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This book has six chapters. First chapter is introductory in nature. The new concept of non-associative semi-linear algebras is introduced in chapter two. This structure is built using groupoids over semi-fields. Third chapter introduces the notion of non-associative linear algebras. These algebraic structures are built using the new class of loops. All these non-associative linear algebras are defined over the prime characteristic field Zp, p a prime. However if we take polynomial non associative, linear algebras over Zp, p a prime; they are of infinite dimension over Zp. We in chapter four introduce the notion of groupoid vector spaces of finite and infinite order and their generalizations. Only when this study becomes popular and familiar among researchers several applications will be found. The final chapter suggests around 215 problems some of which are at research level. ...

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Ln(m) is a loop of order n + 1 that is Ln(m) is always of even order greater than or equal to 6. For more about these loops please refer [37]. All properties discussed in case of groupoids can be done for the case of loops. However the resultant product may not be a loop in general. For the concept of semifield refer [41]. We will be using these loops and groupoids to build linear algebra and semilinear algebras which are non associative. ...

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Preface 5 Chapter One BASIC CONCEPTS 7 Chapter Two NON ASSOCIATIVE SEMILINEAR ALGEBRAS 13 Chapter Three NON ASSOCIATIVE LINEAR ALGEBRAS 83 Chapter Four GROUPOID VECTOR SPACES 111 Chapter Five APPLICATION OF NON ASSOCIATIVE VECTOR SPACES / LINEAR ALGEBRAS 161 Chapter Six SUGGESTED PROBLEMS 163 FURTHER READING 225 INDEX 229 ABOUT THE AUTHORS 231 ...

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This book has six chapters. The first one is introductory in nature. Second chapter introduces complex modulo integer groupoids and complex modulo integer loops using C(Zn). This chapter gives 77 examples and forty theorems. Chapter three introduces the notion of nonassociative complex rings both finite and infinite using complex groupoids and complex loops. This chapter gives over 120 examples and thirty theorems. Forth chapter introduces nonassociative structures using complex modulo integer groupoids and quasi loops. This new notion is well illustrated by 140 examples. These can find applications only in due course of time, when these new concepts become familiar. The final chapter suggests over 300 problems some of which are research problems....

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THEOREM 2.1: Let G = {C(Zn), *, (t, u); t, u ∈ Zn} be a complex modulo integer groupoid. If H ⊆ G is such that H is a Smarandache modulo integer subgroupoid, then G is a Smarandache complex modulo integer groupoid. But every subgroupoid of G need not be a Smarandache complex modulo interger subgroupoid even if G is a Smarandache groupoid. Proof is direct and hence is left as an exercise to the reader. Example 2.28: Consider G = {C(Z8), *, (2, 4)}, a complex modulo integer groupoid....

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This book is organized into seven chapters. Chapter one is introductory in content. The notion of neutrosophic set linear algebras and neutrosophic neutrosophic set linear algebras are introduced and their properties analysed in chapter two. Chapter three introduces the notion of neutrosophic semigroup linear algebras and neutrosophic group linear algebras. A study of their substructures are systematically carried out in this chapter. The fuzzy analogue of neutrosophic group linear algebras, neutrosophic semigroup linear algebras and neutrosophic set linear algebras are introduced in chapter four of this book. Chapter five introduces the concept of neutrosophic group bivector spaces, neutrosophic bigroup linear algebras, neutrosophic semigroup (bisemigroup) linear algebras and neutrosophic biset bivector spaces. The fuzzy analogue of these concepts are given in chapter six. An interesting feature of this book is it contains nearly 424 examples of these new notions. The final chapter suggests over 160 problems which is another interesting feature of this book....

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Now we proceed onto define the notion of neutrosophic subgroup of a neutrosophic group. DEFINITION 1.2: Let N(G) = (GuI) be a neutrosophic group generated by G and I. A proper subset P(G) is said to be a neutrosophic subgroup if P(G) is a neutrosophic group i.e. P(G) must contain a (sub) group. Example 1.3: Let N(Z2) = 􀂢Z2 􀂉 I􀂲 be a neutrosophic group under addition. N(Z2) = {0, 1, I, 1 + I}. Now we see {0, I} is a group under + in fact a neutrosophic group {0, 1 + I} is a group under ‘+’ but we call {0, I} or {0, 1 + I} only as pseudo neutrosophic groups for they do not have a proper subset which is a group. So {0, I} and {0, 1 + I} will be only called as pseudo neutrosophic groups (subgroups). We can thus define a pseudo neutrosophic group as a neutrosophic group, which does not contain a proper subset which is a group. Pseudo neutrosophic subgroups can be found as a substructure of neutrosophic groups. Thus a pseudo neutrosophic group though has a group structure is not a neutrosophic group and a neutrosophic group cannot be a pseudo neutrosophic group. Both the concepts are different. Now we see a neutrosophic group ...

