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...iving by preparing school­people and students (1986­1988). From this short sequence of didactic activities during the "golden days" is brought to ligh... ...ppeared America, paradisul diavolului (America, the Paradise of the Devil),journal of an emigrant, edited by Editura " Aius" Craiova. The majority of ... ... 1991), New York, Colorado (1991, 1992), and Seoul (1991). He also has two journals describing his emigration, with over 1000 pages and four plays, so... ... his literary steps, one can distinguish three: the prose ­ comprising the journal and the plays ­ the paradoxist movement that he promoted, and the p... ...ose in Romania consists only of the book America, the Devil's Paradise ­ a journal of emigration ­ covering the period between 23 March 1990, when he ... ...ved by him after the experience gained within the totalitarian system. The journal reveals lived facts, a concrete reality, with quite a few elements ...

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...[49] and (2001), [50] this constitutes its first appearance in a peer-review journal. The relativistic parameters (Section 3) and particle-fields mo... ...ies: an even-number (α-particle) progression in nucleo protons and Fibonacci sequence in the outer proton, (octet and face) sites. The projection of ... ...of light in refractive transmission is attributed to an absorption-emission sequence of the light by atoms of the matter field; in which, successive... ...ble) scale. SQP-1 Conclusions in MT To summarize, the absorption-emissive sequence in refraction imparts no visible atomic field to the radiation,...

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...ew and not mould or manipulate it. So a shrewd reader may understand that the sequence of answers and questions are also not stereotypes. It was l... ... you think about sex education? : 123. What do you think about yellow journalism and pornographic/blue films? : 124. Different views pr... ...hts at the Workplace: Emerging Challenges and Legal Intervention. The Indian Journal of Social Work, Vol.18 (1). 9. Bandhari, A. (1990) Women an... ...13. Bharat, S. (1995) HIV/AIDS and the Family in Care and Support. The Indian Journal of Social Work, Vol.56 (2). 14. Bollinger, R.C., Tripathy S... ...nting, S. M. et al. (1999) Poor Women Living with HIV: Self Identified Needs, Journal of Community Health Nursing, Vol. 16, 41-52. 20. Cash, K. (... ...ficiency Syndrome: A Historical Perspective on Recent Developments. American Journal of Medicine, Vol. 96, 439-450. 41. Hebb, D.O., (1949) The O...

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...sionmark 200 2nd Ave. SE Cedar Rapids, IA 52401 Chapter 1 Smarandache Sequences In the time since it was first published[ 1], the Smarandache fu... ...order. In this first chapter, we will concentrate on notions that involve sequences, moving on to other, more specific points in the second. The fi... ...t problem we will deal with is number (6) in [5]. Smarandache permutation sequence: 12,1342.135642, 13578642, 1357910864~ 135791112108642,. Or as a... ...)(2n)(2n-2)(2n-4) 642 where SPS is an acronym for Smarandache Permutation Sequence. Note on notation: As a general principle, acronyms will be creat... ...Note on notation: As a general principle, acronyms will be created for all sequences. Consult appendix I for a complete list of all acronyms, the ful... ...ion in the Smarandache Archives at Arizona State Lniversity 9. H ~elson, Journal of Recreational :\1athematics, Vol. 20,1988. 73 In this book, we...

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...I have met the Smarandache's world for the first time about one year ago reading some articles and problems published in the Journal of Recreational Mathematics. From then on I discovered the interesting American Research Press web site dedicated to the Smarandache notions and held by Dr. Perez (address: http://www.gallup.unm.edu/~smarandache/), th...

