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 combinatorics, non-euclidean geometry and topology and their applications to other sciences. Topics in detail to be covered are: Smarandache multi-spaces with applications to other sciences, such as those of algebraic multi-systems, multi-metric spaces,. . . , etc.. Smarandache geometries; Differential Geometry; Geometry on manifolds; Topological graphs; Algebraic graphs; Random graphs; Combinatorial maps; Graph and map enumeration; Combinatorial designs; Combinatorial enumeration; Low Dimensional Topology; Differential Topology; Topology of Manifolds; Geometrical aspects of Mathematical Physics and Relations with Manifold Topology; Applications of Smarandache multi-spaces to theoretical physics; Applications of Combinatorics to mathematics and theoretical physics; Mathematical theory on gravitatio...

Smarandache-Zagreb Index on Three Graph Operators Abstract: Many researchers have studied several operators on a connected graph in which one make an attempt on subdivision of its edges. In this paper, we show how the Zagreb indices, a particular case of Smarandache-Zagreb index of a graph changes with these operators and extended these results to obtain a relation connecting the Zagreb index on operators. Key Words: Subdivision graph, ladder graph, Smarandache-Zagreb index, Zagreb index, graph operators. ...

Contents Smarandache-Zagreb Index on Three Graph Operators BY RANJINI P.S. and V.LOKESHA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 01 Total Minimal Dominating Signed Graph BY P.SIVA KOTA REDDY and S.VIJAY . . . . . . . . . . . . . . . . . . . . . . . . . . 11 The Number of Minimum Dominating Sets in Pn Å~ P2 BY H.B.WALIKAR, K.P. NARAYANKAR and S.S.SHIRAKOL . . . . . . . . . . . . . . . 17 Super Fibonacci Graceful Labeling BY R.SRIDEVI, S.NAVANEETHAKRISHNAN AND K.NAGARAJAN. . . . . . . . . . .22 A Note on Smarandachely Consistent Symmetric n-Marked Graphs BY P.SIVA KOTA REDDY, V. LOKESHA and GURUNATH RAO VAIDYA. . . . . . . . .41 Some Fixed Point Theorems in Fuzzy n-Normed Spaces BY SAYED KHALIL ELAGAN and MOHAMAD RAFI SEGI RAHMAT . . . . . . . . . . 45 A Result of Ramanujan and Brahmagupta Polynomials Described by a Matrix Identity BY R. RANGARAJAN . . . . . . . . . . . . . . . . 57 Biharmonic Slant Helices According to Bishop Frame in E3 BY ESSIN TURHAN and TALAT K¨ORPINAR . . . . . . . . . . . . . . . . . . . . . . 64 Combinatorial Optimization in VLSI Hypergraph Partitioning Using Taguchi Methods...

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 combinatorics, non-euclidean geometry and topology and their applications to other sciences. Topics in detail to be covered are: Smarandache multi-spaces with applications to other sciences, such as those of algebraic multi-systems, multi-metric spaces,. . . , etc.. Smarandache geometries; Differential Geometry; Geometry on manifolds; Topological graphs; Algebraic graphs; Random graphs; Combinatorial maps; Graph and map enumeration; Combinatorial designs; Combinatorial enumeration; Low Dimensional Topology; Differential Topology; Topology of Manifolds; Geometrical aspects of Mathematical Physics and Relations with Manifold Topology; Applications of Smarandache multi-spaces to theoretical physics; Applications of Combinatorics to mathematics and theoretical physics; Mathematical theory on gravitatio...

On the Bicoset of a Bivector Space Abstract: The study of bivector spaces was first intiated by Vasantha Kandasamy. The objective of this paper is to present the concept of bicoset of a bivector space and obtain some of its elementary properties. Key Words: bigroup, bivector space, bicoset, bisum, direct bisum, inner biproduct space, biprojection. ...

Contents On the Bicoset of a Bivector Space BY AGBOOLA A.A.A. AND AKINOLA L.S.. . . . . . . . . . . . . . . . . . . . .01 Smarandachely Bondage Number of a Graph BY KARAM EBADI AND L.PUSHPALATHA . . . . . . . . . . . . . . . . . . . . . 09 Domination Number in 4-Regular Graphs BY H.Abdollahzadeh Ahangar AND Pushpalatha L. . . . . . . . . . . . . . . . . . 20 Computing Smarandachely Scattering Number of Total Graphs BY AYSUN AYTAC AND ELGIN KILIC. . . . . . . . . . . . . . . . . . . . . . .31 On the 3ψ3 Basic Bilateral Hypergeometric Series Summation Formulas BY K. R.VASUKI AND G.SHARATH. . . . . . . . . . . . . . . . . . . . . . . .41 Minimal Retraction of Space-time and Their Foldings BY A. E. El-AHMADY aND H. RAFAT. . . . . . . . . . . . . . . . . . . . . . . .49 Efficient Domination in Bi-Cayley Graphs BY T. TAMIZH CHELVAM AND SIVAGNANAM MUTHARASU. . . . . . . . . .56 Independent Complementary Distance Pattern Uniform Graphs BY GERMINA K.A. AND BEENA KOSHY. . . . . . . . . . . . . . . . . . . . . .63 On Smarandachely Harmonic Graphs BY D.D.SOMASHEKARA AND C.R.VEENA . . . . . . . . . . . . . . . . . . . . . 75 S...

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 combinatorics, non-euclidean geometry and topology and their applications to other sciences. Topics in detail to be covered are: Smarandache multi-spaces with applications to other sciences, such as those of algebraic multi-systems, multi-metric spaces,. . . , etc.. Smarandache geometries; Differential Geometry; Geometry on manifolds; Topological graphs; Algebraic graphs; Random graphs; Combinatorial maps; Graph and map enumeration; Combinatorial designs; Combinatorial enumeration; Low Dimensional Topology; Differential Topology; Topology of Manifolds; Geometrical aspects of Mathematical Physics and Relations with Manifold Topology; Applications of Smarandache multi-spaces to theoretical physics; Applications of Combinatorics to mathematics and theoretical physics; Mathematical theory on gravitatio...

The Characterization of Symmetric Primitive Matrices with Exponent n − 2 Junliang Cai Abstract: In this paper the symmetric primitive matrices of order n with exponent n − 2 are completely characterized by applying a combinatorial approach, i.e., mathematical combinatorics ([7]). Key words: primitive matrix, primitive exponent, graph....

The Characterization of Symmetric Primitive Matrices with Exponent n − 2 BY JUNLIANG CAI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 01 Characterizations of Some Special Space-like Curves in Minkowski Space-time BY MELIH TURGUT AND SUHA YILMAZ . . . . . . . . . . . . . . . . . . . . . . . 17 Combinatorially Riemannian Submanifolds BY LINFAN MAO. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 Smarandache Half-Groups BY ARUN S.MUKTIBODH. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .46 On Smarandache Bryant Schneider Group of a Smarandache Loop BY T. G. JA´IY´EOL´A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 Some Properties of Nilpotent Lattice Matrices BY QIYI FAN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 On the Crossing Number of the Join of Some 5-Vertex Graphs and Pn BY BO LI, JING WANG AND YUANQIU HUANG . . . . . . . . . . . . . . . . . . 70 Identities by L-summing Method (II) BY MEHDI HASSANI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 On the Basis Numbe...

În anul 1972 Florentin Smarandache prezentase o ipoteză supraluminala (prin care susţinea că nu există barieră a vitezei în univers), infirmând postulatul einsteinian. Autorul l-a contrazis din nou pe Einstein în 1982 construind, prin calcule matematice simple, o Teorie Absolută a Relativităţii (T.A.R.), din care erau înlăturate fanteziile ştiinţifice din Teoria Specială a Relativităţii precum dilatare a timpului, contractare a spaţiului, simultaneitate relativistă, sau paradoxuri relativiste. In 1972 Smarandache hypothesis provided a warp (which claims that there is speed barrier in the universe), refuting Einsteinian postulate. Author Einstein contradicted again in 1982 built by simple math, an Absolute Relativity Theory (ART), which were removed scientific fantasies special theory of relativity and time dilation, space contraction, relativistic simultaneity, or paradoxes relativistic....

„Neutrosofia” deschide uşi noi în matematică şi în fizică Florentin Smarandache, şef de promoţie al Facultăţii de Matematică din Craiova, nu este doar matematician, ci şi scriitor (poet, prozator, dramaturg), întemeietor al mişcării literare de avangardă numită de el „Paradoxism” (pentru că utilizează în mod programmatic paradoxuri, antiteze, oximoroane), editând şase antologii internaţionale paradoxiste. Are contribuţii şi în alte ştiinţe (filozofie şi fizică), bazate pe aplicarea paradoxismului în ştiinţă. Pornind de la faptul că pentru o entitate „A” există nu doar opusul ei, „antiA”, ci şi neutrul ei, „neutA” (care nu este nici „A”, nici „antiA”), Florentin Smarandache a generalizat „Dialectica” (un capitol al filozofiei, bazat pe existenţa „contrariilor” – „A” şi „antiA”) în „Neutrosofie” (bazată pe existent „contariilor” şi a „neutraliilor”). ...

22 septembrie 2011: CERN confirmă primul experiment supraluminal - Smarandache Hypothesis, by Philip M. Parker .. . 7 - Un cercetător român a dedus existenţa particulelor cu vitezele supraluminale descoperite recent la CERN, de Prof. Ion Pătraşcu.......... 8 - Un cercetător român postulase că viteza luminii poate fi depăşită, înaintea descoperirii făcute de CERN, de Ichim Vasilică .......... 13 - Profet în Ţara Fizicii: Smarandache confirmat, Einstein infirmat?! de Mircea Monu, fizician....23 - Follow-up on CERN's OPERA Neutrino Results, by Huping Hu & Maoxin Wu ........ 34 04-11 noiembrie 2011: Participare la Conferinţa Internaţională IEEE de Calcul Granular, Universitatea Kaohsiung, Taiwan, cu lucrări despre Logica Neutrosofică - Florentin Smarandache duce neutrosofia şi în Taiwan!, de M. Monu .......... 37 18 noiembrie 2011: Premiul Statului New Mexico la categoria Ştiinţă şi Matematică în Albuquerque - Renaissance Man, Shondiin Silversmith ... . 46 - Un profesor român a câştigat Premiul statului New Mexico (SUA) la Ştiinţă şi Matematică pe anul 2011, de Prof. Mircea Eugen Şelariu ......... 48 premiul statului New M...

