smarandache notions journal, vol. 14

8/14/2019 Smarandache Notions Journal, Vol. 14

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Vol. 14, 2004 ISSN 1084-2810

SMARANDACHE NOTIONS JOURNAL

UNIVERSITY COLLEGE CORK


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This journal is an extension of the "Smarandache Function Journal",ISBN 1053-4792, Vol. 1-6, 1990-1995.

SNJ is yearly published (in the Spring or Fall) in a 300-400 pagesvolume, and 800-1000 copies.

SNJ is a referred journal: reviewed, indexed, cited by thefollowing journals: "Zentralblatt Fr Mathematik" (Germany),"Referativnyi Zhurnal" and "Matematika" (Academia Nauk, Russia),"Mathematical Reviews" (USA), "Computing Review" (USA), "LibertasMathematica" (USA), "Octogon" (Romania), "Indian Science Abstracts"(India), "Ulrich's International Periodicals Directory" (USA),"Gale Directory of Publications and Broadcast Media" (USA),"Historia Mathematica" (USA), "Journal of Recreational Mathematics"(USA), "Abstracts of Papers Presented to the American Mathematical

Society" (USA), "Personal Computer World" (U.K.), "MathematicalSpectrum" (U.K.), "Bulletin of Pure and Applied Sciences" (India),Institute for Scientific Information (PA, USA), "Library ofCongress Subject Headings" (USA).

Referents:Murad A. AlDamen, P. O. Box 713330, Hai Nazzal 11171, Amman,

Jordan.Y. V. Chebrakov, Department of Mathematics, St.-Petersburg

Technical University, Nevsky 3-11, 191186, Russia.Ion Goian, Department of Algebra, Number Theory and Logic,

State University of Kishinev, Republic of Moldova.M. Khoshnevisan, School of Accounting and Finance, Griffith

University, Australia.

Maohua Le, Department of Mathematics, Zhanjiang Normal College,29 Cunjin Road, Chikan, Zhanjiang, Guangdong, P. R. China.Chris Nash, 5000 Bryan Station Road #5, Lexington, KY 40516-9505,

USA.Sebastian Martin Ruiz, Avda. De Regla, 43, Chipiona 11550,

Cadiz, Spain.

Copyright 2004by Sabin & Tatiana Tabirca, University College Cork, Ireland.


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ASSOCIATE EDITORIAL BOARD:

Azmy Ariff, PO Box 444, Jalan Sultan, Petaling Jaya 46750,Malaysia.

Charles Ashbacher, Charles Ashbacher Technologies, Box 294,

119 Northwood Drive, Hiawatha, Iowa 52233, USA.

Krassimir Atanassov, Bulgarian Academy of Sciences, PO Box

12 MRL, Sofia, Bulgaria.Ion Balacenoiu, Department of Mathematics, University of

Craiova, Romania.

Mihaly Bencze, Str. H|rmanului 6, 2212 S|cele 3, Jud. Braov,Romania.

Henry Bottomley, 5 Leydon Close, London SE16 5PF, U.K.Micha Fleuren, Acaciastraat 16, 6598 BC Heyen, The

Netherlands.H. Gunarto, Ritsumeikan Asia-Pacific University, 1-1

Jumonjibaru, Beppu-shi 874-8577, Oita-ken, Japan.

Henry Ibstedt, Glimminge 2036, 280 60 Broby, Sweden.Howard Iseri, Department of Mathematics, Mansfield University,

Mansfield, PA 16933, USA.Muneer Jebreel, SS-Math-Hebron, UNRWA, Field Education

Officer, Box 19149, Jerusalem, Israel. W. B. Vasantha Kandasamy, Indian Institute of Technology,

Madras, Chennay 600 036, India.A.A.K. Majumdar, Department of Mathematics, Jahangirnagar

University, Savar, Dhaka 1342, Bangladesh.Leonardo Fernandes Dias da Motta, Av. Conselheiro Furtado,

1574, Apt. 501, Bairro Batista Campos, Belem, PA 66040-100, Brasil.

Felice Russo, Micron Technology Italy, Avezzano (Aq), Italy.

Vasile Seleacu, Department of Mathematics, University ofCraiova, Romania.

Y. A. Shmagin, Department of Mathematics, St.-PetersburgTechnical University, Nevsky 3-11, 191186, St.-Petersburg,Russia.

Delfim F. M. Torres, Department of Mathematics, Universityof Aveiro, 3810-193, Portugal.

Angela Vasiu, Mathematics Department, Babes-BolyaiUniversity, Cluj-Napoca, Romania.

Bouzza El Wahbi, Dpartment de Mathmatques et

Informatiques, Facult des Sciences, B.P. 2121 Ttouan, Morocco.

Zhang Wenpeng, Department of Mathematics, Xian Universityof Technology, Xian, Shaanxi, P.R. China.