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...A SET OF NEW SMARANDACHE FUNCTIONS, SEQUENCES AND CONJECTURES IN NUMBER THEORY Felice Russo AMERICAN RESEARCH P... ...ime about one year ago reading some articles and problems published in the Journal of Recreational Mathematics. From then on I discovered the interest... ...ddress: http://www.gallup.unm.edu/~smarandache/), the Smarandache Notions Journal always published by American Research Press, and several books on c... ...functions, new conjectures, solved/unsolved problems, new Smarandache type sequences and new Smarandache Notions in number theory. Moreover a chapter ... ...respectively) values. For the first 1000 values of Zt(n) the largest found sequences have k=5 and k=4 respectively. Example: Z... ...repeated application of the Zt function. An n-cycle, instead, is a finite sequence of points 1 , 1 0 , - n Y Y Y K such that, under the function Zt,... ...Totient numbers. Problem 37. Is the number 0.1243549107585.... where the sequence of digits is Zt(n) for 1 ‡ n an irrational or trascendental number... ...ults about four Smarandache U-product sequences, Smarandache Notions Journal, Vol.11 1,2,3 Spring 2000 [7] P. Ribenboim, The book of prime numbe... ...ults about four Smarandache U-product sequences, Smarandache Notions Journal, Nov. 1999 [5] E. Weisstein, CRC Concise Encyclopedia of Mathematic...

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...Jebreel Karama On the m -th power residue of n 25 Li Junzhuang and Zhao Jian Generalization of the divisor products and proper divisor products sequences 29 Liang Fangchi The science of lucky sciences 33 Jon Perry Smarandache Sequence of Unhappy Numbers 37 Muneer Jebreel Karama On m -th power free part of an integer 39 Zhao Xiaopeng and Ren Zhibin On two ...

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...n the primitive numbers of power P and its mean value properties 36 D. Torres and V. Teca : Consecutive, reversed, mirror, and symmetric Smarandache sequence of triangular numbers 39 D. Ren : On the square-free number sequence 46 T. Ramaraj and N. Kannappa : On ¯nite Smarandache near-rings 49 X. Kang : Some interesting properties of the Smarandache function 52 L. Mao ...

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...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 combi...

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...Sequences on Graphs with Symmetries Linfan Mao Chinese Academy of Mathematics and System Science, Beijing, 10080, P.R.China Beijing Institute of Civil Engineering and Architecture, Beijing, 100044, P.R.China E-mail: maoli...

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...Contents Lucas Graceful Labeling for Some Graphs BY M.A.PERUMAL, S.NAVANEETHAKRISHNAN AND A.NAGARAJAN . . . . . 01 Sequences on Graphs with Symmetries BY LINFAN MAO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 Supermagic Coverings of Some Simple Graphs BY P.JEYANTHI AND P.SELVAGOPAL . . . . . . . . . . . . . ....

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...ossible. Short articles are preferable. All that has been accepted for the online issue of Progress in Physics is printed in the paper version of the journal. To order printed issues, contact Chief Editor. This journal is non-commercial, academic edition. It is printed from private donations....

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...ated Themes from Mathematics PROGRESSINPHYSICS A quarterly issue scientifc journal, registered with the Library of Congress (DC). This journal is peer... ...nt) ISSN: 1555-5615 (online) 4 issues per annum Electronic version of this journal: http://www.geocities.com/ptep_online To order printed issues of th... ...rnal: http://www.geocities.com/ptep_online To order printed issues of this journal, con- tact the Editor in Chief. Chief Editor Dmitri Rabounski rabou... ... used in other publica- tions must include an appropriate citation of this journal. Authors of articles published in Progress in Physics retain their ... ...periments [61], [73] whereas a minimal angular velocity has important con- sequences in galactic rotation measurements. The role of the Machian princi... ...e non-cancelled fractions). Their distribution in the plane is defned by a sequence of numbers forming a rational series (Fig. 1). This simplest drawi... ...n this way has analogous se- quences of the (k+1)-th rank and higher. Such sequences fll the whole set of rational numbers. To consider the simplest c... ...must be determined in such a way as to provide a means by which an infnite sequence of particular solutions can be readily constructed. It is from suc... ...al solution must not only result in a means for construction of an infnite sequence of particular solutions, it must also naturally produce the soluti...

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...tions, as well as semigroup-valued multiplicative functions. Chapter 4 discusses certain divisibility problems or questions related especially to the sequence of prime numbers. The author has solved various conjectures by Smarandache, Bencze, Russo etc.; see especially articles 4,5,7,8,9,10. Finally, Chapter 5 studies certain irrationality criteria; some of them giving int...

