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Bio:

Born on 10 December 1954, in Balcesti city, Romania, wrote in three languages: Romanian, French, and English.

Poet, playwright, novelist, writer of prose, tales for children, translator from many languages, experimental painter, philosopher, physicist, mathematician.

American citizen.

He graduated from the Department of Mathematics and Computer Science at the University of Craiova in 1979, earned a Ph. D. in Mathematics from the State University Moldova at Chisinau in 1997, and continued postdoctoral studies at various American Universities such as University of Phoenix, University of Texas at Austin, etc. after emigration in America.

In U.S. he worked as a software engineer for Honeywell (1990-1995), adjunct professor for Pima Community College (1995-1997), in 1997 Assistant Professor at the University of New Mexico - Gallup Campus, promoted to Associate Professor of Mathematics in 2003, and to full Professor in 2008..

Since June 2007 he was Chair of the Department of Math & Sciences.


During the Ceausescu's era he got in conflict with authorities.  In 1986 he did the hunger strike for being refused to attend the International Congress of Mathematicians at the University of Berkeley, then published a letter in the Notices of the American Mathematical Society for the freedom of circulating of scientists, and became a dissident.  As a consequence, he remained unemployed for almost two years, living from private tutoring done to students.  The Swedish Royal Academy Foreign Secretary Olof G. Tandberg contacted him by telephone from Bucharest.

Not being allowed to publish, he tried to get his manuscripts out of the country through

the French School of Bucharest and tourists, but for many of them he lost track.

Escaped from Romania in September 1988 and waited almost two years in the political refugee camps of Turkey, where he did unskilled works in construction in order to survive: scavenger, house painter, whetstoner.   Here he kept in touch with the French Cultural Institutes that facilitated him the access to books and rencontres with personalities.

Before leaving the country he buried some of his manuscripts in a metal box in his parents vineyard, near a peach tree, that he retrieved four years later, after the 1989 Revolution,  when he returned for the first time to his native country.   Other manuscripts, that he tried to mail to a translator in France, were confiscated by the secret police and never returned.

In March 1990 he emigrated to the United States.


He wrote hundreds of pages of diary about his life in the Romanian dictatorship (unpublished), as a cooperative teacher in Morocco ("Professor in Africa", 1999), in the Turkish refugee camp ("Escaped... / Diary From the Refugee Camp", Vol. I, II, 1994, 1998), and in the American exile - diary which is still going on.


But he's internationally known as the literary school leader for the "paradoxism" movement  which has many advocates in the world, that he set up in 1980, based on an excessive use of antitheses, antinomies, contradictions, paradoxes in creation paradoxes - both at the small level and the entire level of the work - making an interesting connection between mathematics, philosophy, and literature

[ http://www.geocities.com/charlestle/paradoxism.html ].

He introduced the 'paradoxist distich', 'tautologic distich', and 'dualistic distich', inspired from the mathematical logic [ http://www.gallup.unm.edu/~smarandache/a/literature.htm ].

Literary experiments he realized in his dramas: Country of the Animals, where there is no dialogue!, and An Upside-Down World, where the scenes are permuted to give birth to one billion of billions of distinct dramas!

[ http://www.gallup.unm.edu/~smarandache/a/theatre.htm ]. 

He stated:

"Paradoxism started as an anti-totalitarian protest against a closed society, where the whole culture was manipulated by a small group. Only their ideas and publications counted. We couldn't publish almost anything.

Then, I said: Let's do literature... without doing literature! Let's write... without actually writing anything. How? Simply: literature-object! 'The flight of a bird', for example, represents a "natural poem", that is not necessary to write down, being more palpable and perceptible in any language that some signs laid on the paper, which, in fact, represent an "artificial poem": deformed, resulted from a translation by the observant of the observed, and by translation one falsifies.

Therefore, a mute protest we did!

Later, I based it on contradictions. Why? Because we lived in that society a double life: an official one - propagated by the political system, and another one real. In mass-media it was promulgated that 'our life is wonderful', but in reality 'our life was miserable'. The paradox flourishing! And then we took the creation in derision, in inverse sense, in a syncretism way. Thus the paradoxism was born. The folk jokes, at great fashion in Ceausescu's 'Epoch', as an intellectual breathing, were superb springs.

