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ALGEBRAS, GROUPS AND GEOMETRIES

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ALGEBRAS, GROUPS AND GEOMETRIES

VOLUME 24, NUMBER 1, MARCH 2007

THE HYPERBOLIC CLIFFORD ALGEBRA OF MULTIVECFORS, 1
W. A. Rodrigues Jr. and Q. A.G. de Souza
Institute of Mathematics, Statistics and Scientific Computation
IMECC- UNICAMP CP 6065
13083-859 Campinas, SP, Brazil

DUALITY PRODUCTS OF MULTIVECTORS AND MULTIFORMS,
AND EXTENSORS, 25
V.V. Ferna~ndez , A. M. Moya, W. A. Rodrigues Jr.
Institute of Mathematics,
Satistics and Scietntifics Computation
IMECC-UNICAMP CP 6068
13083-859, SP, Brazil and
E. Notte- Cuello
Departamento de Matema~ticas
Universidad de La Serena
Av. Cisternas 1200, La Serena-Chile

KOBER FRACTIONAL q-INTEGRAL OF MULTIPLE BASIC
HYPERGEOMETRIC FUNCTIONS, 55
R. K. Yadav
Department of Mathematics and Statistics
Jai Narain Vyas University,
Jodhpur - 342005, Rajasthan (India)
S.D. Purohit
Department of Basic Sciences (Mathematics)
College of Technology and Engineering
M.P. University of Agriculture and Technology
Udaipur- 313001, India and
S.L. Kalla
Department of Mathematics and Computer Science
P.O. Box 5969 , Safat 13060
Kuwait University, Kuwait

VERTICAL AND COMPLETE LIFTS TO VECTOR BUNDLE, 75
Mehmet Yildirim
Department of Mathematics
Faculty of Science and Arts Kirikkale University
71451 Yahsihan, Kirikkale, Turkey and
Erdogan Esin
Department of Mathematics
Faculty of Science and Arts Gazi University
06500 Teknikokullar, Ankara, Turkey

QUATERNION CR-SUBMANIFOLD OF LOCALLY
CONFORMAL QUATERNION KAEHLER MANIFOLD, 87
M.F. Naghi, M.H. Shahil and F.R. Al-Solamy
Departament of Mathematics King Abdul Aziz University
P.O. Box 80015, Jeddah 21589, Saudi Arabia

CHARACTERIZATION OF FGI-DUO-RINGS, 105
Mamadou Barry
De~partement de Mathe~matiques et Informatique
Faculte~ des Sciences et Techniques
Universite~ Cheikh Anta Diop, Dakar, Se~ne~gal
Oumar Diankha and Mamadou Sanghare
De~partement de Mathe~matiques et Informatique
Faculte~ des Sciences et Techniques,
UCAD, Dakar, Senegal

UNIVERSAL COVERS OF TOPOLOGICAL VECTOR SPACES, 119
N. Alemdar and O. Mucuk
Department of Mathematics
Erciyes University
Kayseri 38039, Turkey

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ALGEBRAS, GROUPS AND GEOMETRIES

VOLUME 24, NUMBER 2, JUNE 2007

PARALLELISM STRUCTURE ON A SMOOTH MANIFOLD, 129
V.V. Fernandez, A. M. Moya, W.A. Rodriguez Jr.
Institute of Mathematics, Statistics and Scientific Computation
IMECC-UNICAMP CP 6065, 13083 Campinas, SP, Brazil and
E. Notte-Cuello
Departamento de Matematicas
Universidad de La Serena
Av. Cisternas 1200, La Serena-Chile

COMPORTEMENT DES FONCTIONS BISURHARMONIQUES
ET PROBLEME DE RIQUIER FIN
A LA FRONTIERE DE MARTIN BIHARMONIQUE, 155
M. El Kadiri
B.P. 726, Sale~-Tabriquet, Sale~, Maroc and
S. Haddad
595, rue Tarfaya, El massira 1
Temara, Maroc

ACTIONS OF A 2-GENERATED GROUP ON PL(Fq):
THE PARAMETRIZATION PROBLEM, 187
M. Ashiq
Department of Basic Sciences and Humanities
College of E & ME
National University of Sciences and Technology
Rawalpindi, Pakistan, 46,000 and
Q. Mushtaq
Department of Mathematics
Quaid-i-Azam University
Islamabad, Pakistan

ON THE GENERATION OF CONWAY GROUPS
BY CONJUGATE INVOLUTIONS, 203
Faryad Ali and M. Ali Faya Ibrahim
Department of Mathematics
King Khalid University
Abha, Saudi Arabia

k- LIFTS TO EXTENDED MANIFOLDS , 211
M. Yildirim
Department of Mathematics
Faculty of Science and Arts
Kirikkale University
71451 Yahsihan
Kirikkale, Turkey

COVARIANT DERIVATIVES OF
MULTIVECTOR AND MULTIFORM FIELDS, 221
V.V. Fernandez, A.M. Moya, W.A. Rodrigues Jr.
Institute of Mathematics Statistics and Scientifics Computation
IMECC-UNICAMP CP 6065,
13083-859 Campinas, SP, Brazil and
E. Notte-Cuello
Departamento de Matema~ticas, Universidad de La Serena
Av. Cisternas 1200, La Serena, Chile

COMPLETELY INTEGRABLE DISTRIBUTION METHOD
IN THE THEORY OF OF THE FIRST
INTEGRALS OF ORDINARY DIFFERENTIAL EQUATIONS, 237
Moskaliuk S.S.
Bogolyubov Institute for Theoretical Physics
Metrolohichna Street, 14-b
Kyiv-143, Ukraine, UV- 03143

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ALGEBRAS, GROUPS AND GEOMETRIES

VOLUME 23, NUMBER 1, MARCH 2006

SCHWARTZ LEMMA FOR LOCALLY BOUNDED SPACES, 1
A. Bayoumi
Department of Mathematics
College of Sciences , King Saud University
P.O. Box 2455, Riyadh 11451, Saudi Arabia and
Institute for Basic Research
P.O. Box 1577, Palm Harbor, FL 34682, U.S.A.

THE AXIOM SYSTEM OF THE THIRD TYPE LIMIT
AND ITS APPLICATION -SIMULTANEOUS VERIFICATION
OF GLODBACH CONJECTURE AND FERMAT CONJECTURE, 9
Yingjie Li
Department of Mathematics and Computer Science
Guangdong Medical College
Zhanjiang, Guangdong 524023, P.R. China

ON A GENERALIZED WRIGHT TRANSFORM, 25
R.K. Saxena*, J.Ram*, D.L. Suthar* and S.L. Kalla **
*Department of Mathematics and Statistics
Jai Narain Vyas University, Jodhpur - 342005, Rajasthan (India)
**Department of Mathematics and Computer Science
P.O. Box 5969 , Safat 13060 , Kuwait University, Kuwait

FRATTINI SUBALGEBRAS OF n- LIE ALGEBRAS II , 43
Ruipu Bai, Yu Cheng, Ximei Bai
Department of Mathematics
Hebei University, 071002 Boading, China

CHARACTERIZATIONS OF SOME n- ORDERED TOPOLOGICAL
STRUCTURES FOR RA- RELATIONS, 55
H. Kabadayi
Departament of Mathematics, Science Faculty
Ankara University
Tandogan, Ankara 06100, Turkey
M. V. Mielke<
Department of Mathematics
University of Miami
Coral Gables, FL 33124, USA

DERIVATIONS AS HOMOMORPHISMS AND
ANTI -HOMOMORPHISMS IN s - PRIME RINGS, 67
L. Oukhtite
Universite' Moulay Ismail, Faculte' des Sciences et Techniques
Departement de Mathematiques
B. P. 509 -Boutalamine, Errachidia, Maroc
S. Salhi
Universite' Sidi Mohamed Abdellah, Faculte' des Sciences
Departement de Mathematiques et Informatique
B. P. 1796- Atlas , Fes, Maroc

ENUMERATION OF DERIVATIONS AND SECTIONS, 73
M. Alp
Dumlupinar University,Art and Science Faculty
Department of Mathematics, Kutahya, Turkey

INTERPLAY BETWEEN CR- STRUCTURE
AND f (( k + 1) , (k - 1)- STRUCTURE
SATISFYING f k+1 + f k-1 = 0, 85
L.S. Das
Department of Mathematics
Kent State University
New Philadelphia, OH 44663, U.S.A.

GENERALIZATION OF CHEN¹S INEQUALITY, 93
T. Oprea
University of Bucharest, Faculty of Mathematics
14 Academiei St. , code 010014, Buchares, Romania

MAXIMUM PRINCIPLE AND EXISTENCE OF SOLUTIONS
FOR NON NECESSARILY COOPERATIVE SYSTEMS
INVOLVING SCHRO¤DINGER OPERATORS , 105
H.M. Serag
Mathematics Department, Faculty of Science
Al-Azhar University
Nasr City (11884) Cairo, Egypt
A.H. Quamlo
Mathematics Department, Faculty of Education for Girls
Makka, P.O. Box 3653, Saudi Arabia

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ALGEBRAS, GROUPS AND GEOMETRIES

VOLUME 23, NUMBER 2, JUNE 2006

ON THE NOTIONS OF LAGRANGIAN, FINSLERIAN,
HAMILTONIAN AND CARTANIAN MECHANICAL SYSTEMS, 123
R. Miron
Faculty of Mathematics, University ³Al. I. Cuza²
Iasi, 700506, Romania

THE TRANSLATIONAL HULL OF A- WRPP SEMIGROUPS, 131
Ren. X. M. and Li. S. B.
Department of Mathematics
Xi¹an University of Architecture and Technology
Xi¹an 710055, China
K.P. Shum
Faculty of Science, The Chinese University of Hong Kong
Hong Kong, China (SAR)

SOME OPEN QUESTIONS IN FINITE SEMIFIELDS, 141
G.P. Wene
Department of Applied Mathematics
The University of Texas at San Antonio
6900 North Loop 1604 West
San Antonio, Texas, 78249 U.S.A.

