INFORMATION AXIOM BASED EVALUATION APPROACH TO FACILITY LAYOUT PROBLEM

The facility layout problem belongs to typical multiple-attribute decision-making（MADM） problems. To make the information axiom fit to MADM problems, the original computation method for the information content is improved by increasing the satisfaction degree item. Attribute values are divided into precise type, uncertainty type and fuzzy type. For benefit, cost, fixation, and interval type attributes, the computation methods for the information content on the three types of attribute values are presented. The improved information content can reflect the system success probability and the decision-maker satisfaction degree simultaneously and evaluate the MADM problem including multiple type attribute values. Finally, as a case study, the facility layout alternatives of a welding assembly workshop are evaluated. The result verifies the validity and the feasibility of the improved information axiom on the MADM problems.

西门子AXIOM Artis数字减影X线机在肾外伤DSA中摄影参数的探讨

目的:探讨西门子AXIOMArtis数字减影X线机摄影参数(采集参数、血管造影技术参数)在肾外伤DSA中的选择。方法:选择5例肾外伤患者在常规消毒、铺巾、穿刺、插管下,分别行腹主动脉DSA检查和超选择性肾动脉DSA检查。结果:选择适当的数字减影X线机摄影参数行DSA造影检查,准确显示了肾外伤部位、程度、出血灶及其相邻血管的关系。结论:数字减影X线机摄影参数在肾外伤DSA中的正确选择,对肾外伤性肾内动脉的影像显示、肾外伤的诊疗及患者的安全性,具有重要意义。

布尔模态的公理化(英文)

布尔模态(即模态生成算子补、交、并)涉及到了完全性问题。并模态是模态可定义的,但是补和交都不是。这意味着证明包含这三个模态的逻辑的完全性不是一件简单直接的事情。Gargov和Passy使用复制方法从整体上处理这三个模态,但是,这个方法不适用于强完全性,也不能单独处理这三个模态。本文改进了这个方法,使得改进后的方法更具一般性,并且没有这两个不足之处。

Extension of covariant derivative(Ⅰ): From component form to objective form

This paper extends the covariant derivative un der curved coordinate systems in 3D Euclid space. Based on the axiom of the covariant form invariability, the classical covariant derivative that can only act on components is ex tended to the generalized covariant derivative that can act on any geometric quantity including base vectors, vectors and tensors. Under the axiom, the algebra structure of the gen eralized covariant derivative is proved to be covariant dif ferential ring. Based on the powerful operation capabilities and simple analytical properties of the generalized covariant derivative, the tensor analysis in curved coordinate systems is simplified to a large extent.

Cyberspace Endogenous Safety and Security

Uncertain security threats caused by vulnerabilities and backdoors are the most serious and difficult problem in cyberspace.This paper analyzes the philosophical and technical causes of the existence of so-called"dark functions"such as system vulnerabilities and backdoors,and points out that endogenous security problems cannot be completely eliminated at the theoretical and engineering levels;rather,it is necessary to develop or utilize the endogenous security functions of the system architecture itself.In addition,this paper gives a definition for and lists the main technical characteristics of endogenous safety and security in cyberspace,introduces endogenous safety and security mechanisms and characteristics based on dynamic heterogeneous redundancy(DHR)architecture,and describes the theoretical implications of a coding channel based on DHR.

Generalized covariant differentiation and axiom-based tensor analysis

This paper reports the new progresses in the axiomatization of tensor anal- ysis, including the thought of axiomatization, the concept of generalized components, the axiom of covariant form invariability, the axiomatized definition, the algebraic structure, the transformation group, and the simple calculation of generalized covariant differentia- tions. These progresses strengthen the tendency of the axiomatization of tensor analysis.

Extension of covariant derivative(Ⅱ): From flat space to curved space

This paper extends the classical covariant deriva tive to the generalized covariant derivative on curved sur faces. The basement for the extension is similar to the pre vious paper, i.e., the axiom of the covariant form invariabil ity. Based on the generalized covariant derivative, a covari ant differential transformation group with orthogonal duality is set up. Through such orthogonal duality, tensor analy sis on curved surfaces is simplified intensively. Under the covariant differential transformation group, the differential invariabilities and integral invariabilities are constructed on curved surfaces.