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...ses cer- tain divisibility problems or questions related especially to the sequence of prime numbers. The author has solved various conjectures by Sma... ...e proportion of the notes appearing here have been earlier published in 2 journals in Romania or Hungary (many written in Hungarian or Romanian). We ... ... English versions. Some papers appeared already in the Smarandache Notions Journal, or are under publication (see Final References). The book is concl... ...lation for the function f(x) = ( x + 1) 1=x . For the monotonicity of the sequencesff 1 (k + 1) f 1 (x)g,ff(k + 1) f(k)g it is su cient to study th... ...roved ([6]) that for x 7, the function f(x) is strictly concave. Thus the sequence ( n+1 p (n + 1)! n p n!) is strictly decreasing (answering in thi... ...s totient function, Math. Student 35(1967), 79-80. 15. Smarandache Notions Journal (collection). 119 21 On the diophantine equation a 2 +b 2 = 100a +... ...e the following relations which have appeared in the Smarandache Functions Journal: Let p be a prime number. Then S(p x ) S(p y ) for x y (1) S(p a ... ...ment of 2) for n =p. Then (p) =p + 1 and S(p + 1) p ! 0, wherefpg is the sequence constructed there. 5) Let ’(n) be the Enter totient function. Then... .... Thus (S(p!))p! p!S(p!) S(p!) (p!) p!p = (p!) p! !1: Thus, for the sequencefng =fp!g, the results follows. 135 Bibliography 1. J. S andor, O...

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...PREFACE by Steven James Bartlett xiii SAPPHO’S JOURNAL FOREWORD by Willis Barnstone 3 SAPPHO’S JOURNAL 5 CHRIST’S JOURNAL 155 LEONARDO DA VINCI’S JOURNAL 221 SHAKESPEARE’S JOURNAL 343 LINCOLN’S JOURNAL 511 ABOUT THE AUTHOR 621 COLOPHON 625...

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... VOICES FROM THE PAST A Quintet: SAPPHO’S JOURNAL CHRIST’S JOURNAL LEONARDO DA VINCI’S JOURNAL SHAKESPEARE’S JOURN... ...T’S JOURNAL LEONARDO DA VINCI’S JOURNAL SHAKESPEARE’S JOURNAL LINCOLN’S JOURNAL BOOKS BY PAUL ALEXANDER BARTLETT NOVELS VOIC... ...PAUL ALEXANDER BARTLETT NOVELS VOICES FROM THE PAST: Sappho’s Journal ` Christ’s Journal ` Leonardo da Vinci’s Journal Shakespeare’s Jou... ...s Journal ` Leonardo da Vinci’s Journal Shakespeare’s Journal ` Lincoln’s Journal When the Owl Cries Adiós Mi México Forward, Children! ... ... Artist’s Record VOICES FROM THE PAST A Quintet: SAPPHO’S JOURNAL CHRIST’S JOURNAL LEONARDO DA VINCI’S JOURNAL SHAKESPEARE’S JOURN... ...atise is packed in the third trunk—the one with the smashed lock. I must sequence my drawings: 1 - Skin 2 - Muscles 3 - Tendons 4 - Bones I... ...d it is true I can divide Fibonacci’s number (after the fourteenth in his sequence) by the next highest in number: it is precisely .618034 to 1. .6... ...now it’s late. Tomorrow I will arrange fifteen figures, fifteen nudes, in sequence. On the basis of those drawings I will make various comparisons, ...

