e.Electronic Government Procurement(hereinafter e-GP).Despite passing over an era since its enactment,the role of the PPA,2006 remains seriously under-researched area,specifically there is no research on the issue of the grievance redress mechanisms.The study has been done using a qualitative case study methodology,backed by both primary and secondary documentary analysis.Based on empirical data,this paper explained the role of digitalization in the process of government procurement and depicted changes that have been brought by the implementation of e-GP in government purchases.However,it concluded that the grievance redress mechanism in the process of procurement is only existing in the policy papers which need mandatory implementation for a transparent and accountable governance system.Despite the significant changes and up-gradation in digital government procurement,it is hardly found that the GRM process is digitalized.And the mass tenderers are yet to be acquainted with the improvised system apart from the consistent efforts of the government.

Normalized Wolfe-Powell-type local minimax method for finding multiple unstable solutions of nonlinear elliptic PDEs

The local minimax method(LMM)proposed by Li and Zhou(2001,2002)is an efficient method to solve nonlinear elliptic partial differential equations(PDEs)with certain variational structures for multiple solutions.The steepest descent direction and the Armijo-type step-size search rules are adopted in Li and Zhou(2002)and play a significant role in the performance and convergence analysis of traditional LMMs.In this paper,a new algorithm framework of the LMMs is established based on general descent directions and two normalized(strong)Wolfe-Powell-type step-size search rules.The corresponding algorithm framework,named the normalized Wolfe-Powell-type LMM(NWP-LMM),is introduced with its feasibility and global convergence rigorously justified for general descent directions.As a special case,the global convergence of the NWP-LMM combined with the preconditioned steepest descent(PSD)directions is also verified.Consequently,it extends the framework of traditional LMMs.In addition,conjugate-gradient-type(CG-type)descent directions are utilized to speed up the NWP-LMM.Finally,extensive numerical results for several semilinear elliptic PDEs are reported to profile their multiple unstable solutions and compared with different algorithms in the LMM’s family to indicate the effectiveness and robustness of our algorithms.In practice,the NWP-LMM combined with the CG-type direction performs much better than its known LMM companions.

An Overview of Data Mining and Knowledge Discovery

With massive amounts of data stored in databases, mining information and knowledge in databases has become an important issue in recent research. Researchers in many different fields have shown great interest in data mining and knowledge discovery in databases. Several emerging applications in information providing services, such as data warehousing and on-line services over the Internet, also call for various data mining and knowledge discovery techniques to understand user behavior better, to improve the service provided, and to increase the business opportunities. In response to such a demand, this article is to provide a comprehensive survey on the data mining and knowledge discovery techniques developed recently, and introduce some real application systems as well. In conclusion, this article also lists some problems and challenges for further research.