On an Axiomatic Foundation for a Theory of Everything

Whether a unified theory of everything(TOE)is possible or not is a philosophical question and yes or no can be chosen in a two-valued logic system.Currently the two schools are in conflict with each other.Based on the relativity of simultaneity axiom proposed in this paper,the present author suggests to use a midway philosophy to replace the present materialist philosophy for modern sciences;then this conflict together with many other conflicts among different theories such as classical mechanics(CM),general relativity(GR),and quantum mechanics(QM)can be solved and a unified theory of everything for the world we can observe can be constructed.In this paper,the axiomatic foundation for a TOE is proposed which contains six fundamental axioms.Various problems related to these foundational issues are discussed.It is hoped that the present paper might show a new promise and a new direction for TOE which would be helpful for the further development of modern sciences.

A minimal axiom group for rough set based on quasi-ordering

Rough set axiomatization is one aspect of rough set study to characterize rough set theory using dependable and minimal axiom groups. Thus, rough set theory can be studied by logic and axiom system methods. The classic rough set theory is based on equivalent relation, but rough set theory based on reflexive and transitive relation (called quasi-ordering) has wide applications in the real world. To characterize topological rough set theory, an axiom group named RT, consisting of 4 axioms, is proposed. It is proved that the axiom group reliability in characterizing rough set theory based on similar relation is reasonable. Simultaneously, the minimization of the axiom group, which requires that each axiom is an equation and each is independent, is proved. The axiom group is helpful for researching rough set theory by logic and axiom system methods.

A structural design of multilevel decomposition and domain mapping

An integrated optimization design was described using multilevel decomposition technique on the base of the parametric distribution and independent axiom at the stages of lower level. Based on Pareto optimum solution, the detailed parameters at lower level can be defined into the independent axiom. The suspension design was used as the simulation example. In an axiomatic design for the optimization design, the uncoupled and decoupled designs between functional requirements and design parameters are generally needed. But using the design sensitivity(or screening) of design parameters, the approximate uncoupled design is developed on behalf of the decoupled and coupled designs. Successive design parameters were applied to the suspension of torsion beam axle. The structural performance increases by 18%. The kinematic and compliance performance increases by 6% within the feasible ranges.

A Hierarchy of Axiom Systems for Set Theory

在文献[1,2]中,我们研究了范畴论基础,建立了集合的公理系统ACG,它能够处理超出了集合与类的极其大的汇合。本文进一步推广了系统ACG,建立了集合论公理系统的三个无穷序列:H0,H1,…;J0,J1,…,G0,G1,…。在建立这些公理系统的过程中,我们使用了类型论的方法,它们描述的能力是逐步增长的,

An Equivalent Form of the Dedekind Axiomand Its Application(Ⅱ)——Also on the unity of the Continuous Induction,the Mathem atical Induction and the Transfinite Induction

In this paper,a common characteristic of real number system and well ordered set is revealed and proved to be an equivalent form of the Dedekind Axiom or the Continuous Induction in R. Basing on it,we get the unified form of the mathematical induction,the transfinite induction and the continuous induction and generalize induction to totally ordered set that has the same characteristic.

An Equivalent Form of the Dedekind Axiomand Its Application(Ⅰ)——Also on theunity ofthe ContinuousInduction,theMathem aticalInduction and theTransfiniteInduction

In this paper,a common characteristic of real number system and well ordered set is revealed and proved to be an equivalent form of the Dedekind Axiom or the Continuous Induction in R. Basing on it,we get the unified form of the mathematical induction,the transfinite induction and the continuous induction and generalize induction to totally ordered set that has the same characteristic.

A Comprehensive Overview on Various Mind-Body Models

To understand what the relation between the mind and body is,philosophers and scientists have done quite a lot of work,but their opinions are controversial and this problem is known as mind-body dichotomy.Mind and body are thought to be separated in ancient Greek and ancient India and both of the two civilizations emphasize the dominated role of mind in the mind-body interaction.However,modern sciences such as biology are based on materialism and they think that mental phenomena are entirely dependent upon brain.A series of philosophical groups focusing on the mind-body problem,such as physicalism and dualism,have been developed based on traditional views and scientific advances.In this paper,a comprehensive overview and comparison to various theoretical mind-body models are carried out and based on the relativity of simultaneity axiom we recently proposed,we concluded that mind and body should be two independent existences and any theory based on monist philosophy such as materialism,idealism and Christianity cannot satisfy the logical consistency requirement while the trialism of matter,energy and information is unnecessary.

