This book has seven chapters. Chapter one provides several basic notions to make this book self-contained. Chapter two introduces neutrosophic groups and neutrosophic N-groups and gives several examples. The third chapter deals with neutrosophic semigroups and neutrosophic N-semigroups, giving several interesting results. Chapter four introduces neutrosophic loops and neutrosophic N-loops. Chapter five just introduces the concept of neutrosophic groupoids and neutrosophi...

1.1 Groups, N-group and their basic Properties It is a well-known fact that groups are the only algebraic structures with a single binary operation that is mathematically so perfect that an introduction of a richer structure within it is impossible. Now we proceed on to define a group. DEFINITION 1.1.1: A non empty set of elements G is said to form a group if in G there is defined a binary operation, called the product and denoted by '•' such that

We in this book introduce the notion of pure (mixed) neutrosophic interval bisemigroups or neutrosophic biinterval semigroups. We derive results pertaining to them. The new notion of quasi bisubsemigroups and ideals are introduced. Smarandache interval neutrosophic bisemigroups are also introduced and analysed. Also notions like neutrosophic interval bigroups and their substructures are studied in section two of this chapter. Neutrosophic interval bigroupoids and the ide...

Now we will be using these intervals and work with our results. However by the context the reader can understand whether we are working with pure neutrosophic intervals or neutrosophic of rationals or integers or reals or modulo integers. This chapter has four sections. Section one introduces neutrosophic interval bisemigroups, neutrosophic interval bigroups are introduced in section two. Section three defines biinterval neutrosophic bigroupoids. The final section gives ...

“The Analects of Confucius” are considered a record of the words and acts of Confucius and his disciples, as well as the discussions they held. Written during the Spring and Autumn Period through the Warring States Period（475 BC - 221 BC) the Analects is the representative work of Confucianism and continues to have a tremendous influence on Chinese and East Asian thoughts and values today. In neutrosophy, between two ends there are many, sometimes a continuous range of n...

Negative Part 3 You want to know a person truly, not only to understand this person’s words, but also understand this person’s actions and ideas. Commentary on Negative Part 3 Confucius did not mention to understand people’s ideas. While the words and actions are controlled by the ideas. Neutrosophic Part 3 The person’s time and energy were limited. For knowing a man truly, besides one person’s ability, other person’s help is needed in many cases, sometimes even the...

A book on the contrasts between the eastern Asian culture versus the western culture on topics such as education, medicine, science, and politics.

Is oriental culture a kind of science? There lies a crucial difference in that Western science seeks the exterior solutions outside the heart. However, our ancient sages illustrated that humans are an integral part of the universe, and all the phenomena never skip out of the heart. And very fortunately, many wise men did succeed in cultivating their hearts to testify to the profound truth. So our Eastern classics focus on our inner cultivation. However people, in...

The first chapter is introductory in nature and gives a few essential definitions and references for the reader to make use of the literature in case the reader is not thorough with the basics. The second chapter deals with different types of neutrosophic bilinear algebras and bivector spaces and proves several results analogous to linear bialgebra. In chapter three the authors introduce the notion of n-linear algebras and prove several theorems related to them. Many of ...

pARadOXisMul - ultima avangardă a mileniului doi 1. Definiţie Paradoxismul este o mişcare internaţională de avangardă în literatură, artă, filozofie, chiar şi ştiinţă, bazată pe folosirea excesivă de antiteze, antinomii, contradicţii, oximorone, parabole, paradoxuri în creaţie. A fost înfiinţat de către scriitorul, artistul, şi omul de ştiinţă Florentin Smarandache în anii 1980 în România, care dorea “lărgirea sferei artistice prin elemente neartistice şi prin experim...

L) Limitele filozofiei Întreaga filozofie este un tautologism: adevărat în virtutea de formă, pentru că orice idee lansată pentru prima oară este dovedită ca adevărată de către iniţiatorul(ii) său(i). Prin urmare, filozofia este goală sau dezinformativă, şi reprezintă a priori cunoaşterea. Se poate afirma: Totul este adevărat, chiar si falsul! Şi totuşi, întreaga filozofie este un nihilism: pentru ca orice idee, odată dovedită adevărată, este mai tîrziu dovedită ...

In this book, we consider various many-valued logics: standard, linear, hyperbolic, parabolic, non-Archimedean, p -adic, interval, neutrosophic, etc. We survey also results which show the tree different proof-theoretic frameworks for many-valued logics, e.g. frameworks of the following deductive calculi: Hilbert ’s style, sequent, and hypersequent. Recall that hypersequents are a natural generalization of Gentzen ’s style sequents that was introduced independently by Avr...