AN OPTIMAL SYSTEM AND SYMMETRY
REDUCTION OF THE BURGERS EQUATION, 153
A.Ouhadan and E.H. El Kinani
Moulay Ismail University, Faculty of Science and Technics
Department of Mathematics
Group of Algebras and Applications P.O. BOx 509 Boutalamine, Errachidia, Morocco
UFR de Science de l¹Inge~nieur
Faculte~ des Science et Technique
Boutalamine B.P. 509, Errachidia, Morocco

ON THE MEASURE OF TRANSCENDENCE OF
FORMAL LAURENT SERIES, 167
A. S. Ozdemir
Marmara University, A. Education Faculty
Department of Mathematics Goztepe-Kadikoy
Istanbul, Turkey

CC-ANALOG OF THE THEOREM OF PYTHAGORAS, 179
O. Gelisgen and R. Kaya
University of Eskisehir Osmangazi
Faculty of Science and Art
Department of Mathematics
26480 Eskisehir, Turkey

PSEUDO-RIEMANNIAN STRUCTURES
WITH THE SAME CONNECTION, 189
G. Bercu
University of Galati, Department of Mathematics
48, Domneasca Str., 6200 Galati, Romania

PRIME AND SPECIAL RADICALS IN NEAR-RINGS, 209
H. Altindis, E. Aygu�n
Faculty of Art and Science, Department of Mathematics
University of Erciyes, 38039, Kayseri, Turkey
A.O. Atyagu�n
Yozgat Faculty of Arts and Science, Department of Matmematics
University of Erciyes, 66100, Yozgat, Turkey

AUTOMORPHISMS AND ISOMORPHISMS OF
RESTRICTED WEYL TYPE ALGEBRAS I , 219
Ki-Bong Nam
Department of Mathematics and Computer Science
University of Wisconsin-Whitewather
800 West Main Street
Whitewater, WI 53190 USA

FIFTEEN CONSECUTIVE INTEGERS WITH
EXACTLY k PRIME FACTORS, 229
Chun-Xuan Jiang
Beijing 100854, P.O. Box 3924
P.R.China

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ALGEBRAS, GROUPS AND GEOMETRIES

VOLUME 23, NUMBER 3, SEPTEMBER 2006

MECHANICAL SYSTEMS ON LIE ALGEBROIDS, 235
M. Anastasiei
Institute for Basic Reasearch
Palm Harbor, Fl. 34682, USA and
Department of Geometry
Faculty of Mathematics, University ³Al.I. Cuza²
Bd. Carol I 11, Iasi, Romania

SUPER- DIFFERENTIAL CALCULUS IN F- SPACES, 246
A. Bayoumi
Stockholm University, Department of Mathematics
S- 106 91 Stockholm, Sweden and
Institute for Basic Research
Palm Harbor, Fl 34682, U.S.A

PRIMITIVE LIFTING IN FREE NILPOTENT LIE ALGEBRAS, 273
Z. Ozkurt
Cukurova University
Department of Mathematics
01330- Adana, Turkey

A NOTE ON MAXIMAL CAP- SUBGROUPS OF FINITE GROUPS , 285
Yangming Li
Department of Mathematics
Institute of Education, Guangzhou, 510310, China and
Guojun Wang
Department of Mathematics
Zhejiang University, Hangzhou, 310028, China

ON SEMI-INVARIANT SUBMANIFOLDS OF CONFORMAL K (x)
CONTACT RIEMANNIAN MANIFOLD, 291
L. S. Das
Department of Mathematics
Kent State University
New Philadelphia, OH 44663, USA
Ram Nivas
Department of Mathematics and Astronomy
Lucknow University, Lucknow 226007, India
M. Nazrul I. Khan
Azad Institute of Engineering and Technology
Department of Applied Sciences and Humanities
Natkur, Post-Chadrawal, Bangla Bazar Road
Lucknow 226002, India

FINITE DENSITY EFFECTS IN HOSOTANI MECHANISM
AND A VACUUM GAUGE BALL, 303
Yoshinori Cho and Kiyoshi Shiraishi
Graduate Schol of Science and Engineering
Yamaguchi University
Yamaguchi- shi, Yamaguchi 753-8512, Japan

SUR LES ALGEBRES QUASI- CONSTANTES II, 326
I. Katambe
Department de Mathematiques
Faculte~ des Sciences, Universite~ de Niamey
B.P. 10662, Niamey, Niger
A. Micali
Department de Mathematiques
Universite~ Montpellier II
Place Eugene Bataillon, F34095 Montpellier, France
M. Ouattara
Department de Mathematiques
UFR Sciences Exactes et Appliquees
Universite~ de Ouagadougou
03 B.P. 7021 Ouagadougou 03, Burkina Faso
J. Rodary
I.U.T. de Tremblay
Universite~ Paris VIII, Rue de la Raperie
F93290 Tremblay-en-France, France

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ALGEBRAS, GROUPS AND GEOMETRIES

VOLUME 23, NUMBER 4, DECEMBER 2006

q- ANALOGUES OF SOME OPERATIONAL FORMULAS , 354
Thomas Ernst
Department of Mathematics
Uppsala University, P.O. Box 480
SE- 751 06 Uppsala, Sweden

AUTOMORPHISMS OF TYPE I
SEMIFIELDS QUADRATIC OVER A WEAK NUCLEUS, 375
G.P. Wene
Department of Mathematics
University of Texas at San Antonio, One UTSA Circle
San Antonio, Texas 78249-0624

AN ADJOINTNESS PROPERTY FOR REPRESENTATIONS
OF GRADED LIE ALGEBRAS, 387
L. A-M. Hanna
Kuwait University, Faculty of Science
Department of Mathematics and Computer Science
P.O. Box 5969, Safat 13060, Kuwait

OPERATEURS B-FREDHOLM NON BORNES
SUR DES ESPACES DE BANACH, 393
L. Saddek et M. Sarih
Laboratoire de Mathe~matiques et leurs Applications
Department de Mathematiques et Informatique
Faculte~ des Sciences, Universite~ Moulay Ismail
B.P 11201 Zitoune Mekne`s, Maroc

COMPLETELY NON- SYMMETRIC ALGEBRAS , 407
Ki-Bong Nam
Department of Mathematics and Computer Science
University of Wisconsin- Whitewater
800 West Main Street
Whitewater, WI 53190, USA

NATURAL WEAK AUTOMORPHISMS OF P2- LATTICES I, 417
K.I. Tabash
Islamic University of Gaza
Mathematics Department
P.O.Box 108, Gaza, Palestine

ON RANK 2 RED ROOT SYSTEMS, 425
M.Q. Hailat
Department of Mathematical Sciences
University of South Carolina Aiken, Aiken, SC 29801
F. M. Sarhan
Department of Mathematics
Jordan University of Science and Technology
Irbid, Jordan

A STUDY ON PRIME SUBMODULES, 455
U. Tekir
University of Marmara,
Department of Mathematics
Ziverbey- Goztepe, Istanbul

ON THE DISTANCE FORMULAE
IN THREE DIMENSIONAL TAXICAB SPACE, 463
Z. Akca and R. Kaya
Osmangazi University
Department of Mathematics
26480, Eskisehir, Turkiye

INDEX Vol. 23, 2006 , 475

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ALGEBRAS, GROUPS AND GEOMETRIES

VOLUME 22, NUMBER 1, MARCH 2005

EXTREME POINTS AND APPLICATIONS TO NON CONVEX ANALYSIS AND OPERATIONS RESEARCH, 1 A. Bayoumi
Department of Mathematics, College of Sciences
King Saud University
P.O. Box 2455, Riyadh 11451, Saudi Arabia and
Institute for Basic Research
P.O. Box 1577, Palm Harbor, FL 34682, U.S.A.

SPACELIKE PARALLEL pi-EQUIDISTANT RULED SURFACES IN THE MINKOWSKI 3-SPACE R31, 13
M. Masal
Ondokuz Mayis University, Faculty of Arts and Science Department of Mathematics, 55139 Kurupelit, Samsun, Turkey N. Kuruoglu
Bahcesehir University, Faculty of Arts and Science
Department of Mathematics and Computer Sciences
34538, Bahcesehir, Istanbul, Turkey

HOMOMORPHISM THEOREMS FOR ORDERED GROUPOIDS, 25
N. Kehayopulu and M. Tsingelis
University of Athens, Department of Mathematics
Panepistimiopolis, Athens 15784, Greece and
K. P. Shum
Faculty of Science, The Chinese University of Hong Kong
Shatin, Hong Kong SAR, China

A QUANTITATIVE CHARACTERIZATION OF THE LINEAR GROUP IN DIMENSION ELEVEN OVER THE BINARY FIELD, 37
M. R. Darafsheh and Y. Farjami
Department of Mathematics
Statistics and Computer Science, Faculty of Science
University of Teheran, Teheran, Iran

SUR LA GAMETISATION ET LE RETROCROISEMENT, 49
Ch. Mallol
Dpto. de Ingeneria Matematica, UFRO
Casilla 54-D, Temuco, Chile and
R. Varo
Dpt. de Mathematiques et Informatique
U. P. V., 34199 Montpellier, France

HARMONIC MORPHISM ON ALMOST r - CONTACT METRIC MANIFOLDS, 61
L. S. Das
Department of Mathematics, Kent State University, Tuscarawas
New Philadelphia, Ohio 44663, U. S. A. and
R. Nivas
Department of Mathemaics and Astronomy
Lucknow University, Lucknow 226007, India

ON A GENERALIZED BETA FUNCTION AND ASSOCIATED STATISTICAL DISTRIBUTION, 69
M. Garg, R. Mishra
Department of Mathematics, University of Rajasthan
Jaipur-302004, Rajasthan, India and
S. L. Kalla
Department of Mathematics and Computer Science
Kuwait University P.O. Box 5969, Safat 13060, Kuwait

THE UNIVERSAL ENVELOPING ALGEBRA OF A TRAIN ALGEBRA OF RANK 31, 83
I. Correa,
Departamento de Matematicas Universidad de la Serena
Avda. Cisternas 1200, La Serena-Chile
R. Costa,
Departamento de Matematica, Universidad de Sao Paulo
Caixa Postal 6628105315-970, Sao Paolo, Brasil and
A. Labra
Departemento de Matematica, Facultad de Ciencias
Universidad de Chile, Casilla 653, Santiago, Chile

ABSENCE DE POINTS CONJUGUES ET COURBURE INTEGRALE DANS Rn, 93
M. Sarhi
Department de Mathematiques et Informatique
Faculte des Sciences et Techniques de Settat
Universite Hassan 1er
B.P. 577, 26000 Settat, Morocco

MARTINDALE po-RING AND DERIVATIONS ON (SEMI) PRIME l-RINGS, 109
M. M. Ebrahimi, H. Pajoohesh, and M. Mahmoudi
Department of Mathematics, Shahid Beheshti University
19839, Tehran, Iran

TWO OPERATIONS IN TRIANGLE PLANE, 117
N. Omur and S. Bilir
University of Kocaeli, Department of Mathematics
Ataturk Bulvari
Izmit, Turkey

DISPROOFS OF RIEMANN'S HYPOTHESIS, 123
Chun-Xuan, Jiang
P.O. Box 3924, Beijing 100854, China and
Institute for Basic Research
P.O. Box 1577, Palm Harbor, FL 34682, U.S.A.

