3D Fractals, Axiom of Algebra (Δn)n = +1

After having laid down the Axiom of Algebra, bringing the creation of the square root of -1 by Euler to the entire circle and thus authorizing a simple notation of the nth roots of unity, the author uses it to organize homogeneous divisions of the limited development of the exponential function, that is opening the way to the use of a whole bunch of new primary functions in Differential Calculus. He then shows how new supercomplex products in dimension 3 make it possible to calculate fractals whose connexity depends on the product considered. We recall the geometry of convex polygons and regular polygons.

The Evaluation of Risk-Based Resource Allocation Alternatives Based on Fuzzy Information Axiom

This paper presents an analysis of the challenges in risk-based resource allocation in engineering projects.Sub-sequently,an alternative resource allocation evaluation method based on language information and information axioms is proposed.Firstly,the evaluation team uses language information to give the evaluation information of the alternatives of risk resource allocation and provides the corresponding expected information for each resource.Secondly,according to the transformation formula of language information and fuzzy numbers,the above information is transformed into the evaluation information and expected information of the alternatives of risk-based resource allocation.Thirdly,according to the transformation formula of language information and fuzzy numbers,the above information is transformed into evalu-ation information and expectation information of alternative risk resource allocation.Finally,according to the information amount of each risk resource and the corresponding weight,the comprehensive information amount of the expected risk-based resource allocation alternatives is determined.

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。

多元性与普遍性的弥合--章太炎以“齐物”解构“公理”的后果

章太炎在与《新世纪》派论战的过程中,深感“公理”对于个体的压制。他从“公理”观念形成的认识论基础与话语霸权两方面对其进行了批判,并提出以“齐物”思想取代“公理”的观点。为了避免“齐物”观念同样面临从认识论层面被解构的风险,他将“齐物”的合法性建立在否定名相以体证“真如”的基础之上,然而这却致使其价值指向徘徊于多元性与普遍性之间。章太炎最终以当下历史情境中的“人民”弥合了二者之间的裂隙。因此,“齐物”思想的价值指向并非多元或者普遍,而是回归于“人民”这一历史主体之上。

章太炎齐物哲学对中国文化的破与立

近代中国受到西方文化的强势入侵,大量传统学者对西方文化的理性、智识等观念极为推崇,而章太炎则以庄子的齐物观念对这些西方思想予以批评。在《辨性下》中章太炎认为文教国民更具智力,但却远离真如本性,陷入对概念系统的执着。这源于章太炎以其齐物哲学体系对进化以及西方现代性思想的批判,也与章太炎反对维新的彻底革命立场相关。按章太炎齐物哲学,传统学术与西方现代思想都属于世间范畴,不悟本真,所以不能定一者为“公理”。不过中国文化追求“愚菴(愚钝)”这种“大智慧”,离本真更近,因此在文化选择,即“回真向俗”的过程中,应该尊重中华传统文化,而非一味追求西化。

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.

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.

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.

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 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,

Pre—Separation Axioms in Fuzzifying Topology

In the present paper we introduce and study pre-T0-,pre-R0-,pre-R1-,pre-T2(pre-Hausdorff)-,pre-T3(pre-regularity)-,pre-T4(pre-normality)-,pre-strong T3- and pre-strong T4-separation axioms in fuzzifying topology and give some of their characterisations as well as the relations of these axioms and other separation axioms in fuzzifying topology introduced by Shen[7].

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.

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.

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.

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.

On Axiom A + no-cycles

In this paper, we give another description of Axiom A plus no cycles condition.

Axiom Cosmology: A New Direction

In this work we have to deal with the axiomatization of cosmology, but it is only recently that we have hit upon a new mathematical approach to capitalize on our new set identities for the basic laws of cosmology. So our proposal of settlement is that we will propose some new laws (e.g., formation of the black hole). We introduce the concept of axiom cosmology. This principle describes the cosmology which can get freedom from the notion of the induction. We present a large-scale structure model of the universe, and this leads to successfully explanation of problem of closed universe or open universe (because from the outset it is theorem and its succinct proof). In this paper we prove that the non-singular point theorem means that a singularity cannot be mathematically defined nor physical. It allows us to overcome the mysterious, physical singularity conundrum and explain meaningful antimatter annihilations for general configurations.

The Physical Laws and Mathematical Axioms of the Brain’s OS and the Traditional Fundamental Laws of Thought of Logic and Philosophy

This article presents four (4) additions to a book on the brain’s OS published by SciRP in 2015 [1]. It is a kind of appendix to the book. Some familiarity with the earlier book is presupposed. The book itself proposes a complete physical and mathematical blueprint of the brain’s OS. A first addition to the book (see Chapters 5 to 10 below) concerns the relation between the afore-mentioned blueprint and the more than 2000-year-old so-called fundamental laws of thought of logic and philosophy, which came to be viewed as being three (3) in number, namely the laws of 1) Identity, 2) Contradiction, and 3) the Excluded Middle. The blueprint and the laws cannot both be the final foundation of the brain’s OS. The design of the present paper is to interpret the laws in strictly mathematical terms in light of the blueprint. This addition constitutes the bulk of the present article. Chapters 5 to 8 set the stage. Chapters 9 and 10 present a detailed mathematical analysis of the laws. A second addition to the book (Chapter 11) concerns the distinction between the laws and the axioms of the brain’s OS. Laws are part of physics. Axioms are part of mathematics. Since the theory of the brain’s OS involves both physics and mathematics, it exhibits both laws and axioms. A third addition (Chapter 12) to the book involves an additional flavor of digitality in the brain’s OS. In the book, there are five (5). But brain chemistry requires a sixth. It will be called Existence Digitality. A fourth addition (Chapter 13) concerns reflections on the role of imagination in theories of physics in light of the ignorance of deeper causes. Chapters 1 to 4 present preliminary matter, for the most part a brief survey of general concepts derived from what is in the book [1]. Some historical notes are gathered at the end in Chapter 14.