1.1 Neutrality concept in logic Every point of view A tends to be neutralized, diminished, balanced by Non-A. At the same time, in between A and Non-A there are infinitely many points of view Neut-A. Let’s note by A an idea, or proposition, theory, event, concept, entity, by Non-A what is not A, and by Anti-A the opposite of A. Neut-A means what is neither A nor Anti-A, i.e. neutrality is also in between the two extremes.

The experimental digital arts on the front and back covers represent the “World Trade Center Towers before 9/11” and respectively an “Aquatic Monster” done by the cyberartist.

Science and Art resemble Horace’s concordia discors (discordant harmony) from his “Epistles” and both are built on imagination. Imagination is a quality given a man to compensate him for what he is not, and a sense of humor was provided to console him for what he is (Oscar Wilde). Every great advance in science has issued from a new audacity of imagination (John Dewey). And similarly for the advance in art and letters.

This book has eight chapters. The first chapter is introductory in nature. Polynomials with matrix coefficients are introduced in chapter two. Algebraic structures on these polynomials with matrix coefficients is defined and described in chapter three. Chapter four introduces natural product on matrices. Natural product on super matrices is introduced in chapter five. Super matrix linear algebra is introduced in chapter six. Chapter seven claims only after this notion be...

In this chapter we only indicate as reference of those the concepts we are using in this book. However the interested reader should refer them for a complete understanding of this book. In this book we define the notion of natural product in matrices so that we have a nice natural product defined on column matrices, m * n (m ≠ n) matrices. This extension is the same in case of row matrices. We make use of the notion of semigroups and Smarandache semigroups. Also the noti...

This book has three chapters. In the first chapter the notion of n-vector spaces of type II are introduced. This chapter gives over 50 theorems. Chapter two introduces the notion of n-inner product vector spaces of type II, n-bilinear forms and n-linear functionals. The final chapter suggests over a hundred problems. It is important that the reader should be well versed with not only linear algebra but also n-linear algebras of type I.

In this chapter we for the first time introduce the notion of n-vector space of type II. These n-vector spaces of type II are different from the n-vector spaces of type I because the n-vector spaces of type I are defined over a field F where as the n-vector spaces of type II are defined over n-fields. Some properties enjoyed by n-vector spaces of type II cannot be enjoyed by n-vector spaces of type I. To this; we for the sake of completeness just recall the definition of...

This book has four chapters. The first chapter just introduces n-group which is essential for the definition of n-vector spaces and n-linear algebras of type I. Chapter two gives the notion of n-vector spaces and several related results which are analogues of the classical linear algebra theorems. In case of n-vector spaces we can define several types of linear transformations. The applications of these algebraic structures are given in Chapter 3. Chapter four gives some...

n-VECTOR SPACES OF TYPE I AND THEIR PROPERTIES In this chapter we introduce the notion of n-vector spaces and describe some of their important properties. Here we define the concept of n-vector spaces over a field which will be known as the type I n-vector spaces or n-vector spaces of type I. Several interesting properties about them are derived in this chapter. DEFINITION 2.1: A n-vector space or a n-linear space of type I (n  2)

The fourth volume, in my book series of “Collected Papers”, includes 100 published and unpublished articles, notes, (preliminary) drafts containing just ideas to be further investigated, scientific souvenirs, scientific blogs, project proposals, small experiments, solved and unsolved problems and conjectures, updated or alternative versions of previous papers, short or long humanistic essays, letters to the editors

This short technical paper advocates a bootstrapping algorithm from which we can form a statistically reliable opinion based on limited clinically observed data, regarding whether an osteo-hyperplasia could actually be a case of Ewing’s osteosarcoma. The basic premise underlying our methodology is that a primary bone tumour, if it is indeed Ewing’s osteosarcoma, cannot increase in volume beyond some critical limit without showing metastasis. We propose a statistical meth...

We have used the 2-adaptive fuzzy model having the two fuzzy models, fuzzy matrices model and BAMs viz. model to analyze the views of public about HIV/ AIDS disease, patient and the awareness program. This book has five chapters and 6 appendices. The first chapter just recalls the definition of four fuzzy models used in this book and gives illustration of some of them. Chapter two introduces the new n-adaptive fuzzy models. Chapter three uses for the first time 2 adaptiv...

In this chapter for the first time we introduce the new class of n-adaptive fuzzy models (n a positive integer and n ≥ 2) and illustrate it. These n-adaptive fuzzy models can analyze a problem using different models so one can get in one case the hidden pattern, in one case the maximum time period in some case output state vector for a given input vector and so on. So this new model has the capacity to analyze the problem in different angles, which can give multiple sugg...

This book was intended to discuss some paradoxes in Quantum Mechanics from the viewpoint of Multi-Valued-logic pioneered by Lukasiewicz, and a recent concept Neutrosophic Logic. Essentially, this new concept offers new insights on the idea of ‘identity’, which too often it has been accepted as given.