GENERAL TWO PARAMETER MOTION, 137
M. K. Karacan and Y. Yayli
Ankara University
Faculty of Sciences
Department of Mathematics
06100 Tandogan, Ankara, Turkey

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ALGEBRAS, GROUPS AND GEOMETRIES

VOLUME 22, NUMBER 2, JUNE 2005

A SIMPLE EMBEDDING OF MEROMORPHIC FUNCTIONS INTO COMPLEX NUMBERS, 147
M. Golasinski
Faculty of Mathematics and Computer Science
Nicholas Copernicus University
Chopina 12/18
87-100 Torun, Poland

FINSLERIAN MECHANICAL SYSTEMS, 151
R. Miron
Department of Geometry, Faculty of Mathematics
University "Al. I. Cuza"
Bd. Copou 11, Iasi, 6600, Romania and
C. Frigioiu
Department of Mathematics, "Al. I. Cuza"
Domneasca Street 47, Galati, 6200, Romania

LIMITS AND COLIMITS IN CATEGORIES OF UNIVERSAL HYPERALGEBRAS, 169
A. Karimi
Department of Mathematics, Shahid Beheshti University
Tehran 19839, Iran and
Department of Mathematics and Statistics
University of Agricultural Sciences and Natural Resources
Gorgan, Iran and
Department of Mathematics, Islamic Azad University
Gorgan, Iran and
M. M. Ebrahimi and M. Mahmoudi
Dept. of Mathematics, Shahid Beheshti University
Tehran 19839, Iran

INDUCED STRUCTURES ON THE TANGENT BUNDLE OF AN e- FRAMED METRIC MANIFOLD, 183
L. Das
Kent State University, Tuscarawas, Dept. of Mathematics
New Philadelphia, OH 44663, U.S.A. and
S. K. Srivastava
Dept. of Mathematics, Govt. P.G. College
Dhantari, Raipur (C.G.)

OPERADS AND DEFORMATIONS, 193
E. Paal
Department of Mathematics
Tallinn University of Technology
Ehitajate tee 5, 19086 Tallinn, Estonia

SUM OF TWO SQUARES IN A CYCLOTOMI-QUADRATIC FIELD, 201
A. Asimi and A Lbekkouri
Department de Mathematiques et Informatique
Faculte des Sciences de Rabat
B.P. 1014 Rabat, Maroc

PRO-C COMPLETIONS OF CROSSED MODULES OF COMMUTATIVE ALGEBRAS, 215
M. Kocak
Department of Mathematics
Art and Science Faculty
Osmangazi University 26480, Eskisehir, Turkey

SEMISIMPLE ALGEBRA WITH A POSITIVE INVOLUTION, 223
L. Oukhtite
Moulay Ismail University, Faculty of Sciences and Techniques
Department of Mathematics
P.O. Box 509 Boutalamine, Errachidia, Morocco and
M. Boulagouaz
Sidi Mohamed Ben Abdellah University
Faculty of Sciences and Techniques
Department of Mathematics
P.O. Box 2202 Fez-Saiss, Fez, Morocco

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ALGEBRAS, GROUPS AND GEOMETRIES

VOLUME 22, NUMBER 3, SEPTEMBER 2005

GROUPS ASSOCIATED WITH GRAPHS, 273
M.R. Adikari and L.K. Pramanik
Department of Pure Mathematics
University of Calcutta
35 Ballygunge Circular Road
Kolkata - 700019, India

A NOTE BI-INVARIANT METRIC ON LIE GROUPS, 281
Ryad Ghanam
Department of Mathematics
University of Pittsburgh at Greensburg
Greensburg, PA 15601, U.S.A.

NONLINEAR EIGENCURVES AND APPLICATIONS
TO THE STUDY OF THE STRICT MONOTONY OF THE
SECOND EIGENVALUE FOR THE p - LAPLACIAN WITH WEIGHT, 293
M. Hadda and A. Dakkan
De~partement de Mathe~matiques
Groupe d¹Analyse non Line~aire
Faculte~ de Sciences at Techniques
52000 Boutalamine Errachidia, Maroc
C. Ziti
Departement de Mathe~matiques et Informatique
Faculte~ des Sciences de Mekne`s, Universite~ Moulay Ismail
BP 4010 Beni M¹hamed, Mekne`s, Maroc

THE BIVARIANT DIHEDRAL COHOMOLOGY, 311
E. Cerati and I. Schwer
Departamento de Matema~tica, Facultad de Ingenieria Quimica
Universidad National del Litoral
Santiago del Estero 2829 - Santa Fe - Argentina

THE LIFTS OF JET VECTOR FIELDS, 331
C. Aycan and S. Civelek
Osmangazi University and Pamukkale University
Department of Mathematics
Eskisehir- Denizli- Tu�rkiye

DERIVATION OF SYMMETRIC NON- ASSOCIATIVE ALGEBRA I, 341
Seul Hee Choi
Department of Mathematics
University of Jeonju, Chon- ju 560-759, Korea
Ki- Bong Nam
Department of Mathematics and Computyer Science
University of Wisconsin- Whitewater
800 West Main Strret
Whitewater , WI 53190, USA

MEAN -VALUE THEOREM FOR DEFINITE INTEGRALS OF
VECTOR- VALUED FUNCTIONS OF p- BANACH SPACES, 353
A. Bayoumi
King Saud University , Mathematics Department
P.O. Box 2455, Riyadh 11451, Saudi Arabia and
Institute for Basic Research
P.O.Box 1577, Palm Harbor, Fl 34682, U.S.A

SOME RESULTS ON TOPOLOGICAL
COLIMIT PRESERVING EQUALIZERS, 365
Gh. Mirhosseinkhani and S.N. Hosseini
Department of Mathematics
Shahid Bahonar University of Kerman, Iran

RINGS WITH A SPECIAL s - DERIVATION, 375
L. Oukhtite
Universite~ Moulay Ismail, Faculte~ des Sciences et Techniques
De~partement de Mathe~matiques , B. P. 509 Boutalamine
Errachidia, Maroc
S.Salhi
Universite~ Sidi Mohamed Abdellah, Faculte~ des Sciences
De~partement de Mathe~matiques et Informatique
B. P. 1796 Atlas-Fe`s, Maroc

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ALGEBRAS, GROUPS AND GEOMETRIES

VOLUME 22, NUMBER 4, DECEMBER 2005

A CHARACTERIZATION OF A CLASS OF GROUPS
OF ORDER 32 BY THEIR ENDOMORPHISM SEMIGROUPS, 387
T.Gramushnjak
Department of Mathematics,Tallinn Pedagogical University
Narva Road 25, Tallinn,Estonia
P. Puusemp
Department of Mathematics,Tallinn University of Technology
Ehitajate tee 5,19086 Tallinn, Estonia

CARTESIAN PRODUCTS SPACE OF r -MANIFOLDS, 413
L.S. Das
Department of Mathematics, Kent State University
New Philadelphia , OH 44663, U.S.A.
R. Nivas
Department of Mathematics and Astronomy
Lucknow University ,Lusknow,India
D. Singh
Northern India Engineering College
Lucknow,India

LIE SYMMETRIES AND PRELIMINARY CLASSIFICATION
OF GROUP-INVARIANT SOLUTIONS OF THOMAS EQUATION, 423
A Ouhadan and E.H.El Kinani
Moulay Ismail University,Faculty of Sciences and Technics
Department of Mathematics, Group of Algebras and Applications
P.O. Box 509 Boutalamine, Errachidia ,Morocco and
UFR de Sciences de l¹Inge~nieur et Technique
Boulamanie B.P. 509 ,Errachidia , Morocco

THE EQUIVALENCE OF TOPOLOGICAL 2- GROUPOIDS
AND TOPOLOGICAL CROSSED MODULES, 447
M. Habil Gu¤rsoy, I. Icen and A. Faith O¤zcan
Ino¤nu¤ University, Science and Art Faculty
Department of Mathematics, Malatya -Turkey

FUZZY TOPOLOGICAL DIVISORS
OF ZERO IN A FUZZY NEIGHBORHOOD RING, 457
T.M.G. Ahsanullah
Department of Mathematics King Saud University, Riyadh 11451, Saudi Arabia
M A Basha, S. Shirin
Department of Mathematics, University of Dhaka
Dhaka 1000, Bangladesh

STUDIES ON A CLASS OF LIE - ADMISSIBLE SOLID ALGEBRAS, I , 473
Seul Hee Choi
Department of Mathematics University of Jeonju , Chon-ju 560-759,Korea
G. Samaranayake and Ki-Bong Nam
Department of Mathematics and Computer Science
University of Wisconsin -Withewater,
800 West Main Street,Withewater,WI 53190 U.S.A

SYMETRISATION DU TRESSAGE DANS UNE CATEGORIE
TENSORIELLE ET ALGEBRE ENVELOPPANTE TRESSEE, 486
H. Choulli et A . Haddi
De~partement de Mathe~matiques et Informatiques
Universite~ Abdelmalek Essaadi , Faculte~ des Sciences
B.P. 2121 Tetounan, Maroc

INDEX, 387

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ALGEBRAS, GROUPS AND GEOMETRIES

VOLUME 21, NUMBER 1, MARCH 2004

OPERADS AND COHOMOLOGY, 1
L. Kluge and E. Paal
Department of Mathematics, Tallinn Technical University
Ehitaja tee 5, 19086 Tallinn, Estonia

A SURVEY OF FOUR-DIMENSIONAL
C- ASSOCIATIVE ALGEBRAS, 9
S. C. Althoen, K.D. Hansen, and L.D. Kugler
Department of Mathematics, University of Michigan-Flint
Flint, Michigan 48502-1950