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...nction ¼ 2 (n)9 2 A2. Three formulae for n-thprimeandsix formulae for n-thtermoftwinprimes 98 A3. Explicit formulae for the n-th term of the twin prim... ...{ the twin primes counting function, i.e., ¼ 2 (n)denotesthe number of primes p such that p·n and p+2isalsoaprime; p 2 (n){n-th term of the twin prime... ...31;::: 9 1. ON THE 2-ND SMARANDACHE'S PROBLEM 1 The second problem from [13] (see also 16-th problem from [24]) is the following: Smarandache circula... ... the largest natural number strongly smaller than the real (positive) number x. For instance, ]7:1[=7, but ]7[=6. Let f(n)bethen-th member of the abov... ...:: 0001100011000::: ::: 0011000001100::: ::: 0 110000000110 ::: ::: 0011000001100::: ... ... 2 The results in this section are taken from [38] 13 Thi... ...che's Problems. Amer- ican Research Press, Lupton, 1999. [3] Atanassov K., Remarks on some of the Smarandache's prob- lems. Part 1. Smarandache Notion... ...e l'Academie Bulgare des Sciences, Vol. 54, 2001, No. 7, 5-6. [5] Atanassov K. On the 20-th and the 21-st Smarandache's prob- lems. Smarandache Notion... ...ems. Smarandache Notions Journal, Vol. 12, No. 1-2-3, Spring 2001, 111-113. [6] Atanassov K. On four prime and coprime functions. Smaran- dache Notion... .... Smaran- dache Notions Journal, Vol. 12, No. 1-2-3, Spring 2001, 122- 125. [7] Atanassov, K. On the 17-th Smarandache's problem. Smaran- dache Notion...

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... pay for information (with precious few exceptions, like the "Wall Street Journal"'s electronic edition). Moreover, the Internet, with 3 billion page... ...shing Service is about empowerment. The price of scholarly, peer- reviewed journals has skyrocketed in the last few years, often way out of the limite... ...ve and authenticated knowledge has declined as the number of professional journals has proliferated. This is not to mention the long (and often cruc... ...tomated and very short. The system includes a long series of thematic journals. These journals self-assemble, in accordance with the call number... ... with certain call numbers will automatically be included in the relevant journals. The fly in the ointment is the absence of peer review. As t... ...friendliness (i.e., the interfaces require specific knowledge and specific sequences of specific commands). Even the most "user-friendly" interface ...

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...t result. This might be comparable to approximating the limit of a convergent sequence, calculating more and more terms, or by calculating the limit... ...4/935277052-999. [28] Le, Charles T., The Smarandache Class of Paradoxes, in “Journal of Indian Academy of Mathematics”, Bombay, India, No. 18, 53-... ...ss, NJ, 1976. [38] Shafer, Glenn, The Combination of Evidence, International Journal of Intelligent Systems, Vol. I, 155-179, 1986. [39] Smarand... ...just know that the cardinality numbers of follow the integers of the Dedekind’s sequence minus one when Card increases. Examples 1. If we consider (em... ...ations in the mathematical community. Cardinality numbers follow the Dedekind’s sequence (minus one), i.e. when Card . 4.3 General basic assignment n... ...pp. 325 339, 1967. [12] Dempster A.P.,“A Generalization of Bayesian Inference”, Journal of the Royal Statistical Society, Serie B, Vol. 30, pp. 205 24... ...is D., Prade H.,“On the Unicity of Dempster Rule of Combination”, International Journal of Intelligent Sys tems, Vol. 1, pp. 133 142, 1986. [17] Dubo... ...Functions”, Comm. Pure Appl. Math., 23, pp. 299 312, 1970. [55] Sloane N.J.A., “Sequences A006826/M2469, A007153/M3551, and A014466”, in “An On Line V... ...153/M3551, and A014466”, in “An On Line Version of the Encyclopedia of Interger Sequences” (http://www.research.au.com/˜njas/sequences/eisonline.html)...

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... Smarandache prime function Chapter 5: The general term of the prime number sequence and the Smarandache prime function Chapter 6:Expressions of th... ...ller: To Enjoy is a Permanent Component of Mathematics. SMARANDACHE NOTIONS JOURNAL Vol. 9 No 1-2, (1998) pp 21-26 8 Chapter... ...ller: To Enjoy is a Permanent Component of Mathematics. SMARANDACHE NOTIONS JOURNAL VOL 9:, No. 1-2 (1998) pp 21-26. ... ... all positive integer values of k?. Reference: [1] Smarandache Notions Journal, Vol. 9, No. 1-2, (1998), pp. 21-26. ... ...1997. 18 Chapter 5: The general term of the prime number sequence and the Smarandache prime function. Let is consider the funct... ...epends on n , this expression will be the general term of the prime numbers sequence, since π is in function with G and G does with d(i) that is exp... ...o be very probable; we will have that the general term of the prime numbers sequence is: ∑                        ... ...cha Fleuren, “Smarandache Factors and Reverse Factors”, Smarandache Notions Journal, Vol. 10, www.gallup.unm.edu/~smarandache/ 2. Chris Caldwell, ...