2 Lukasiewicz Multi-Valued-logic: History and Introduction to Multi- Valued Algebra 2.1 Introduction to trivalent logic and plurivalent logic We all have heard of typical binary logic, Yes or No. Or in a famous phrase by Shakespeare: “To be or not to be.” In the same way all computer hardwares from early sixties up to this year are built upon the same binary logic. It is known that the Classical Logic, also called Bivalent Logic for taking only two values {0, 1...

The fourth volume, in my book series of “Collected Papers”, includes 100 published and unpublished articles, notes, (preliminary) drafts containing just ideas to be further investigated, scientific souvenirs, scientific blogs, project proposals, small experiments, solved and unsolved problems and conjectures, updated or alternative versions of previous papers, short or long humanistic essays, letters to the editors

This short technical paper advocates a bootstrapping algorithm from which we can form a statistically reliable opinion based on limited clinically observed data, regarding whether an osteo-hyperplasia could actually be a case of Ewing’s osteosarcoma. The basic premise underlying our methodology is that a primary bone tumour, if it is indeed Ewing’s osteosarcoma, cannot increase in volume beyond some critical limit without showing metastasis. We propose a statistical meth...

Noi pledăm pentru un proces cogniscibil care să nu aibă îngrădiri de nici o formă. Din această cauză, hermeneutica se presupune a fi cât mai diversificată. Interviurile următoare împletesc cultura, ştiinţa, tehnica şi viaţa într-un multi-eu. De aceea volumul se numeşte multirelavititate: adică idei şi metodologii privite din unghiuri cât. We advocate for a process that does not have restrictions of any form. Therefore, hermeneutics is assumed to be more diversified. N...

Scriitorul şi omul de ştiinţă Florentin Smarandache, cunoştiinţă deosebită, specială, de aproape 20 de ani, este permanent pe drumuri, cu carneţelul de însemnări în buzunar. Este un ambasador autentic al inteligenţei şi talentului românilor, în aceeaşi măsură, acest Geo Bogza al zileleor noastre gata permanent să noteze tot ce trebuie să fie marcat în vreun fel în istoria locurilor pe care le parcurge cu: piciorul, maşina, vaporul, avionul şi nu rareori cu gândul şi ochi...

A book on Smarandache's achievements throughout his life time with a short history on his personal life.

In the beginning, this international avant-garde was a mutism: to make literature by not writing literature at all!! (any mathematical/chemical/physical etc. abstract sign, any drawing, draft, picture, graffito (having no words, no letters) could mean a poem; the non-literature created became, paradoxically, a new kind of literature; later the paradoxism has generalized the old term of for the n-dimensional and other scientific (Lobacevsky, Riemann, Banach, etc.) spaces...

Vă mulţumesc că m-aţi dispreţuit, umilit, că m-aţi împins spre emigrare unde nu mai sunt dispreţuit, nu mai sunt umilit, mi se respectă creaţiile şi persoana. Şi pentru toate acestea, mă simt mai patriot ca niciodată.

Bere cu cântec În restaurant, bând bere cu prietenii de clasă, și fredonând toți cântece pentru… copii de grădiniță: Înfloresc grădinile, Ceru-i ca oglinda, Fluturii cu miile Au pornit colinda!... Și consumatorii de la mesele din jur — uitându-se surprinși la noi, neștiind ce să creadă! Beer song The restaurant, drinking beer with friends and class humming all songs ... kindergarten children: Blooming gardens, He asked her the mirror, Butterflies by the t...

The authors in this book have analyzed the socio-economic and psychological problems faced by People with Disabilities (PWDs) and their families. The study was made by collecting data using both fuzzy linguistic questionnaire by interviews in case they are not literates from 2,15,811 lakhs people. This data was collected using the five Non Government Organizations (NGOs) from northern Tamil Nadu.

The main objective of this was to understand the basic psychological and social problems faced by the PWDs and their caretakers. To interpret the collected data, tabulations and analysis were made. Efforts were made to highlight the inferences in each table and in few places comments were made in order to use it for fuzzy analysis. Following is the list of organizations and the total population from 5 blocks is listed below.

A book on Florentin Smarandache's travels through Russia.

Rusia – mamă vitregă pentru România! În Moscova, sunt 11 linii de metrou. Pe hartă, apar cu diverse culori. Vechiul oraş e cuprins în interiorul liniei 5 (centura). Nouln oraş s-a dezvoltat împrejur. Tunelul metroului trece când pe sub râuln Moscova, când pe deasupra, pe poduri solide. Până la aeroport, am schimbat două autobuze şi două metrouri. Dmitri şi Larissa m au condus. Îmi părea rău de despărţire, dar mă bucuram de întoarcerea acasă – am atâtea de făcut (s-au ad...