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The purpose of this book is to postulate some theories and test them numerically. Estimation is often a difficult task and it has wide application in social sciences and financial market. In order to obtain the optimum efficiency for some classes of estimators, we have devoted this book into three specialized sections: Part 1. In this section we have studied a class of shrinkage estimators for shape parameter beta in failure censored samples from two-parameter Weibull distribution when some 'apriori' or guessed interval containing the parameter beta is available in addition to sample information and analyses their properties. Some estimators are generated from the proposed class and compared with the minimum mean squared error (MMSE) estimator. Numerical computations in terms of percent relative efficiency and absolute relative bias indicate that certain of these estimators substantially improve the MMSE estimator in some guessed interval of the parameter space of beta, especially for censored samples with small sizes. Subsequently, a modified class of shrinkage estimators is proposed with its properties. Part2. In this section we h...

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... M. Khoshnevisan, S. Saxena, H. P. Singh, S. Singh, F. Smarandache RANDOMNESS AND OPTIMAL ESTIMATION IN DATA SAMPLI... ...RE Cut-off Point 2 M. Khoshnevisan, S. Saxena, H. P. Singh, S. Singh, F. Smarandache RANDOMNESS AND OPTIMAL ESTIMATION IN DATA SAMPLI... ...artment of Mathematics and statistics.University of Saskatchewan, Canada. Dr. Florentin. Smarandache, Department of Mathematics, UNM, USA. ... ...Mathematics and statistics.University of Saskatchewan, Canada. Dr. Florentin. Smarandache, Department of Mathematics, UNM, USA. Ameri... ...ks can be downloaded from our E-Library of Science: http://www.gallup.unm.edu/~smarandache/eBooks-otherformats.htm This book has been peer re... ...a P. Singh 1 , Sharad Saxena 1 , Mohammad Khoshnevisan 2 , Sarjinder Singh 3 , Florentin Smarandache 4 1 School of Studies in Statistics, Vikram ... ...ling Mohammad Khoshnevisan 1 , Housila P. Singh 2 , Sarjinder Singh 3 , Florentin Smarandache 4 1 School of Accounting and Finance, Gri... ...sence of Measurement Errors Mohammad Khoshnevisan 1 , Housila P. Singh 2 , Florentin Smarandache 3 1 School of Accounting and Finance, Griffi... ... by Housila P. Singh, Sharad Saxena, Mohammad Khoshnevisan, Sarjinder Singh, Florentin Smarandache …………………………………………………….…..5 A General Class o...

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Abstract. The goal of this paper is to experiment new math concepts and theories, especially if they run counter to the classical ones. To prove that contradiction is not a catastrophe, and to learn to handle it in an (un)usual way. To transform the apparently unscientific ideas into scientific ones, and to develop their study (The Theory of Imperfections). And finally, to interconnect opposite (and not only) human fields of knowledge into a.s-heterogeneous-as-possible another fields. The author welcomes any co=ents, notes, articles on this paper and/or the 120 open questions bothering him, which will be published in a collective monograph about the paradoxist mathematics....

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The "Paradoxist Mathematics" may be understood as Experimental Mathematics, NonMathematics, or even Anti-Mathematics: not in a nihilistic way, but in positive one. The truly innovative researchers will banish the old concepts in oder of check, by heuristic processes, some new ones: their opposites. Don't simply follow the crowd, and don't accept to be manipulated by any (political, economical, social, even scientific, or artistic, cultural, etc.) media! Learn to conradict everuthing and everybody!! "Duibito, ergo cogito; cogito, ergo sum", said Rene Descartes, "I doubt, therefore I think; I think, therefore I exist" (metaphysical doubt). See what happens if you deny the classics' theory?...

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...n the Number Theory .82 -- Contributii la Studiul unor Functii §i Conjecturi in Teoria Numerelor .85 -- "The Function that You Bear its Name" .112 -- Smarandache Type Functions Obtained by Duality .113 -- Func!;ii Analitice .129 -- Funct;ii Prime §i Coprime .137 -- Asupra unor Conjecturi §i Probleme Nerezolvate Referitoare la 0 Funct;ie in Teoria l'\umerelor 138 -- K-Divis...