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...ty traits, or behaviour patterns. But too little is known to establish irrefutable sequences of causes-and-effects. Even less is proven about the i... ...ity traits, or behavior patterns. But too little is known to establish irrefutable sequences of causes-and-effects. Even less is proven about the i... ...ecause a minimum number of axioms and hypotheses yield, in an inexorable deductive sequence, everything else known in the field the theory pertains... ...nt to foreign RND ventures and to governments on macro-economic matters. Freelance journalist and analyst for various media in the USA. 1990 to 19... ...2003 Senior Business Correspondent for United Press International (UPI). Web and Journalistic Activities Author of extensive Web sites in: – P...

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...is the progeny of Charles Dow of Dow Jones fame and the founder of the "Wall Street Journal". He devised a method to discern cyclical patterns in sh... ... Dr. Sam Vaknin Also published by United Press International (UPI) The Wall Street Journal has recently published an elegiac list: "Twenty years a... ...to monopolies, attract less attention from trustbusters. Quoted in the Wall Street Journal on March 8, 1999, Galambos wrote: "Oligopolistic competi... ...s University's Center for the Study of Drug Development, quoted in The wall Street Journal. In a paper titled "If Cartels Were Legal, Would Firms F... ... hazard" are frequently ill- informed and haphazard. Even the venerable Wall Street Journal fell in this fashionable trap. It labeled the Long Term ... ..., to obtain any meaningful data, one has to observe behaviour in time, to obtain a sequence of reactions and actions. To isolate, observe and manip... ...mental variables and study human interactions. No snapshot can approximate a video sequence where humans are concerned. Return Financial Crises, ... ...nature itself. Every economic cycle invariably starts with inflation. The previous sequence having ended – and the new one just begun – the environ...

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... 1998. 2. R. Padilla, Smarandache Algebraic Structures, Smarandache Notions Journal, USA, Vol.9, No. 1-2, 36-38, (1998). 3. R. Padilla. Smarand... ....B.Vasantha Kandasamy, New classes of finite groupoids using Z n , Varahmihir Journal of Mathematical Sciences, Vol 1, 135-143, (2001). 45 ... ....B.Vasantha Kandasamy, New classes of finite groupoids using Z n , Varahmihir Journal of Mathematical Sciences, Vol 1, 135-143, (2001). 69 ... ....B.Vasantha Kandasamy, New classes of finite groupoids using Z n , Varahmihir Journal of Mathematical Sciences, Vol 1, 135-143, (2001). 4. W. B. V... ...quential operations. Thus, it is reasonable to consider the set of all finite sequences of elements of the set A including the empty sequence Λ. ... ...B. Vasantha Kandasamy, New classes of finite groupoids using Z n , Varahmihir Journal of Mathematical Sciences, Vol. 1, 135-143, (2001). 4. W. B. ...

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...h Perez of the American Research Press, editor of the Smarandache Notions Journal, a close research associate and inspiration-provider par excellenc... ...eal of R and 0 < α < 1. DEFINITION 1.4.9: A finite strictly increasing sequence of prime ideals of a ring R, P 0 ⊂ P 1 ⊂ P 2 ⊂ …⊂ P n is call... ...ver some set X. X X F X g N h f 117 DEFINITION 1.8.34: A finite sequence N = N 0 ⊃ N 1 ⊃ N 2 ⊃ … ⊃ N t = {0} of sub- binear-rings N i ... ... {0} of sub- binear-rings N i of the binear-ring N is called the binormal sequence of N if and only if for all i ∈ {1, 2, …, t}, N i is a bi-ideal ... ...n all the N i 's are bi-ideals of the binear-ring N, we call the binormal sequence an bi-invariant sequence. DEFINITION 1.8.35: Let P be a bi-ide... .... i. λ ∈ F 2 (D). ii. (a) λ ∈ F 1 (D) and (b) given d ∈ D there exists sequences {a n }, {b n } in D such that d = a n b n and ) d ( )} b ( ), ...