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 combinatorics, non-euclidean geometry and topology and their applications to other sciences. Topics in detail to be covered are: Smarandache multi-spaces with applications to other sciences, such as those of algebraic multi-systems, multi-metric spaces,. . . , etc.. Smarandache geometries; Differential Geometry; Geometry on manifolds; Topological graphs; Algebraic graphs; Random graphs; Combinatorial maps; Graph and map enumeration; Combinatorial designs; Combinatorial enumeration; Low Dimensional Topology; Differential Topology; Topology of Manifolds; Geometrical aspects of Mathematical Physics and Relations with Manifold Topology; Applications of Smarandache multi-spaces to theoretical physics; Applications of Combinatorics to mathematics and theoretical physics; Mathematical theory on gravitatio...

Duality Theorems of Multiobjective Generalized Disjunctive Fuzzy Nonlinear Fractional Programming Abstract: This paper is concerned with the study of duality conditions to convex-concave generalized multiobjective fuzzy nonlinear fractional disjunctive programming problems for which the decision set is the union of a family of convex sets. The Lagrangian function for such problems is defined and the Kuhn-Tucker Saddle and Stationary points are characterized. In addition, some important theorems related to the Kuhn-Tucker problem for saddle and stationary points are established. Moreover, a general dual problem is formulated together with weak; strong and converse duality theorems are proved. Key Words: Generalized multiobjective fractional programming; Disjunctive programming; Convexity; Concavity; fuzzy parameters Duality. ...

Contents Duality Theorems of Multiobjective Generalized Disjunctive Fuzzy Nonlinear Fractional Programming BY E.E.AMMAR . . . . . . . . . . . . . . . . . . . . 01 Surface Embeddability of Graphs via Joint Trees BY YANPEI LIU. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .15 Plick Graphs with Crossing Number 1 BY B.BASAVANAGOUD AND V.R.KULLI . . . . . . . . . . . . . . . . . . . . . . 21 Effects of Foldings on Free Product of Fundamental Groups BY M.El-GHOUL, A. E.El-AHMADY, H.RAFAT AND M.ABU-SALEEM. . . . . . . 29 Absolutely Harmonious Labeling of Graphs BY M.SEENIVASAN AND A.LOURDUSAMY . . . . . . . . . . . . . . . . . . . . 40 The Toroidal Crossing Number of K4n BY SHENGXIANG LV, TANG LING AND YUANGQIU HUANG . . . . . . . . . . 52 On Pathos Semitotal and Total Block Graph of a Tree BY MUDDEBIHAL M. H. AND SYED BABAJAN. . . . . . . . . . . . . . . . . . 64 Varieties of Groupoids and Quasigroups Generated by Linear-Bivariate Polynomials Over Ring Zn BY E.ILOJIDE, T.G.JAIYEOLA AND O.O.OWOJORI . . . . . 79 New Characterizations for Bertrand Curves in Minkowski 3-Space BY BAHADDIN BUKCU, MURAT K...

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 combinatorics, non-euclidean geometry and topology and their applications to other sciences. Topics in detail to be covered are: Smarandache multi-spaces with applications to other sciences, such as those of algebraic multi-systems, multi-metric spaces,. . . , etc.. Smarandache geometries; Differential Geometry; Geometry on manifolds; Topological graphs; Algebraic graphs; Random graphs; Combinatorial maps; Graph and map enumeration; Combinatorial designs; Combinatorial enumeration; Low Dimensional Topology; Differential Topology; Topology of Manifolds; Geometrical aspects of Mathematical Physics and Relations with Manifold Topology; Applications of Smarandache multi-spaces to theoretical physics; Applications of Combinatorics to mathematics and theoretical physics; Mathematical theory on gravitatio...

x4: Radio labeling of P3n for n is less than or equal to 5 or n = 7 In this section we determine radio numbers of cube path of small order as a special case....

This book will take you on a journey, through the eyes and minds of two unlikely heroes. These two amazing, inventive & creative young souls find adventure & create solutions through the use of mathematics, "Om technology", and sharo-logical edutainment as well as creating a multitude of "Harmless but helpful inventions that assist themselves & those that they meet. These heroes make friends where ever they may go while solving many of what some may call "the worlds problems" along the way. This dynamic duo as well as their amazing group of friends find as much joy in Action sports as they do in listening to all of the great adventures of people that have been alive many more years then them. Love, respect, caring, self-confidence,responsibility and joy are the tools of their trade, and they believe that all people can be truly amazing! Get your copy of "An Essential Book of Good" here today so you can feel, and be even more amazing today!...

"There were no great walls that could stop a free thinking minds path". One just has to simply do the math, create a plan and then just actually commit, and then do whatever the task". "If one was to study the magic of Mathematics or the physics of lifting off, one could create solutions to even inventing a flying skate-snow or surfboard that levitates effortlessly without even the slightest of sounds"....

Introduction 1) Essential Fabric & Style 2) Fish Faith 3) Life Keys for you & me 4) A Gift for you 5) Then and Now 6) Strange Days 7) Dream Seeds 8) The Great Storm 9) A Brand New Day 10) A friend in Need is a Friend Indeed 11) Success with Persistence ~ The Golden Envelope...

Creaţia este un risc Prefaţă Cei care construiesc şi cei care se căsătoresc nu sunt niciodată în siguranţă, sună un proverb suedez. Deci creaţia, care este o c-o-n-s-t-r-u-c-ţ-i-e, presupune un risc, atrăgând prieteni dar şi duşmani, şi lăsând o a treia categorie de oameni indiferenţi (ca-n logica neutrosofică). În a doua jumătate a vieţii producţia-mi literară s-a redus în cantitate, eu fiind absorbit în (şi sponsorizat pentru) creaţia ştiinţifică aplicată (matematică folosită în inginerie, robotică, medicină, aeronautică, sau încercări sporadice de fizică teoretică). În afara unor autotraduceri, şi-acelea înaintând greu din lipsă de timp, iar în domeniul plastic al ‘artei electronice’ (pe computer), mai scriu ca “literatură” doar memoriile despre diversele conferinţe ştiinţifice internaţionale la care sunt invitat să prezint lucrări de cercetare ori seminarii. Memorii care, de fapt, sunt nişte reportaje, îmbinate cu expunerea de idei şi teorii ştiinţifice, documentarii istorice, geografice, filozofice, antropologice, religioase, artistice, etc. de la diversele muzee, galerii de artă, monumente şi locuri culturale ...

Cifrele au început să vibreze mi-am încărcat buzunarele cu cifre şi pătrate şi am vâslit hoinar pe drumuri la fiecare colţ al liniei curbe a vieţii aruncam cu cercuri şi triunghiuri în mulţime şi ele rezonau cu cifre am pavat şoseaua iar sub paşii mei au început să vibreze când mi-am umplut plămânii de ele s-au convertit în litere şi am descins pe drumul poeziei...

Prefaţă: Creaţia este un risc: 5 INTERVIURI: 6 Legătura dintre paradoxism şi Teoria Dezert-Smarandache (Interviu cu Flavia Teoc): 7 Exil sau diasporă? (Interviu cu Silvia Constantinescu): 11 God does play dice! (Interview with Ovidiu Bufnilă): 21 “Totul este posibil, chiar şi imposibilul!” (Interviu cu Tudor Negoescu): 22 Literatura şi ştiinţa experimentală (Interviu cu Adrian Lesenciuc): 28 Gândirea pozitivistă (Interviu cu Gabriel Stănescu): 33 "Rămân emigranţii fideli valorilor culturii de origine?” (Chestionar de Gabriel Stănescu): 36 O luptă permanentă cu viaţa (Interviu cu Crenguţa Ţolea): 38 A fi sau a nu fi paradoxist (Taifas electronic cu Mircea Monu): 47 Nichita versus Florentin (Dialog cu M. N. Rusu): 55 Paradoxism şi (Aut-)Artă: o nouă (dez)ordine culturală? (Interviu cu Mugur Grosu şi Mircea Ţuglea): 56 SCURTE ESEURI: 86 Aut-Artă: 87 Ab ovo: 89 Un Om şi-o Operă (Aurel M. Buricea la 65 de ani): 91 Pasiunea de Dascăl şi Creator: 92 Prolificitatea Profesorului Bencze: 94 Aniversare Alpha: 95 Nuvele serioase în neseriozitatea lor: 96 La frontiera onirismului: 99 Un nou gen literar: 100 Vorbe de duh: 1...

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 combinatorics, non-euclidean geometry and topology and their applications to other sciences. Topics in detail to be covered are: Smarandache multi-spaces with applications to other sciences, such as those of algebraic multi-systems, multi-metric spaces,. . . , etc.. Smarandache geometries; Differential Geometry; Geometry on manifolds; Topological graphs; Algebraic graphs; Random graphs; Combinatorial maps; Graph and map enumeration; Combinatorial designs; Combinatorial enumeration; Low Dimensional Topology; Differential Topology; Topology of Manifolds; Geometrical aspects of Mathematical Physics and Relations with Manifold Topology; Applications of Smarandache multi-spaces to theoretical physics; Applications of Combinatorics to mathematics and theoretical physics; Mathematical theory on gravitatio...

Contents On the Crypto-Automorphism of the Buchsteiner Loops BY J.O.AD´EN´IRN and Y.T.OYEBO. . . . . . . . . . . . . . . . . . . . . . . . .01 Generalizations of Poly-Bernoulli Numbers and Polynomials BY HASSAN JOLANY, M.R.DARAFSHEH AND R.EIZADI ALIKELAYE . . . . 07 Open Alliance in Graphs BY N.JAFARI RAD AND H.REZAZADEH . . . . . . . . . . . . . . . . . . . . . 15 The Forcing Weak Edge Detour Number of a Graph BY A.P.SANTHAKUMARAN AND S.ATHISAYANATHAN . . . . . . . . . . . . . 22 Special Smarandache Curves in the Euclidean Space BY AHMAD T. ALI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 The H-Line Signed Graph of a Signed Graph BY R.RANGARAJAN, M. S. SUBRAMANYA AND P. SIVA KOTA REDDY. . . .37 Min-Max Dom-Saturation Number of a Tree BY S. ARUMUGAM AND S. SUDHA . . . . . . . . . . . . . . . . . . . . . . . 45 Embeddings of Circular graph C(2n + 1, 2) (n ≥ 2) on the Projective Plane BY XINQIU LIU, YUANQIU HUANG AND JING WANG. . . . . . . . . . . . .53 A Note On Jump Symmetric n-Sigraph BY H. A.MALATHI AND H. C.SAVITHRI . . . . . . . . . . . . . . . . . . . . 65 New Families of Mean Graphs ...