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...Professor Florentin Smrandache is invited to spend a period of three months time at the Research Institute of Extension Engineering at Guangdong University of Technology in China in order to conduct research on extenics....

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Cu moralul extrem de ridicat, alerg pe autostrada I-40 din Gallup spre aeroportul din Albuquerque. Urlă muzica. Ferestrele deschise. Muzică populară românească, din Banat şi Oltenia, la casetă. Am înregistraţi şi pe cântăreţii mei din Bălceşti: Vasile Oprea (Vasilică a lu’ Tirina, vecinul meu), Mărin Covrig (coleg de şcoală primară şi generală), Gheorghe Lupu (mai mare cu doi ani ca mine, stătea peste drum de casa mea)....

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Application / 3 Invitation / 8 Extensica. Fotojurnal instantaneu din Canton / 9 Certificate / 170 Letter / 171

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This book aims to assist social scientists to analyze their problems using fuzzy models. The basic and essential fuzzy matrix theory is given. The book does not promise to give the complete properties of basic fuzzy theory or basic fuzzy matrices. Instead, the authors have only tried to give those essential basically needed to develop the fuzzy model. The authors do not present elaborate mathematical theories to work with fuzzy matrices; instead they have given only the needed properties by way of examples. The authors feel that the book should mainly help social scientists who are interested in finding out ways to emancipate the society. Everything is kept at the simplest level and even difficult definitions have been omitted. Another main feature of this book is the description of each fuzzy model using examples from real-world problems. Further, this book gives lots of references so that the interested reader can make use of them. This book has two chapters. In Chapter One, basic concepts about fuzzy matrices are introduced. Basic notions of matrices are given in section one in order to make the book self contained. Section two g...

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Preface 4 Dedication 6 Chapter One BASIC MATRIX THEORY AND FUZZY MATRIX THEORY 7 1.1 Basic Matrix Theory 7 1.2 Basic Concepts on Fuzzy Matrices 33 1.3 Basic Concepts on Graphs 47 Chapter Two DESCRIPTION OF SIMPLE FUZZY MODELS AND THEIR APPLICATIONS TO REAL WORLD PROBLEMS 71 2.1 Description of Simple Fuzzy Matrix Model 72 2.2 Definition of Fuzzy Cognitive Maps with real world model representation 146 2.3 Definition and Illustration of Fuzzy Relational Maps 205 2.4 Introduction to Bidirectional Associative Memories (BAM) Model and their Application 238 2.5 Description of Fuzzy Associative Memories (FAM) model and their illustrations 264 2.6 Fuzzy Relational Equations (FRE) and their application 277 REFERENCE 317 INDEX 345 ABOUT THE AUTHORS 352...

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

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This short technical paper advocates a bootstrapping algorithm from which we can form a statistically reliable opinion based on limited clinically observed data, regarding whether an osteo-hyperplasia could actually be a case of Ewing’s osteosarcoma. The basic premise underlying our methodology is that a primary bone tumour, if it is indeed Ewing’s osteosarcoma, cannot increase in volume beyond some critical limit without showing metastasis. We propose a statistical method to extrapolate such critical limit to primary tumour volume. Our model does not involve any physiological variables but rather is entirely based on time series observations of increase in primary tumour volume from the point of initial detection to the actual detection of metastases....

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.......................................6 ASTRONOMY..................................14 1. First Lunar Space Base, project proposal, by V. Christianto, Florentin Smarandache..15 2. On Recent Discovery of New Planetoids in the Solar System and Quantization of Celestial System, by V. Christianto, F. Smarandache..................28 3. Open and Solved Elementary Questions in A...