THE CENTROID OF n-LIE ALGEBRAS, 29
B. Ruipu
Department of Mathematics, Hebei University
(071002) Baoding, China
Department of Mathematics, NanKai University
(300071) Tianjin, China
Department of Mathematics, Hebei University
(300071) Tianjin, China
M. Daoji
Department of Mathematics, NanKai University
(300071) Tianjin, China

ETUDE TENSORIELLE ET GEOMETRIQUE
D'UN ALGORITHME DE NORMES
TENSORIELLES RAISONNABLES, 39
M. Archoun
Universite Moulay Ismail
Faculte des Sciences
Departement de Mathematiques et Informatique
U.F.R. AFACS
BP 4010 Zitoune, Meknes, Maroc

INVARIANTS OF BASS, CATENARITY AND TAUVEL'S HEIGHT FORMULA IN SOME EXTENSIONS
OF FILTERED RINGS, 57
T. Guedenon
Faculty of Applied Sciences
Free University of Brussels, VUB
B-1050 Brussels, Belgium

DOLD-KAN THEOREM FOR N-CROSSED
OF COMMUTATIVE ALGEBRAS, 29
I. Akca and Z. Arvasi
Osmangazi University, Department of Mahtematics
26480 Eskisehir, Turkey

ON FACTORIZATION IN COEFFICIENTS
OF POWER SERIES RINGS, 111
M. Golasinski
Faculty of Mathematics and Computer Science
Nicholas Copernicus University
Chopina 12/18, 87-100 Torun, Poland

ON FREE LIE PRODUCT OF LIE p-ALGEBRAS, 115
A. Temizyurek
Cukurova Univrsitesi Matematik Bolumu
01330 Adana, Turkey

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ALGEBRAS, GROUPS AND GEOMETRIES

VOLUME 21, NUMBER 2, JUNE 2004

ON ABE-IIYORI'S PROBLEMOF FINITE SIMPLE GROUPS, 127
Jianxing Bi
Department of Mathematics, Liaoning University
Shenyang, 110036, People's Republic of China and
Xianhua Li
Department of Mathematics, Suzhou University
Suzhou, 215006, People's Republic of China

A SEMIDIRECT PRODUCT OF CYCLIC GROUPS
AND ITS ENDOMORPHISM SEMIGROUP, 137
P. Puusemp
Department of Mathematics, Tallinn Technical University
Ehitajate tee 5, Tallinn 19086, Estonia

STUDY OF A FORMALISM MODELING MASSIVE PARTICLES AT THE SPEED OF LIGHT ON A MACHIAN BASIS, 153
B. Gokden
Middle East Technical University
Ankara 06531, Turkey

FITTING IDEALS AND CANONICAL FORMS
FOR FINITELY GENERATED MODULES, 181
I. Akharraz and M.E. Charkani
Faculty of Sciences - Dhar Mahraz
B.P. 1796 Atlas Fez, Morocco

SEMIPRIME SUBMODULES AND QUOTIENT MODULES, 191
H.A. Tavallaee
Department of Mathematics
Iran University of Science and Technology
Narmak, Tehran 16844, Iran
M.J. Nikmehr
Department of Mathematics
K.N.T. University of Technology
Tehran

DIAGONAL Z-AUTOMORPHISMS OF
Z(x1, x2, ....., xn), 201
J. M. Habeb
Department of Mathematics
Yarmouk University
Irbid, Jordan
M. Hajja
Department of Mathematics
Yarmouk University
Irbid, Jordan

APPLICATIONS OF FREE CROSSED SQUARE OF A FREE SIMPLICIAL GROUP WITH GIVEN CW-BASIS, 211
A. Mutlu
University of Celal Bayar
Faculty of Science, Department of Mathematics
Muradiye Campus
45047 Manisa, Turkey

ALGEBRES MONOMIALES CONSTANTES
DE DEGRE 4, 231
C. Mallol
Departamento de Ingeneria Matematica
Universidad de La Frontera
Casilla 54-D, Temuco, Chile
M. Nourigat and R. Varro
Departement de Mathematiques et Informatique Appliquees
Universite Paul Valery, 34199 Montpellier, France

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ALGEBRAS, GROUPS AND GEOMETRIES

VOLUME 21, NUMBER 3, SEPTEMBER 2004

Conference on Differential Geometry:
Lagrange and Hamilton Spaces

M. Anastasiei, Editor

In honour of Prof. Dr. Radu Miron on the occasion of his 75th Birthday
Foreword by M. Anastasiei

GEOMETRY OF BERWALD VECTOR BUNDLES, 251
M. Anastasiei
Faculty of Mathematics
University "l.I. Cuza," Iasi
6600, Iasi, Romania

EXTENDED MAXWELL EQUATIONS WITH SOURCES IN GEOMETRIZED JET FRAMEWORK, 263
V. Balan
Department of Mathematics I
Politehnica University of Bucharest
Splaiul Independentei 313, RO-77206, Bucharest, Romania and
P.C. Stavrinos
Department of Mathematics
Universiy of Athens, Panepistemiopolis
GR-15784 Athens, Greece

TZITZEICA INDICATRICES IN LAGRANGE GEOMETRY, 277
M. Crasmareanu
Faculty of Mathematics
University "Al.I. Cusa," Iasi, 6000, Romania

ON THE NOTION OF SEMISPRAY GEOMETRICAL OBJECT FIELD AND ITS LIE DERIVATIVE, 285
M. Isu
Faculty of Education
Fukushima University, Japan

NON-COMMUTATIVE GEOMETRY AND APPLICATIONS IN PHYSICS, 291
A. Jannussis, V. Papatheou and K. Vlachos
Departament of Physics, University of Patras, Greece

ON THE HAMILTON-JACOBI EQUATIONS OF THE HAMILTONIANS OF ORDER k ¾ 1, 311
R. Miron
Faculty of Mathematics
University "Al.I. Cuza," Iasi
6600 Iasi, Romania

HOLOMORPHIC SUBSPACES OF A COMPLEX LAGRANGE SPACES, 317
G. Munteanu and G. Pitis
Transilvania University
Faculty of Mathematics and Informatics
2200, Brasov, Romania

SPIN-LAPLACIANS ON THE TOTAL SPACE OF A FIBER BUNDLE, 331
O. Munteanu
Faculty of Mathematics and Informatics
Transilvania University of Brasov
Brasov, Romania

RULED SURFACES IN EUCLIDIAN SPACES, 341
G. Neagu
Faculty of Sciences
University of Bacau
5500, Romania

GENERALIZED SPHERES ON RIEMANNIAN MANIFOLDS, 349
G. T. Pripoae
University of Bucharest
Faculty of Mathematics and Informatics
Str. Academiei nr. 14 , Bucharest, Romania

ON THE SECOND COVARIANT DERIVATIVES OF RIEMANNIAN CURVATURE TENSOR
M. Yawata and H. Hashiguchi
Shibazono Narashino, Chiba 275-0023, Japan

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ALGEBRAS, GROUPS AND GEOMETRIES

VOLUME 21, NUMBER 4, DECEMBER 2004

ON MILNOR¹S REGULARITY AND THE PATH-FUNCTOR FOR THE CLASS OF INFINITE DIMENSIONAL LIE ALGEBRAS OF CBH TYPE, 367
Th. Robart
Departamentof Mathematics
Howard University, Washington, DC, 20059

THE BAR-RADICAL OF JORDAN BARIC ALGEBRAS, 387
J.C.M. Ferreira
Universidade Federal de Mato Grosso do Sul
Departamento de Matematica
Caixa Postal 549
79070-900, Campo Grande, MS, Brazil and
H. Guzzo Jr
Universidade de Sao Paulo
Instituto de Matematica e Estatistica
Caixa Postal 66281
05315-970, Sao Paulo-SP, Brazil

ON TENSOR PRODUCTS OF REAL ALGEBRAS, 399
Zeng Guangxing
Department of Mathematics, Nanchang University
Nanchang 330047, China amd
Li Yangming
Department of Mathematics, Guangdong Education College
Guangzhou 501303, China

ON THE STATISTICAL CONVERGENCE IN R m , 413
A.N. Guncan
Deparment of Mathematics, Su¤leyman Demirel University
32260 Isparta, Turkey

GENERAL MEAN-VALUE THEOREM AND TAYLOR EXPANSIONS FOR m-QUASI-DIFFERENTIABLE FUNCTIONS OF LOCALLY BOUNDED SPACES, 421
A. Bayoumi
Department of Mathematics, College of Sciences
King Saud University
P.O. Box 2455, Riyadh 11451, Saudi Arabia and
Institute for Basic Research
P.O. Box 1577, Palm Harbor, FL 34682, U.S.A.

FUZZY n-PRIME AND FUZZY STRONGLY n-PRIME SEMI-IDEALS IN SEMILATTICES, 437
Wu Congxin
Department of Mathematics
Harbin Institute of Technnology
Harbin, 150001, P.R. China and
K.P. Shum
Faculty of Science
The Chinese University of Hong Kong
Shatin, New Territories, Hong Kong

A CHAOTIC INFLATIONARY COSMOLOGICAL MODEL WITH INTERACTING SCALAR FIELDS, 451
V. Pankovic and M. Predojevic
Institute of Physics, Faculty of Sciences
21000 Novi Sad, Trg Dositeja Obradovica 4
Serbia and Montenegro

DERIVATIONS DANS LES ALGEBRES DE LOTKA-VOLTERRA, 471
H. Boujemaa et M. Rachidi
Departement de Mathematiques et Informatique
Faculte des Sciences, Universite Mohammed V-Agdal
Avenue Ibn Battouta, B.P. 1014, Rabat, Maroc and
A. Micali
Department des Sciences Mathematiques
Universite Montpellier II
Place Eugene Battaillon, 34095 Montpellier, France

REDUCED QUADRATIC MODULES AND SIMPLICIAL GROUPS, 489
E. Ulualan
Osmangazi University
Department of Mathematics
26480, Eskisehir, Turkey

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ALGEBRAS, GROUPS AND GEOMETRIES

VOLUME 20, NUMBER 1, MARCH 2003

STUDIES ON THE TSAGAS-SOURLAS-SANTILLI ISOTOPOLOGY, 1
R.M. Falcon and J. Nunez
Dpto Geometria y Topologia. Facultad de Matematicas
Universidad de Sevilla, Aptdo 1160 41080, Sevilla, Spain

This issue is dedicated to the memory of
Professor GRIGORIOS T.TSAGAS
Editor, Algebras, Groups and Geometries
Chairman, Department of Mathematics
Aristotle University, Thessaloniki, Greece

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ALGEBRAS, GROUPS AND GEOMETRIES

VOLUME 20, NUMBER 2, JUNE 2003

A STANDARD WREATH PRODUCT OF GROUPS AND
ITS ENDOMORPHISM SEMIGROUP, 101
P. Puusemp
Institute of Mathematics
Tallinn Technical University
Ehitajate tee 5
Tallinn 19086, Estonia

CYCLIC NEOFIELDS SATISFYING (1+x)(1+(-x))=1, 117
C.P. Johnson
Department of Mathematics and Statistics
Mississippi State University
P.O. Drawer MA
Mississippi State, MS 39762
Errata Corrige. This article was previously published incomplete.