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 combinatorics, non-euclidean geometry and topology and their applications to other sciences. Topics in detail to be covered are: Smarandache multi-spaces with applications to other sciences, such as those of algebraic multi-systems, multi-metric spaces,. . . , etc.. Smarandache geometries; Differential Geometry; Geometry on manifolds; Topological graphs; Algebraic graphs; Random graphs; Combinatorial maps; Graph and map enumeration; Combinatorial designs; Combinatorial enumeration; Low Dimensional Topology; Differential Topology; Topology of Manifolds; Geometrical aspects of Mathematical Physics and Relations with Manifold Topology; Applications of Smarandache multi-spaces to theoretical physics; Applications of Combinatorics to mathematics and theoretical physics; Mathematical theory on gravitatio...

Abstract: In this paper we find the interrelations and the hidden pattern of the problems faced by the PWDs and their caretakers using Fuzzy Relational Maps (FRMs). Here we have taken the problems faced by the rural persons with disabilities in Melmalayanur and Kurinjipadi Blocks, Tamil Nadu, India. This paper is organized with the following four sections. Section one is introductory in nature giving the overall contents from the survey made about PWDs in the above said Blocks. Section two gives description of FRM models and the attributes taken for the study related with the PWDs and the caretakers, the FRM model formed using these attributes and their analysis. The third section gives the suggestions and conclusions derived from the survey as well as the FRM model. Key Words: FRM model, fixed point, hidden pattern, relational matrix, limit cycle. AMS(2000): 04A72....

Study of the Problems of Persons with Disability (PWD) Using FRMs BY W.B.VASANTHA KANDASAMY, A.PRAVEEN PRAKASH AND K.THIRUSANGU 01 Topological Multi-groups and Multi-fields BY LINFAN MAO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 08 Shortest Co-cycle Bases of Graphs BY HAN REN AND JING HAN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 On Involute and Evolute Curves of Spacelike Curve with a Spacelike Principal Normal in Minkowski 3 -Space BY BAHADDIN BUKCU AND MURAT KEMAL KARACAN . . . . . . . . . . . . . . . 27 Notes on the Curves in Lorentzian Plane L2 BY S¨ UHA YILMAZ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 Cycle-Complete Graph Ramsey Numbers r(C4,K9), r(C5,K8) ≤ 33 BY M.M.M. JARADAT AND B.M.N. ALZALEQ . . . . . . . . . . . . . . . . . . . . 42 Smarandache Breadth Pseudo Null Curves in Minkowski Space-time BY MELIH TURGUT. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 Smarandachely k -Constrained labeling of Graphs BY SHREEDHARK, B. SOORYANARAYANA AND RAGHUNATHP . . . . . . . . . . .50 Equiparity Path D...

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 combinatorics, non-euclidean geometry and topology and their applications to other sciences. Topics in detail to be covered are: Smarandache multi-spaces with applications to other sciences, such as those of algebraic multi-systems, multi-metric spaces,. . . , etc.. Smarandache geometries; Differential Geometry; Geometry on manifolds; Topological graphs; Algebraic graphs; Random graphs; Combinatorial maps; Graph and map enumeration; Combinatorial designs; Combinatorial enumeration; Low Dimensional Topology; Differential Topology; Topology of Manifolds; Geometrical aspects of Mathematical Physics and Relations with Manifold Topology; Applications of Smarandache multi-spaces to theoretical physics; Applications of Combinatorics to mathematics and theoretical physics; Mathematical theory on gravitatio...

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: maolinfan@163.com Abstract: An interesting symmetry on multiplication of numbers found by Prof.Smarandache recently. By considering integers or elements in groups on graphs, we extend this symmetry on graphs and find geometrical symmetries. For extending further, Smarandache’s or combinatorial systems are also discussed in this paper, particularly, the CC conjecture presented by myself six years ago, which enables one to construct more symmetrical systems in mathematical sciences. Key Words: Smarandache sequence, labeling, Smarandache beauty, graph, group, Smarandache system, combinatorial system, CC conjecture...

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 . . . . . . . . . . . . . . . . . . . . . . . 33 Elementary Abelian Regular Coverings of Cube BY FURONG WANG AND LIN ZHANG. . . . . . . . . . . . . . . . . . . . . .49 Super Fibonacci Graceful Labeling of Some Special Class of Graphs BY R.SRIDEVI, S.NAVANEETHAKRISHNAN AND K.NAGARAJAN. . . . . . . . 59 Surface Embeddability of Graphs via Tree-travels BY YANPEI LIU. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .73 Edge Maximal C3 and C5-Edge Disjoint Free Graphs BY M.S.A.BATAINEH AND M.M.M.JARADAT . . . . . . . . . . . . . . . . . . 82 A Note on Admissible Mannheim Curves in Galilean Space G3 BY S.ERSOY, M.AKYIGIT AND M.TOSUN . . . . . . . . . . . . . . . . . . . . 88 The Number of Spanning Trees in Generalized Complete Multipartite Graphs of Fan-Type BY JUNLIANGE CAI AND XIAOLI LIU . . . . . ....

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 combinatorics, non-euclidean geometry and topology and their applications to other sciences. Topics in detail to be covered are: Smarandache multi-spaces with applications to other sciences, such as those of algebraic multi-systems, multi-metric spaces,. . . , etc.. Smarandache geometries; Differential Geometry; Geometry on manifolds; Topological graphs; Algebraic graphs; Random graphs; Combinatorial maps; Graph and map enumeration; Combinatorial designs; Combinatorial enumeration; Low Dimensional Topology; Differential Topology; Topology of Manifolds; Geometrical aspects of Mathematical Physics and Relations with Manifold Topology; Applications of Smarandache multi-spaces to theoretical physics; Applications of Combinatorics to mathematics and theoretical physics; Mathematical theory on gravitatio...

§1. Why is the WORLD a Combinatorial One? The multiplicity of the WORLD results in modern sciences overlap and hybrid, also implies its combinatorial structure. To see more clear, we present two meaningful proverbs following. Proverb 1. Ames Room An Ames room is a distorted room constructed so that from the front it appears to be an ordinary cubic-shaped room, with a back wall and two side walls parallel to each other and perpendicular to the horizontally level floor and ceiling. As a result of the optical illusion, a person standing in one corner appears to the observer to be a giant, while a person standing in the other corner appears to be a dwarf. The illusion is convincing enough that a person walking back and forth from the left corner to the right corner appears to grow or shrink. ...

Contents Combinatorial Fields - An Introduction BY LINFAN MAO. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .01 A Spacetime Geodesics of the Schwarzschild Space and Its Deformation Retract BY H. RAFAT. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .23 On Degree Equitable Sets in a Graph BY A. ANITHA, S. ARUMUGAM AND E. SAMPATHKUMAR . . . . . . . . . . . . 32 Smarandachely k-Constrained Number of Paths and Cycles BY P. DEVADAS RAO, B. SOORYANARAYANA, M. JAYALAKSHMI . . . . . . . . . 48 On Functions Preserving Convergence of Series in Fuzzy n-Normed Spaces BY SAYED ELAGAN AND MOHAMAD RAFI SEGI RAHMAT . . . . . . . . . . . . 61 Achromatic Coloring on Double Star Graph Families BY VERNOLD VIVIN J., VENKATACHALAM M. AND AKBAR ALI M.M. . . . . . 71 Some Results on Super Mean Graphs BY R.VASUKI AND A.NAGARAJAN. . . . . . . . . . . . . . . . . . . . . . . . .82 Chromatic Polynomial of Smarandache νE-Product of Graphs BY KHALIL PARYAB AND EBRAHIM ZARE. . . . . . . . . . . . . . . . . . . .97 Open Distance-Pattern Uniform Graphs BY BIBIN K. JOSE . . . . . . . . . . . . . . . . . ....

The present book discusses, among other things, various quantization phenomena found in Astrophysics and some related issues including Brownian Motion. With recent discoveries of exoplanets in our galaxy and beyond, this Astrophysics quantization issue has attracted numerous discussions in the past few years. Most chapters in this book come from published papers in various peer-reviewed journals, and they cover different methods to describe quantization, including Weyl geometry, Supersymmetry, generalized Schrödinger, and Cartan torsion method. In some chapters Navier-Stokes equations are also discussed, because it is likely that this theory will remain relevant in Astrophysics and Cosmology While much of the arguments presented in this book are theoretical, nonetheless we recommend further observation in order to verify or refute the propositions described herein. It is of our hope that this volume could open a new chapter in our knowledge on the formation and structure of Astrophysical systems. ...

Abstract We explore Yang’s Noncommutative space-time algebra (involving two length scales) within the context of QM defined in Noncommutative spacetimes and the holographic area-coordinates algebra in Clifford spaces. Casimir invariant wave equations corresponding to Noncommutative coordinates and momenta in d-dimensions can be recast in terms of ordinary QM wave equations in d + 2-dimensions. It is conjectured that QM over Noncommutative spacetimes (Noncommutative QM) may be described by ordinary QMin higher dimensions. Novel Moyal-Yang-Fedosov-Kontsevich star products deformations of the Noncommutative Poisson Brackets are employed to construct star product deformations of scalar field theories. Finally, generalizations of the Dirac-Konstant and Klein-Gordonlike equations relevant to the physics of D-branes and Matrix Models are presented. ...

In these proceedings of the second international conference on smarandache type notions in mathematics and quantum physics (december 21-24, 2000, university ofcraiova, romania; organizers: v. Seleacu and m. L perez) are collected articles and notes: in mathematics: related to smarandache anti-geometry, function, f-inferior part function, k-k additive relationships, 2-2 subtractive relationships, sequences, coprime functions, double factorial function, magic squares, problems, conjectures, equations, partitions, paradoxes, series, algebraic structures, pseodo-smarandache function, erdos-smarandache moments numbers; and in physics: related to smarandache hypothesis that there is no speed barrier in the universe, srm-theory of the possibility of constructing arbitrary speeds, and quantum smarandache paradoxes....

Flatland: A Romance of Many Dimensions is an 1884 science fiction novella by the English schoolmaster Edwin Abbott Abbott. As a satire, Flatland offered pointed observations on the social hierarchy of Victorian culture. However, the novella's more enduring contribution is its examination of dimensions; in a foreword to one of the many publications of the novella, noted science writer Isaac Asimov described Flatland as The best introduction one can find into the manner of perceiving dimensions. As such, the novella is still popular amongst mathematics, physics and computer science students....