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

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This short technical paper advocates a bootstrapping algorithm from which we can form a statistically reliable opinion based on limited clinically observed data, regarding whether an osteo-hyperplasia could actually be a case of Ewing’s osteosarcoma. The basic premise underlying our methodology is that a primary bone tumour, if it is indeed Ewing’s osteosarcoma, cannot increase in volume beyond some critical limit without showing metastasis. We propose a statistical method to extrapolate such critical limit to primary tumour volume. Our model does not involve any physiological variables but rather is entirely based on time series observations of increase in primary tumour volume from the point of initial detection to the actual detection of metastases....

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.......................................6 ASTRONOMY..................................14 1. First Lunar Space Base, project proposal, by V. Christianto, Florentin Smarandache..15 2. On Recent Discovery of New Planetoids in the Solar System and Quantization of Celestial System, by V. Christianto, F. Smarandache..................28 3. Open and Solved Elementary Questions in A...

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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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This paper contains exercises and problems of algebra and grouped chapters, the upper classes of secondary schools and coli culture media general. Its purpose is to prepare students from high schools mathematics categories and will be helpful in working independently. Also work can be used for extra school work because the reader will find in it important formulas, theorems, concepts, and basic definitions which are not always included in school textbooks....

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Prezenta lucrare conţine exerciţii §i probleme de algebră, grupate pe capitole, pentru clasele superioare de licee §i §coli medii de cultură generală. Scopul ei este pregătirea matematică a elevilor din liceele de toate categoriile §i va fi utilă în lucrul de sine stătător. De asemenea, lucrarea poate fi folosită pentru lucrul extra§colar, deoarece cititorul va găsi în ea teoreme §i formule importante, noţiuni §i definiţii de bază care nu întotdeauna sunt incluse în manualele §colare....

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In this book authors study and analyze the problem of school dropouts and their life after. The problems can by no means be analyzed by collecting the numerical data. For such data can only serve as information beyond that the data can be of no use, for the school dropouts suffer an environment change after becoming a school dropout. Thus the emotions of the school dropout; is technically involved....

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The basic tools used in the analysis of the problem of school dropout and their life after are described briefly in this chapter. We provide also the references for these concepts. Bart Kosko introduced the Fuzzy Cognitive Maps (FCMs) in the year 1986. Fuzzy Cognitive Maps are fuzzy structures that strongly resemble neural networks, and they have powerful and far-reaching consequences as a mathematical tool for modeling complex systems. FCM was a fuzzy extension of the cognitive map pioneered in 1976 by political scientist Robert Axelord, who used it to represent knowledge as an interconnected, directed, bilevel-logic graph....

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Preface 5 Chapter One INTRODUCTION 7 Chapter Two BASIC CONCEPTS 21 Chapter Three CAUSES OF SCHOOL DROPOUTS – A MATHEMATICAL ANALYSIS 35 Chapter Four SCHOOL DROPOUTS AS CHILD LABOURERS 59 Chapter Five SCHOOL DROPOUTS AS RAG PICKERS USING FUZZY MODELS 79 Chapter Six PERFORMANCE ASPECTS OF SCHOOL STUDENTS USING RULE BASED CONTROL SYSTEM 89 Chapter Seven MIGRATION OF PARENTS AND THE SCHOOL DROPOUTS A STUDY USING THE FUZZY RELATIONAL MAPS MODEL 99 Chapter Eight THE IMPACT OF MISSIONARY INTERVENTIONS ON THE EDUCATION AND REHABILITATION OF DEPRIVED CHILDREN – A FUZZY ANALYSIS 117 Chapter Nine CONCLUSIONS AND SUGGESTIONS 129 FURTHER READING 139 INDEX 143 ABOUT THE AUTHORS 145...

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This book has five chapters. In Chapter I, we give a brief description of the sixteen sutras invented by the Swamiji. Chapter II gives the text of select articles about Vedic Mathematics that appeared in the media. Chapter III recalls some basic notions of some Fuzzy and Neutrosophic models used in this book. This chapter also introduces a fuzzy model to study the problem when we have to handle the opinion of multiexperts. Chapter IV analyses the problem using these models. The final chapter gives the observations made from our study....