ON SOME PERMUTATION MODULES OF
THE GENERAL LINEAR GROUP, 125
M.R. Darafsheh and M. Khademi
Department of Mathematics, Statistics and Computer Science
Faculty of Science, University of Teheran
Teheran, Iran

THE RIEMANN-ROCH THEOREM
ON RIEMANN SURFACES, 141
I.I. Akca
Osmangazi University
Department of Mathematics
26480 Eskisehir,Turkey

PRIME THEOREM IN SANTILLI'S
ISONUMBER THEORY (II), 149
Chun-Xuan Jiang
P.O. Box 3924, Beijing 100854
P.R. China

RADICALS OF TRIPLE SYSTEMS, 171
N. Kamiya
Center for Mathematical Sciences
University of Aizu
Aizuwakamatsu

NEW RESULTS ON
SEMIPERFECT ASSOCIATIVE PAIRS.
SEMIPERFECT RINGS WITHOUT IDENTITY, 181
M.A. Fortes Escalona
Departamento de Matematica Aplicada
E.U. Arquitectura Tecnica
Universidad de Granada
C/Severo Ochoa, s/n. Campus de Fuentenueva
18071 Granada, Spain
I. de las Penas Cabrea
Departamento de Matematica Aplicada
E.U. Politecnica Universidad de Malaga
Campus Universitario El Ejido
29071 Malaga, Spain
E. Sanchez Campos
Departemnto de Algebra
Geometria y Topologia
Facultad de Ciencias
Universidad de Malaga
Apartado 59, 29080 Malaga, Spain

STATIONARY LORENTZ
CURVES IN FIRST-ORDER JET SPACES.
NUMERICAL SIMULATION V. Balan
Department of Mathematics
Politehnica University of Bucharest
Splaiul Independentei 313
RO-77206, Bucharest, Romania
K. Trencevski
Institute of Mathematics
St. Cyril and Methodius University
1000 Skopje, Macedonia
Dedicated to Prof. Dr. Radu Miron
Member of the Romaniean Academy, at his 75th Anniversary

STUDY OF A PARAMETERIZED SYSTEM OF EQUATIONS AND INEQUATIONS IN THE NEIGHBORHOOD OF A SINGLE POINT APPLICATION TO OPTIMIZATION, 211
H. Zouaki
Universite Moulay Ismail
Faculte des Sciences
BP 4010, Beni M'hamed
5000 Meknes, Maroc

SOME RESULTS ON THE WRIGHT'S GENERALIZED HYPERGEOMETRIC FUNCTION, 229
L. Galue'
Centro de Investigacion de Matematica Aplicada (C.I.M.A.)
Facultad de Ingenieria
La Universidad del Zulia
Apartado Postal 10482
Maracaibo-Venezuela

RINGS DERIVED FROM SEMIHYPER-RINGS, 245
B. Davvaz
Department of Mathematics
Yazd University
Yazd, Iran

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ALGEBRAS, GROUPS AND GEOMETRIES

VOLUME 20, NUMBER 3, SEPTEMBER 2003

ON THE GEOMETRY OF THE BIG BANG, 253
K. Buechner
Zentrum Mathematik der Technischen Universitaet
D-80290 Muenchen, Germany and
G.G.L. Nashed
Mathematics Department, Faculty of Science
Ain Shams University, Cairo, Egypt

LOCAL STRUCTURE OF SUBALGEBRAS
AROUND 1- HEIGHT MAXIMAL IDEALS AND
DESINGULARIZATIONS. II, 263
A. Constantinescu
Institute of Mathematics
Romanian Academy of Sciences
P.O. Box 1-764, 70700 , Bucharest, Romania

THE GEOMETRY OF LIGHT CONE
OF THE ANTI-MACH SPACE-TIME, 279
M. Abdel-Megied
Mathematics Department, Faculty of Science
Minia University, El-Minia, Egypt

VARIATIONAL PROBLEM IN FINSLER SPACES
WITH ( a, b) - METRIC, 285
R. Miron
University Al.I. Cuza Iasi, Romania and
B.T. Hassan
Cairo University, Giza, Egypt

ON A THEOREM OF CILIBERTO AND SERNESI, 301
O. Pasarescu
Institute of Mathematics
Romanian Academy of Sciences
P.O. Box 1-764, 70700, Bucharest, Romania

GENERAL RANDERS SPACES AND ITS HOMOGENEOUS NONLINEAR CONNECTION, 313
M.R. Roman
Technical University Gh. Asachi
Department of Mathematics
Bd. Carol, No.11, Iasi, Romania

SOME QUESTIONS REGARDING THE AREA IN FINSLER AND AREAL SPACES, 323
L. Tamassy
Institute of Mathematics and Informatics
Debrecen University
H-4010 Debrecen, P.O. Box 12, Hungary

THE CATEGORY OF K- ALMOST LINEAR SPACES, 337
A. Sava
V. Alecsandri College, Iasi, 6600, Romania and
M. Roman
Technical University Gh. Asachi
Department of Mathematics
Bd. Carol, No.11, Iasi, Romania

FROM GEOMETRY TO QUANTUM, 345a
M.I. Wanas
Astronomy Department, Faculty of Science
Cairo University, Giza, Egypt

ON THE DEVELOPMENT OF THE EXTENSIONS
THEOREM OF SYMMETRIC RELATIONS IN HILBERT SPACE, 345
A.A. El-Sabbagh
Department of Mathematics, Faculty of Engineering
Shoubra, Zagazig University
108 Shoubra Street, Cairo, Egypt

FUZZY SETS. APPLICATIONS IN ECONOMICAL PROBLEMS, 353
B. Andronic
University Petre Andrei of Iasi, 6600 Romania

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ALGEBRAS, GROUPS AND GEOMETRIES

VOLUME 20, NUMBER 4, DECEMBER 2003

RELATIONS CONNECTING MULTIINDEX
MITTAG-LEFFLER FUNCTIONS AND
RIEMANN-LIOUVILLE FRACTIONAL CALCULUS, 363
R. K. Saxena
Department of Mathematics and Statistics
Jai Narain Vyas University, Jodhpur - 342001, India,
S. L. Kalla
Department of Mathematics and Computer Science
Kuwait University, P.O. Box 5969, Safat 13060, Kuwait and
V. S. Kiryakova
Institute of Mathematics and Informatics
Bulgarian Academy of Sciences, Sofia 1090, Bulgaria

EQUIVALENT EXTENSIONS OF ORDERED SETS, 387
N. Kehayopulu
Department of Mathematics, University of Athens
Panepistimioupolis, GR - 157 84, Athens, Greece
K.P. Shum
Faculty of Science, The Chinese University of Hong Kong
Hong Kong, China (SAR)

LIGHTLIKE SUBMANIFOLDS OF SEMI-RIEMANNIAN
WARPED PRODUCT MANIFOLD, 403
E. Kilic, B. Sahin, and M. Atceken
Inonu University, Faculty of Science and Art
Department of Mathematics, Malatya, 44069, Turkey

AN ISOGENIC CHARACTERIZATION
OF L* - ALGEBRAS, 419
A.J. Calderon Martin
Departamento de Matematicas, Universidad de Cadiz
11510 Puerto Real, Cadiz, Spain

GENERATING ALTERNATING GROUPS, 435
R. Nekkoei
Mathematics Department
Shahid Bahonar University of Kerman, Kerman, Iran and A. Jabari
Mathematics and Statistics Department
Ferdosi University of Mashhad, Mashhad, Iran

ALGEBRES ASSOCIE~ES AUX TRAIN ALGEBRES DE RANG 3, 443
Ch. Mallol
Departamento de Ingenieria Matematica
Universidad de La Frontera, Casilla 54-D, Temuco, Chile and
R. Varro
Departement de Mathematiques et Informatique Appliquees
Universite Paul Valery
34199 Montpellier, France

STRONGLY REGULAR ( l-) RINGS AND DERIVATIONS ON THEM, 451
M.M. Ebrahimi
Mathematics Department, Shahid Beheshti University
Tehran 19839, Iran and
Department of Mathematics, McMaster University
Hamilton, Ontario L8S-4K1 and
H. Pajoohesh
Mathematics Department, Shahid Beheshti University
Tehran 19839, Iran

POINTS ALGEBRIQUES DE DEGRE AU PLUS 3
SUR LA QUARTIQUE DE KLEIN, 461
O. Sall
U.F.R. de Mathematiques, Universite Paris 7 - Denis Diderot
175, rue de Chevaleret, 75013 Paris, France ou
Departement de Mathematiques et Informatique
Faculte des Sciences et Techniques
Universite Cheikh Anta Diop de Dakar, Senegal

ON TOPOLOGICAL COLIMIT PRESERVING EQUALIZERS, 475
S.N. Hosseini and Gh. Mirhosseinkhani
Department of Mathematics, Shahid Bahonar University, Kerman, Iran

HOMOMORPHIC IMAGES of D (2,3,9) AS SUBGROUPS OF PGL (2, q), 485
Q. Mushtaq
Department of Mathematics Quaid-i-Azam University, Islamabad, Pakistan, T. Maqsood
Department of Computer Science (MCS)
National University of Sciences and Technology, Rawalpindi, Pakistan,
M. Aslam
Department of Mathematics and Statistics, Allama Iqbal Open University
Islamabad, Pakistan and
M. Ashiq
Department of Basic Sciences, College of E & ME
National University of Sciences and Technology, Rawalpindi, Pakistan

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ALGEBRAS, GROUPS AND GEOMETRIES

VOLUME 19, NUMBER 1, MARCH 2002

COHERENT DIRECT SYSTEMS OF L* - TRIPLES , 1
A.J. Calderon Martin
Departamento de Matematicas
Universidad de Cadiz
11510 Puerto Real, Cadiz, Spain