Lamarr Widmer, Department of Mathematics, Messiah College,Grantham, PA 17027, USA.

INDICATION TO AUTHORS


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Authors of papers concerning any of Smarandache type functions,numbers, sequences, integer algorithms, paradoxes, Non-Euclideangeometries, etc. are encouraged to submit manuscripts to Editors:

Prof. Sabin & Tatiana TabircaDepartment of Mathematics

University College Cork, Ireland.

The submitted manuscripts may be in the format of remarks,conjectures, solved/unsolved or open new proposed problems,notes, articles, miscellaneous, etc. They must be original workand camera ready [typewritten/computerized, format: 8.5 x 11

inches (. 21,6 x 28 cm)]. They are not returned, hence weadvise the authors to keep a copy.

The title of the paper should be writing with capital letters.

The author's name has to apply in the middle of the line, nearthe title. References should be mentioned in the text by anumber in square brackets and should be listed alphabetically.Current address followed by e-mail address should apply at theend of the paper, after the references.

The paper should have at the beginning an up to a half-pageabstract, followed by the key words.

All manuscripts are subject to anonymous review by two or moreindependent sources.

Every letter will be answered.

The authors will receive free copies of the journal.

Papers in electronic form are accepted. They can be e-mailedin Microsoft Word XP (or lower), WordPerfect 7.0 (or lower), PDF6.0 or lower.


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C O N T E N T S

MATHEMATICS:

PAULO D. F. GOUVEIA, DELFOM F. M. TORRES, Smarandache Sequences: Explorationsand Discoveries with a Computer Algebra System .... 5

HENRY IBSTEDT, Palindrome Studies (Part I: the Palindrome Concept and Its Applicationsto Prime Numbers) .....23

A. S. MUKTIBODH, V. M. WAGH, Chains of Smarandache Semifields ...36

CHARLES ASHBACHER, On Numbers That Are Pseudo-Smarandache and SmarandachePerfect ...40

A. W. VYAWAHARE, K. M. PUROHIT, Near Pseudo-Smarandache Function ....42

ZHANG TIANPING, On the k-Power Free Number Sequence 62

ZHU WEIYI, On the k-Power Complement and k-Power Free Number Sequence 66

HE XIAOLIN, GUO JINBAO, On the 80-th Problem of F. Smarandache (I) 70

HE XIAOLIN, GUO JINBAO, On the 80-th Problem of F. Smarandache (II) ..74

MUNEER JEBREEL KARAMA, Smarandache Concatenated Magic Squares ..80

ZHENG JIANFENG, Proof of Functional Smarandache Iterations .. 84

ZHENG JIANFENG, On the Inferior and Superior k-th Power Part of a Positive Integer andDivisor Function ..88A. A. MAJUMDAR, H. GUNARTO, On Some Recurrence Type Smarandache sequences 92

ADRIAN VASIU, ANGELA VASIU, The Fulfilled Euclidean Plane 113

DELFIM F. M. TORRES, Nmeros Felizes e Sucesses de Smarandache Digresses com oMaple.119JOHN PERRY, Calculating the Smarandache Numbers 124

JZSEF SNDOR, On Additive Analogues of Certain Arithmetic Functions ..128

SABIN TABIRCA, KIERAN REYNOLDS, Recursive Prime Numbers ..133

MUNEER JEBREEL, Smarandache Sequence of Happy Cube Numbers .139

ZHU WEIYI, On the Divisor Product Sequence ..144

ZHANG TIANPING, On the Cubic Residues Numbers and k-Power Complement Numbers.....147

MAOHUA LE, A Conjecture Concerning the Smarandache Dual Function 153LIU HONGYAN, LOU YUANBING, A Note on the 29-th Smarandaches Problem ....156

XU ZHEFENG, On the k-Full Number Sequence ..159

LIU HONGYAN, ZHANG WENPENG, A Note on the 57-th Smarandaches Problem ...164

SEBASTIAN MARTIN RUIZ, Diverse Algorithms to Obtain Prime Numbers Based on thePrime Function of Smarandache .166


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LIU HONGYAN, ZHANG WENPENG, On the Simple Numbers and the Mean ValueProperties ...171

MOHUA LE, The Divisibility of the Smarandache Combinatorial Sequence of Degree Two.176

MAOHUA LE, The Smarandache Sequence ...178

MAOHUA LE, Two Functional Equations ..180

MAOHUA LE, Two Formulas for Smarandache LCM Ratio Sequences ..183

MAOHUA LE, An Equation Concerning the Smarandache LCM Functions ...186

GAO JING, LIU HUANING, On the 45-th Smarandaches Problem 189

GAO JING, LIU HUANING, On the Mean Value of Smarandache Double Factorial Function.193

