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Introduction to Bimetrics

By: Florentin Smarandache

Matrix theory has been one of the most utilised concepts in fuzzy models and neutrosophic models. From solving equations to characterising linear transformations or linear operators, matrices are used. Matrices find their applications in several real models. In fact it is not an exaggeration if one says that matrix theory and linear algebra (i.e. vector spaces) form an inseparable component of each other. The study of bialgebraic structures led to the invention of n...

Matrices provide a very powerful tool for dealing with linear models. Bimatrices which we are going to define in this chapter are still a powerful and an advanced tool which can handle over one linear model at a time. Bimatrices will be useful when time bound comparisons are needed in the analysis of the model.

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Introduction to Linear Bialgebra

By: Florentin Smarandache

The algebraic structure, linear algebra happens to be one of the subjects which yields itself to applications to several fields like coding or communication theory, Markov chains, representation of groups and graphs, Leontief economic models and so on. This book has for the first time, introduced a new algebraic structure called linear bialgebra, which is also a very powerful algebraic tool that can yield itself to applications. With the recent introduction of bimatric...

In this section we give the definition of linear algebra and just state the few important theorems like Cayley Hamilton theorem, Cyclic Decomposition Theorem, Generalized Cayley Hamilton Theorem and give some properties about linear algebra.

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Begin the Adventure : How to Break the Light Barrier

By: Florentin Smarandache

For most of the 20th century, both relativity and star travel fascinated this writer. The reasons Albert Einstein concluded there is an absolute barrier at the speed of light seemed at first clear, then later not so clear upon closer examination. "The speed of light relative to what?" I often asked anyone who would listen. The common response was, "Light needs no specification of that kind; its speed is the same no matter who measures it." "That's true." I would respo...

One's reach should exceed one's grasp. Thus we reach for Alpha Centauri with a round-trip manned and womanned mission as the proposed overarching goal under a clear plan of exploration - a grand experiment described in later chapters. Whether or not we succeed in grasping the goal under this or under any plan is not as important as it is to set a definite plan and work towards its goal. The plan outlined here is in two phases: Phase one has a high probability of succe...

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Asupra Unor Noi Functii in Teoria Numerelor

By: Florentin Smarandache

Performantele matematicii actuale,ca si descoperirile din viitor isi au,desigur, inceputul in cea mai veche si mai aproape de filozofie ramura a matematicii, in teoria numerelor. Matematicienii din toate timpurile au fost, sunt si vor fi atrasi de frumusetea si varietatea problemelor specifice acestei ramuri a matematicii. Regina a matematicii, care la randul ei este regina a stiintelor, dupa cum spunea Gauss, teoria numerelor straluceste cu lumina si atractiile ei, fa...

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On Some of Smarandache's Problems

By: Krassimir T. Atanassov

In 1996 the author wrote reviews for "Zentralblatt fUr Mathematik" for books [11 and [21 and this was him first contact of with the Smarandache's problems. In [1] Florentin Smarandache formulated 105 unsolved problems, while in [21 C. Dumitrescu and V. Seleacu formulated 140 unsolved problems. The second book contains almost all problems from [11, but now everyone problem has unique number and by this reason the author will use the numeration of the problems from [2]...

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An Introduction to the Smarandache Function

By: Charles Ashbacher

The creation of a book is an act that requires several preconditions. I) An interesting and worthwhile subject; 2) A fair, yet demanding editor.; 3) Someone willing to put the words on paper. Given the existence of these three items, the leap to making the book a good one becomes the responsibility of the author. The Smarandache function is simultaneously a logical extension to earlier functions in number theory as well as a key to many future paths of exploration. As...

As one of the oldest of mathematical disciplines, the roots of number theory extend back into antiquity. Problems are often easy to state, but extremely difficult to solve. Which is the origin of much of their charm. All mathematicians, amateurs and professionals alike, have a soft spot in their hearts for the "purity" of the integers. When "Fermat's Last Theorem" was finally proven after centuries of effort, the result was discussed on many major news shows in the U...

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Pluckings from the Tree of Smarandache Sequences and Functions

By: Charles Ashbacher

In writing a book, one encounters and overcomes many obstacles. Not the least of which is the occasional case of writer’s block. This is especially true in mathematics where sometimes the answer is currently and may for all time be unknown. There is nothing worse than writing yourself into a corner where your only exit is to build a door by solving unsolved problems. In any case, it is my hope that you will read this volume and come away thinking that I have overcome eno...