ON THE EXTENSION OF SYMMETRIC INVARIANT BILINEAR FORMS ON TWISTED INNER DERIVATION TRIPLE SYSTEM, 19
L Xuewen
School of Mathematical Sciences
Peking University
Beijing 1000871, China and
Z. Zhixue
Department of Mathematics
Hebei University
Baoding 071002, China

CYCLIC NEOFIELDS SATISFYING (1+x) (1+(-x)) = 1, 31
C.P. Johnson
Department of Mathematics and Statistics
Mississippi State University
P.O. Drawer MA
Mississippi State, MS 39762

DUALITY IN FUZZY LINEAR PROGRAMMING, 39
R.N. Gasimov and K. Yenilmez
Osmangazi University
Department of Mathematics
26480 Eskisehir, Turkey

ON SOME PARTICULAR CHARACTER AND EXPONENTIAL SUMS, 57
G. Danas
Department of Mathematics,
Technological Educational Institution
Thessalonikiv School of Sciences
P.O. Box 14561. GR-54631, Thessaloniki, Greece

ON A CLASS OF NONASSOCIATIVE ALGEBRAS:
A REDUCTION THEOREM FOR THEIR ASSOCIATED
QUADRATIC SYSTEMS, 73
H. Boujemaa and M. Rachidi
Departement de Mathematiques et Informatique
Faculte des Sciences
Universite Mohammed V-Agdal
Avenue Ibn Battouta B.P. 1014, Rabat, Maroc and
A. Micali
Departement des Sciences Mathematiques
Universite Montpellier II
Place Eugene Bataillon, 34095 Montpellier, France

FACTORING LARGE NUMBERS, 85
Chun-Xuan Jiang
P. O. Box 3924, Beijing 100854
P. R. China

ALGEBRES w -MONOMIALES
ASSOCIATIVES NON COMMUTATIVES, 97
C. Mallol
Departamento de Ingenieria Matematica
Universidad de La Frontera
Casilla 54-D, Temuco Chile and
C. Burgueno
Departamento de Matematica y Estadistica
Universidad de La Frontera
Casilla 54-D, Temuco, Chile

SOME RESULTS ON BARIC ALGEBRAS, 109
F. Zitan
Department de Mathematiques et Informatique
Universite Moulay Ismail
Faculte des Sciences
B.P. 4010, Beni M'hamed, Meknes, Maroc

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ALGEBRAS, GROUPS AND GEOMETRIES

VOLUME 19, NUMBER 2, JUNE 2002

HIGHER-DIMENSIONAL FREE CROSSED MODULES OF COMMUTATIVE ALGEBRAS, 129
Z. Arvasi and U. Ege
Department of Mathematics
Faculty of Arts and Science
University of Osmangazi
26480 Eskisehir, Turkey

2-STEP SOLVABLE LIE ALGEBRAS ASSOCIATED TO
NONSPLIT 7- DIMENSIONAL FUNDAMENTAL ALGEBRAS, 147
R. Campoamor-Stursberg
Departamento de Geometria Topologia
Facultad CC. Matematicas Univ. Complutense
28040 Madrid, Spain

ORTHONORMAL EIGENBASES OVER THE OCTONIONS, 163
T. Dray
Department of Mathematics
Oregon State University
Corvallis, OR. 97331, U.S.A. and
C. A. Manogue
Department of Physics Oregon State University
Oregon State University
Corvallis, OR 97331, U.S.A. and
S. Okubo
Department of Physics and Astronomy
University of Rochester
Rochester, NY 14627

EQUALITIES AND INEQUALITIES FOR TRACES OF
QUATERNIONIC MATRICES, 181
Yongge Tian
Department of Mathematics and Statistics
Queen's University
Kingston, Ontario, Canada K7L 3N6

ON THE DEFINABILITY OF A SEMIDIRECT PRODUCT OF CYCLIC GROUPS BY ITS ENDOMORPHISM SEMIGROUP, 195
P. Puusemp
Department of Mathematics
Tallinn Technical University
Ehitajate tee 5
Tallinn 19086, Estonia

GEOMETRICAL PROPERTIES OF MODEL METABELAN LIE ALGEBRAS, 213
J.R. Gomez
Dpto. Matematica Aplicada I
Facud de Informatica
Universidad de Sevilla
41012, Sevilla, Spain and
I. Rodriguez
Departamento de Matematicas
Escuela Politecnica Superior
Universidad de Huelva
21819, Palos de la Frontera
Huelva, Spain

A CHARACTERIZATION OF E 6(Q), 225
Behrooz Khosravi and Behnam Khosravi
241, Golnaz Street, Golbahar Street
Daneshjou Blvd, Velenjak
Tehran, 19847, Iran

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ALGEBRAS, GROUPS, AND GEOMETRIES

VOLUME 19, NUMBER 3, SEPTEMBER 2002

ON A PROBABILITY DISTRIBUTION INVOLVING A
CONFLUENTHYPERGEOMETRIC FUNCTION
OF TWO VARIABLES, 254
B.N. Al-Saqabi, S.L. Kalla, and A. Shafea
Department of Mathematics and Computer Science
Kuwait University
P.O. Box 5969, Safat 13060, Kuwait

ON ASSOCIATED FRECHET VECTOR BUNDLES, 277
E. E. Vassiliou
Department of Mathematics
University of Athens
Panepistimiopolis
GR-157 84 Athens, Greece and
G.N. Galanis
Hellenic Naval Academy
Hatzikyriakion
Gr-145 10 Piraeus, Greece

2-ORDERED TOPOLOGICAL STRUCTURES
IN FILTER CONVERGENCE SPACES, 289
H. Kabadayi
Department of Mathematics
Science Faculty, Ankara University
Tandogan, Ankara 06100, Turkey

0-SEMIDIRECT PRODUCTS OF 0-SEMILATTICES WITH
PRIMITIVE INVERSE SEMIGROUPS, THEIR INVERSE
0-SUBSEMIGROUPS AND 0-RESTRICTED HOMOMORPHIC
IMAGES, 295
Zhonghao Jiang
Department of Mathematics
Northern Jiaotong Universit
100044, Beijing, China

SUR UNE CLASSE D'ALGEBRES D'EVOLUTION, 315
J. Bayara and M. Ouattara
Universite Polytechnique
de Bobo-Dioulasso (U.P.B.)
01 BP 1091 Bobo-Dioulasso 01
Burkina, Faso and
A. Micali
Departement des Sciences Mathematiques
Universite Montpellier II
place Euge`ne Bataillon
34095 Montpellier, France and
J. Carlos da Motta Ferreira
Departmento de Matematica
Universidade Federal de Mato Grosso do Sul
Caixa Postal 549
79070-900 Campo Grande, MS, Brasil

SANTILLI ISOMANIFOLDS IN
ARBITRARY DIMENSIONS, 347
M.R. Molaei
Department of Mathematics
University of Kerman, Kerman, Iran and
F. Farmitani
Department of Mathematics
Azad University of Kerman, Kerman, Iran

POSITIVE LIAPUNOV EXPONENTS FOR FAMILIES OF
MULTIMODAL CIRCLE MAPS, 357
F.H. Ghane
Department of Mathematics
Ferdowsi University, Mashhad
1159-91775, Iran and
B. Honary
Department of Mathematics
Shahid Beheshti University
19834, Tehran

FIRST ORDER LIFTS OF COMPLEX STRUCTURES , 373
M. Tekkoyun and S. Civelek
Osmangazi University
Department of Mathematics
Eskisehir, Turkey

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ALGEBRAS, GROUPS AND
GEOMETRIES

VOLUME 19, NUMBER 4, DECEMBER 2002

A CONTRACTION FORMULA FOR THE INVARIANTS
OF THE COADJOINT REPRESENTATION OF LIE ALGEBRAS, 385
R. Campoamor-Stursberg
Depto. Geometria y Topologia
Fac. CC. Matematicas U.C.M.
E-28040 Madrid, Spain

SUR QUELQUES TRAIN ALGE`BRES
ASSOCIATIVES NON COMMUTATIVES, 395
C. Mallol
Departamento de Ingenieria Matematica
Universidad de La Frontera
Casilla 54-D, Temuco, Chile

GRADING ISOMANIFOLDS AND
SUPER ISOMANIFOLDS, 409
N. Gerami
Dept. of Math., Faculty of Mathematics and Computer Sciences
Shahid Bahonar University of Kerman
Kerman, Iran and
G.R. Rezaei
Dept. of Math., Sistan and Baluchestan University
Zahedan, Iran

DERIVATIVES IN Nth -ORDER BERNSTEIN ALGEBRAS, III, 442
H. Guzzo Jr.
Instituto de Matematica e Estatistica
Universidade de Sao Paulo
Caixa Postal 66281, 05315-970-Sao Paulo, Brazil and
P. Vicente
Universidad de Leon, Departamento de Matematicas
Campus de Vegazana, 24071-Leon, Spain

A TREATMENT OF SECOND-ORDER SINGULAR LAGRANGIANS AS CONTENEOUS SYSTEMS, 445
N.I. Farahat and Kh. Ramadan
Department of Physics
The Islamic University of Gaza
P.O. Box 108
Gaza, Palestine

BASIC SETS OF BRAUER CHARACTERS OF
THE SPORADIC MONSTER GROUP, III, 459
K. Ikeda
Department of Mathematics
Kyushu Sangyo University
Fukuoka 813-8503, Japan

PRIME THEOREM IN SANTILLI'S ISONUMBER THEORY, 475
pn=ap1m +P2+...+Pn-1 ±b
Chun-Xuan Jiang
P.O. Box 3924, Beijing 100854
P.R. China

SUR LES SOUS-ALGEBRES MONOGENES
D'ALGEBRES D'EVOLUTION STATIONNAIRE, 490

A. Conseibo et M. Quattara
Departement de Mathematiques et Informatique
Universite Polytechnique de Bobo-Dioulasso
o1 B.P. 1091 Bobo-Dioulasso 01
Burkina Faso

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ALGEBRAS, GROUPS AND GEOMETRIES

VOLUME 18, NUMBER 1, MARCH 2001

QUASILINEAR HYPERBOLIC SYSTEMS WITH HEXAGONAL THREE-WEB OF CHARACTERISTICS IN MECHANICS, 1
H. Kilp
Institute of Pure Mathematics
University o
Tartu 51014, Estonia