The Resolution of the Great 20th Century Debate in the Foundations of Mathematics

The paper resolves the great debate of the 20th century between the three philosophies of mathematics-logicism, intuitionism and formalism—founded by Bertrand Russell and A. N. Whitehead, L. E. J. Brouwer and David Hilbert, respectively. The issue: which one provides firm foundations for mathematics? None of them won the debate. We make a critique of each, consolidate their contributions, rectify their weakness and add our own to resolve the debate. The resolution forms the new foundations of mathematics. Then we apply the new foundations to assess the status of Hilbert’s 23 problems most of which in foundations and find out which ones have been solved, which ones have flawed solutions that we rectify and which ones are open problems. Problem 6 of Hilbert’s problems—Can physics be axiomatized?—is answered yes in E. E. Escultura, Nonlinear Analysis, A-Series: 69(2008), which provides the solution, namely, the grand unified theory (GUT). We also point to the resolution of the 379-year-old Fermat’s conjecture (popularly known as Fermat’s last theorem) in E. E. Escultura, Exact Solutions of Fermat’s Equations (Definitive Resolution of Fermat’s Last Theorem), Nonlinear Studies, 5(2), (1998). Likewise, the proof of the 274-year-old Goldbach’s conjecture is in E. E. Escultura, The New Mathematics and Physics, Applied Mathematics and Computation, 138(1), 2003.

A MULTIDIMENSIONAL CENTRAL LIMIT THEOREM WITH SPEED OF CONVERGENCE FOR AXIOM A DIFFEOMORPHISMS

Let T：X → X be an Axiom A diffeomorphism,m the Gibbs state for a Hlder continuous function ɡ. Assume that f：X → R^d is a Hlder continuous function with ∫_X^（fdm） = 0.If the components of f are cohomologously independent, then there exists a positive definite symmetric matrix σ~2：=σ~2 （f ） such that S^fn √ n converges in distribution with respect to m to a Gaussian random variable with expectation 0 and covariance matrix σ~2 . Moreover, there exists a real number A 〉 0 such that, for any integer n ≥ 1,Π（ m＊（ 1√ nS f n ）,N （0,σ~2 ） ≤A√n, where m＊（1√ n S^fn）denotes the distribution of 1√ n S^fn with respect to m, and Π is the Prokhorov metric.

A New Minimal Rough Set Axiom Group

Rough set axiomatization is one aspect of rough set study, and the purpose is to characterize rough set theory using independable and minimal axiom groups. Thus, rough set theory can be studied by logic and axiom system methods. To characterize rough set theory, an axiom group named H consisting of 4 axioms, is proposed. That validity of the axiom group in characterizing rough set theory is reasonable, is proved. Simultaneously, the minimization of the axiom group, which requires that each axiom is an inequality and each is independent, is proved. The axiom group is helpful for researching rough set theory by logic and axiom system methods. Key words rough set - lower approximation - axioms - minimization CLC number TP 18 Foundation item: Supported by the 973 National Basic Research Program of China (2002CB312106) and Science & Technology Program of Zhejiang Province (2004C31G101003)Biography: DAI Jian-hua (1977-), male, Ph. D, research direction: data mining, artificial intelligence, rough sets, evolutionary computation.

Fuzzy rough sets in Sostak sense

In this paper,we defined the fuzzy operator Φ_(λ) in a fuzzy ideal approximation space(X,R,I)associated with a fuzzy rough set λ in Sostak sense.Associated with Φ_(λ),there are fuzzy ideal interior and closure operators int_(Φ)^(λ) and cl_(Φ)^(λ),respectively.r-fuzzy separation axioms,r-fuzzy connectedness and r-fuzzy compactness in fuzzy ideal approximation spaces are defined and compared with the relative notions in r-fuzzy approximation spaces.There are many differences when studying these notions related with a fuzzy ideal different from studying these notions in usual fuzzy approximation spaces.Lastly,using a fuzzy grill,we will get the same results given during the context.

Separation axioms in topological ordered spaces

The Ti-axiom,the Ti-ordered axiom and Ti-pairwise axiom(i = 0,1,2,3,4) of topological ordered space are discussed and proved that they are equivalence under the certain conditions.

Stability of Hausdorff dimension of Axiom A attractors under random perturbations

This paper proves that the Hausdorff dimension of an Axiom A attractor is stable under random perturbations.