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 Book Id: WPLBN0002097119 ► Abstract Full Text Search Details...ss (DC). This journal is peer reviewed and included in the abstracting and indexing coverage of: Mathematical Reviews and MathSciNet (AMS, USA), DOAJ ... ... Chief Editor Dmitri Rabounski rabounski@yahoo.com Associate Editors Prof. Florentin Smarandache smarand@unm.edu Dr. Larissa Borissova lborissova@yaho... ...ioned equations m 0 cF αβ U β =0 (31), being taken in contravariant (upper-index) form, are m 0 cF α∙ ∙σ U σ =0, (59) whereU σ is the four-dimensional... ...the chr.inv.-feld strength tensorU ik , can be written in covariant (lower index) form as follows U ik =p 0 h ik −α ik =ph ik −β ik , (72) where α ik ... ... c 2 F j A ij =κJ i , (6.14) ∂D ik ∂t −(D ij +A ij ) D j k +A ∙j k∙ +DD ik + +3A ij A ∙j k∙ + 1 2 ( ∇ i F k + ∇ k F i )− 1 c 2 F i F k − −c ... ... the most general static metric for the point-mass is, ds 2 =A(D)dt 2 −B(D)dD 2 −C(D) dθ 2 +sin 2 θdϕ 2 , D =|r−r 0 |, A,B,C>0, where r 0 is an ar... ... The radius of curvature isR= p C(D) . 3. The proper radius isR p = Rp B(D)dD . 3 The equatorial orbit The general Kerr-Newman form in Boyer-Lindquist... ...d in the General Theory of Relativity Dmitri Rabounski, Larissa Borissova, Florentin Smarandache Dept. of Mathematics, University of New Mexico, 200 C... ... Experiments, More Types of Unmatter, and a Quantum Chromodynamics Formula Florentin Smarandache Dept. of Mathematics, University of New Mexico, 200 C...
 Book Id: WPLBN0002097044 Collections: Math, Literature, Algebra, Authors Community, Mathematics ► Abstract Description Details.... vector spaces) form an inseparable component of each other. The study of bialgebraic structures led to the invention of new notions like birings, Smarandache birings, bivector spaces, linear bialgebra, bigroupoids, bisemigroups, etc. But most of these are abstract algebraic concepts except, the bisemigroup being used in the construction of biautomatons. So we felt it... Full Text Search Details...36, India e-mail: vasantha@iitm.ac.in web: http://mat.iitm.ac.in/~wbv Florentin Smarandache Department of Mathematics University of New Mexic... ... e-mail: vasantha@iitm.ac.in web: http://mat.iitm.ac.in/~wbv Florentin Smarandache Department of Mathematics University of New Mexico Gallup,... ...ity, Atlanta, GA 30302, USA Copyright 2005 by W. B. Vasantha Kandasamy, Florentin Smarandache and K. Ilanthenral Layout by Kama Kandasamy.... ...57 Chapter Four SUGGESTED PROBLEMS 159 BIBLIOGRAPHY 169 INDEX 175 ABOUT THE AUTHORS 181 5 Preface Matri... ... and Kama Kandasamy for formatting this book. W.B.VASANTHA KANDASAMY FLORENTIN SMARANDACHE K. ILANTHENRAL 7 Chapter One BIMATRI... ...ince [ ] 12 B( B, B) T = = D = D 1 ∪ D 2 i.e., [ ] 12 12 12 (B B B ) TT DD =∪ ∪= ∪ . i.e. [ ] [ ] 12 1212 BB TTDD ∪=∪ if and only if T α i =... ... ⎢⎥ ⎢⎥ ∪ ⎢⎥ ⎢⎥ ⎢⎥ ⎢⎥ ⎢⎥ ⎢⎥ ⎣⎦ ⎣⎦ where 12 ii II ∪ is the ( ) 1122 iiii dd, dd ×× identity bimatrix. From the bimatrix we make the following two... ...the biproduct of linear factors f = f 1 ∪ f 2 = ()() 11 22 lk ' lk ' dd dd 1122 lk1k ' xc xc , ( xc) ( xc) ⎛⎞ −−−− ⎜⎟ ⎝⎠ . 127 If the f... ... D., A first course in Linear Algebra, Academic Press, 1973. 175 INDEX B Bisingular, 75 Bibasis, 101-2 Bicoefficients, 90-1 Bicofac...