Fiction, Science fiction, Satire

Jules Henri Poincaré (1854 – 1912) was one of France's greatest mathematicians and theoretical physicists, and a philosopher of science. As a mathematician and physicist, he made many original fundamental contributions to pure and applied mathematics, mathematical physics and celestial mechanics. He was responsible for formulating the Poincaré conjecture, one of the most famous problems in mathematics. In his research on the three-body problem, Poincaré became the first person to discover a chaotic deterministic system which laid the foundations of modern chaos theory. He is considered to be one of the founders of the field of topology. Poincaré introduced the modern principle of relativity and was the first to present the Lorentz transformations in their modern symmetrical form. He discovered the remaining relativistic velocity transformations and recorded them in a letter to Lorentz in 1905. Thus he obtained perfect invariance of all of Maxwell's equations, an important step in the formulation of the theory of special relativity. (Summary from Wikipedia)...

Science

This is an introduction to Einstein’s space-bending, time-stretching theory of Relativity, written by the master himself. Special and General relativity explain the structure of space time and provide a theory of gravitation, respectively. Einstein’s theories shocked the world with their counterintuitive results, including the dissolution of absolute time. In this book he brings a simplified form of his profound understanding of the subject to the layperson. In the words of Einstein: “The present book is intended, as far as possible, to give an exact insight into the theory of Relativity to those readers who, from a general scientific and philosophical point of view, are interested in the theory, but who are not conversant with the mathematical apparatus of theoretical physics.” The book is challenging at times but, when approached patiently, proves itself one of the most lucid explanations of Relativity to be found anywhere. [Due to transcription or optical character recognition errors in creating online texts, and because of less-than-clear fonts in some printed texts, the variables as read in some of the equations here are not as...

Science

Scientia Magna is published annually in 200-300 pages per volume and 1,000 copies on topics such as mathematics, physics, philosophy, psychology, sociology, and linguistics....

A structure theorem of right C-rpp semigroups1 Abstract A new method of construction for right C-rpp semigroups is given by using a right cross product of a right regular band and a strong semilattice of left cancellative monoids. Keywords Right C-rpp semigroups, right cross products, right regular bands, left cancellative monoids. x1. Introduction Recall that a semigroup S is called an rpp semigroup if all its principal right ideals aS1, regarded as right S1-systems, are projective. According to J.B. Fountain[5], a semigroup S is rpp if and only if, for any a 2 S, the set Ma=fe 2 E j S1a µ Se and for all x; y 2 S1, ax = ay ) ex = eyg is a non-empty set, where E is the set of all idempotents of S. An rpp semigroup S is called strongly rpp if for every a 2 S, there exists a unique idempotent e in Ma such that ea=a. It is easy to see that regular semigroups are rpp semigroups and completely regular semigroups are strongly rpp semigroups. Thus, rpp semigroups are generalizations of regular semigroups. A strongly rpp semigroups S is said to be a right C-rpp semigroup if L. _ R is a congruence on S and Se µ eS for all e 2 E(...

X. Pan and B. Liu : On the irrational root sieve sequence 1 H. Liu : Sub-self-conformal sets 4 K. Liu : On mean values of an arithmetic function 12 L. Wang and Y. Liu : On an infinite series related to Hexagon-numbers 16 X. Ren, etc. : A structure theorem of right C-rpp semigroups 21 A. R. Gilani and B. N. Waphare : Fuzzy extension in BCI-algebras 26 A. S. Shabani : The Pell's equation x2 ¡ Dy2 = §a 33 L. Cheng : On the mean value of the Smarandache LCM function 41 W. Guan : Four problems related to the Pseudo-Smarandache-Squarefree function 45 Y. Lou : On the pseudo Smarandache function 48 J. L. Gonzalez : A miscellaneous remark on problems involving Mersenne primes 51 Y. Liu and J. Li : On the F.Smarandache LCM function and its mean value 52 N. T. Quang and P. D. Tuan : A generalized abc-theorem for functions of several variables 56 W. Liu, etc. : An assessment method for weight of experts at interval judgment 61 Y. Xue : On the F.Smarandache LCM function SL(n) 69 Y. Zheng : On the Pseudo Smarandache function and its two conjectures 74 Z. Ding : Diophantine equations and their positive integer solutions 77 S. Gou ...

Scientia Magna is published annually in 200-300 pages per volume and 1,000 copies on topics such as mathematics, physics, philosophy, psychology, sociology, and linguistics....

Abstract In this paper, we use 4-cyclotomic cosets of modulo n and generator polynomials to describe quaternary simple-root cyclic codes of length n = 85. We discuss the conditions under which a quaternary cyclic codes contain its dual, and obtain some quantum error-correcting codes of length n = 85, three of these codes are better than previous known codes. Keywords Quaternary cyclic code, self-orthogonal code, quantum error-correcting code. x1. Introduction Since the initial discovery of quantum error-correcting codes, researchers have made great progress in developing quantum error-correcting codes. Many code construction are given. Reference [1] gives a thorough discussion of the principles of quantum coding theory. Many good quantum error-correcting codes were constructed from BCH codes, Reed-Muller codes, Reed-Solomon codes and algebraic geometric codes, see [2-6]. So it is natural to construct quantum error-correcting codes from quaternary cyclic codes. It is known that there is a close relation between cyclotomic coset and cyclic codes. Suggested by this relation, we use 4-cyclotomic coset modulo n and generator polyn...

S. M. Khairnar and M. More : Subclass of analytic and univalent functions in the unit disk 1 Y. Ma, etc. : Large quaternary cyclic codes of length 85 and related quantum error-correcting 9 J. Chen : Value distribution of the F.Smarandache LCM function 15 M. Bencze : About a chain of inequalities 19 C. Tian and N. Yuan : On the Smarandache LCM dual function 25 J. Caltenco, etc. : Riemannian 4-spaces of class two 29 Y. Xue : On a conjecture involving the function SL¤(n) 41 Y. Wang : Some identities involving the near pseudo Smarandache function 44 A. Gilani and B. Waphare : On pseudo a-ideal of pseudo-BCI algebras 50 J. Chen : An equation involving the F.Smarandache multiplicative function 60 M. Enciso-Aguilar, etc. : Matrix elements for the morse and coulomb interactions 66 Y. Xu and S. Li : On s¤¡Supplemented Subgroups of Finite Groups 73 C. Tian : Two equations involving the Smarandache LCM dual function 80 W. Zheng and J. Dou : Periodic solutions of impulsive periodic Competitor- Competitor-Mutualist system 86 X. Zhang : On the fourth power mean value of B(Â) 93 Z. Lv : On the F.Smarandache function and its mean val...

In this work the authors apply concepts of Neutrosophic Logic to the General Theory of Relativity to obtain a generalisation of Einstein’s four dimensional pseudo-Riemannian differentiable manifold in terms of Smarandache Geometry (Smarandache manifolds), by which new classes of relativistic particles and non-quantum teleportation are developed....

1.2 The basics of neutrosophy Neutrosophy studies the origin, nature, and scope of neutralities, as well as their interactions with different ideational spectra. It considers that every idea tends to be neutralized, balanced by ideas; as a state of equilibrium. Neutrosophy is the basis of neutrosophic logic, neutrosophic set which generalizes the fuzzy set, and of neutrosphic probability and neutrosophic statistics, which generalize the classical and imprecise probability and statistics respectively. Neutrosophic Logic is a multiple-valued logic in which each proposition is estimated to have percentages of truth, indeterminacy, and falsity in T, I, and F respectively, where T, I, F are standard or non-standard subsets included in the non-standard unit interval ] −0, 1+[. It is an extension of fuzzy, intuitionistic, paraconsistent logics. ...

Preface of the Editor 4 Chapter 1 PROBLEM STATEMENT . THE BASICS OF NEUTROSOPHY 1.1 Problem statement 5 1.2 The basics of neutrosophy 8 1.3 Neutrosophic subjects 13 1.4 Neutrosophic logic. The origin of neutrosophy 14 1.5 Definitions of neutrosophic 16 Chapter 2 TRAJECTORIES AND PARTICLES 2.1 Einstein’s basic space-time 18 2.2 Standard set of trajectories and particles. A way to expand the set 22 2.3 Introducing trajectories of mixed isotropic/non-isotropic kind 28 2.4 Particles moving along mixed isotropic/non-isotropic trajectories 31 2.5 S-denying the signature conditions. Classification of the expanded spaces 35 2.6 More on an expanded space-time of kind IV 45 2.7 A space-time of kind IV: a home space for virtual photons 52 2.8 A space-time of kind IV: non-quantum teleportation of photons 55 2.9 Conclusions 59 Chapter 3 ENTANGLED STATES AND QUANTUM CAUSALITY THRESHOLD 3.1 Disentangled and entangled particles in General Relativity. Problem statement 61 3.2 Incorporating entangled states into General Relativity 64 3.3 Quantum Causality Threshold in General Relativity 69 3.4 Conclusions 72 Biblio...

The present book covers a wide-range of issues from alternative hadron models to their likely implications in New Energy research, including alternative interpretation of low energy reaction (coldfusion) phenomena. While some of these discussions may be found a bit too theoretical, our view is that once these phenomena can be put into rigorous theoretical framework, thereafter more 'openminded' physicists may be more ready to consider these New Energy methods more seriously. Our basic proposition in the present book is that considering these new theoretical insights, one can expect there are new methods to generate New Energy technologies which are clearly within reach of human knowledge in the coming years....

In the preceding article we argue that biquaternionic extension of Klein-Gordon equation has numerical solution with sinusoidal form, which differs appreciably from conventional Yukawa potential. In the present article we interpret and compare this result from the viewpoint of EQPET/TSC model described by Takahashi. Further observation is of course recommended in order to refute or verify this proposition....

Peer-reviewers ii Abstract iii Preface by D. Rapoport iv Contents vi Foreword viii Prologue: Socio-economic impact of New Energy technologies xi Contributors to this volume xiv Short biography of Contributors xv Free energy and Topological Geometrodynamics 1. Nuclear string hypothesis – M. Pitkanen 1 2. The notion of free-energy and many-sheeted Space-Time concept – M. Pitkanen 44 3. Prediction and calculation of New Energy development – Fu Yuhua 111 4. Some unsolved problems in the physics of elementary particle – V. Christianto & F. Smarandache (PiP, vol. 3 no. 4, 2007) 127 5. About some unsolved problems in physics – M. Pitkanen 132 Beyond Standard Model, Unmatter and Yang-Mills Field 6. Bifurcations and pattern formation in particle physics: an introductory study – E. Goldfain (submitted to APS conference, 2008) 151 7. Dynamics of Neutrino oscillations and the Cosmological constant problem – E. Goldfain 168 8. Fractional dynamics and the Standard Model of Elementary particles – E. Goldfain (Comm. In Nonlin. Science and Numerical. Simulation, 2007) 176 9. A new possible form of Matter, Unmatter – formed by parti...