CHARLES ASHBACHER, LORI NEIRYNCK, The Density of Generalized SmarandachePalindromes 196

ZHU WEIYI, On the Cube Free Number Sequence 199GAO JING, On the 49-th Smarandaches Problem .203

HOWARD ISERI, Paper Models of Surfaces with Curvature Creative Visualization Labs ..205

CHARLES T. LE, BERND HUTSCHENREUTHER, Die Smarandachesche Klasse vonParadoxien . ...211

BOUAZZA EL WAHBI, Convergence of the Smarandache General Continued Fraction ...213

MUNEER JEBREEL, The first 10-th Smarandache Symmetric Numbers 215

LIU HUANING, ZHANG WENPENG, On the 57-th Smarandaches Problem 218

MAOHUA LE, Some Problems Concerning the Smarandache Square Complementary

Function (I) 220JASON EARLS, Some Results Concerning the Smarandache Deconstructive Sequence .222

LOU YUANBING, An Asymptotic Formula Involving Square Complement Numbers .227

FELICE RUSSO, On A Problem Concerning the Smarandache Left-Right Sequences ...230

CHARLES ASHBACHER, Some Properties of the Happy Numbers and the Smarandache H-Sequence .236

JASON EARLS, Some Smarandache-Type Sequences and Problems Concerning Abundantand Deficient Numbers ..243

JASON EARLS, On Smarandache Repunit n Numbers .251

CHARLES ASHBACHER, Some Simple Advantages of Reasoning in IntuitionisticNeutrosophic Logic 257

JASON EARLS, Smarandache Iterations of the First Kind on Functions Involving Divisorsand Prime Numbers ...259

JASON EARLS, The Smarandache Sum of Composites between Factors Function 265

YAO WEILI, On the Mean Value of m-th Power Free Numbers ...271


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JASON EARLS, A Note on the Smarandache Divisors of Divisors Sequence and Two similarSequences ...274

SEBASTIAN MARTIN RUIZ, Formula to Obtain the Next Prime Number in Any IncreasingSequence of Positive Integer Numbers .276

W. B. VASANTHA KANDASAMY, Smarandache Non-Associative (SNA-) Rings ...281

W. B. VASANTHA KANDASAMY, Smarandache Pseudo-Ideals ..294

HOWARD ISERI, Impulse Gauss Curvature ..299

W. B. VASANTHA KANDASAMY, Smarandache-Galois Fields ...310

W. B. VASANTHA KANDASAMY, Smarandache Near-Rings and Their Generalizations ..315

W. B. VASANTHA KANDASAMY, Smarandache Semi-Automaton and Automaton ..320

W. B. VASANTHA KANDASAMY, Smarandache Zero Divisors ...325

MAOHUA LE, Some Problems Concerning the Smarandache Square ComplementaryFunction (II) ..330

MAOHUA LE, Some Problems Concerning the Smarandache Square ComplementaryFunction (III) .333

MAOHUA LE, Some Problems Concerning the Smarandache Square ComplementaryFunction (IV) .335

MAOHUA LE, Some Problems Concerning the Smarandache Square ComplementaryFunction (V) ...338

MAOHUA LE, The Smarandache Combinatorial Sequences .341

MAOHUA LE, A Conjecture Concerning Indexes of Beauty .343

MAOHUA LE, The Smarandache-Riemann Zeta Sequence ..346

LI HAILONG, On Third Power Mean Values Computation of Digital Sum Function in Base n..348

HENRY BOTTOMLEY, A Lucky Derivative ...352

HOWARD ISERI, A Classification of S-Lines in a Closed S-Manifold .354

SEBASTIAN MARTIN RUIZ, AZMY ARIFF, A Basic Characteristic of Twin Primes and ItsGeneralization 357

SEBASTIAN MARTIN RUIZ, Formula to Obtain the Next Prime in an ArithmeticProgression .363

SHYAM SUNDER GUPTA, Smarandache Sequence of Triangular Numbers .366

PHYLOSOPHYFENG LIU, Truth and Absolute Truth in Neutrosophic Logic ..369

FENG LIU, Toward Excitation and Inhibition in Neutrosophic Logic ..381

FLAVIAN VASILE, Processes of Consciousness 389

CHENG-GUI HUANG, A Note on Neutrosophy and Buddhism 398


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PHYSICS:HOMER B. TILTON, Reverse Engineer the Universe! ...399

SOCIEDAD ESPAOLA DE EXOBIOLOGIA, HG Wells Telecom (Pregntale al Cientfico)

.404SOCIEDAD ESPAOLA DE EXOBIOLOGIA, Estacin Central Tiempo (Pregntale alCientfico) ...407

J. HARRI T. TIAINEN, The Schrdinger Cat Thought Experiment Land (The SCTE Land).409

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