 Book Id: WPLBN0002097105 ► Abstract Full Text Search Details... W. B. VASANTHA KANDASAMY FLORENTIN SMARANDACHE FUZZY RELATIONAL MAPS AND NEUTROSOPHIC... ...600036, India e-mail: vasantha@iitm.ac.in web: http://mat.iitm.ac.in/~wbv Florentin Smarandache Department of Mathematics University of New M... ...Mysore, Karnataka, India. Copyright 2004 by W. B. Vasantha Kandasamy and Florentin Smarandache Layout by Kama Kandasamy. Cover design by... ...orld problems 272 Chapter Five SUGGESTED PROBLEMS 279 Bibliography 283 Index 295 About the Authors 301 6 GM... ...) = r ik contains unknown p ij identified only by one particular value of the index i, that is, the unknown p ij distinguished by different value... ...P(X, Y), P j (X, Y), Q(Y, Z), Q j (Y, Z) and R(Z, V) where j takes values in an index set J, the following are basic properties of the Sup-i composi... ... subsets of disorders which are not singletons. Eq. (3) is then extended by DD = {D ∈ DD ⊆ 2 D , M(D) + ⊆ − M and ⊆ M(D) – ⊆ + M (12) f... ... (12) for the subsets of disorders which jointly may explain M + and M – . DD can obviously be refined by extending the counterparts of (10) or... ...fining “relevant” subsets of disorders; for instance (10) is generalized by DD = {D∈ DD M(d) + ∩ M + ≠ 0 / or M(d) – ∩ M – ≠ 0 / }. (13...
 Book Id: WPLBN0002097043 ► Abstract Description Details...to applications. With the recent introduction of bimatrices (2005) we have ventured in this book to introduce new concepts like linear bialgebra and Smarandache neutrosophic linear bialgebra and also give the applications of these algebraic structures.... Full Text Search Details...6, India e-mail: vasantha@iitm.ac.in web: http://mat.iitm.ac.in/~wbv Florentin Smarandache Department of Mathematics University of New Mexico... ...e-mail: vasantha@iitm.ac.in web: http://mat.iitm.ac.in/~wbv Florentin Smarandache Department of Mathematics University of New Mexico Gallup, ... ...sore, Karnataka, India. Copyright 2005 by W. B. Vasantha Kandasamy, Florentin Smarandache and K. Ilanthenral Layout by Kama Kandasamy. ... ...191 Chapter Five SUGGESTED PROBLEMS 201 BIBLIOGRAPHY 223 INDEX 229 ABOUT THE AUTHORS 238 5 Preface The alg... ...ent in every manner made this book possible. W.B.VASANTHA KANDASAMY FLORENTIN SMARANDACHE K. ILANTHENRAL 7 Chapter One I... ...c polynomial p (x). Suppose the characteristic polynomial p(x) = ()() 1k dd 1k x ... x −α −α 109 where α i ∈ K, 1 ≤ i ≤ K and d 1 +…+ d k = n... ...t 2 the demand neutrosophic bivector d = d 1 ∪ d 2 d = 12 11 12 kk dd dd ⎡ ⎤⎡⎤ ⎢ ⎥⎢⎥ ∪ ⎢ ⎥⎢⎥ ⎢ ⎥⎢⎥ ⎣ ⎦⎣⎦ at time t 1 and t 2 respecti... ...eristic bipolynomial of T = T 1 ∪ T 2 is f = f 1 ∪f 2 = {(x – 11 1k dd 11 1k c ) ... (x c ) − } ∪ ()() { } 22 1k dd 22 1k xx . . .xc −− and ... ... A first course in Linear Algebra, Academic Press, 1973. 229 INDEX A Adjoint linear operator, 13-4 B Best approximation...
 Book Id: WPLBN0002097108 ► Abstract Full Text Search Details... W. B. VASANTHA KANDASAMY FLORENTIN SMARANDACHE FUZZY RELATIONAL MAPS AND NEUTROSOPHIC... ...600036, India e-mail: vasantha@iitm.ac.in web: http://mat.iitm.ac.in/~wbv Florentin Smarandache Department of Mathematics University of New M... ...Mysore, Karnataka, India. Copyright 2004 by W. B. Vasantha Kandasamy and Florentin Smarandache Layout by Kama Kandasamy. Cover design by... ...orld problems 272 Chapter Five SUGGESTED PROBLEMS 279 Bibliography 283 Index 295 About the Authors 301 6 GM... ...) = r ik contains unknown p ij identified only by one particular value of the index i, that is, the unknown p ij distinguished by different value... ...P(X, Y), P j (X, Y), Q(Y, Z), Q j (Y, Z) and R(Z, V) where j takes values in an index set J, the following are basic properties of the Sup-i composi... ... subsets of disorders which are not singletons. Eq. (3) is then extended by DD = {D ∈ DD ⊆ 2 D , M(D) + ⊆ − M and ⊆ M(D) – ⊆ + M (12) f... ... (12) for the subsets of disorders which jointly may explain M + and M – . DD can obviously be refined by extending the counterparts of (10) or... ...fining “relevant” subsets of disorders; for instance (10) is generalized by DD = {D∈ DD M(d) + ∩ M + ≠ 0 / or M(d) – ∩ M – ≠ 0 / }. (13...
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