As someone who works heavily in both math and computers, I can truly appreciate the role that logic plays in our modern world. One cannot understand the foundations of mathematics while lacking knowledge of the basics of logic and how proofs are constructed. Two of the first classes I took as a graduate student in mathematics were in the foundations of mathematics, and hardly a day goes by where I do not use some topic from those courses. Logic is also a fundamental component of advanced computer classes. I am currently teaching advanced courses in assembly language programming and computer organization. Reference is constantly being made to how the rules of logic are incorporated into the fundamental circuits of a computer. The logic used in these classes is known as classical or Boolean logic. Neutrosophic logic is an extension of classical logic, but as you will see in the book, there are two intermediate steps between them. Neutrosophic logic is yet another idea generated by Florentin Smarandache, who seems to be a perpetual idea machine. Like classical logic, it can be used in many ways, everywhere from statistics to quantum me...

For most of the 20th century, both relativity and star travel fascinated this writer. The reasons Albert Einstein concluded there is an absolute barrier at the speed of light seemed at first clear, then later not so clear upon closer examination. "The speed of light relative to what?" I often asked anyone who would listen. The common response was, "Light needs no specification of that kind; its speed is the same no matter who measures it." "That's true." I would respond; "That's just the second postulate of special relativity which is not in doubt; but that postulate applies to light, and we're talking about rocketships here." However it seemed that no one understood what I was saying. By referring to the universal constant c= 299.792 458 megameters per second as "the speed of light," we paint ourselves into a logical corner in which light is automatically taken as the subject of discussion even when it is not. The careful reader will know not to immediately think "light" when he hears or reads "the speed of light." But it is better to have a neutral name for that universal constant. It has been called the Lorentz speed; Ignaz...

One's reach should exceed one's grasp. Thus we reach for Alpha Centauri with a round-trip manned and womanned mission as the proposed overarching goal under a clear plan of exploration - a grand experiment described in later chapters. Whether or not we succeed in grasping the goal under this or under any plan is not as important as it is to set a definite plan and work towards its goal. The plan outlined here is in two phases: Phase one has a high probability of success, given the required propulsion system; the chances of phase two working will be indicated by results obtained from phase one. A fundamental problem is the one of propulsion. It is important to the working of this plan, a highly optimistic one, that the engine be capable of a sustained acceleration of ¼ G in phase one and 1G in phase two. (1G = 9.80665 m/s2) Such an engine is within the reach of present ideas....

Prefaces. 6 -- Ch.1. Introduction . 11 -- Ch.2. The Human Barrier. 14 -- Ch.3. An Overview. 18 -- Ch.4. Acceleration Due to Light Pressure. 21 -- Ch.5. Light Sailing is Not All There Is. 27 -- Ch.6. Einstein's Light Barrier. 32 -- Ch.7. The Phase One Experiment: The First Starship. 37 -- Ch.8. The Phase Two Experiment: Alpha Centauri or Bust!. 45 -- Ch.9. Voyage to the Center of the Galaxy. 50 -- Ch.10. An Hypothesis: There is no Speed Barrier in the Universe. 52 --...

Philosophiæ Naturalis Principia Mathematica, Latin for "Mathematical Principles of Natural Philosophy", often referred to as simply the Principia, is a work in three books by Sir Isaac Newton, first published 5 July 1687. Newton also published two further editions, in 1713 and 1726. The Principia states Newton's laws of motion, forming the foundation of classical mechanics, also Newton's law of universal gravitation, and a derivation of Kepler's laws of planetary motion (which Kepler first obtained empirically). The Principia is "justly regarded as one of the most important works in the history of science". The French mathematical physicist Alexis Clairaut assessed it in 1747: "The famous book of mathematical Principles of natural Philosophy marked the epoch of a great revolution in physics. The method followed by its illustrious author Sir Newton, spread the light of mathematics on a science which up to then had remained in the darkness of conjectures and hypotheses." A more recent assessment has been that while acceptance of Newton's theories was not immediate, by the end of a century after publication in 1687, "no one could deny...

Scientia Magna is published annually in 200-300 pages per volume and 1,000 copies on topics such as mathematics, physics, philosophy, psychology, sociology, and linguistics. ...

x3. Some Observations Some observations about the Pseudo-Smarandache Function are given below : Remark 3.1. Kashihara raised the following questions (see Problem 7 in [1]) : (1) Is there any integer n such that Z(n) > Z(n + 1) > Z(n + 2) > Z(n + 3)? (2) Is there any integer n such that Z(n) < Z(n + 1) < Z(n + 2) < Z(n + 3)? The following examples answer the questions in the affirmative: ...

A. Majumdar : A note on the Pseudo-Smarandache function 1 S. Gupta : Primes in the Smarandache deconstructive sequence 26 S. Zhang and C. Chen : Recursion formulae for Riemann zeta function and Dirichlet series 31 A. Muktibodh : Smarandache semiquasi near-rings 41 J. Sandor : On exponentially harmonic numbers 44 T. Jayeo. la : Parastrophic invariance of Smarandache quasigroups 48 M. Karama : Perfect powers in Smarandache n-expressions 54 T. Jayeo. la : Palindromic permutations and generalized Smarandache palindromic permutations 65 J. Sandor : On certain inequalities involving the Smarandache function 78 A. Muktibodh : Sequences of pentagonal numbers 81 J. Gao : On the additive analogues of the simple function 88 W. Zhu : On the primitive numbers of power p 92 A. Vyawahare : Smarandache sums of products 96 N. Yuan : On the solutions of an equation involving the Smarandache dual function 104 H. Zhou : An in¯nite series involving the Smarandache power function SP(n) 109...

Research papers presented in this collection manifest only a few of many possible applications of neutrosophic logics to theoretical physics. Most of these applications target the theory of relativity and quantum physics, but other sections of physics are also possible to be considered....

We apply the S-denying procedure to signature conditions in a four-dimensional pseudo-Riemannian space — i. e. we change one (or even all) of the conditions to be partially true and partially false. We obtain five kinds of expanded space-time for General Relativity. Kind I permits the space-time to be in collapse. Kind II permits the space-time to change its own signature. Kind III has peculiarities, linked to the third signature condition. Kind IV permits regions where the metric fully degenerates: there may be non-quantum teleportation, and a home for virtual photons. Kind V is common for kinds I, II, III, and IV....

Preface, by Dmitri Rabounski ............................5 General Relativity, Gravitation, and Cosmology................6 S-Denying of the Signature Conditions Expands General Relativity’s Space, by Dmitri Rabounski, Florentin Smarandache, Larissa Borissova, Progress in Physics, 13-19, Vol. 3, 2006.......7 Positive, Neutral, and Negative Mass-Charges in General Relativity, by Larissa Borissova and Florentin Smarandache, Progress in Physics, 51-54, Vol. 3, 2006. .............14 Extension of the Big Bang Theory, by Florentin Smarandache, Bulletin of Pure and Applied Sciences, 139-140, Vol. 23D, No. 2, 2004. .....................18 What Gravity Is. Some Recent Considerations, by Vic Christianto and Florentin Smarandache, Progress in Physics, 63-67, Vol. 3, 2008. .......................20 A Few Remarks on the Length of Day: A Cosmological Perspective, by Vic Christianto, Matti Pitkaneny, and Florentin Smarandache, Progress in Physics, L3-L4, Vol. 1, 2009............25 Quantum Physics and Statistics .......................27 A Note on Unified Statistics Including Fermi-Dirac, Bose-Einstein, and Tsallis Statistic...

Scientia Magna is published annually in 200-300 pages per volume and 1,000 copies on topics such as mathematics, physics, philosophy, psychology, sociology, and linguistics....

An identity involving the function ep(n) Abstract The main purpose of this paper is to study the relationship between the Riemann zeta-function and an in¯nite series involving the Smarandache function ep(n) by using the elementary method, and give an interesting identity. Keywords Riemann zeta-function, in¯nite series, identity. x1. Introduction and Results Let p be any fixed prime, n be any positive integer, ep(n) denotes the largest exponent of power p in n. That is, ep(n) = m, if pm j n and pm+1 - n. In problem 68 of [1], Professor F.Smarandache asked us to study the properties of the sequence fep(n)g. About the elementary properties of this function, many scholars have studied it (see reference [2]-[7]), and got some useful results. For examples, Liu Yanni [2] studied the mean value properties of ep(bk(n)), where bk(n) denotes the k-th free part of n, and obtained an interesting mean value formula for it. That is, let p be a prime, k be any fixed positive integer, then for any real number x ¸ 1, we have the asymptotic formula....

F. Ayatollah, etc. : Some faces of Smarandache semigroups' concept in transformation semigroups' approach 1 G. Feng : On the F.Smarandache LCM function 5 N. Quang and P. Tuan : An extension of Davenport's theorem 9 M. Zhu : On the hybrid power mean of the character sums and the general Kloosterman sums 14 H. Yang and R. Fu : An equation involving the square sum of natural numbers and Smarandache primitive function 18 X. Pan and P. Zhang : An identity involving the Smarandache function ep(n) 26 A.A.K. Majumdar : A note on the Smarandache inversion sequence 30 F. Li : Some Dirichlet series involving special sequences 36 Y. Wang : An asymptotic formula of Sk(n!) 40 S. Gao and Z. Shao : A fuzzy relaxed approach for multi-objective transportation problem 44 J. Li : An infinity series involving the Smarandache-type function 52 B.E. Carvajal-Gamez, etc. : On the Lorentz matrix in terms of Infeld-van der Waerden symbols 56 X. Li : On the mean value of the Smarandache LCM function 58 K. Ran and S. Gao : Ishikawa iterative approximation of fixed points for multi-valued Ástrongly pseudo-contract mappings 63 X. Fan : On the divisi...

This issue of the journal is devoted to the proceedings of the third International Conference on Number Theory and Smarandache Problems. The conference was a great success and will give a strong impact on the development of number theory in general and Smarandache problems in particular. In this volume we assemble not only those papers which were presented at the conference but also those papers which were submitted later and are concerned with the Smarandache type problems or other mathematical problems. Other papers are concerned with the number-theoretic Smarandache problems and will enrich the already rich stock of results on them. Readers can learn various techniques used in number theory and will get familiar with the beautiful identities and sharp asymptotic formulas obtained in the volume....