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Collection of Problems on Smarandache Notions

By: Charles Ashbacher

A Smarandache notion is an element of an ill-defined set, sometimes being almost an accident oflabeling. However, that takes nothing away from the interest and excitement that can be generated by exploring the consequences of such a problem It is a well-known cliche among writers that the best novels are those where the author does not know what is going to happen until that point in the story is actually reached. That statement also holds for some of these problems. ...

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Smarandache Sequences, Stereograms and Series

By: Charles Ashbacher

F. Smarandache has defined many sequences of integers formed by concatenating the positive integers in specific ways. A question that is often asked about most of these sequences concerns the number of primes in the sequence. As Paul Erdos pointed out, determining how many primes are in sequences of this type is a problem that the current state of mathematical knowledge is unprepared to solve. In general, the sequences grow rather fast, so after a very short time, t...

Using the bases from three through nine to form new sequences, we can then ask the same question regarding the number of primes in the sequence. That appears to be a question just as difficult as the one for base ten numbers, and is summarized in the following statement.

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Antichambers, Antipoesies, Bizarreries

By: Florentin Smarandache

Un costaud force une traInee a fuir sa villa. II entretient des relations avec une autredes relations de sang. Le gars court la gueuse jusqu' au bOI-del, ou il est -a la botte d'une prostituee dlkllaussee. Le male lui rcgarde en face son dos puis il met a nu cette femelle deja deshabillee.

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Algebra-Russian

By: Florentin Smarandache

This is Smarandache's Russian translation from Romanian on Algebra.

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Algebra-Romanian

By: Florentin Smarandache

Prezenta lucrare contine exercitii §i probleme de algebra, grupate pe capitole, pentru clasele superioare de licee §i §coli medii de cultura generala. Scopul ei este pregatirea matematica a elevilor din liceele de toate categoriile §i va fi utila in lucrul de sine statator. De asemenea, lucrarea poate fi folosita pentru lucrul extra§colar, deoarece cititorul va gasi in ea teoreme §i for mule importante, notiuni §i definitii de baza care nu intotdeauna sunt incluse in manualele §colare.

Teoria axiomatica a multimilor este foarte dificila pentru a fi expusa la un nivel elementar, de aceea, intuitiv, prin multime vom in1elege o colec1ie de obiecte pe care Ie vom numi elemente sau puncte ale acestei mul1imi. 0 mul1ime este definita daca sunt date elementele sale sau daca se da 0 proprietate pe care 0 au toate elementele sale, proprietate care Ie deosebe§te de elementele altei mul1imi. Ulteror mul1imile Ie vom nota cu majuscule: A, B, C, .. . , X, Y, ...

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Afinitati

By: Florentin Smarandache

Din nevoie deoarece m aflam într'un lagr de refugiaÛi politici in Turcia Õi mi se lungiser ochii dup viza americana de emigrare, viz care se tot lsa aÕteptat pân la disperare! Aproape doi ani de nerbdri Õi descumpniri am înscris în memoria mea... Destui colegi, nerezistând, îÕi luau lumea'n cap Õi fugeau din lagr haihui prin Europa, trecând clandestin frontierele în Grecia Õi-apoi tind-o spre inima continentului în Germania, Belgia, care pe unde nimerea, ba ascunÕ...

Structura roman; a celui mai frumos pod; care a rezistat unui cutremur -; în timp ce cldirile înalte cdeau precum copacii; - destul de tare s Ûin greutatea; atâtor armate Õi caravane spre vechiul oraÕ; care st la intersecÛia Europei....

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Essays

By: Michel Eyquem de Montaigne

(Author to reader)--Reader, loe here a well-meaning Booke. It doth at the first entrance forewarne thee, that in contriving the same I have proposed unto my selfe no other than a familiar and private end: I have no respect or consideration at all, either to thy service, or to my glory: my forces are not capable of any such desseigne. I have vowed the same to the particular commodity of my kinsfolk and friends: to the end, that losing me (which they are likely to do ere...

They have a secret, unperceived and delicate beauty; he had neede of a cleere, farreseeing and true-discerning sight that should rightly discover this secret light. Is not ingenuity (according to us) cosin germaine unto sottishnesse, and a quality of reproach? Socrates maketh his soule to moove, with a naturall and common motion. Thus saith a plaine Country-man, and thus a seely Woman: Hee never hath other people in his mouth than Coach-makers, Joyners, Coblers, and Masons.