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...emerged. Actual Causality The Dynamic of Actual Causality is a connected sequence of events. Every cause is an effect, and every effect is a c... ... cause. It is the Dynamic which actually causes things to happen in a strict sequence. Cause and Effect can also be defined by Newton’s Third Law ... ...use-effect-cause-effect-cause-effect-cause-effect-cause effect By tracing a sequence of events backwards: forensic experts can go into a burned ou... ...One: The Universe 2 make them tip over in one direction in a strict causal sequence of events. You can also tip them over in the opposite direct... ... did not appear by magic out of nowhere; they were created in a strict causal sequence. Our Universe existed first as a Causal Infinite Totality th... ...hment, his Theory of Relativity would never have been published in scientific journals and his ideas would never have gained worldwide fame. After ... ...ot talk back to you… and cannot attack you. And then publish it in a Science Journal as a bunch of facts with no opinion, no conclusion, no underst... ...ot allowed to publish their findings or conclusions or opinions in scientific journals. This way nobody can question your dead detached ideas. Do... ... the closed doors of your tiny scientific clique. Then publish it in obscure journals that nobody reads. Only people involved in your specialized ...

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...ing businesses and the nonprofits, as well as government. The book's chapters are sequenced to suit the reader having little or no familiarity with ... ...s delivered to a consuming audience. Indeed, the term "vehicle" is used to mean a journal said to "carry" the article. Abstract products need the ... ...pter 2. In conventional product management, idea generation is only the first of a sequence of R & D steps -concept screening, concept testing, tech... ...er and Greenberg 1978, p. 355). The study produced the following list of issues, sequenced, as before, in order of importance to members: 1. Need... ...ting field. What is perhaps the foremost scholarly vehicle read by marketers, the Journal of Consumer Research, bills itself as "an interdisciplinar... ...on of the idea, or having some capability useful to its marketing. These are then sequenced hierarchically in flowchart format and what results is ... ... Bagozzi, Richard P. 1977. "Structural Equation Models in Experimental Research.” Journal of Marketing Research 14, 209-26. -----. 1975. "Marketin... ... Journal of Marketing Research 14, 209-26. -----. 1975. "Marketing as Exchange.” Journal of Marketing 39, 32-39. -----. 1974. "Marketing as an Org... ...39, 32-39. -----. 1974. "Marketing as an Organized Behavioral System of Exchange." Journal of Marketing 38, 77-81. Bagozzi, Richard P. and M. Franc...

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...illions of professionals - judges, police officers, criminologists, psychologists, journalists, publishers, prosecutors, lawyers, social workers, p... ...ther necessitates the effect, or is a sufficient condition for its occurrence. The sequence is either inevitable, or possible. The meaninglessness ... ...heir true accomplishments. A celebrity is famous for being famous. Of course, such journalists will likely to fall prey to up and coming colleagues... ...e in the past, then eternity would have elapsed up to the present. Thus an infinite sequence would have been completed. Since this is impossible, th... ...obert Merton - quoted in Sigma 3/2001 - described in the Winter 1992 issue of the "Journal of Applied Corporate Finance" the various phases of the ... ...ty traits, or behaviour patterns. But too little is known to establish irrefutable sequences of causes-and-effects. Even less is proven about the i... ...tations, including those related to human life directly. We even issue patents for sequences of human DNA. And people do own forests and rivers and... ...the Government, was the media coerced to publish it by a major advertiser, was the journalist arrested after the publication? The circumstances sur... ...re carefully "selected" for some purpose, within a certain pattern and in a certain sequence. What could that purpose be? Probably, the extension an...

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... simple. DEFINITION 1.1.7: A subnormal series of a group G is a finite sequence H 0 , H 1 , …, H n of subgroups of G such that H i is a norma... ...f H i+1 with H 0 ={e} and H n = G. A normal series of G is a finite sequence H 0 , H 1 , … , H n of normal subgroups of G such that H i ⊂ H... ...ot found in any ring theory texts but only in research papers published by journals. So some of these concepts, which may be really good, do not find... ...asamy W.B., Idempotents in the group ring of a cyclic group, Vikram Math. Journal, Vol. X, 59-73, (1990). 87. Vasantha Kandasamy W.B., Regularly p... ...B., Smarandache Semirings and Smarandache Semifields, Smarandache Notions Journal, American Research Press, Vol. 13, 88-91, (2002). 157. Vasanth...

