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Mathematics


The category of mathematics are works on the abstract study of subjects encompassing quantity, structure, space, change, and more; it has no generally accepted definition.

 
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DSmT 理论 及其在信息融合中的应用 (文集) (Advances and Applications of DSmT for In...

By: Florentin Smarandache; Jean Dezert

The Chinese edition of Advances and Applications of DSmT for Information Fusion (Collected Works) that explains the Dezert-Smarandache Theory.

作者在近年来 提出的似是而非和自相矛盾推理,DSmT,可以看作是 经典的 DSmT 的扩展,但是它们又存在着重要的差异。比如,DSmT 可以处理由 信度函数表示的任意类型独立信息源间的信息融合问题,但它的重点是处理不确 定、高度冲突和不精确的证据源的融合问题。DSmT 能够不受 DST 框架的限制, 处理复杂的静态或动态融合问题,特别是当信息源间的冲突非常大时,或者是所考 虑问题的框架(一般情况下用Θ表示)由于Θ中命题 之间的界限模糊、不确定、 不精确而很难细分时,DSmT 便发挥了它的优势。

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Advances and Applications of DSmT for Information Fusion (Collecte...

By: Florentin Smarandache; Jean Dezert

Applications demonstrate the power of the DSmT framework. In this third Volume, DSmT is applied to the entire spectrum of the Information Fusion that would interest any reader in data, sensor, information, and mathematical fusion topics. Highlighted in Figure 1 are the contemporary issues that include the links between (1) data conditioning and information management, (2) combined situation and impact assessment, and (2) knowledge representation between machine processin...

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Advances and Applications of DSmT for Information Fusion (Collecte...

By: Florentin Smarandache; Jean Dezert

This second book devoted on advances and applications of Dezert-Smarandache Theory (DSmT) for information fusion collects recent papers from different researchers working in engineering and mathematics. Part 1 of this book presents the current state-of-the-art on theoretical investigations while, Part 2 presents several applications of this new theory. Some ideas in this book are still under current development or improvements, but we think it is important to propose the...

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Advances and Applications of DSmT for Information Fusion (Collecte...

By: Florentin Smarandache; Jean Dezert

This book is devoted to an emerging branch of Information Fusion based on new approach for modeling the fusion problematic when the information provided by the sources is both uncertain and (highly) conflicting. This approach, known in literature as DSmT (standing for Dezert-Smarandache Theory), proposes new useful rules of combinations. We gathered in this volume a presentation of DSmT from the beginning to the latest development. Part 1 of this book presents the curren...

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DSm Super Vector Space of Refined Labels : Volume 2

By: W. B. Vasantha Kandasamy; Florentin Smarandache

In this book authors for the first time introduce the notion of supermatrices of refined labels. Authors prove super row matrix of refined labels form a group under addition. However super row matrix of refined labels do not form a group under product; it only forms a semigroup under multiplication. In this book super column matrix of refined labels and m Å~ n matrix of refined labels are introduced and studied. We mainly study this to introduce to super vector space of ...

THEOREM 1.1.1: Let S = {(a1 a2 a3 | a4 a5 | a6 a7 a8 a9 | … | an-1, an) | ai ∈ R; 1 ≤ i ≤ n} be the collection of all super row vectors with same type of partition, S is a group under addition. Infact S is an abelian group of infinite order under addition. The proof is direct and hence left as an exercise to the reader. If the field of reals R in Theorem 1.1.1 is replaced by Q the field of rationals or Z the integers or by the modulo integers Zn, n < ∞ still the conclusi...

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Definitions, Solved and Unsolved Problems, Conjectures, and Theore...

By: Florentin Smarandache; M L. Perez, Editor

Florentin Smarandache, an American mathematician of Romanian descent has generated a vast variety of mathematical problems. Some problems are easy, others medium, but many are interesting or unsolved and this is the reason why the present book appears. Here, of course, there are problems from various types. Solving these problems is addictive like eating pumpkin seed: having once started, one cannot help doing it over and over again.

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Data Madministration : A Paradox Style

By: Florentin Smarandache

This is a how-not-to-do book about codification, indexing, information, computer science, peripherals and terminals. The data entries are unselected and stored in a database. Afterwards, they are disorganized, unstructured and then manufactured. A data mudflow is designed later in order to misdirect all information. A nonquality control personnel filters and trashes all high valued documents and restores the chaos in the institution. The book helps with the malfunctionin...

The illogical mudflow of a quarterly non-production process In looking at the illogical mudflow of a quarterly non-production process, it is very imperative for us to take into account several non-practical factors that take place during such non-production process. These factors include: - Tools under maintenance - Contracts - Transportation - Supply Below is an illustration of the two major phases that are not usually encountered during the execution of a non-production process.

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Cultural Advantages for Cities : An Alternative for Developing Cou...

By: Florentin Smarandache; V. Christianto

We focus our discussions in this book on cities, because in our opinion a city is the smallest economic entity which has ‘self-organizing’ character, in a sense that a city can grow by itself (with minimum intervention). Nonetheless, this book will not discuss the self-organization character itself, but a new concept called ‘Cultural Economy’ development. Cultural Economic here is part of leisure and tourism industry, and depends on taste, advertisement, history, and the...