RADICALS OF TRIPLE SYSTEMS, 17
N. Kamiya
University of
965-8580, Japan

QUASI-SIMILATTICE DECOMPOSITIONS
OF SEMIGROUPS WITH ZERO, 27
M. Ciric and S. Bogdanovic
University of Nis
Faculty of Sciences and Mathematics
Cirila i Metodija 2, P. O. Box 91
18000 Nis, Yugoslavia

DE NOUVEAUX RESULTATS SUR
SPEC (A [X1,........., Xn] ), 35
R. Chibloun
Departement de Mathematique et Informatique
Universite Moulay Ismail
Faculte des Sciences
B.P. 4010, Beni M'hamed
Meknes, Maroc

COMPLEMENT OF AN F- HYPEROPERATION, 43
A. Iranmanesh and M. N. Iradmusa
Department of Mathematics
Tarbiat Modarres University
P. O. Box 14115-137
Teheran, Iran and
Center for Theoretical Physics and Mathematics
P.O. Box 11365-8486, AEOI
Teheran, Iran

TENSOR INVARIANTS ASSOCIATED WITH GOOD LIE SUPERALGEBRAS.
TOWARDS A NEW CLASSIFICATION OF SIMPLE LIE ALGEBRAS, 53
M. El Houari
Instituto de Matematica e Estatistica-USP
Departamento de Matematica, Universidade de Sao Paulo
Rua do Matao, 1010 - Cidade Universitaria
05315-970 Sao Paulo-SP, Brazil

DERIVATIONS DE PEIRCE ET STRUCTURE D'ALGEBRE: COMPLEMENTS, 79
C. Burgueno et C. Mallol
Departmento de Matematica y Estadistica
Universidad de La Frontera
Casilla 54-D
Temuco, Chile

RESTRICTION OF SOME DISCRETE SERIES REPRESENTATIONS, 85
J. A. Vargas
FAMAF
Universidad Nacional de Cordoba
5000 Cordoba, Argentina

A GENERALIZED STIRLING INVERSION
FORMULA, 101
Fethi Bin Muhammad Belgacem
Department of Mathematics and Computer Science
Faculty of Science, Kuwait University
P. O. Box 5969
Safat 13060, Kuwait

SOUS-ALGEBRES DE CARTAN D'UNE
SUPERALGEBRE DE MALCEV, 115
A. Koulibaly et J. Come Bere
Department de Mathematiques et Informatique
Faculte des Sciences et Techniques
Universite de Ouagadougou
03 B. P. 7021 Ouagadougou 03
Burkina Faso and
Saliou Toure
Institut de Recherche Mathematiques
08 B.P. 2030 Abidjan 08
Cote d'Ivoire

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ALGEBRAS, GROUPS AND GEOMETRIES

VOLUME 18, NUMBER 2, JUNE, 2001

ENDOMORPHISM SEMIGROUPS
OF SCHMIDT GROUPS, 139
P. Puusemp
Department of Mathematics
Tallinn Technical University
Ehitajate tee 5
Tallinn 19086, Estonia

LOCALISATION ET FORMULE DES HAUTEURS DE
TAUVEL DANS LES ANNEAUX DE POLYNOMES TORDUS, 153
T. Guedenon
U. F. R. de Mathematiques
Universite des Sciences et Technologies de Lille
59655 Villeneuve d'Ascq, France

SUR LES CHAINES DE VALUATIONS ET
D'IDEAUX PREMIERS DES ANNEAUX DE POLYNOMES,184
R. Chibloun
Department de Mathematiques et Informatique
Universite Moulay Ismail, Faculte des Sciences
B. P. 4010, Beni M¹hamed, Meknes, Maroc

ABOUT x4=w ( x ) 3x TRAIN ALGEBRAS, 193
R. Benavides and C. Mallol
Universidad de la Frontera - Facultad de Ingenieria
Departamento de Matematica
Casilla 54-D
Temuco, Chile and
R. Costa
Instituto de Matematica e Estatistica - USP
Caixa Postal 66281- CEP 05389-970 - Ag. Cidade de Sao Paulo
Sao Paulo, SP - Brazil

AUTOMORPHISMES DANS LES ALGEBRES DE
LOTKA-VOLTERRA, 203
H. Boujemaa et M. Rachidi
Department de Mathematiques et Informatique
Faculte des Sciences, Universite Mohammed V-Agdal
Avenue Ibn Battouta, B. P. 1014
Rabat, Maroc and
A. Micali
Departement des Sciences Mathematiques
Universite Montpellier II
Place Eugene Bataillon
34095 Monpellier, France

DIRECT LIMITS OF L* -TRIPLES, 223
A. J. Calderon Martin
Departamento de Matematicas, Universidad de Cadiz
11510 Puerto Real
Cadiz, Spain and
C. Martin Gonzalez
Departamento de Algebra, Geometria y Topologia
Universidad de Malaga
Apartado 59, 29080
Malaga, Spain

SUPERPREHOLOMORPHIC SECTIONS ON A COMPLEX SUPERMANIFOLD, 233
M. Mostafavi and Y. Bahrampour
Department of Mathematics
Shahid Bahonar University of Kerman
Kerman, Iran

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ALGEBRAS, GROUPS AND GEOMETRIES

VOLUME 18, NUMBER 3, SEPTEMBER 2001

SABININ SPACES AND MOUFANG LOOPS, 259
N. Castaneda
Department of Mathematical Sciences
Central Connecticut State University
New Britain, CT 06053

A CHARACTERIZATION OF SOME SYMMETRIC AND
LINEAR GROUPS, 281
M. R. Darafsheh
Department of Mathematics and Computer Sciences
Faculty of Science
University of Tehran
Tehran, Iran and
A. R. Moghaddamfar
Department of Mathematics
Iran University of Science and Technology
Narmak, Tehran 16844, Iran and
A. R. Zokayi
Department of Mathematics
Faculty of Science
K.N.T. University of Technology
Tehran Iran

EACTNESS OF BRS COHOMOLOGY SEQUENCE IN R...... FORMULATION OF THE ABELIAN HIGGS MODEL, 301
N. Motoyui and M. Yamada
Department of Mathematical Sciences, Faculty of Science
Ibaraki University, Bunkyo 2-1-1
Mito, 310-8512 Japan

HALIDON RINGS AND GROUP ALGRBRAS, 317
A. Telveenus
Department of Mathematics
Fatima Mata National College
Quilon, Kerala State, S. India

RELATION BETWEEN CROSSED SQUARE AND CROSSED CORNER, 331
M. Alp
Dumlupinar Universitesi
Fen-Edebiyat Fakultesi
Matematik Bolumu
Kutahya, Turkey

ON THE DIVISION ALGEBRAS IN R......, 341
Y. Yayli and H. H. Hacisalihoglu
Department of Mathematics, Faculty of Sciences, Ankara
University 06100, Tandogan, Ankara, Turkey and
A. A. Ergin
Department of Mathematics, Faculty of Arts and Sciences,
Akdeniz University, Antalya, Turkey

ON THE GROUP WITH THE SAME ORDERS
OF SYLOW NORMALIZERS AS THE FINITE
SIMPLE GROUP S....., 349
Jianxing Bi
Department of Mathematics
Liaoning University
Shenyang, 110036 P. R. China

A CLASS OF GENERALIZED ELLIPTIC-TYPE INTEGRALS..., 357
A. Al-Zamel
Department of Mathematics and Computer Science
Kuwait University
P.O. Box, 5969
Safat 13060, Kuwait

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ALGEBRAS, GROUPS AND GEOMETRIES

VOLUME 18, NUMBER 4, DECEMBER 2001

CONVOLUTIONS OF CERTAIN ANALYTIC
FUNCTIONS, 375
S. Saita
Department of Mathematics
Kinki University
Higashi-Osaka, Osaka 577-8502, Japan and
S. Owa
Department of Mathematics
Kinki University
Hiigashi-Osaka, Osaka 577-8502, Japan

ON BOREL SUBSYSTEMS OF LIE TRIPLE SYSTEMS, 385
Y. S. Daoji Meng
Department of Mathematics, Nankai University
Tianjin P. R. China, 300071
Member of the PMC Key Lab., ME of China

CHARACTERISTICALLY NILPOTENT EXTENSIONS OF NILRADICALS OF SOLVABLE RIGID LAWS, 393
Jose Maria Ancochea Bermudez
Rutwig Campoamor
Departamento de Geometria y Topologia
Fac. CC. Matematicas Univ. Complutense
28040 Madrid, Spain

TOPOLOGICAL CROSSED MODULES AND G-GROUPOIDS, 401
I. Icen and A. Fatih Ozcan
Inonu University
Faculty of Science and Art
Department of Mathematics
Malatya, Turkey

PROOF OF SCHINZEL'S HYPOTHESIS, 411
C. Jiang
P. O. Box 3924
Beijing 100854
P. R. China

THE PUSH -OUT SPACE OF SPHERICALLY IMMERSED SURFACES, 421
S. Carter and Y. Kaya
Department of Pure Mathematics
University of Leeds
Leeds LS2 9JT, England

THE ACTION OF AutII2 ... ON THE SET OF REGULAR
UNBRANCHED Dp - AND Q8 - COVERINGS OF S2, 434
M. Kazaz
Department of Mathematics
Faculty of Science
University of Celal Bayar
Muradiye Campus, 45047
Manisa, Turkey

SUPERMULTIPLETS AND RELATIVISTIC PROBLEMS:
BHABHA EQUATIONS IN HAMILTONIAN FORM, 445
R.-K. Loide
Department of Physics
Tallinn Technical University
Ehitajate tee 5, 19086 Tallinn, Estonia and
I. Ots
Institute of Physics, University of Tartu
Riia 142, 51014 Tartu, Estonia and
R. Saar
Institute of Theoretical Physics
University of Tartu
Tahe 4, 51010 Tartu, Estonia

EXTENSIONS OF GRADED
FILIFORM LIE ALGEBRAS, 461
J. Reyes
Departamento de Matematica
Escuela Politecnica Superior
Universidad de Huelva
21819, Palos de la Frontera
Huelva, Spain

ON THE SET OF ORDER ELEMENTS OF G = PSL3 (q)
WHEN EXTENDED BY A SUBGROUP OF OUT (G), 473
M. R. Darafsheh and N. S. Karamzadeh
Department of Mathematics and Computer Science
Faculty of Science, University of Tehran
Tehran, Iran

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ALGEBRAS, GROUPS AND GEOMETRIES