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I and Thou

By: Martin Bube

Tms work in its oripl, German form has already, since its publication fourteen years ago, exercised. on the Continent an influence, quite out of proportion to its slender size. In view of this influence alone it may be affirmed that 1 and Thou will rank &8 one of the epoch-making books 9f our generation. It has hitherto been eomparatively Unknown among English-speaking students of philosophy and theology.

The primal natm:e of the effort to establish relation is already to be seen in the earliest and most confined stage. Before anything isolated can be perceived, timid glances mOve out into indistinct space, towards something indefinite; and in times when there seems to be no desire for nourishment, hands sketch delicately and dimly in the empty air, apparently aimlessly seeking and reaching out to meet something indefinite. You may, if you wish, call this an animal acti...

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Report on Orphaned Works

By: Marybeth Peters

This Report addresses the issue of “orphan works,” a term used to describe the situation where the owner of a copyrighted work cannot be identified and located by someone who wishes to make use of the work in a manner that requires permission of the copyright owner. Even where the user has made a reasonably diligent effort to find the owner, if the owner is not found, the user faces uncertainty – she cannot determine whether or under what conditions the owner would permi...

We also recommend one other threshold requirement for a user to qualify for the orphan works limitations on remedies: throughout the use of the work, the user must provide attribution to the author and copyright owner of the work if such attribution is possible and as is reasonably appropriate under the circumstances. The idea is that the user, in the course of using a work for which he has not received explicit permission, should make it as clear as possible to the publ...

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Information Technology Tales

By: Brad Bradford

This book also begins with that wondrous first Information Technology and then moves on to tales about the wonders of the written word—great stories, many of them likely new to most readers. In them, you‘ll find all the backgrounds, foregrounds, premises, conclusions, and surprises that make up the best and most valuable books. This book also begins with that wondrous first Information Technology and then moves on to tales about the wonders of the written word—great st...

Way back in the fifteenth century a man named Johann Gutenberg invented the ?printing press. More than 400 years passed before Ottmar Mergenthaler found a way in the late 1880s to mechanize that historic invention. Then, less than a century later – in the 1980s – digital printing displaced Mergenthaler’s wondrous Linotypes.

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On the Babylonian Captivity of the Church

By: Martin Luther

Martin Luther goes through the seven sacraments of the medieval Catholic Church with his interpretation of the Bible. He teaches his opinions on the different pratices taken place within the Catholic Church and what they should or do represent. The book is seemingly set in an "angry tone" as this was the first time he accused the pope of being the Antichrist. Luther's book was further published in German by his opponent Franciscan Thomas Murner, in hopes that he would...

“Rise up then, you popish flatterers, one and all! Get busy and defend yourselves against the charges of impiety, tyranny, and lèse-majesté against the gospel, and of the crime of slandering your brethren. You decry as heretics those who refuse to contravene such plain and powerful words of Scripture in order to acknowledge the mere dreams of your brains! If any are to be called heretics and schismatics, it is not the Bohemians or the Greeks,47 for they take their stand ...

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Sextus Empiricus and Greek Scepticism

By: Mary Mills Patrick

The following treatise on Sextus Empiricus and Greek Scepticism has been prepared to supply a need much felt in the English language by students of Greek philosophy. For while other schools of Greek philosophy have been exhaustively and critically discussed by English scholars, there are few sources of information available to the student who wishes to make himself familiar with the teachings of Pyrrhonism. The aim has been, accordingly, to give a concise presentation of...

“Interest has revived in the works of Sextus Empiricus in recent times, especially, one may say, since the date of Herbart. There is much in the writings of Sextus that finds a parallel in the methods of modern philosophy. There is a common starting-point in the study of the power and limitations of human thought. There is a common desire to investigate the phenomena of sense-perception, and the genetic relations of man to the lower animals, and a common interest in the ...

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Allegorical Expositions of the Holy Laws

By: Philo of Alexandria

Philo used philisophical representations to fuse and harmonize Jewish traditions and Greek philosophy. It interprets both Jewish and historic Greek philosophies.

“It is a melancholy reflection upon the history of the Jews that they have failed to pay due honor to their two greatest philosophers. Spinoza was rejected by his contemporaries from the congregation of Israel; Philo Judaeus was neglected by the generations that followed him.”

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