The "No" and "Anti" from my paradoxist manifestos had a creative character, not at all nihilistic." Paradoxism, following the line of dadaism, lettrism, absurd theatre, is a kind of up-side down writings!

In 1992 he was invited speaker in Brazil (Universidad do Blumenau, etc.).


He did many poetical experiments within his avant-garde and published paradoxist manifestos: "Le Sens du Non-Sens" (1983), "Anti-chambres/Antipoésies/Bizarreries" (1984, 1989), "NonPoems" (1990), changing the French and respectively English linguistics clichés.  While "Paradoxist Distichs" (1998) introduces new species of poetry with fixed form.

Eventually he edited three International Anthologies on Paradoxism (2000-2004) with texts from about 350 writers from around the world in many languages.


"MetaHistory" (1993) is a theatrical trilogy against the totalitarianism again, with dramas that experiment towards a total theatre: "Formation of the New Man", "An Upside - Down World", "The Country of the Animals".  The last drama, that pioneers no dialogue on the stage, was awarded at the International Theatrical Festival of Casablanca (1995). 

He translated them into English as "A Trilogy in pARadOXisM: avant-garde political dramas"; and they were published by ZayuPress (2004).

"Trickster's Famous Deeds" (1994, auto-translated into English 2000), theatrical trilogy for children, mixes the Romanian folk tradition with modern and SF situations. 


His first novel is called "NonNovel" (1993) and satirizes the dictatorship in a gloomy way, by various styles and artifice within one same style.


"Faulty Writings" (1997) is a collection of short stories and prose within paradoxism, bringing hybrid elements from rebus and science into literature.


His experimental albums "Outer-Art" (Vol. I, 2000 & Vol. II: The Worst Possible Art in the World!, 2003) comprises over-paintings, non-paintings, anti-drawings, super-photos, foreseen with a manifesto: "Ultra-Modernism?" and "Anti-manifesto"

[ http://www.gallup.unm.edu/~smarandache/a/oUTER-aRT.htm ].

Art was for Dr. Smarandache a hobby.  He did:

- graphic arts for his published volumes of verse: "Anti-chambres/ Anti-poésies/ Bizarreries" (mechanical drawings), "NonPoems" (paradoxist drawings), "Dark Snow" & "Circles of light" (covers);

- paradoxist collages for the "Anthology of the Paradoxist Literary Movement", by J. -M. Levenard, I. Rotaru, A. Skemer;

- covers and illustrations of books, published by "Dorul" Publ. Hse., Aalborg, Denmark;

- illustrations in the journal: "Dorul" (Aalborg, Denmark).

Many of his art works are held in "The Florentin Smarandache Papers" Special Collections at the Arizona State University, Tempe, and Texas State University, Austin (USA), also in the National Archives of Valcea and Romanian Literary Museum (Romania), and in the Musee de Bergerac (France).


Twelve books were published that analyze his literary creation, among them: "Paradoxism's Aesthetics" by Titu Popescu (1995), and "Paradoxism and Postmodernism" by Ion Soare (2000).

In 1999 he was nominated for the Nobel Prize in Literature.


In mathematics he introduced the degree of negation of an axiom or of a theorem in geometry (see the Smarandache geometries which can be partially Euclidean and partially non-Euclidean, 1969), the multi-structure (see the Smarandache n-structures, where a weak structure contains an island of a stronger structure), and multi-space (a combination of heterogeneous spaces).

He created and studied many sequences and functions in number theory. 

He generalized the fuzzy, intuitive, paraconsistent, multi-valent, dialetheist logics to the 'neutrosophic logic' (also in the Denis Howe's Dictionary of Computing, England) and, similarly, he generalized the fuzzy set to the 'neutrosophic set' (and its derivatives: 'paraconsistent set', 'intuitionistic set', 'dialethist set', 'paradoxist set', 'tautological set').


