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Geometrie (clasa a IX-a). 4 -- Geometrie §i trigonometrie. 27 -- Probleme diverse. 47 -- Probleme recapitulative. 56 -- Geometrie spatiala. 61 -- Drepte §i plane. 85 -- Probleme recapitulative. 97 -- Proectii. 128 -- Geornetrie §i trigonormtrie (clasa a X-a). 144 --...

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This book contains a collection of poetry compiled by the author Florentin Smarandache.

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In chapter 1, following the Special Theory of Relativity, we generalize the Lorentz Contraction Factor C(v) to an Oblique-Contraction Factor OC(v, θ), which gives the contraction factor of the lengths moving at an oblique angle with respect to the motion direction. In the chapters 2-5 we show several inconsistencies, contradictions, and anomalies in the Special and General Theories of Relativity...

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1.3. Oblique-Length Contraction Factor The Special Theory of Relativity asserts that all lengths in the direction of motion are contracted, while the lengths at right angles to the motion are unaffected. But it didn’t say anything about lengths at oblique angle to the motion (i.e. neither perpendicular to, nor along the motion direction), how would they behave? This is a generalization of Galilean Relativity, i.e. we consider the oblique lengths. The length contraction factor in the motion direction is: C(v) = The square root of (1 – (v squared divided by c squared )(5) Suppose we have a rectangular object with width W and length L that travels at a constant speed v with respect to an observer on Earth. ...

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Chapter 1. Contraction and Dilation Factors in The Special Theory of Relativity: 15 Chapter 2. New Paradoxes for The Special Theory of Relativity: 38 Chapter 3. Other Paradoxes for The Special Theory of Relativity: 53 Chapter 4. Dilemmas for The General Theory of Relativity: 77 Chapter 5. Open Questions and Remarks: 101 ...

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This book is the Spanish translation of Applications of Smarandache Function, and Prime and Coprime Functions.

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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, fascinandu-ne si usurandu-ne drumul cunoasterii legitatilor ce guverneaza macrocosmosul si microcosmosul. De la etapa antichitatii, cand teoria numerelor era cuprinsa in aritrnetica, la etapa aritrneticii superioare din perioada Renasterii, cand teoria numerelor a de venit parte de sine statatoare si ajungand la etapa moderna din secolele XIX si XXcand in teoria numerelor isi fac loc metode de cercetare din domenii vecine, ca teoria functiilor de variabila complexa si analiza matematicii drumul este lung, insa dens, cu rezultate surprinzatoare, ingenioase si culte nu numai teoriei propriuzise a numerelor, dar si altor domenii ale cunoasterii, atat teoretice cat si pra...

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

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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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The submitted manuscripts may be in the format of remarks, conjectures, solved/unsolved or open new problems, notes, articles, miscellaneous, etc. They must be original work and camera ready [typewritten/computerized, format: 8.5 x 11 inches (z 21,6 x 28 centimetres)]. They are not returned, hence we advise the authors to keep a copy...

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This book has four chapters. In chapter one we just recall the notion of RD codes, MRD codes, circulant rank codes and constant rank codes and describe their properties. In chapter two we introduce few new classes of codes and study some of their properties. In this chapter we introduce the notion of fuzzy RD codes and fuzzy RD bicodes. Rank distance m-codes are introduced in chapter three and the property of m-covering radius is analysed. Chapter four indicates some applications of these new classes of codes....

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DEFINITION 1.12: The ‘norm’ of a word v _ VN is defined as the ‘rank’ of v over GF(2) (By considering it as a circulant matrix over GF(2)). We denote the ‘norm’ of v by r(v). We just prove the following theorem. THEOREM 1.2: Suppose ____GF(2N) has the polynomial representation g(x) over GF(2) such that the gcd(g(x), xN +1) has degree N – k, where 0 _ k _ N. Then the ‘norm’ of the word generated by _ is ‘k’. ...

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Preface 5 Chapter One BASIC PROPERTIES OF RANK DISTANCE CODES 7 Chapter Two RANK DISTANCE BICODES AND THEIR PROPERTIES 25 Chapter Three RANK DISTANCE m-CODES 77 Chapter Four APPLICATIONS OF RANK DISTANCE m-CODES 131 FURTHER READING 133 INDEX 144 ABOUT THE AUTHORS 150...