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Combinatorial Geometry with Applications to Field Theory : Second ...

By: Linfan Mao

In The 2nd Conference on Combinatorics and Graph Theory of China (Aug. 16-19, 2006, Tianjing), I formally presented a combinatorial conjecture on mathematical sciences (abbreviated to CC Conjecture), i.e., a mathematical science can be reconstructed from or made by combinatorialization, implicated in the foreword of Chapter 5 of my book Automorphism groups of Maps, Surfaces and Smarandache Geometries (USA, 2005). This conjecture is essentially a philosophic notion for de...

1.5 ENUMERATION TECHNIQUES 1.5.1 Enumeration Principle. The enumeration problem on a finite set is to count and find closed formula for elements in this set. A fundamental principle for solving this problem in general is on account of the enumeration principle: For finite sets X and Y , the equality |X| = |Y | holds if and only if there is a bijection f : X → Y . Certainly, if the set Y can be easily countable, then we can find a closed formula for elements in X.

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Smarandache 问题研究 (Smarandache Problems), Volume 1

By: Yi Yuan; Kang Xiaoyu

A book on problems arising with some of Florentin Smarandache's theories.

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关于一些 Smarandache 问题的研究 (Research On A Number of Smarandache Proble...

By: Huaning Liu; Jing Gao

This book systematically introduces the works obtained by using analytic methods on Smarandache problems, the book includes the basic knowledge of analytic number theory, mean value on some Smarandache sequences, infinite series involving some Smarandache functions, hybrid mean value of divisor function and so on. This book could open up the reader’s perspective, and inspire the reader to these fields.

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关于Smarandache问题 研究的新进展 (On the Smarandache Problem : New Progress)...

By: Guo Xiaoyan; Yuan Xia

A book on number theory.

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Smarandache 未解决问题研究 (Smarandache Unresolved Problems), Volume 5

By: Jianghua Li; Yanchun Guo

前言 数论这门学科最初是从研究整数开始的, 所以叫做整数论. 后来整数 论又进一步发展, 就叫做数论了. 确切的说, 数论就是一门研究整数性质 的学科. 它是最古老的数学分支. 按照研究方法来说, 数论可以分成初等 数论, 解析数论, 代数数论, 超越数论, 计算数论, 组合数论等. Foreword Number theory, this discipline was originally started from the study integer, so called Number Theory. Later integer on further development of number theory called it. Rather, number theory is an integer nature of disciplines and it is the oldest branch of mathematics concerned by the study methods, can be divided in...

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关于 Smarandache 理论 及其有关问题 (On the Smarandache Notions and Related P...

By: Wang Yu; Su Juanli

前言 数论这门学科最初是从研究整数开始的, 所以叫做整数论. 后来整数 论又进一步发展, 就叫做数论了. 确切的说, 数论就是一门研究整数性质 的学科. 在我国, 数论也是发展最早的数学分支之一. 许多著名的数学著 作中都有关于数论内容的论述, 比如求最大公约数、勾股数组、某些不 定方程整数解的问题等等... Foreword Number theory, this discipline was originally started from the study integer, so called Number Theory. Later integer on further development of number theory called it. Rather, number theory is an integer nature of Discipline in our country, the development of number theory is one of the oldest branche...

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Smarandache未解决的问题 及其新进展 (Smarandache Unsolved Problems and New Pro...

By: Liu Yanni; Li Ling

This book will mainly make part of the research results of current domestic and foreign scholars on Smarandache problems and unsolved problems into a book. Its main purpose is to introduce some of the research of Smarandache problems to readers, comprehensively and systematically, including the mean value of arithmetic functions, identities and inequalities, infinite series, the solutions of special equations, and put forward to some new interesting problems. We hope t...

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Smarandache 问 题 新 进 展 (Smarandache Question : New Exhibition), Vol...

By: Chen Guohui

This book includes part of the research results about the Smarandache problems written by Chinese scholars at present, and its main purpose is to introduce various results about the Smarandache problems, such as Smarandache function and its asymptotic properties, series convergence, solutions about special equations. At the same time, we put forward to some new interesting problems either in order to research further. We hope this booklet will guide and inspire readers to these fields.

前言 数论这门学科最初是从研究整数开始的, 所以叫整数数论. 后来整数 数论又进一步发展, 就叫做数论了. 确切地说, 数论就是一门研究整数性 质的学科. 数论和几何学一样, 是古老的数学分支. 数论在数学中的地位是特殊的, 高斯曾经说过:“数学是科学的皇后, 数论是数学中的皇冠”. 虽然数论中的许多问题在很早就开始了研究, 并得到了丰硕的成果, 但是至今仍有许多被数学家称之为“皇冠上的明 珠”的悬而未解的问题等待人们去解决. 正因如此, 数论才能不断地充 实和发展, 才能既古老又年轻, 才能始终活跃在数学领域的前沿. Foreword Number theory, this discipline was originally started from the study integer, so called integer number theory. Later integer further development of number theory, number theory called up. Rather, nu...