Also, he proposed an extension of the classical probability and the imprecise probability to the 'neutrosophic probability', that he defined as a tridimensional vector whose components are real subsets of the non-standard interval ]-0, 1+[.

He's organizing the 'First International Conference on Neutrosophics' at the University of New Mexico, 1-3 December 2001

[ http://www.gallup.unm.edu/~smarandache/FirstNeutConf.htm ].


Since 2002, together with Dr. Jean Dezert from Office National de Recherches Aeronautiques in Paris, worked in information fusion and generalized the Dempster-Shafer Theory to a new theory of plausible and paradoxist fusion (Dezert-Smarandache Theory):http://www.gallup.unm.edu/~smarandache/DSmT.htm .

In 2004 he designed an algorithm for the Unification of Fusion Theories and rules (UFT) used in bioinformatics, robotics, military.


In physics he found a series of paradoxes (see the quantum smarandache paradoxes), and 

emitted the hypothesis that there is no speed barrier in the universe, which is very contradictory among scientists.  Also, considered the possibility of a third form of matter, called unmatter, which is combination of matter and antimatter (or quarks and antiquarks):

http://www.geocities.com/m_l_perez/QuantumPhysics.html ].


In philosophy he introduced in 1995 the 'neutrosophy', as a generalization of Hegel's dialectic, which is the basement of his researches in mathematics and economics, such as 'neutrosophic logic', 'neutrosophic set', 'neutrosophic probability', 'neutrosophic statistics'.

Neutrosophy is a new branch of philosophy that studies the origin, nature, and scope of neutralities, as well as their interactions with different ideational spectra. This theory considers every notion or idea together with its opposite or negation and the spectrum of "neutralities" (i.e. notions or ideas located between the two extremes, supporting neither nor ). The and ideas together are referred to as .  According to this theory every idea tends to be neutralized and balanced by and ideas - as a state of equilibrium

[ http://www.gallup.unm.edu/~smarandache/neutrosophy.htm ].


Other small contributions he had in psychology:

[ http://www.gallup.unm.edu/~smarandache/psychology.htm ],

 and in sociology: [ http://www.gallup.unm.edu/~smarandache/sociology.htm ].


Invited to lecture at University of Berkeley (2003), Jadavpur University-India (2004), NASA Langley Research Center-USA (2004), NATO Advance Study Institute-Bulgaria (2005), Institute of Theoretical and Experimental Biophysics-Russia (2005), Bloomsburg University-USA (1995), University Sekolah Tinggi Informatika & Komputer Indonesia-Malang and University Kristen Satya Wacana Salatiga-Indonesia (2006), Minufiya University (Shebin Elkom) – Egypt (2007), etc.

Presented papers at many Sensor or Information Fusion International Conferences (Australia, Sweden, USA, Spain, Italy, Belgium, Canada, Germany).


Very prolific, he is the author, co-author, and editor of over 150 books published by thirty five publishing houses (such as university and college presses, professional scientific and literary presses, such as Springer Verlag (in print), Univ. of Kishinev Press, Pima College Press, ZayuPress, Haiku, etc.) in ten countries and in many languages, over 180 scientific articles and notes, and contributed to over 100 literary and 50 scientific journals from around the world.


He published many articles on international journals, such as: Multiple-Valued Logic - An International Journal (now called Multiple-Valued Logic & Soft Computing), International Journal of Social Economics, International Journal of Applied Mathematics, International Journal of Tomography & Statistics, Far East Journal of Theoretical Statistics, International Journal of Applied Mathematics and Statistics (Editor-in-Chief), Gaceta Matematica (Spain), Humanistic Mathematics Network Journal, Bulletin of Pure and Applied Sciences, Progress in Physics, Infinite Energy (USA), Information & Security: An International Journal, InterStat - Statistics on the Internet (Virginia Polytechnic Institute and State University, Blacksburg, USA), American Mathematical Monthly, Mathematics Magazine, Journal of Advances in Information Fusion (JAIF), Zentralblatt Für Mathematik (Germany; reviewer), Nieuw Archief voor Wiskunde (Holland), Advances in Fuzzy Sets and Systems, Intelligencer (Gottingen, Germany), Notices of the American Mathematical Society, etc. and on many International Conference Proceedings.