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We then remove the common factor if any from each and we find x + 1 staring us in the face i.e. x + 1 is the HCF. Two things are to be noted importantly. (1) We see that often the subsutras are not used under the main sutra for which it is the subsutra or the corollary. This is the main deviation from the usual mathematical principles of theorem (sutra) and corollaries (subsutra). (2) It cannot be easily compromised that a single sutra (a Sanskrit word) can be mathematically interpreted in this manner even by a stalwart in Sanskrit except the Jagadguru Puri Sankaracharya. We wind up the material from the book of Vedic Mathematics and proceed on to give the opinion/views of great personalities on Vedic Mathematics given by Jagadguru. Since the notion of integral and differential calculus was not in vogue in Vedic times, here we do not discuss about the authenticated inventor, further we have not given the adaptation of certain sutras in these fields. Further as most of the educated experts felt that since the Jagadguru had obtained his degree with mathematics as one of the subjects, most of the results given in book on Ve...

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Preface 5 Chapter One INTRODUCTION TO VEDIC MATHEMATICS 9 Chapter Two ANALYSIS OF VEDIC MATHEMATICS BY MATHEMATICIANS AND OTHERS 31 2.1 Views of Prof. S.G.Dani about Vedic Mathematics from Frontline 33 2.2 Neither Vedic Nor Mathematics 50 2.3 Views about the Book in Favour and Against 55 2.4 Vedas: Repositories of Ancient Indian Lore 58 2.5 A Rational Approach to Study Ancient Literature 59 2.6 Shanghai Rankings and Indian Universities 60 2.7 Conclusions derived on Vedic Mathematics and the Calculations of Guru Tirthaji - Secrets of Ancient Maths 61 Chapter Three INTRODUCTION TO BASIC CONCEPTS AND A NEW FUZZY MODEL 65 3.1 Introduction to FCM and the Working of this Model 65 3.2 Definition and Illustration of Fuzzy Relational Maps (FRMS) 72 3.3 Definition of the New Fuzzy Dynamical System 77 3.4 Neutrosophic Cognitive Maps with Examples 78 3.5 Description of Neutrosophic Relational Maps 87 3.6 Description of the new Fuzzy Neutrosophic model 92 Chapter Four MATHEMATICAL ANALYSIS OF THE VIEWS ABOUT VEDIC MATHEMATICS USING FUZZY MODELS 95 4.1 Views of students about the use of Vedic Mathematics in their c...

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We have used the 2-adaptive fuzzy model having the two fuzzy models, fuzzy matrices model and BAMs viz. model to analyze the views of public about HIV/ AIDS disease, patient and the awareness program. This book has five chapters and 6 appendices. The first chapter just recalls the definition of four fuzzy models used in this book and gives illustration of some of them. Chapter two introduces the new n-adaptive fuzzy models. Chapter three uses for the first time 2 adaptive fuzzy models to study psychological and sociological problems about HIV/AIDS. Chapter four gives an outline of the interviews. Chapter five gives the suggestions and conclusion based on our study. Of the 6 appendices four of them are C-program made to make the working of the fuzzy model simple....