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Teoria Analitics a Numerelor reprezents pentru mine 0 pasiune. Rezultatele expuse mai departe constituie rodul catorva ani buni de cercetsri si csutsri. Lucrarea de fass se compune din 9 articole, publicate toate prin reviste de matematics romanesti sau strsine, iar unele prezentate chiar la congrese si conferinse nasionale cat si internasionale [vezi "Lista publicasiilor autorului pe tema tezei"). Ea se structureazs in patru capitole: - in primele trei capi tole se introduc noi funsii in teoria numerelor, se studiazs proprietssile lor, probleme nerezol vate legate de ele, implicasii in lumea stiinsific! internasional! (ce alsi matematicieni au abordat nosiunile acestea), conexisi cu alte funcsii bine stiute, importansa rezultatelor obsinute: - in ul timul capitol se aduc contribusii la studierea unei- funsii cunoscute in teoria numerelor (totient sau phi a lui Euler), in principal referitoare la conjectura lui carmichael. [Exist! referinse particulare dup! fiecare paraqraf (articol), iar referinse generale in finalul tezei.)...

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Ne bucuram exprimAnd mult-umirile noast.re f'at-a de t.ot-i acei.cunescut- i sau mai put-in cunoscut-i.care de-a Iungul aniler ne-au ajut.at. sa ajungem la aceast.a cart.e.Sunt. mult-i.sunt. f'oart.e mult-i cei care ne-au ajut.at. ... Unii ne-au dat. sugest.ii.alsii ne-au oferit. idei. uneori ne-am st.raduit. impreunA sa descif'ram un amanunt. nelamurit.. alleori Invst-am din Int.rebarile mest.esugit.e sau poale chiar naive ale inlerloculorilor nost.rii:...

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Mi-a sosit, de curand, cu po~ta aeriana, 0 carte din Amcrica. Era expcdiata de Florentin Smarandache, din Phoenix. Arizona. un valcean de-al nostru din Balce~ti, fugit Inainte de revolutic prin Turcia ~i "aclimatizat" In Statele Unite. Cinc e Florentin Smarandache: profesor de matematica, aut or a peste cincisprczece volume. poet. initiator al curentului paradoxise acum cercetator la Corporatia de computere Honeywell. Arizona. L-am cunoscut bine pe acest domn In perioada studentiei, cand incerca sa publice la revista studentcasca pe care 0 conduceam, tot felul de jocuri matematice. pe care nici nu Ie Intelegeam, nici nu Ie gustam, dar pe care Ie-am publicae in final. de dragul omului....

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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]. Also, in [2] there are some problems, which are not included in [1]. On the other hane, there are problems from [1], which are not included in [2]. One of them is Problem 62 from [1], which is included here under the same number. In the summer of 1998 the author found the books in his library and for a first time tried to solve a problem from them. After some attempts one of the problems was solved and this was a power impulse for the next research. In the present book are collected the 27 problems solved by the middle of February 1999....

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Preface 5 -- 1. On The 4-Th Smarandache's Problem 7 -- 2. On The 16-Th Smarandache's Problem 12 -- 3. On The 22-Nd, The 23-Rd, And The 24th -- Smarandache's Problems 16 -- 4. On The 37-Th And The 38th -- Smarandache's Problems 22 -- 5. On The 39-Th, The 40-Th, The 41st, And -- The 42-Nd Smarandache's Problems 27 -- 6. On The 43-Rd And 44-Th Smarandache's -- Problems 33 -- 7. On The 61-St, The 62-Nd, And The 63red -- Smarandache's Problems 38 -- 8. On The 97-Th, The 98-Th, And The 99th -- Smarandache's Problems 50 -- 9. On The 100-Th, The 101-St, And The 102nd -- Smarandache's Problems 57 -- 10. On The Ll7-Th Smarandache's Problem 62 -- Ll. On The Ll8-Th Smarandache's Problem 64 -- 12. On The 125-Th Smarandache's Problem 66 -- 13. On The I26-Th Smarandache's Problem 68 -- 14. On The 62-Nd Smarandache's Problem 71 -- Is. Conclusion 74 -- 16. Appendix 76 -- References 83 -- Curriculum Vitae Of K. Atanassov 86 --...

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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 refined labels using matrices....