Some of them can be downloaded from the LANL / Cornell University (http://arXiv.org) and the CERN web sites.


Hundreds of articles, books, and reviews have been written about his activity around the world.  The books can be downloaded from this

Digital Library of Science:

http://www.gallup.unm.edu/~smarandache/eBooks-otherformats.htm

and from the Digital Library of Arts & Letters:

http://www.gallup.unm.edu/~smarandache/eBooksLiterature.htm .


As a Globe Trekker he visited over 35 countries that he wrote about in his memories.


International Conferences:

   First International Conference on Smarandache Type Notions in Number Theory,

August 21-24, 1997, organized by Dr. C. Dumitrescu & Dr. V. Seleacu, University of Craiova, Romania.

   International Conference on Smarandache Geometries, May 3-5 2003, organized by Dr. M. Khoshnevisan, Griffith University, Gold Coast Campus, Queensland, Australia. 

   International Conference on Smarandache Algebraic Structures, December 17-19, 2004, organized by Prof. M. Mary John, Mathematics Department Chair, Loyola College,  Madras, Chennai - 600 034 Tamil Nadu, India.

General Information:
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  • Cover Image

Lyriphotons : At Mind's Infinite Speed

By: by Florentin Smarandache

A lyriphoton nuclear reaction occurs when the high-energy lyriphotons collide with an atomic literary nucleus and disintegrate it (lyriphotofission) into words [lyrics] and images [photo(n)s]. See below.

- Go big or go home - Oh, what minute minute! - I come in the afternoon or after afternoon - This abstract has no dimensions. That's the long and the short of it!

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Life Strategies Part Three : Theatrical & Non-Novel Strategies

By: by Florentin Smarandache

This small book, which is rather a draft, comprises a collection of ideas, viewpoints and methods in various aspects of theater, performance arts, non-novel1 etc. If for no other reason, the ideas listed here at least can stimulate further thoughts and research – for instance, young writers may use these ideas to make his/her drama or novel more enthralling.

• The best functions of the theatre are none! (but the theatre itself); • Fatal attraction theatre; • A personage has a man’s mask taped on his bottom which faces the spectators and “talks” like this; • On a cross is crucified a book, or a lamb, or a pork, other object (crucified with the legs up) [which should symbolize something]; • On stage, place some cosmic objects (for example make visible a part of the Earth, or a Lunar Base, …); • Theatre for deaf and mute p...

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Life Strategies Part Two : Literature

By: by Florentin Smarandache

If for nothing else, the (random) sentences listed here at least can stimulate further thoughts and ideas – for instance, young writers and artists may find plenty of interesting ideas for their next literary work (or best-selling novels) in ‘Experimental Literature’ section. In a sense, this book itself is an experimental one. Needless to say, the readers may find that some of these ideas are quite absurd or seemingly outlandish

• Literary disorder; • Self abandonment; • Be an action man; • Abstract theatre (Felix Aderca); • The auto-destruction and the death of literature (Adrian Marino); antipoetic, antiauthor, anti-talent, anti-vocation; the surpassing of the literature; anti-literature; ultraliterature; par-literature; a-literature; “On one side, nothing is literature, on the other side everything is or could be literature. The notion of literary genus disappears.” The literature conditi...

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Life Strategies Part One : Works

By: by Florentin Smarandache

These ideas were either collected or inspired from author's various lectures of books, journals, newspapers, tv and radio shows, personal conversations. I started to write down such ideas since I was a high school student and continue even today - I always bear with me a small pen and small notebook where I write in the plane, or driving my car, or even in class room. Despite three decades of postponement, I hope this booklet will keep on inspiring the reader, as good id...

• Be competitive; • Don’t be panic, when under pressure; • Use probabilities (how much % you’re expected to produce); • Infiltrate in certain organizations; • To have power of influence; • Charm those who interact with you; • Be firm and fast in decisions; • To make a plan for a long period of time and subdivide it in smaller sub-plans for short periods of time

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Laws of Internal Composition : Poems With Problems!