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Preface 5 Chapter One INTRODUCTION 7 Chapter Two SET NEUTROSOPHIC LINEAR ALGEBRA 13 2.1 Type of Neutrosophic Sets 13 2.2 Set Neutrosophic Vector Space 16 2.3 Neutrosophic Neutrosophic Integer Set Vector Spaces 40 2.4 Mixed Set Neutrosophic Rational Vector Spaces and their Properties 52 Chapter Three NEUTROSOPHIC SEMIGROUP LINEAR ALGEBRA 91 3.1 Neutrosophic Semigroup Linear Algebras 91 3.2 Neutrosophic Group Linear Algebras 113 Chapter Four NEUTROSOPHIC FUZZY SET LINEAR ALGEBRA 135 Chapter Five NEUTROSOPHIC SET BIVECTOR SPACES 155 Chapter Six NEUTROSOPHIC FUZZY GROUP BILINEAR ALGEBRA 219 Chapter Seven SUGGESTED PROBLEMS 247 FURTHER READING 277 INDEX 280 ABOUT THE AUTHORS 286 ...

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This book has four chapters. Chapter one is introductory in nature, for it recalls some basic definitions essential to make the book a self-contained one. Chapter two, introduces for the first time the new notion of neutrosophic rings and some special neutrosophic rings like neutrosophic ring of matrix and neutrosophic polynomial rings. Chapter three gives some new classes of neutrosophic rings like group neutrosophic rings, neutrosophic group neutrosophic rings, semigroup neutrosophic rings, S-semigroup neutrosophic rings which can be realized as a type of extension of group rings or generalization of group rings. Study of these structures will throw light on the research on the algebraic structure of group rings. Chapter four is entirely devoted to the problems on this new topic, which is an added attraction to researchers. A salient feature of this book is that it gives 246 problems in Chapter four. Some of the problems are direct and simple, some little difficult and some can be taken up as a research problem....

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Now we proceed onto define the notion of neutrosophic subgroup of a neutrosophic group. DEFINITION 1.1.2: Let N(G) = 〈G ∪ I〉 be a neutrosophic group generated by G and I. A proper subset P(G) is said to be a neutrosophic subgroup if P(G) is a neutrosophic group i.e. P(G) must contain a (sub) group. Example 1.1.3: Let N(Z2) = 〈Z2 ∪ I〉 be a neutrosophic group under addition. N(Z2) = {0, 1, I, 1 + I}. Now we see {0, I} is a group under + in fact a neutrosophic group {0, 1 + I} is a group under ‘+’ but we call {0, I} or {0, 1 + I} only as pseudo neutrosophic groups for they do not have a proper subset which is a group. So {0, I} and {0, 1 + I} will be only called as pseudo neutrosophic groups (subgroups). We can thus define a pseudo neutrosophic group as a neutrosophic group, which does not contain a proper subset which is a group. Pseudo neutrosophic subgroups can be found as a substructure of neutrosophic groups. Thus a pseudo neutrosophic group though has a group structure is not a neutrosophic group and a neutrosophic group cannot be a pseudo neutrosophic group. Both the concepts are different. Now we see a neutrosophi...

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Preface 5 Chapter One INTRODUCTION 1.1 Neutrosophic Groups and their Properties 7 1.2 Neutrosophic Semigroups 20 1.3 Neutrosophic Fields 27 Chapter Two NEUTROSOPHIC RINGS AND THEIR PROPERTIES 2.1 Neutrosophic Rings and their Substructures 29 2.2 Special Type of Neutrosophic Rings 41 Chapter Three NEUTROSOPHIC GROUP RINGS AND THEIR GENERALIZATIONS 3.1 Neutrosophic Group Rings 59 3.2 Some special properties of Neutrosophic Group Rings 73 3.3 Neutrosophic Semigroup Rings and their Generalizations 85 Chapter Four SUGGESTED PROBLEMS 107 REFERENCES 135 INDEX 149 ABOUT THE AUTHORS 154 ...