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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 conclusion of the theorem 1.1.1 is true. Further the same conclusion holds good if the partitions are changed. S contains only same type of partition. However in case of Zn, S becomes a finite commutative group....

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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....

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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 n-fields in section one and n-vector spaces of type II are defined in section two and some important properties are enumerated....

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Preface 5 Chapter One n-VECTOR SPACES OF TYPE II AND THEIR PROPERTIES 7 1.1 n-fields 7 1.2 n-vector Spaces of Type II 10 Chapter Two n-INNER PRODUCT SPACES OF TYPE II 161 Chapter Three SUGGESTED PROBLEMS 195 FURTHER READING 221 INDEX 225 ABOUT THE AUTHORS 229...

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The function named in the title of this book is originated from the e:riled Romanian mathematician Florentin Smaranda.che, who has significant contributions not only in mathematics, but also in li~ratuIe. He is the father of The Paradorut Literary Movement and is the author of many stories, novels, dramas, poems....

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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 enough of those obstacles to make the book worthwhile. As always, your comments and criticisms are welcome. Feel free to contact me using any of the addresses listed below, although e-mail is the preferred method....

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In this book authors for the first time introduce the notion of super interval matrices using the special intervals of the form [0, a], a belongs to Z+ ∪ {0} or Zn or Q+ ∪ {0} or R+ ∪ {0}....

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SUPER INTERVAL SEMILINEAR ALGEBRAS In this chapter we for the first time introduce the notion of semilinear algebra of super interval matrices over semifields of type I (super semilinear algebra of type I) and semilinear algebra of super interval matrices over interval semifields of type II (super semilinear algebra of type II) and study their properties and illustrate them with examples. DEFINITION 4.1: Let V be a semivector space of super interval matrices defined over the semifield S of type I. If on V we for every pair of elements x, y ∈ V; x . y is in V where ‘.’ is the product defined on V, then we call V a semilinear algebra of super interval matrices over the semifield S of type I. We will illustrate this situation by some examples. Example 4.1: Let V = {([0, a1] [0, a2] | [0, a3] [0, a4] | [0, a5] [0, a6] | [0,a7]) | ai ∪ Z+ ∪ {0}; 1 ≤ i ≤ 7} be a semivector space of super interval matrices defined over the semifield S = Z+ ∪ {0} of type I. Consider x = ([0, 5] [0, 3] | [0, 9] [0, 1] [0, 2] [0, 8] | [0, 6]) and y =([0, 1] [0, 2] | [0, 3] [0, 5] [0, 3] [0, 1] | [0, 5]) in V. We define the product ‘.’ on V as x.y =...

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CONTENTS Preface 5 Chapter One INTRODUCTION 7 Chapter Two INTERVAL SUPERMATRICES 9 Chapter Three SEMIRINGS AND SEMIVECTOR SPACES USING SUPER INTERVAL MATRICES 83 Chapter Four SUPER INTERVAL SEMILINEAR ALGEBRAS 137 Chapter Five SUPER FUZZY INTERVAL MATRICES 203 5.1 Super Fuzzy Interval Matrices 203 5.2 Special Fuzzy Linear Algebras Using Super Fuzzy Interval Matrices 246 Chapter Six APPLICATION OF SUPER INTERVAL MATRICES AND SET LINEAR ALGEBRAS BUILT USING SUPER INTERVAL MATRICES 255 Chapter Seven SUGGESTED PROBLEMS 257 FURTHER READING 281 INDEX 285 ABOUT THE AUTHORS 287...

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Prima culegere de "Problemes avec et sans …problemes!" a aparut in Maroc in 1983. Am strans aceste proleme, aparute prill diverse reviste romanel;lti sau straine (printre care: "Gazeta Matematica", revista Ia care Ill-am format ca problemisi, "American Mathematical Monihly", "Crux Mathematicorum" (Canada), "E1emcllte del' Mathematik" (Elvetia), "Gaceta Matematica" (Spania), "Nieuw voor Archief" (Olanda), etc.) ori inedite intr-un al doilea volum....

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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. In mathematics, one often does not know what the consequences of a statement are. Cnlike a novel however, there are no complete plot resolutions in mathematics as there are no villains to rub out. As the French emphatically say in another context, "Vive la difference'"...

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The methodology of how mathematics is untaught.