By: by Florentin Smarandache

A book of poems written by Florentin Smarandache whilst he was experiencing a dark time in life.

EPILOGUE I leave you with my poems. Feel through me! I have achieves this volume in three years, but read it in T E N! It is a hut from the outside, and maybe a castle inside. (this volume holds connections with the earth!) The book has me between its covers - but now it is in its agony:

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În Vestul Nesălbatic : Fotojurnal Instantaneu

By: by Florentin Smarandache; Gheorge Niculescu, Editor

A journal on Florentin Smarandache's road trip to the western states in America.

În statul… colorat Pe autostrada I 511 spre localitatea Ignacio. Intrăm în Colorado, statul „plin de culori” (conform adjectivului spaniol colorado/colorada = colorat/colorată). Galben de toamnă, grena, verde şters – pomii. Pompe automate de extras ţiţei. În Ignacio, vizităm galeria de artă „Dancing Spirit”. Drumul de la Durango la Silverton urcă în creierul munţilor. Vârfuri roşii de piatră. Nişte stânci au marginile drepte, de zici că-s tăiate cu cuţitul. Sculpturi...

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Interval Neutrosophic Sets and Logic : Theory and Applications in ...

By: by Florentin Smarandache; Haibin Wang

Chapter 1 first introduces the interval neutrosophic sets which is an instance of neutrosophic sets. In this chapter, the definition of interval neutrosophic sets and set-theoretic operators are given and various properties of interval neutrosophic set are proved. Chapter 2 defines the interval neutrosophic logic based on interval neutrosophic sets including the syntax and semantics of first order interval neutrosophic propositional logic and first order interval neutros...

The neutrosophic set generalizes the above mentioned sets from philosophical point of view. From scientific or engineering point of view, the neutrosophic set and set-theoretic operators need to be specified. Otherwise, it will be difficult to apply in the real applications. In this chapter, we de_ne the set theoretic operators on an instance of neutrosophic set called Interval Neutrosophic Set (INS). We call it as “interval" because it is subclass of neutrosophic set, t...

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Innovative Uses of Matrices

By: by Florentin Smarandache; W. B. Vasantha Kandasamy

This book is organized into seven chapters. The first one is introductory in nature. In the second chapter authors give the unique and new way of analyzing the data which is time dependent. In chapter three the authors for the first time define the new concept of matrices with linguistic variables. In chapter four authors have used super matrices in super fuzzy models like super FCMs, super FRMs super FAMs etc. In chapter five we define interval matrix and matrix interva...

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În Exerciţiul Funcţiunii : Haz de Necaz (In the Discharge of One's...

By: by Florentin Smarandache

A collection of poems organized over a period of thirteen days.

Fac jocul femeii „De - ţi vine ţie pe chelie Să mă trimiţi pe mine-n vie”, Să sap, să leg, să copilesc … Nu vezi cum fug ca să iubesc?! I play women "De - and comes to you on baldness Send me on my live-in " To dig to tie to child ... I do not see how they run to love!

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Methods in Industrial Biotechnology for Chemical Engineers

By: by Florentin Smarandache; W. B. Vasantha Kandasamy

This book has six chapters. First chapter gives a brief description of biotechnology. Second chapter deals will proper proportion of mix of raw materials in cement industries to minimize pollution using fuzzy control theory. Chapter three gives the method of determination of temperature set point for crude oil in oil refineries. Chapter four studies the flow rates in chemical industries using fuzzy neutral networks. Chapter five gives the method of minimization of waste ...

2.4 Finding the MIX of raw materials in proper proportion and minimize the waste dust using fuzzy neural network. The study of proper proportions of material mix during the clinkerization process is very difficult due to inconsistency in the chemical and mineralogical composition and the variation of these characteristic affects kiln operation, fuel consumption, clinker quality and above all the amount of CKD vent into the atmosphere. Further the raw mix should mainta...