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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 identities satisfied by them are studied in section three of this chapter. The final section of chapter one introduces the notion of neutrosophic interval biloops and studies them. Chapter two of this book introduces the notion of neutrosophic interval birings and bisemirings. Several results in this direction are derived and described. Even new bistructures like neutrosophic interval ring-semiring or neutrosophic interval semiring-ring are introduced and analyzed. Further in this chapter the concept of neutrosophic biinterval vector spaces or neutrosophic interval bivector spaces are introduced and their properties are described. In the third chapter we introduce the n...

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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 notion of neutrosophic interval biloops....

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Preface 5 Chapter One BASIC CONCEPTS 7 1.1 Neutrosophic Interval Bisemigroups 8 1.2 Neutrosophic Interval Bigroups 32 1.3 Neutrosophic Biinterval Groupoids 41 1.4 Neutrosophic Interval Biloops 57 Chapter Two NEUTROSOPHIC INTERVAL BIRINGS AND NEUTROSOPHIC INTERVAL BISEMIRINGS 75 2.1 Neutrosophic Interval Birings 75 2.2 Neutrosophic Interval Bisemirings 85 2.3 Neutrosophic Interval Bivector Spaces and their Generalization 93 Chapter Three NEUTROSOPHIC n- INTERVAL STRUCTURES (NEUTROSOPHIC INTERVAL n-STRUCTURES) 127 Chapter Four APPLICATIONS OF NEUTROSOPHIC INTERVAL ALGEBRAIC STRUCTURES 159 Chapter Five SUGGESTED PROBLEMS 161 FURTHER READING 187 INDEX 189 ABOUT THE AUTHORS 195 ...

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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 the classical theorems for neutrosophic algebras are proved with appropriate modifications. Chapter four indicates the probable applications of these algebraic structures. The final chapter suggests about 80 innovative problems for the reader to solve....

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Dedication 5 Preface 7 Chapter One INTRODUCTION TO BASIC CONCEPTS 9 1.1 Introduction to Bilinear Algebras and their Generalizations 9 1.2 Introduction to Neutrosophic Algebraic Structures 11 Chapter Two NEUTROSOPHIC LINEAR ALGEBRA 15 2.1 Neutrosophic Bivector Spaces 15 2.2 Strong Neutrosophic Bivector Spaces 32 2.3 Neutrosophic Bivector Spaces of Type II 50 2.4 Neutrosophic Biinner Product Bivector Space 198 Chapter Three NEUTROSOPHIC n-VECTOR SPACES 205 3.1 Neutrosophic n-Vector Space 205 3.2 Neutrosophic Strong n-Vector Spaces 276 3.3 Neutrosophic n-Vector Spaces of Type II 307 Chapter Four APPLICATIONS OF NEUTROSOPHIC n-LINEAR ALGEBRAS 359 Chapter Five SUGGESTED PROBLEMS 361 FURTHER READING 391 INDEX 396 ABOUT THE AUTHORS 402...

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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 becomes popular we can find interesting applications of them. The final chapter suggests over 100 problems some of which are at research level....

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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 notion of semirings, Smarandache semirings, semi vector spaces and semifields are used....

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This book has four chapters. Chapter one is introductory in nature. The reader is expected to have a good background of algebra and graph theory in order to derive maximum understanding of this research. The second chapter represents groups as graphs. The main feature of this chapter is that it contains 93 examples with diagrams and 18 theorems. In chapter three we describe commutative semigroups, loops, commutative groupoids and commutative rings as special graphs. The final chapter contains 52 problems....

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Preface 5 Chapter One INTRODUCTION TO SOME BASIC CONCEPTS 7 1.1 Properties of Rooted Trees 7 1.2 Basic Concepts 9 Chapter Two GROUPS AS GRAPHS 17 Chapter Three IDENTITY GRAPHS OF SOME ALGEBRAIC STRUCTURES 89 3.1 Identity Graphs of Semigroups 89 3.2 Special Identity Graphs of Loops 129 3.3 The Identity Graph of a Finite Commutative Ring with Unit 134 Chapter Four SUGGESTED PROBLEMS 157 FURTHER READING 162 INDEX 164 ABOUT THE AUTHORS 168...