Abstract : Let k be any ¯xed positive integer, n be any positive integer, Sk(n) denotes the smallest positive integer m such that m! is divisible by kn: In this paper, we use the elementary methods to study the asymptotic properties of Sk(n), and give an interesting asymptotic formula for it. Keywords : F. Smarandache problem, primitive numbers, asymptotic formula. ...

J. Wang : Cube-free integers as sums of two squares 1 G. Liu and H. Li : Recurrences for generalized Euler numbers 9 H. Li and Q. Yang : Some properties of the LCM sequence 14 M. Liu : On the generalization of the primitive number function 18 Z. Lv : On the F. Smarandache LCM function and its mean value 22 Q. Wu : A conjecture involving the F. Smarandache LCM function 26 S. Xue : On the Smarandache dual function 29 N. Yuan : A new arithmetical function and its asymptotic formula 33 A. Muktibodh, etc. : Sequences of pyramidal numbers 39 R. Zhang and S. Ma : An e±cient hybrid genetic algorithm for continuous optimization problems 46 L. Mao : An introduction to Smarandache multi-spaces and mathematical combinatorics 54 M. Selariu : Smarandache stepped functions 81 X. Zhang and Y. Zhang : Sequences of numbers with alternate common di®erences 93 Y. Zhang : On the near pseudo Smarandache function 98 A. Muktibodh : Smarandache mukti-squares 102...

Scientia Magna is published annually in 200-300 pages per volume and 1,000 copies on topics such as mathematics, physics, philosophy, psychology, sociology, and linguistics....

0. In 1999, the second author of this remarks published a book over 30 of Smarandache's problems in area of elementary number theory (see [1, 2]). After this, we worked over new 20 problems that we collected in our book [28]. These books contain Smarandache's problems, described in [10, 16]. The present paper contains some of the results from [28]. In [16] Florentin Smarandache formulated 105 unsolved problems, while in [10] C.Dumitresu and V. Seleacu formulated 140 unsolved problems of his. The second book contains almost all the problems from [16], but now each problem has unique number and by this reason in [1, 28] and here the authors use the numeration of the problems from [10]. In the text below the following notations are used....

V. Mladen and T. Krassimir : Remarks on some of the Smarandache's problem. Part 2 1 W. Kandasamy : Smarandache groupoids 27 L. Ding : On 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 : On Automorphism Groups of Maps, Surfaces and Smarandache Geometries 55 L. Ding : On the mean value of Smarandache ceil function 74 M. Le : An equation concerning the Smarandache function 78 M. Bayat, H. Teimoori and M. Hassani : An extension of ABC-theorem 81 J. Ma : An equation involving the Smarandache function 89 C. Chen : Inequalities for the polygamma functions with application 91 W. Vasantha and M. Chetry : On the number of Smarandache zero-divisors and Smarandache weak zero-divisors in loop rings 96 M. Le : The function equation S(n) = Z(n) 109 Z. Li : On the Smarandache Pseudo-number Sequences 111 D. Mehendale :...

This book was intended to discuss some paradoxes in Quantum Mechanics from the viewpoint of Multi-Valued-logic pioneered by Lukasiewicz, and a recent concept Neutrosophic Logic. Essentially, this new concept offers new insights on the idea of ‘identity’, which too often it has been accepted as given....

2 Lukasiewicz Multi-Valued-logic: History and Introduction to Multi- Valued Algebra 2.1 Introduction to trivalent logic and plurivalent logic We all have heard of typical binary logic, Yes or No. Or in a famous phrase by Shakespeare: “To be or not to be.” In the same way all computer hardwares from early sixties up to this year are built upon the same binary logic. It is known that the Classical Logic, also called Bivalent Logic for taking only two values {0, 1}, or Boolean Logic from British mathematician George Boole (1815-64), was named by the philosopher Quine (1981) “sweet simplicity.” [57] But this typical binary logic is not without problems. In the light of aforementioned ‘garment analogue’, we can compare this binary logic with a classic black-and-white tuxedo. It is timeless design, but of course you will not wear it for all occasions. Aristotle himself apparently knew this problem; therefore he introduced new terms ‘contingency’ and ‘possibility’ into his modal logic [5]. And then American logician Lewis first formulated these concepts of logical modality. ...

Contents Foreword 6 1 Introduction: Paradoxes, Lukasiewicz, Multi-Valued logic 7 2 Lukasiewicz Multi-Valued Logic: History and Introduction to Multi-Valued Algebra 10 2.1. Introduction to trivalent logic and plurivalent logic 10 2.2. History of Lukasiewicz and Multi-Valued Logic 12 2.3. Introduction to Multi-Valued Algebra, Chang’s Notation 15 2.4. Linkage between Multi-Valued Logic and Quantum Mechanics 15 2.5. Exercise 17 3 Neutrosophy 25 3.1. Introduction to Neutrosophy 25 3.2. Introduction to Non-Standard Analysis 26 3.3. Definition of Neutrosophic Components 27 3.4. Formalization 28 3.5. Evolution of an Idea 30 3.6. Definition of Neutrosophic Logic 31 3.7. Differences between Neutrosophic Logic and IFL 32 3.8. Operations with Sets 33 3.9. Generalizations 34 4 Schrödinger Equation 39 4.1. Introduction 39 4.2. Quantum wave dynamics and classical dynamical system 43 4.3. A new derivation of Schrödinger-type Equation 45 5 Solution to Schrödinger’s Cat Paradox 47 5.1. Standard interpretation 47 5.2. Schrödinger’s Cat Paradox 48 5.3. Hidden-variable hypothesis 50 5.4. Hydrodynamic viewpoint and diffusion i...

Applications demonstrate the power of the DSmT framework. In this third Volume, DSmT is applied to the entire spectrum of the Information Fusion that would interest any reader in data, sensor, information, and mathematical fusion topics. Highlighted in Figure 1 are the contemporary issues that include the links between (1) data conditioning and information management, (2) combined situation and impact assessment, and (2) knowledge representation between machine processing and user coordination. Various applications leverage DSmT “Advances” listed above along with DSmH (hybrid), DSmP (Probabilistic), and DSmT theoretical insights. The third volume attacks these application issues of coordination between the “levels” of information fusion....

Part I Advances on DSmT 1 Chapter 1 An introduction to DSmT 3 by J. Dezert and F. Smarandache 1.1 Introduction . . . . . . . . . . 4 1.2 Foundations of DSmT . . . . . . . . . 4 1.2.1 The power set, hyper-power set and super-power set . . 6 1.2.2 Notion of free and hybrid DSm models . . . . 18 1.2.3 Generalized belief functions . . . . . . 20 1.2.4 The classic DSm rule of combination . . . . . 21 1.2.5 The hybrid DSm rule of combination . . . . . 22 1.2.6 Examples of combination rules . . . . . . 24 1.2.7 Fusion of imprecise beliefs . . . . . . 29 1.3 Proportional Conflict Redistribution rule . . . . . 33 1.3.1 PCR formulas . . . . . . . . . 34 1.3.2 Examples . . . . . . . . . 35 1.3.3 Zadeh’s example . . . . . . . . 39 1.4 Uniform and partially uniform redistribution rules . . . 41 1.5 RSC Fusion rules . . . . . . . . . 43 1.6 The generalized pignistic transformation (GPT) . . . . 45 1.6.1 The classical pignistic transformation . . . . 45 1.6.2 Notion of DSmcardinality . . . . . . 46 1.6.3 The Generalized Pignistic Transformation . . . 47 1.7 The DSmP transformation . . . . . . . 48 1.7.1 The Probabilistic In...

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 investigations while, Part 2 presents several applications of this new theory. Some ideas in this book are still under current development or improvements, but we think it is important to propose them in order to share ideas and motivate new debates with people interested in new reasoning methods and information fusion. So, we hope that this second volume on DSmT will continue to stir up some interests to researchers and engineers working in data fusion and in artificial intelligence....

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 rule . . . . . . . . . 6 1.2.3 The disjunctive rule . . . . . . . . . 8 1.2.4 Dempster’s rule of combination . . . . . . . 8 1.2.5 Smets’ rule of combination . . . . . . . 9 1.2.6 Yager’s rule of combination . . . . . . . 9 1.2.7 Dubois & Prade’s rule of combination . . . . . . 9 1.2.8 The hybrid DSm rule . . . . . . . . 10 1.3 The general weighted operator (WO) . . . . . . . 11 1.4 The weighted average operator (WAO) . . . . . . . 12 1.4.1 Definition . . . . . . . . . 12 1.4.2 Example for WAO . . . . . . . . . 13 1.4.3 Limitations of WAO . . . . . . . . . 13 1.5 Daniel’s minC rule of combination . . . . . . . 14 1.5.1 Principle of the minC rule . . . . . . . 14 1.5.2 Example for minC . . . . . . . . . 15 1.6 Principle of the PCR rules . . . . . . . . . 20 1.7 The...

In The 2nd Conference on Combinatorics and Graph Theory of China (Aug. 16-19, 2006, Tianjing), I formally presented a combinatorial conjecture on mathematical sciences (abbreviated to CC Conjecture), i.e., a mathematical science can be reconstructed from or made by combinatorialization, implicated in the foreword of Chapter 5 of my book Automorphism groups of Maps, Surfaces and Smarandache Geometries (USA, 2005). This conjecture is essentially a philosophic notion for developing mathematical sciences of 21st century, which means that we can combine different fields into a union one and then determines its behavior quantitatively. It is this notion that urges me to research mathematics and physics by combinatorics, i.e., mathematical combinatorics beginning in 2004 when I was a post-doctor of Chinese Academy of Mathematics and System Science. It finally brought about me one self-contained book, the first edition of this book, published by InfoQuest Publisher in 2009. This edition is a revisited edition, also includes the development of a few topics discussed in the first edition....

1.5 ENUMERATION TECHNIQUES 1.5.1 Enumeration Principle. The enumeration problem on a finite set is to count and find closed formula for elements in this set. A fundamental principle for solving this problem in general is on account of the enumeration principle: For finite sets X and Y , the equality |X| = |Y | holds if and only if there is a bijection f : X → Y . Certainly, if the set Y can be easily countable, then we can find a closed formula for elements in X....