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În Doi Timpi Si Trei Miscari : Afurisisme

By: by Florentin Smarandache

Spontaneous notations, old books reprinted from 20 years ago, we started to shy love poem to a woman inaccessible. Phrases, quips, annotations, locuþiuni (nouns, verbs, adjective, etc..) Clichés idiomatic, construction, regional, archaic ideas / thoughts rãzleþe, Thoughts short templates language, zicãturi, afurisenii - mostly taken from folklore, others extracted from various readings. Order: no order!

Profund profundã. Legalizarea mãsurilor nelegale. Medile eu le fac ochiometric. Ai împãtrat-o cubic! Nu se potrivesc ele cinci degete la o mânã. Legislaþie antilegislatorialã. Bãtrâneþea e o boalã. Sãptãmâna oarbã. Deeply profound. Legalizing illegal measures. I do ochiometric Media. Do you have a cubic fourfold! Do they fit five fingers on a hand. Legislation antilegislatorialã. Old age is a disease. Week blind.

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Impresii Si Expresii (Reviews and Expressions)

By: by Florentin Smarandache; Gheorge Niculescu

A book of poems, short stories, and sayings in Romanian.

Aşa precum poetul Tagore glăsuieşte, „Nimic nu este veşnic, nimic nu dăinuieşte!” Oricât de rău ne este sau bun de ne e traiul, Aicea este Iadul şi tot aici şi Raiul. Nu vrăjmăşiţi, nu faceţi păcate, nici în gând! Iubiţi-vă, că Raiul i-aicea, pe Pământ! Făceţi-vă prieteni, iertaţi-i pe duşmani! Nu fiţi robii averii. Dă-i dracului de bani! Trăieşte în decenţă, fii vesel şi curat; De ură şi prostie, nu fi încătuşat! Trăieşte-ţi viaţa sfântă, în fiecare zi; Gânde...

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International Journal of Mathematical Combinatorics : Volume 4, De...

By: by Linfan Mao

Aims and Scope: The International J.Mathematical Combinatorics (ISSN 1937-1055) is a fully refereed international journal, and published quarterly comprising 100-150 pages approx. per volume, which publishes original research papers and survey articles in all aspects of Smarandache multi-spaces, Smarandache geometries, mathematical combinatorics, non-euclidean geometry and topology and their applications to other sciences. Topics in detail to be covered are: Smarandache...

On (∈ vq)-Fuzzy Bigroup Abstract: In this paper, we introduce the concept of fuzzy singleton to bigroup, and uses it to define (∈ v q)- fuzzy bigroup and discuss its properties. We investigate whether or not the fuzzy point of a bigroup will belong to or quasi coincident with its fuzzy set if the constituent fuzzy points of the constituting subgroups both belong to or quasi coincident with their respective fuzzy sets, and vise versa. We also prove that a fuzzy bisubset ...

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International Journal of Mathematical Combinatorics : Volume 4, Ja...

By: by Linfan Mao

Aims and Scope: The International J.Mathematical Combinatorics (ISSN 1937-1055) is a fully refereed international journal, and published quarterly comprising 100-150 pages approx. per volume, which publishes original research papers and survey articles in all aspects of Smarandache multi-spaces, Smarandache geometries, mathematical combinatorics, non-euclidean geometry and topology and their applications to other sciences. Topics in detail to be covered are: Smarandache...

On the Bicoset of a Bivector Space Abstract: The study of bivector spaces was first intiated by Vasantha Kandasamy. The objective of this paper is to present the concept of bicoset of a bivector space and obtain some of its elementary properties. Key Words: bigroup, bivector space, bicoset, bisum, direct bisum, inner biproduct space, biprojection.

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International Journal of Mathematical Combinatorics : Volume 3, Oc...

By: by Linfan Mao

Aims and Scope: The International J.Mathematical Combinatorics (ISSN 1937-1055) is a fully refereed international journal, and published quarterly comprising 100-150 pages approx. per volume, which publishes original research papers and survey articles in all aspects of Smarandache multi-spaces, Smarandache geometries, mathematical combinatorics, non-euclidean geometry and topology and their applications to other sciences. Topics in detail to be covered are: Smarandache...