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

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Chapter One SOME BASIC FUZZY MODELS WITH ILLUSTRATIONS 1.1 Fuzzy matrices and their applications 9 1.2 Definition and illustration of Fuzzy Relational Maps (FRMs) 16 1.3 Some basic concepts of BAM with illustration 20 1.3.1 Some basic concepts of BAM 22 1.3.2 Use of BAM Model to study the cause of vulnerability to HIV/AIDS and factors for migration 28 1.4 Introduction to Fuzzy Associative Memories (FAM) 35 Chapter Two ON A NEW CLASS OF N-ADAPTIVE FUZZY MODELS WITH ILLUSTRATIONS 2.1 On a new class of n-adaptive fuzzy models with illustrations 39 2.2 Some special n-adaptive models 49 Chapter Three USE OF 2-ADAPTIVE FUZZY MODEL TO ANALYZE THE PUBLIC AWARENESS OF HIV/AIDS 3.1 Study of the psychological and social problems the public have about HIV/AIDS patients using CETD matrix 52 3.2 Use of 2 adaptive fuzzy model to analyze the problem 72 Chapter Four PUBLIC ATTITUDE AND AWARENESS ABOUT HIV/AIDS 4.1 Introduction 77 4.2 Interviews 81 Chapter Five CONCLUSIONS 167 Appendix 1. Questionnaire 177 2. Table of Statistics 191 3. C-program for CETD and RTD Matrix 198 4. C-program for FRM 202 5. C-program for CFRM 2...

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The new concept of fuzzy interval matrices has been introduced in this book for the first time. The authors have not only introduced the notion of fuzzy interval matrices, interval neutrosophic matrices and fuzzy neutrosophic interval matrices but have also demonstrated some of its applications when the data under study is an unsupervised one and when several experts analyze the problem....

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1.2 Definition of Fuzzy Cognitive Maps In this section we recall the notion of Fuzzy Cognitive Maps (FCMs), which was introduced by Bart Kosko in the year 1986. We also give several of its interrelated definitions. FCMs have a major role to play mainly when the data concerned is an unsupervised one. Further this method is most simple and an effective one as it can analyse the data by directed graphs and connection matrices. DEFINITION 1.2.1: An FCM is a directed graph with concepts like policies, events etc. as nodes and causalities as edges. It represents causal relationship between concepts. Example 1.2.1: In Tamil Nadu (a southern state in India) in the last decade several new engineering colleges have been approved and started. The resultant increase in the production of engineering graduates in these years is disproportionate with the need of engineering graduates. ...

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Dedication 5 Preface 6 Chapter One BASIC CONCEPTS 1.1 Definition of Interval Matrices and Examples 8 1.2 Definition of Fuzzy Cognitive Maps 9 1.3 An Introduction to Neutrosophy 13 1.4 Some Basic Neutrosophic Structures 16 1.5 Some Basic Notions about Neutrosophic Graphs 22 1.6 On Neutrosophic Cognitive Maps with Examples 28 1.7 Definition and Illustration of Fuzzy Relational Maps (FRMs) 33 1.8 Introduction to Fuzzy Associative Memories 40 1.9 Some Basic Concepts of BAM 43 1.10 Properties of Fuzzy Relations and FREs 49 1.11 Binary Neutrosophic Relations and their Properties 56 Chapter Two INTRODUCTION TO FUZZY INTERVAL MATRICES AND NEUTROSOPHIC INTERVAL MATRICES AND THEIR GENERALIZATIONS 2.1 Fuzzy Interval Matrices 68 2.2 Interval Bimatrices and their Generalizations 76 2.3 Neutrosophic Interval Matrices and their Generalizations 92 Chapter Three FUZZY MODELS AND NEUTROSOPHIC MODELS USING FUZZY INTERVAL MATRICES AND NEUTROSOPHIC INTERVAL MATRICES 3.1 Description of FCIMs Model 118 3.2 Description and Illustration of FRIM Model 129 3.3 Description of FCIBM model and its Generalization 139 3.4 FRIBM model and i...

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...This second book devoted on advances and applications of Dezert-Smarandache Theory (DSmT) for information fusion collects recent papers from different researchers working in engineering and mathematics. Part 1 of this book presents the current state-of-the-art on theoretical investigation...

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...Preamble iii Prefaces v Part I Advances on DSmT 1 Chapter 1 Proportional Conflict Redistribution Rules for Information Fusion 3 by Florentin Smarandache and Jean Dezert 1.1 Introduction . . . . . . . . . . . 3 1.2 The principal rules of combination . . . . . . . 6 1.2.1 Notion of total and partial conflicting masses . . . . . 6 1.2.2 The conjunctive ...