Contents Preface to the Second Edition . . . . . . . . . . . . . . . . . . . i Chapter 1. Combinatorial Principle with Graphs . . . . . . . . . . 1 1.1 Multi-sets with operations. . . . . . . . . . . . . . . . . . . . .2 1.1.1 Set . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.1.2 Operation . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.1.3 Boolean algebra . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.1.4 Multi-Set . . . . . . . . . . . . . . . . . . . . . . . . . .8 1.2 Multi-posets . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.2.1 Partially ordered set . . . . . . . . . . . . . . . . . . . . .11 1.2.2 Multi-Poset . . . . . . . . . . . . . . . . . . . . . . 13 1.3 Countable sets . . . . . . . . . . . . . . . . . . . . . . . . 15 1.3.1 Mapping . . . . . . . . . . . . . . . . . . . . . . . . . 15 1.3.2 Countable set . . . . . . . . . . . . . . . . . . . . 16 1.4 Graphs . . . . . . . . . . . . . . . . . . . . . . . . 18 1.4.1 Graph. . . . . . . . . . . . . . . . . . . . . . . . . . . .18 1.4.2 Subgraph . . . . . . . . . . . . . . . . . . . . . . . . 21 1.4.3 Labeled graph. . . . . . ...

Progress and development in our knowledge of the structure, form and function of the Universe, in the true sense of the word, its beauty and power, and its timeless presence and mystery, before which even the greatest intellect is awed and humbled, can spring forth only from an unshackled mind combined with a willingness to imagine beyond the boundaries imposed by that ossified authority by which science inevitably becomes, as history teaches us, barren and decrepit. Revealing the secrets of Nature, so that we truly see ‘the sunlit plains extended, and at night the wondrous glory of the everlasting stars’*, requires far more than mere technical ability and mechanical dexterity learnt from books and consensus. The dustbin of scientific history is replete with discredited consensus and the grand reputations of erudite reactionaries. Only by boldly asking questions, fearlessly, despite opposition, and searching for answers where most have not looked for want of courage and independence of thought, can one hope to discover for one’s self. From nothing else can creativity blossom and grow, and without which the garden of science can o...

After the experiments were completed, the life span of such “atoms” was calculated theoretically in Chapiro’s works [61,62,63]. His main idea was that nuclear forces, acting between nucleon and anti-nucleon, can keep them far away from each other, hindering their annihilation. For instance, a proton and anti-proton are located at the opposite side of the same orbit and move around the orbit’s centre. If the diameter of their orbit is much larger than the diameter of the “annihilation area”, they can be kept from annihilation (see fig. 3). But because the orbit, according to Quantum Mechanics, is an actual cloud spreading far around the average radius, at any radius between the proton and the anti-proton there is a probability that they can meet one another at the annihilation distance. Therefore the nucleon---anti-nucleon system annihilates in any case, as this system is unstable by definition having a life span no more than 10-20 sec....

Contents Preface 5 Foreword 6 1 Unsolved Problems in Theoretical Physics 8 1.1. Problems related to elementary particles 8 1.2. Problems related to Unmatter 11 1.3 Some unresolved problems, questions and applications of the Brightsen nucleon cluster model 21 2 Unsolved Problems in Mathematics 24 2.1. Maximum number of circles 25 2.2. Consecutive sequence 25 2.3. Diophantine equation 25 2.4. Van Der Waerden Theorem 26 2.5. Differential equation with fractional power 26 2.6. Representation of odd number with prime 26 2.7. Magic square problem 27 2.8. Palindromic number and iteration 27 2.9. Non-Euclidean geometry by giving up its fifth postulate 28 2.10. Smarandache Geometry and Degree of Negation in Geometries 28 2.11. Non-Archimedean triangle theorem 33 2.12. The cubic Diophantine equation 33 2.13. Multispaces and applications in physics 34 3 Unsolved Problems in Astrophysics 35 3.1. Unsolved problems in Celestial Mechanics 35 3.2. Unsolved problems in Astrophysics 37 4 Unsolved Problems in Geophysics 45 4.1. Introduction 45 4.2. Some new questions 45 5 Unsolved Problems in Sorites Quantum Paradox and Sm...

Scientia Magna is published annually in 200-300 pages per volume and 1,000 copies on topics such as mathematics, physics, philosophy, psychology, sociology, and linguistics....

Smarandache inversion sequence Abstract We study the Smarandache inversion sequence which is a new concept, related sequences, conjectures, properties, and problems. This study was conducted by using (Maple 8){a computer Algebra System. Keywords Smarandache inversion, Smarandache reverse sequence. Introduction In [1], C.Ashbacher, studied the Smarandache reverse sequence: 1; 21; 321; 4321; 54321; 654321; 7654321; 87654321; 987654321; 10987654321; 1110987654321; (1) and he checked the _rst 35 elements and no prime were found. I will study sequence (1), from different point of view than C. Ashbacher. The importance of this sequence is to consider the place value of digits for example the number 1110987654321, to be considered with its digits like this : 11; 10; 9; 8; 7; 6; 5; 4; 3; 2; 1, and so on. (This consideration is the soul of this study because our aim is to study all relations like this (without loss of generality). Definition. The value of the Smarandache Inversions (SI) of a positive integers, is the number of the relations i > j ( i and j are the digits of the positive integer that we concern with it), where i alw...

M. Karama : Smarandache inversion sequence 1 W. He, D. Cui, Z. Zhao and X. Yan : Global attractivity of a recursive sequence 15 J. Earls : Smarandache reversed slightly excessive numbers 22 X. Ren and H. Zhou : A new structure of super R¤-unipotent semigroups 24 J. Li : An equation involving the Smarandache-type function 31 P. Zhang : An equation involving the function ±k(n) 35 Y. B. Jun : Smarandache fantastic ideals of Smarandache BCI-algebras 40 T. Jayeo. la : On the Universality of some Smarandache loops of Bol-Moufang type 45 W. Kandasamy, M. Khoshnevisan and K. Ilanthenral : Smarandache representation and its applications 59 Y. Wang, X. Ren and S. Ma : The translational hull of superabundant semigroups with semilattice of idempotents 75 M. Bencze : Neutrosophic applications in ¯nance, economics and politics|a continuing bequest of knowledge by an exemplarily innovative mind 81 J. Fu : An equation involving the Smarandache function 83 W. Zhu : The relationship between Sp(n) and Sp(kn) 87 X. Du : On the integer part of the M-th root and the largest M-th power not exceeding N 91 J. Earls : On the ten's complement fa...

The Incunabula Papers are arguably the first immersive online legend complex that introduced readers to a host of content, including what religious historian Robert Ellwood has called the “alternative reality tradition. – Legend-Tripping Online: Supernatural Folklore and the Search for Ong’s Hat...

INCUNABULA A Catalog of Rare Books, Manuscripts & Curiosa Conspiracy Theory, Frontier Science & Alternative Worlds Emory Cranston, Prop.Incunabulum: cocoon; swaddling clothes; cradle; in-cunae, in the cradle; koiman, put to sleep, winding- sheet; koimetarium (cemetery); printed books before 1501, hence by extension any rare & hermetic book… Introduction This catalog is a reproduction. This is not a commercial advertisement. ECommerce links to the available books are offered a as courtesy to researchers. Consider this first file an unusually complete bibliography to the story that unravels in the companion files. No book for sale here was actually printed before 1501, but they all answer to the description ” rare and hermetic” – even the mass market paperbacks, not to mention the xeroxes of unpublished manuscripts, which cannot be obtained from any other source! The symbol INCUNABULA was chosen for our company for it’s shape – cocoon, egg-like, gourd-like, the shape of Chaos according to Chaung Tzu. Cradle: beginnings. Sleep: dreams. Silken white sheets of birth and death; books, white pages, the cemetery of ideas. Thi...

. Incunabula A Catalogue of Rare Books, Manuscripts & Curiosa. 2. Ong's Hat: Gateway to the Dimensions! A full color brochure for the Institute of Chaos Studies and the Moorish Science Ashram in Ong's Hat, New Jersey. 4. Joseph Matheny's Journal 3. Advances in Skin Science: Quantum Tantra...

This book is devoted to an emerging branch of Information Fusion based on new approach for modeling the fusion problematic when the information provided by the sources is both uncertain and (highly) conflicting. This approach, known in literature as DSmT (standing for Dezert-Smarandache Theory), proposes new useful rules of combinations. We gathered in this volume a presentation of DSmT from the beginning to the latest development. Part 1 of this book presents the current state-of-the-art on theoretical investigations while Part 2 presents several applications of this new theory. We hope that this first book on DSmT will stir up some interests to researchers and engineers working in data fusion and in artificial intelligence. Many simple but didactic examples are proposed throughout the book. As a young emerging theory, DSmT is probably not exempt from improvements and its development will continue to evolve over the years. We just want through this book to propose a new look at the Information Fusion problematic and open a new track to attack the combination of information....

Preamble xi Prefaces xiii I Advances on DSmT 1 1 Presentation of DSmT 3 1.1 Introduction . . . . . 3 1.2 Short introduction to the DST . . . . 5 1.2.1 Shafer’s model and belief functions . . . 5 1.2.2 Dempster’s rule of combination . . . 5 1.2.3 Alternatives to Dempster’s rule of combination . . . 6 1.2.4 The discounting of sources of evidence . . . 10 1.3 Foundations of the DSmT . . . . 11 1.3.1 Notion of free and hybrid DSm models . . . 11 1.3.2 Notion of hyper-power set D_ . . . 13 1.3.3 Generalized belief functions . . . . 15 1.3.4 The classic DSm rule of combination . . . 16 1.3.5 The hybrid DSm rule of combination . . . 17 1.3.6 On the refinement of the frames . . . 18 1.3.7 On the combination of sources over different frames . . . 20 1.4 Comparison of different rules of combinations . . . 21 1.4.1 First example . . . . . 21 1.4.2 Second example . . . . 25 1.4.3 Third example . . . . 26 1.4.4 Fourth example . . . . 27 1.4.5 Fifth example . . . . . 27 1.5 Summary . . . . . 29 1.6 References . . . . . 31 2 The generation of hyper-power sets 37 2.1 Introduction . . . . . 37 2.2 Definition of hyper-po...

In the volume we assemble not only those papers which were presented at the conference but also those papers which were submitted later and are concerned with the Smarandache type problems. There are a few papers which are not directly related to but should fall within the scope of Smarandache type problems. They are 1. L. Liu and W. Zhou, On conjectures about the class number of binary quadratic forms; 2. W. Liang, An identity for Stirling numbers of the second kind; 3. Y. Wang and Z. Sheng, Two formulas for x^n in terms of Chebyshev polynomials. Other papers are concerned with the number-theoretic Smarandache problems and will enrich the already rich stock of results on them. Readers can learn various techniques used in number theory and will get familiar with the beautiful identities and sharp asymptotic formulas obtained in the volume....