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...998. 2. R. Padilla, Smarandache Algebraic Structures, Smarandache Notions Journal, USA, Vol.9, No. 1-2, 36-38, (1998). 3. R. Padilla. Smarandac... ... Kandasamy, W. B. Smarandache Semirings and Semifields, Smarandache Notions Journal, Vol. 7, 1-2-3, 88-91, 2001. http://www.gallup.unm.edu/~smarand... ...71. 9. Padilla, R. Smarandache Algebraic Structures. Smarandache Notions Journal, USA, Vol.9, No. 1-2, 36-38, 1998. 10. Padilla, R. Smarandach... ..., 1984. 13. Vasantha Kandasamy, W.B. Semi-idempotents in semigroup rings. Journal of Guizhou Inst. of Tech., Vol. 18, 73 – 74, 1989. 14. Vasan... ...ndasamy, W.B. Idempotents in the group ring of a cyclic group. Vikram Math. Journal, Vol. X, 59-73, 1990. 15. Vasantha Kandasamy, W.B. Filial semi... ...nding chain condition (S-dcc) on S-ideals S i if every strictly decreasing sequence of S-ideals N 1 ⊃ N 2 ⊃ N 3 ⊃… in S is of finite length. The...

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... encouragement given by Dr. Minh Perez, editor of the Smarandache Notions Journal for writing this book-series. As an algebraist, for the past one-y... ...exists an ideal J in N such that N = I + J. DEFINITION 1.6.10: A finite sequence N = N 0 ⊃N 1 ⊃ N 2 ⊃ … ⊃ N n = {0} of subnear- rings N i of N... ... 1 ⊃ N 2 ⊃ … ⊃ N n = {0} of subnear- rings N i of N is called a normal sequence of N if and only if for all i ∈ {1, 2, …, n}; N i is an ideal of... ...m k are juxtaposed and m i, m j, m k, ∈ L. iv. We assume only finite sequence of elements of the form m 1 m 2 …m k ∈ DL. v. m i m j = m j ... ... near-ring are replaced by S-ideals of a near-ring. Smarandache normal sequence and Smarandache invariant sequence are defined by replacing the s... ...te spanning dimension (S-finite spanning dimension) if for any decreasing sequence of Smarandache NS-subsemigroups (S-NS-subsemigroups); X ⊃ X 1 ... ... 44. RAUL, Padilla, Smarandache Algebraic Structures, Smarandache Notions Journal, 9, 36-38 (1998). 45. RAMAKOTAIAH, Davuluri and PRABHAKARA RAO K.... ...0 115. VASANTHA KANDASAMY, W. B., Smarandache loops, Smarandache Notions Journal, 13, 252-258 (2002). http://www.gallup.unm.edu/~smarandache/Loops... ...NDASAMY, W. B., Smarandache semirings and semifields, Smarandache Notions Journal, 13, 88-91(2002). http://www.gallup.unm.edu/~smarandache/SemiRings...

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...is the progeny of Charles Dow of Dow Jones fame and the founder of the "Wall Street Journal". He devised a method to discern cyclical patterns in sh... ...e Mason University - School of Management, and published in the Financial Analysts Journal, Vol. 59, No. 6, pp. 66-74, November/December 2003, yiel... ... from the visitors' gallery - incurring a loss of $10-14 billion. The Wall Street Journal warned naive investors: "Many are looking for technical... ...g term average. Contrast this with an article published in June 1990 issue of the "Journal of Economic History" by Robert Barsky and Bradford De Lo... ... the Lessons of History" published by the Friedberg Mercantile Group, this was the sequence in London in 1720 (the infamous "South Sea Bubble"), an... ...ack arguments arising out of the Central Bank case. As I maintained in the American Journal of Trial Advocacy, the real significance of the Supreme ...