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This book has six chapters. The first one is introductory in nature just giving only the needed concepts to make this book a self contained one. Chapter two introduces the notion of refined plane of labels, the three dimensional space of refined labels DSm vector spaces. Clearly any n-dimensional space of refined labels can be easily studied as a matter of routine....

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Preface 5 Chapter One INTRODUCTION 7 Chapter Two DSm VECTOR SPACES 17 Chapter Three SPECIAL DSm VECTOR SPACES 83 Chapter Four DSm SEMIVECTOR SPACE OF REFINED LABELS 133 Chapter Five APPLICATIONS OF DSm SEMIVECTOR SPACES OF ORDINARY LABELS AND REFINED LABELS 173 Chapter Six SUGGESTED PROBLEMS 175 FURTHER READING 207 INDEX 211 ABOUT THE AUTHORS 214...

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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 malfunctioning of an administrative system....

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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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Contents Forward and Backward.........3 Chapter 1 ...................................5 Non-Basic symbols misused in Computer Science .....................5 Unintelligent terminal .........................9 The illogical mudflow of a quarterly non-production process ...............12 Chapter 2 ..................................15 The computer coding misused in Computer Science ...................15 Codification problems ..............................17 Codes misclassification .............................18 Chapter 3 ..................................21 Miscomputing the time for creating an application misusing the mudflow scrambles ........21 Misinformation deregistration and non-identification in files...............27 Chapter 4 ..................................29 Data storage and types of non-peripheral devices .....................29 Representation of Misinformation in internal memory ..............30 External non-peripherals ............................31 Printing paper ................................34 Magnetic band ...............................34 Magnetic disks ...............................35 The non-...

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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 that the readers could be interested in these issues. At the same time, this book could open up the reader’s perspective, guide and inspire the readers to these fields....

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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....

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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 wheat etc. (see Shabbir and Gupta (2006)). In such situations, taking the advantage of point biserial correlation between the study variable and the auxiliary attribute, the estimators of parameters of interest can be constructed by using prior knowledge of the parameters of auxiliary attribute....

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Preface...............................................4 1.Ratio Estimators in Simple Random Sampling Using Information on Auxiliary Attribute...............................................7 2.Ratio-Product Type Exponential Estimator for Estimating Finite Population Mean Using Information on Auxiliary Attribute......................18 3.Improvement in Estimating the Population Mean Using Exponential Estimator in Simple Random Sampling....................................33 4.Almost Unbiased Exponential Estimator for the Finite Population Mean......................41 5.Almost Unbiased Ratio and Product Type Estimator of Finite Population Variance Using the Knowledge of Kurtosis of an Auxiliary Variable in Sample Surveys....................................54 6.A General Family of Estimators for Estimating Population Variance Using Known Value of Some Population Parameter(s).....................62-73...

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Etimologic, aforism + flori = af(L)orism, deci un “aflorism” este o mică reflecție scrisă pe un dizain floral, ori un poem scurt pe un fond artistic.

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Cost piperat Sau ţi-o pune aşa un preţ ..să pici în coadă!

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Cuprins Cuprins..................................................5 Cât vreau eu..................................................25 Dezolare........................................................25 Lucrătură proastă....................................................25 Ridicol..................................................25 Dispreţuitor...................................................25 Încearcă pastile, că..................................................26 Dreptul de alegere..................................................26 Mister..................................................26 Unul sus pus..................................................26 Needucat.......................................................26 Ingâmfatul.....................................................27 Dublă condamnare..................................................27 Iritant sonor..................................................27 Iscoditor........................................................27 Sunt edificat..................................................27 Zăpacit de fericire...................................................

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This is a book on empirical number theory concentrating on the analysis of number sequences. Its focus is on a small part of a very large number of integer sequences defined by Florentin Smarandache. The author has. however. when appropriate included some other of his research results which organically belongs to this area. The content is organized into chapters according to the main considerations to make when programming the analysis. They are not mutually exclusive. As in my previous book Surfing on the ocean of numbers - a few Smarandache Notions and Similar Topics an attempt has been made to present results so that they are easy to understand and not to burdensome to read. There are many tables. some of which may be used for reference. but in general they are there to show the overall results obtained at a glance. In most cases it is the way in which sequences behave. not the individual figures. which is of importance. Some graphs have been included to illustrate important findings....