On Algebraic Multi-Vector Spaces Abstract A Smarandache multi-space is a union of n spaces A1;A2;An with some additional conditions hold. Combining these Smarandache multi-spaces with linear vector spaces in classical linear algebra, the conception of multi-vector spaces is introduced. Some characteristics of multi-vector spaces are obtained in this paper. Keywords Vector, multi-space, multi-vector space, dimension of a space. x1. Introduction These multi-spaces was introduced by Smarandache in under his idea of hybrid mathematics: combining different fields into a unifying field, which can be formally defined with mathematical words by the next definition. ...

L. Mao : On Algebraic Multi-Vector Spaces 1 L. Liu and W. Zhou : On conjectures concerning class number of binary quadratic forms 7 W. Zhai and H. Liu : On square-free primitive roots mod p 15 X. Pan : A new limit theorem involving the Smarandache LCM sequence 20 M. Le : The Smarandache Perfect Numbers 24 N. Yuan : On the solutions of an equation involving the Smarandache dual function 27 J. Wang : Mean value of a Smarandache-Type Function 31 H. Yang and R. Fu : On the mean value of the Near Pseudo Smarandache Function 35 W. Liang : An Identity of Stirling Numbers of the Second Kind 40 R. Ma : On the F.Smarandache LCM Ratio Sequence 44 L. Mao : On Algebraic Multi-Ring Spaces 48 Y. Han : On the Product of the Square-free Divisor of a Natural Number 55 P. Zhang : Some identities on k-power complement 60 Y. Wang and Z. Sheng : Two Formulas for xn being Represented by Chebyshev Polynomials 64 X. Chen : Two Problems About 2-Power Free Numbers 70 X. Ma : The Asymptotic Formula of P n·x log Pad(n) 72 Q. Tian : On the K-power free number sequence 77 C. Lv : On a generalized equation of Smarandache and its integer sol...

Scientia Magna is published annually in 200-300 pages per volume and 1,000 copies on topics such as mathematics, physics, philosophy, psychology, sociology, and linguistics....

x1. Introduction The study of Smarandache loops was initiated by W.B. Vasantha Kandasamy in 2002. In her book [19], she defined a Smarandache loop (S-loop) as a loop with at least a subloop which forms a subgroup under the binary operation of the loop. For more on loops and their properties, readers should check [16], [3], [5], [8], [9] and [19]. In her book, she introduced over 75 Smarandache concepts on loops. In her ¯rst paper [20], she introduced Smarandache : left(right) alternative loops, Bol loops, Moufang loops, and Bruck loops. But in this paper, Smarandache : inverse property loops (IPL), weak inverse property loops (WIPL), G-loops, conjugacy closed loops (CC-loop), central loops, extra loops, A-loops, K-loops, Bruck loops, Kikkawa loops, Burn loops and homogeneous loops will be introduced and studied relative to the holomorphs of loops. Interestingly, Adeniran [1] and Robinson [17], Oyebo [15], Chiboka and Solarin [6], Bruck [2], Bruck and Paige [4], Robinson [18], Huthnance [11] and Adeniran [1] have respectively studied the holomorphs of Bol loops, central loops, conjugacy closed loops, inverse property loops, A-loops,...

T. Jayeo. la : An holomorphic study of the Smarandache concept in loops 1 Z. Xu : Some arithmetical properties of primitive numbers of power p 9 A. Muktibodh : Smarandache Quasigroups 13 M. Le : Two Classes of Smarandache Determinants 20 Y. Shao, X. Zhao and X. Pan : On a Subvariety of + S` 26 T. Kim, C. Adiga and J. Han : A note on q-nanlogue of Sandor's functions 30 Q. Yang : On the mean value of the F. Smarandache simple divisor function 35 Q. Tian : A discussion on a number theoretic function 38 X. Wang : On the mean value of the Smarandache ceil function 42 Y. Wang : Some identities involving the Smarandache ceil function 45 J. Yan, X. Ren and S. Ma : The Structure of principal lters on po-semigroups 50 Y. Lu : F. Smarandache additive k-th power complements 55 M. Le : The Smarandache reverse auto correlated sequences of natural numbers 58 M. Karama : Smarandache partitions 60 L. Mao : On Algebraic Multi-Group Spaces 64 F. Russo : The Smarandache P and S persistence of a prime 71 Y. Lu : On the solutions of an equation involving the Smarandache function 76 H. Ibstedt : A Random Distribution Experiment 80 L. Mao...

The 2000 year history of the atom and chemistry, from the Classic Greek Era to the present, is described in 800 pages, depicted with some 300 pictures and illustrations. This history of the atom and chemistry discusses the lives of about 180 chemists and physicists, through the evolution of several stages of development, representing the most important scientific accomplishments. The most significant discoveries in chemistry and physics are presented chronologically to illustrate their contributions to the creation of the chemical sciences during the last 21 centuries....

INTRODUCTION It is a genuine pleasure and challenge for me to try to express the full extent of my emotions and reasons for writing this book on the STORY OF THE ATOM AND THE SCIENCES, with special reference to the CHEMICAL SCIENCES. In one sentence, I can distill the essence of the purpose for this study by simply stating that it has been a labor of love that transcended the written word because sentiments and ideas belong in the realm of the ethereal and the philosophical as well as in the domain of LITERATURE and SCIENCE. Ever since a young and impressionable student attending a country school in a community of a few hundred people, began to be introduced to the world of knowledge over 65 years ago, the sciences became to me what water is to fish, air is to birds and earth is to humanity. The introduction to the mathematical, physical, chemical and biological sciences felt like reading a beautiful poem or listening to a romantic melody. In essence, it was truly a joyful experience, full of the enigmatic, the mysterious and the fantastic, beyond my wildest imagination. The words used in the title of this book, were car...

TABLE OF CONTENTS INTRODUCTION 1 THE STORY OF THE ATOM AND CHEMISTRY 7 THE CAVE MAN 7 ABSTRACT ON THE CONCEPT OF PERSPECTIVE AND SENSE OF DUTY 8 THE MIGRATORY AND THE SEDENTARY MAN 9 ABSTRACT ON THE ATOM AND ITS ENERGY 11 THE CLASSIC GREEK AND ROMAN PHILOSOPHERS 17 EMPEDOCLES (492-432 BC) Greek Philosopher 20 Proposed the four basic elements: earth, water, air and fire. DEMOCRITUS (470-380 BC) Greek Philosopher 22 The founder of the atomic theory of antiquity. CLAUDIUS PTOLEMY (100-170) Greek Astronomer 24 Proponent of the geocentric theory of our solar system with the Earth and not the Sun at its center. ABSTRACT ON THE GENESIS OF AN ORDERLY AND SYSTEMATIC UNIVERSE 25 THE ALCHEMY OF ANTIQUITY AND THE MIDDLE AGES 32 THE METAL INDUSTRY OF ANTIQUITY 33 Mercury, Copper, Bronze, Iron and Steel. GEBER (721-815) Arabian Alchemist 38 One of the first scholars and alchemists of the Islamic world. OMAR KHAYYAM (12th Century). Persian Scientist and Astronomer 38 Brilliant astronomer and alchemist of the 12th Century. BERNARDO TREVISAN (1406 -1490) Italian Alchemist 39 One of the most famous alchemists of th...

The whole paradoxist distich should be as a geometric unitary parabola, hyperbola, ellipse at the borders between art, philosophy, rebus, and mathematics – which exist in complementariness. The School of Paradoxist Literature, which evolved around 1980s, continues through these bi-verses closed in a new lyric exact formula, but with an opening to essence. For this kind of procedural poems one can elaborate mathematical algorithms and implement them in a computer: but, it is preferable a machine with … soul!...

I M M O D E S T With the shame Shamelessness U N D E C I D E D Fighting Himself J A Z Z ( I ) Melodious Anarchy J A Z Z ( I I ) Anarchic Melody...

Fore/word and Back/word _________ 3 The making of the distich : _____ 3 Characteristics: ______________ 3 Historical considerations: _____ 5 Types of Paradoxist distiches ___ 8 1. Clichés paraphrased: ___ 8 2. Parodies: _____________ 8 3. Reversed formulae: ____ 8 4. Double negation _______ 8 5. Double affirmation, ____ 8 6. Turn around on false tracks: _________________ 8 7. Hyperboles (exaggerated): __________________ 8 8. With nuance changeable from the title: ________ 8 9. Epigrammatic: ________ 8 10. Pseudo-paradoxes: ___ 8 11. Tautologies: ________ 9 12. Redundant: _________ 9 13. Based on pleonasms: _ 9 14. or on anti-pleonasms: 9 15. Substitution of the attribute in collocations ___ 9 16. Substitution of the complement in collocations 9 17. Permutation of various parts of the whole: ___ 9 18. The negation of the clichés ______________ 10 19. Antonymization (substantively, adjectively, etc.) ________________ 10 20. Fable against the grain: _________________ 10 21. Change in grammatical category (preserving substitutions’ homonymy): ________________ 10 22. Epistolary or colloquia style: _________...

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...

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....

Collected Eclectic Ideas - preface by the author.............................3 Contents....................................................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 Astronomy, by Florentin Smarandache.. 36 BIOLOGY......................................40 4. Statistical Modeling of Primary Ewing Tumors of the Bone, by Sreepurna Malakar, Florentin Smarandache, Sukanto Bhattacharya, in in , Vol. 3, No. JJ05, 81-88, 2005................41 CALCULUS....................................53 5. A Triple Inequality with Series and Improper Integrals, by Florentin Smarandache, in Bulletin of Pure and Applied Sciences, Vol. 25E, No. 1, 215-217, 2006.........54 6. Immediate Calculation of Some Poisson Type Integrals Using SuperMathematics Circular Ex-Centric Functions, by Florentin Smarandache & Mircea Eugen................................

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...

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....

Collected Eclectic Ideas - preface by the author.............................3 Contents....................................................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 Astronomy, by Florentin Smarandache.. 36 BIOLOGY......................................40 4. Statistical Modeling of Primary Ewing Tumors of the Bone, by Sreepurna Malakar, Florentin Smarandache, Sukanto Bhattacharya, in in , Vol. 3, No. JJ05, 81-88, 2005................41 CALCULUS....................................53 5. A Triple Inequality with Series and Improper Integrals, by Florentin Smarandache, in Bulletin of Pure and Applied Sciences, Vol. 25E, No. 1, 215-217, 2006.........54 6. Immediate Calculation of Some Poisson Type Integrals Using SuperMathematics Circular Ex-Centric Functions, by Florentin Smarandache & Mircea Eugen................................