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Auxiliary Information and A Priori Values in Construction of Impro...

By: Florentin Smarandache; Rajesh Singh

This volume is a collection of six papers on the use of auxiliary information and a priori values in construction of improved estimators. The work included here will be of immense application for researchers and students who employ auxiliary information in any form.

Introduction In survey sampling, the use of auxiliary information can increase the precision of an estimator when study variable y is highly correlated with the auxiliary variable x. but in several practical situations, instead of existence of auxiliary variables there exists some auxiliary attributes, which are highly correlated with study variable y, such as (i) Amount of milk produced and a particular breed of cow. (ii) Yield of wheat crop and a particular variety of...

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A Unifying Field in Logics : Neutrosophic Logic, Neutrosophy, Neut...

By: Florentin Smarandache; Feng Lui, Translator

科学面临的难题 _ 中智学为何诞生 中智学(neutrosophy)起源于1995年美国, 它站在东西文化交融的立场上, 从对立统一的角度探索从科学技术到文学艺术的一切宏观及微观结构, 构造超越一切学科、超越自然科学与社会科学界限的统一场, 以解决当今认知科学、信息科学、系统科学、经济学、量子力学等科学技术前沿难题——非确定性问题。中智学努力通过新型开放模式改造当今各自然科 与社会科学, 实现它们的新陈代谢、改革创新和更新换代。中智学在我们中国还属空白, 故借 对学科正式命名并引入中国。

中智学, 新的哲学分支 _(Neutrosophy - A New Branch of Philosophy) 摘要: 本文推出了一个新的哲学分支, 中智学 _(neutrosphy), 研究中性的起源、本质和范畴以及和不同思想观念的作用。它的基本点是: 任何观念具有T%的真实性、I%的不确定性以及 的谬误性, 其中T, I, F为╟-0, 1+╢的标准或非标准子集。 _基本理论:任何观念 _ 趋于被 _ 所中和、削弱和平衡 _(不仅仅是被黑格尔主 的), 达到一种平衡状态。 中智学是中智逻辑学 _(在模糊逻辑的基础上总结出来的多值逻辑)、中智集合论 _(模糊 合论的概括总结)、中智概率论和中智统计学 _(分别是经典及非精确概率论、统计学的概括 结) 的基础。 _ 关键字与短语: 非标准分析, 超实数, 无穷小, 单子, 非标准实数单位区间, 集合运算。 _

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A Unifying Field in Logics : Neutrosophic Logic, Neutrosophy, Neut...

By: Florentin Smarandache; Feng Lui, Translator

1. 科学面临的难题 中智学为何诞生 中智学(neutrosophy)起源于1995年美国, 它站在东西文化交融的立场上, 从对立统一的角度探索从科学技术到文学 艺术的一切宏观及微观结构, 构造超越一切学科、超越自然科学与社会科学界限的统一场, 以 决当今认知科学、信息 科学、系统科学、经济学、量子力学等科学技术前沿难题——非确定性问题。中智学努力通 新型开放模式改造当今 各自然科学与社会科学, 实现它们的新陈代谢、改革创新和更新换代。中智学在我们中国还 空白, 故借此对学科正式 命名并引入中国。

中智学, 新的哲学分支(Neutrosophy - A New Branch of Philosophy) 摘要: 本文推出了一个新的哲学分支, 中智学 (neutrosphy), 研究中性的起源、本质和范畴以及和不同思想观念的 作用。它的基本点是: 任何观念具有T%的真实性、I%的不确定性以及 F%的谬误性, 其中T, I, F 为╟-0, 1+╢的标准或 非标准子集。 基本理论:任何观念 趋于被 所中和、削弱和平衡 (不仅仅是被黑格尔主张的), 达到一种 平衡状态。 中智学是中智逻辑学 (在模糊逻辑的基础上总结出来的多值逻辑)、中智集合论 (模糊集合论的概括总结)、中智概 率论和中智统计学 (分别是经典及非精确概率论、统计学的概括总结) 的基础。 关键字与短语: 非标准分析, 超实数, 无穷小, 单子, 非标准实数单位区间, 集合运算。

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Artificial Intelligence and Responsive Optimization (Second Edition)

By: Florentin Smarandache; M. Khoshnevisan

In part 1, we have defined a fuzzy utility system, with different financial goals, different levels of risk tolerance and different personal preferences, liquid assets, etc. In part 2, we have defined a computational model for a simple portfolio insurance strategy using a protective put and computationally derive the investor’s governing utility structures underlying such a strategy under alternative market scenarios. In Part 3, it is proposed an artificial classificati...

In this paper we have designed our fuzzy system so that customers are classified to belong to any one of the following three categories: *Conservative and security-oriented (risk shy) *Growth-oriented and dynamic (risk neutral) *Chance-oriented and progressive (risk happy) A neutrosophic system has three components – that’s why it may be considered as just a generalization of a fuzzy system which has only two components. Besides being useful for clients, investor cla...

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