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... input path of υ if i. ν 1 has no input or has only an external input sequence; ii. ν i , 1 < i < r do not belong to any circle of υ; ν 1 is c... ...ome static after L inference interactions unless it has an external input sequence, where L is the length of the longest path of the FCM. The pro... ...ecome static after L inference iterations unless it has an external input sequence, where L is the length of the path. DEFINITION [136]: A vertex... ...200 35. Eden, C., F.Ackerman, and S.Cropper. The Analysis of Cause Maps, Journal of Management Studies, 29 (1992) 309-323. 36. Fuzzy Thought Ampli... ... Markovian Modeling of User's Web Behaviour, Invited Paper, International Journal of Computation Cognition, (http://www.YangSky.com/yangijcc.htm) 1 ... ...ozar, and I. Zigurs. Group Support Systems Approach to Cognitive Mapping, Journal of Management Information Systems, 11 (1994) 31-57. 88. Silva, P... ...omputing Appraoch for Modelling the Supervisory of Manufacturing Systems, Journal of Intelligent and Robotic Systems, 26 (1999) 389-403. 99. Styli...

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...ternal. After we die we eventually enter new bodies and the endless cyclic sequence of birth, life, and death continues on through all eternity. The w... ...us understanding which he could not find among the orthodox whites. In his Journal of 1672, Fox recounts numerous such occurrences. We may take one ac... ... includes all the Buddhas and in effect ultimately all 91. George Fox, The Journal of George Fox, (revised edition) Cambridge University Press, Cambri... ...f such symptoms as consequences of later visions which he discusses in his Journal. 98. I made this diagnosis on the basis of a close reading of his J... ...g, quite alarming. A quick read- ing through of the initial parts of Fox’s Journal indi- cates the desperation which he had reached. At this point the... ...ing a distinction is particularly obvious in the case of George Fox, whose Journal stresses not only severe depressive states but also apparent swings... ...ars to share some dreams with friends, and at one time I was a member of a sequence of small dream groups that met to share and discuss dreams over a ...

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... are allowed to reiterate before the first appearance of some others). The data sequence is described as (A (υ) , B (υ) ), ν∈N, where (A (υ) , B (... ...llowing theorem can be had from [53]. THEOREM 1.15.1. If {W (t)} is a weight sequence of the fuzzy δ rule, then it is a monotone decreasing seque... ...for the reader if need be refer [55]. THEOREM 1.17.1: If {W(t)} is a weight sequence of the fuzzy δ rule J, then it is a monotone decreasing seq... ...{x}) for x ∈ X. We note that α q ~ : ζ (X) → ζ(X). For α ∈ [0, 1] and x ∈ X, a sequence { } ,... 1 , 0 ) ( ~ = α k k x q is defined iteratively by ... ... i,k = R(x i , x k ) for i, k = 1,…, n. Matrix R will also be described as a sequence of columns: R = (r 1 ,…, r n ), r k = ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ... ... Plant using Hierarchical Genetic Fuzzy Control Algorithms, Vikram Mathematical Journal, 19 (1999) 48- 59. [199] 98. Vasantha Kandasamy, W.B., and P...

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...donian Literary Society was established in 1891 and started publishing "Loza", its journal a year thereafter. Krste Misirkov, Dimitrija Cupovski, t... ...om asphyxiating Turkish rule). But to many outside observers (with the exception of journalists like John Sonixen or John smith), the IMRO was indis... ...d on a rampage of imprisonment, unjust dismissals of Albanians (mainly of teachers, journalists, policemen and judges) and the occasional torture or... ...or grandiose fantasies ("vision"). More about this here: http://samvak.tripod.com/journal37.html Narcissists are aided, abetted and facilitated by ... ...t optimism of the abused never ceases to amaze (read this: http://samvak.tripod.com/journal27.html). Narcissists are an elusive breed, hard to spot,... ...ity traits, or behavior patterns. But too little is known to establish irrefutable sequences of causes-and-effects. Even less is proven about the i...

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...dasein refers mostly to the sentimental aspect of Being in its substantial sequence. In other words, from the escatological point of view, dasein inc... ... the American Research Press in the triple issue 1-2- 3/200 of the NOTIONS JOURNAL, dedicated to professor Florentin Smarandache). 102 Explanato...