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

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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....

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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, Z, iar elementele lor cu minuscule: a, b, c, ... , x, y, z etc....

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This volume contains basic mathematics (in Hawaiian). It teaches you the numbers in Hawaiian up to one hundred and also basio useful mathematics.

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Ehia kahi iloko o ka 10? He 10 a me na kahi ehia iloko o ka 12? He 10 a me na kahi ehia iloko o ka 13? 14? 16? 19? 15? 18? 17? 11? Ehia na umi iloko o ka 20? iloko o ke 30? 40? 60? 80? 60? 70? 50? 90? 100? Ehia na umi a me na kahi iloko o ka 21? iloko o ka 23? 28? 26? 32? 35? 37? 44? 49? 41? 53? 57? 62? 65? 68? 71? 76? 99? 85? 87? 88? 92? 94? 99? He umi a me 1, heaha ia? 10 me 3? 10 me 7? 10 me 9? 2 umi? 2 umi me 1? 2 umi me 5? 2 umi me 7? 3 umi? 3 umi me 2? 3 umi me 8? 4 umi? me 6? 5 umi? 5 umi me 3? 5 umi me 5? 6 umi? 6 umi me 4? 7 umi? 8 umi? 8 umi me 6? 9 umi? 9 umi me 2? 9 umi me 9? 10 ka umi? E kakau oe ma na huahelu i ka papa i hookahi; i elua; a pela a hiki i ka umi. E kakau ma na huahelu i ka umikumamaha, umikumamaono, a hiki i ka iwakalua, a hiki i ke kanakolu, a ke kanaha, a ke kanalima, a ke kanaono, a hiki i ka haneri....

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În perioada 24-25 aprilie 2010 s-a desfăşurat A Şasea Conferinţă Internaţională în Teoria Numerelor şi Noţiuni Smarandache la Universitatea Normală din Tianshui, China. Organizatorii conferinţei au fost prof. univ. dr. Zhang Wenpeng de la Universitatea Nordvest din Xi’an şi prof. univ. dr. Wangsheng He de la Universitatea Normală din Tianshui. Lucrările conferinţei au fost publicate într-un volum special în care se găsesc şi articole matematice despre noţiuni legate de cercetările omului de ştiinţă roman, Florentin Smarandache, precum: semigrupuri, inele neasociative, funcţii aritmetice, şi conjecturi sau probleme Smarandache etc. Cartea poate fi descărcată din site-ul. During the period 24 to 25 April 2010 was conducted Sixth International Conference on Number Theory and Smarandache Notions of Tianshui Normal University, China. Conference organizers were prof. Dr. Zhang Wenpeng together from Northwest University in Xi'an and prof. Dr. Wangsheng He Tianshui Normal University. The conference proceedings were published in a special volume that are mathematics articles about concepts and research related to Romanian scientist, Flore...

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În loc de prefaţă – de Ion Pătraşcu .................................... 8 I. Pe aripile... zborului, în Dayton – Ohio! ........................ 11 . „Înaripare” spre Dayton ............................................. 12 . DWF – marele „nod aerian” ...................................... 13 . Conferinţă de... 1 Mai! ............................................... 16 . La Muzeul Naţional al Aviaţiei Militare .................... 19 . Paradoxurile Fraţilor Wright ...................................... 28 . Totuşi, cine a zburat primul? ..................................... 26 . „Nebuni” contra curentului ........................................ 28 . „Aripile de liliac” ....................................................... 30 . Bimotorul mamut ....................................................... 32 . Cu avionul priponit pe... gheaţă! ................................ 33 . Motorul cu... aer comprimat! ..................................... 34 . De la motorul cu aburi, la cel cu kerosen ................... 35 . Un inventator ciudat ................................................... 37 . Prototipul avionului uşor ........

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A collection ot papers concerninq Smarandache type functions, numbers, sequences, inteqer alqoritbms, paradoxes, experimental qeometries, alqebraic structures, neutrosophic probability, set, and loqic, etc. is published this year....

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Florentin Smarandache, a lliathematician from Eastern Europe, escaped fran his country because the communist authorities had prohibited the publication of his resea~ch papers and his participation in international congresses. After two years of waiting in a political ~efugee camp in Turkey, he emigrated to the united states. As research workers, receiving our co-worker, we decided to publish a selection of his papers....