Smarandache-Zagreb Index on Three Graph Operators Abstract: Many researchers have studied several operators on a connected graph in which one make an attempt on subdivision of its edges. In this paper, we show how the Zagreb indices, a particular case of Smarandache-Zagreb index of a graph changes with these operators and extended these results to obtain a relation connecting the Zagreb index on operators. Key Words: Subdivision graph, ladder graph, Smarandache-Zagreb ...

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International Journal of Mathematical Combinatorics : Volume 3, Oc...

By: by Linfan Mao

Aims and Scope: The International J.Mathematical Combinatorics (ISSN 1937-1055) is a fully refereed international journal, and published quarterly comprising 100-150 pages approx. per volume, which publishes original research papers and survey articles in all aspects of Smarandache multi-spaces, Smarandache geometries, mathematical combinatorics, non-euclidean geometry and topology and their applications to other sciences. Topics in detail to be covered are: Smarandache...

§1. Why is the WORLD a Combinatorial One? The multiplicity of the WORLD results in modern sciences overlap and hybrid, also implies its combinatorial structure. To see more clear, we present two meaningful proverbs following. Proverb 1. Ames Room An Ames room is a distorted room constructed so that from the front it appears to be an ordinary cubic-shaped room, with a back wall and two side walls parallel to each other and perpendicular to the horizontally level floor ...

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International Journal of Mathematical Combinatorics : Volume 3, Oc...

By: by Linfan Mao

Aims and Scope: The International J.Mathematical Combinatorics (ISSN 1937-1055) is a fully refereed international journal, and published quarterly comprising 100-150 pages approx. per volume, which publishes original research papers and survey articles in all aspects of Smarandache multi-spaces, Smarandache geometries, mathematical combinatorics, non-euclidean geometry and topology and their applications to other sciences. Topics in detail to be covered are: Smarandache...

Extending Homomorphism Theorem to Multi-Systems Abstract: The multi-laterality of WORLD implies multi-systems to be its best candidate model for ones cognition on nature, which is also included in an ancient book of China, TAO TEH KING written by Lao Zi, an ancient philosopher of China. Then how it works to mathematics, not suspended in thought? This paper explains this action by mathematical logic on mathematical systems generalized to Smarandache systems, or such syst...

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International Journal of Mathematical Combinatorics : Volume 2, Ju...

By: by Linfan Mao

Aims and Scope: The International J.Mathematical Combinatorics (ISSN 1937-1055) is a fully refereed international journal, and published quarterly comprising 100-150 pages approx. per volume, which publishes original research papers and survey articles in all aspects of Smarandache multi-spaces, Smarandache geometries, mathematical combinatorics, non-euclidean geometry and topology and their applications to other sciences. Topics in detail to be covered are: Smarandache...

Duality Theorems of Multiobjective Generalized Disjunctive Fuzzy Nonlinear Fractional Programming Abstract: This paper is concerned with the study of duality conditions to convex-concave generalized multiobjective fuzzy nonlinear fractional disjunctive programming problems for which the decision set is the union of a family of convex sets. The Lagrangian function for such problems is defined and the Kuhn-Tucker Saddle and Stationary points are characterized. In additio...

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International Journal of Mathematical Combinatorics : Volume 2, Ju...

By: by Linfan Mao

Aims and Scope: The International J.Mathematical Combinatorics (ISSN 1937-1055) is a fully refereed international journal, and published quarterly comprising 100-150 pages approx. per volume, which publishes original research papers and survey articles in all aspects of Smarandache multi-spaces, Smarandache geometries, mathematical combinatorics, non-euclidean geometry and topology and their applications to other sciences. Topics in detail to be covered are: Smarandache...

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  • Cover Image

International Journal of Mathematical Combinatorics : Volume 2, Ju...

By: by Linfan Mao

Aims and Scope: The International J.Mathematical Combinatorics (ISSN 1937-1055) is a fully refereed international journal, and published quarterly comprising 100-150 pages approx. per volume, which publishes original research papers and survey articles in all aspects of Smarandache multi-spaces, Smarandache geometries, mathematical combinatorics, non-euclidean geometry and topology and their applications to other sciences. Topics in detail to be covered are: Smarandache...

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