VOLUME 17, NUMBER 1, MARCH 2000

INVARIANT TRACE FIELDS AND IDEAL TRIANGULATIONS OF CUSPED HYPERBOLIC 3-MANIFOLDS, 1
H. Akyoshi,
Graduate School of Mathematics, Kyushu University,
Fukuoka 812-8581, Japan

GEOMETRIC QUANTIZATION,
OF GENERALIZED OSCILLATOR, 11
S.V. Zuev
Department of Theoretical Physics
Penza State Pedagogical University
440039 Penza, Russia

ANNEAUX MUNIS D'UNE ACTION DE
GROUPE SUPERRESOLUBLE, 17
T. Guedenon
21, Avenue de Versailles,
75016 Paris, France

LATTICES ASSOCIATED WITH COVERING SPACES, 49
M. R. Adikari and P. Das
Department of Mathematics
Burdwan University, Burdwan 713104
West Bengal, India

ONE KIND OF COMPLETE LIE ALGEBRAS, 57
Lin Sheng Zhu
Department of Mathematics
Changshu College, Changshu 2150
Jiangsu, China
and
Department of Mathematics
Nanki University, Tianjin 300071, China and
Daoji Meng
Department of Mathematics
Nankai University
Tianjin 300071, China

ON A NEW CLASSIFICATION OF SIMPLE LIE ALGEBRAS, 73
M. El Houari
Instituto Matematica e Estatistica-USP
Departamento de Matematica
Universidade de Sao Paulo
Rua do Matao, 1010 - Cidade Universitaria
05315-970 Sao Paulo-SP, Brasil

PREHOLOMORPHIC SECTIONS
ON COMPLEX MANIFOLDS, 89
M.Ebrahimi, N. Gerami and R. Nekooei
Department of Mathematics
Shahid Bahonar University of Kerman
P.O. Box 76135-133
Kerman, Iran

ON CERTAIN FLAT FRECHET BUNDELS
AND THEIR HOLONOMY HOMOMORPHISMS, 105
E.E. Vassiliou
Department of Mathematics
University of Athens, Panepistimiopolis
GR-157 84 Athens, Greece and
G.N. Galanis
Hellenic Naval Academy, Terma Hatzikyriakou
GR-185 39 Piraeus, Greece

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ALGEBRAS, GROUPS AND
GEOMETRIES

VOLUME 17, NUMBER 2, JUNE 2000

FOUR-DIMENSIONAL REAL ALGEBRAS
SATISFYING MIDDLE ASSOCIATIVITY, 123
S.C. Althoen, K.D. Hansen, and L.D. Kugler
Department of Mathematics
The University of Michigan-Flint
Flint, Michigan 48502-1950

DERIVATIONS AND AUTOMORPHISMS
IN THE TWISTED POLYNOMIAL ALGEBRA, 149
E. Cerati and I. Schwer
Departamento de Matematica, Facultad de Ingenieria Quimica
Universidad Nacional del Litoral
Santiago del Estero 2829-3000 Santa Fe, Argentina

EXAMPLES OF HYPOSPECIAL LOOPS II, 167
A.Nourou Issa
Institut de Mathematiques et de Sciences Physiques
Universite Nationale du Benin
B.P. 613 Porto Novo, Benin

ON COMPUTING EIGENVALUES
AND DOUBLE BRACKET ALGEBRAS, 177
K.R. Driessel and I.R. Henzel
Mathematics Department
400 Carver Hall
Iowa State University
Ames, Iowa 50011

SOME WHITTAKER MODELS FOR ........, 211
R. Johnson
Instituto de Matematica
Universidad Catolica de Valparaiso
Casilla 4059 , Valparaiso, Chile

MEUSNIER¹S THEOREM FOR SURFCES IN
n-DIMENSIONAL LORENTZIAN SPACE L, 233
E. Iyigun and E. Ozdamar
Uludag University
Department of Mathematics
16059 Gorukle
Bursa, Turkey

BOOK REVIEW, H.M. Srivastava, 249

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ALGEBRAS, GROUPS AND GEOMETRIES

VOLUME 17, NUMBER 3, SEPTEMBER 2000

Proceedings of the 11-th National Conference
on Finsler, Lagrange and Hamilton Geometry
held in Craicova, Romania
February 2000

SOME RIEMANNIAN ALMOST PRODUCT STRUCTURES
ON TANGENT MANIFOLD, 253
M. Anastasiei
Faculty of Mathematics
University ³Al.I. Cuza² Iasi
6600 Iasi, Romania

THE BEHAVIOR OF TEST PARTICLE ON A PLANAR
SPACE-TIME STRUCTURE, 263
I. Astefanoaei and Gh. Maftei,
A.I. Cuza University
Department of Physic
Blvd. Copou no. 11
66oo, Romania

MOVING FRAMES OF RIEMANNIAN SURFACES
IN GL3- SPACES, 273
V. Balan
Department of Mathematics
Politehnica University of Bucharest
Splaiul Independentei 313
RO-77206, Bucharest, Romania

THE NONHOLONOMIC MANIFOLD IN THE HIGHER
ORDER LAGRANGE SPACES, 283
R. Miron
Faculty of Mathematics
University ³Al.I.Cuza²
Iasi, 6600, Romania

COMPLEX HAMILTON SPACES, 293
Gh. Munteanu
³Transilvania² University
Faculty of Science
2200, Brasov, Romania

SINGULAR FINSLER SPACES, 303
T. Nagano
Siebold University of Nagasaki
822 Yoshimuta Goh, Nagayo Cho
Nishisonogi gun, Nagasaki. Pref.
855551-2195, Japan

RIEMANNIAN DEFORMATION CONSTANT
OF A FINSLER SPACE AND QUASI CONFORMALITY, 31
A. Neagu and V.T. Borcea
Technical University ³Gh. Asachi²
Department of Mathematics
Bd Carol, Nr. 11
Iasi - 6600, Romania

ON THE HOMOGENEOUS HYPERBOLIC LIFT OF A
FINSLERIAN METRIC, 323
M. Roman
Technical University ³Gh. Asachi² Iasi
Department of Mathematics
Iasi, 6600, Romania

A CLASS OF METRICAL ALMOST 2- p
STRUCTURES ON TANGENT BUNDLE, 331
A. Sandovici
High School ³Gh. Cartianu²
5600, Piatra, Neamt, Romania and
V. Blanuta
Department of Mathematics
Bacau University
Str. Marasesti 157
5500, Bacau, Romania

A RIGIDITY THEOREM FOR FINSLER SUBMANIFOLDS, 341
Z. Shen
Mathematics Department
Indiana University-Purdue University
Indianapolis, In 46202-3216, U.S.A.

ON THE LINEARIZED FIELD THEORY OF FINSLER AND LAGANGE SPACES, 351
P.C. Stavrinos
Department of Mathematics
University of Athens, Greece

THE CARTAN-CLIFTON METHOD OF
THE MOVING FRAME: FINSLERIAN
BUNDLE ON RIEMANNIAN DISTANCES, 361
J. G. Vargas and D. G. Torr
Department of Physics
University of South Carolina
Columbia, SC 29208, USA

EINSTEIN-YANG-MILLS MODELS FOR GRAVITY, 375
G. Zet
Department of Physics
Technical University ³Gh. Asachi²
Iasi 6600, Romania

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ALGEBRAS, GROUPS AND
GEOMETRIES

VOLUME 17, NUMBER 4, DECEMBER 2000

A CLASS OF NEW NILPOTENT LIE ALGEBRAS, 383
Zhu Lin Sheng
Department of Mathematics
Changshu College
Changshu 215500, China and
Department of Mathematics
Nankai University
Tianjin 300071, China and
Meng Dao Ji
Department of Mathematic
Nankai University
Tianjin 300071, China

ON CONTACT METRIC 3-MANIFOLDS
WITH R (X, x)x = 0, 393
F. Gouli-Andreou
Aristotle University of Thessaloniki
Department of Mathematics
Thessaloniki-540 06, Greece

A CLASS OF CONTACT METRIC 3-MANIFOLDS
WITH x e N (k,m) AND k, m FUNCTIONS, 401
F. Gouli-Andreou and P. J. Xenos
Aristotle University of Thessaoniki
Department of Mathematics
Thessaloniki - 540 60, Greece and
Ph.J. Xenos
Aristotle University of Thessaloniki
School of Technology
Mathematics Division
Thessaloniki - 540 06, Greece

NEOFIELDS SATISFYING 1+1 = 0, 408
C. Powell Johnson
Department of Mathematics and Statistics
Mississippi State University
P.O. Drawer MA
Mississippi State, MS 39762, USA

BASIC SETS OF BRAUER CHARACTERS OF
THE SPORADIC MONSTER GROUP, II, 417
M. Muta and K. Ikeda
Department of Mathematics
Kyushu Sangyo University
Fukuoka 813-8503, Japan

SUR l¹INVERSIBILITE QUADRATIQUE DANS UNE
ALGEBRE VERIFIANT L¹ IDENTITE X X2= X 2X , 435
B. Habib
Departement de Mathematiques et Informatiques
Faculte des Sciences de Mekne`s
B.P. 4010, Zitoune, Mekne`s
Maroc, and
K. Amin
Departamento de Anlysis Matematico
Facultad de Ciencias Experimentales
Universitad de Almeria, La Canada, Almeria

ON COALGEBRAS RELATED TO SUPERPREHOLOMORPHIC FUNCTIONS, 449
M. Sabzevary and Y. Bahrampour
Department of Mathematics
Shahid Bahonar University of Kerman
Kerman, Iran
SPECIAL CASES OF CAT1- GROUPS, 468
M. Alp
Dumlupinar Universitesi
Fen-Edebiyat Fakultesi
Matematik Bolumu
Kutahya, Turkey

CHARACTERIZATION OF A SEMIDIRECT
PRODUCT OF CYCLIC GROUPS BY ITS
ENDOMORPHISM SEMIGROUPS, 479
P. Puusemp
Department of Mathematics
Tallinn Technical University
Ehitajate tee 5
Tallinn 19086, Estonia

ON THE SHEAF OF TRIAD HOMOTOPY GROUPS
AND SOME CHARACTERIZATIONS, 499
A. Serbetci
Ankara University
Faculty of Science
Department of Mathematics
06100 Tandogan, Ankara, Turkey

INDEX, 507

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ALGEBRAS, GROUPS AND GEOMETRIES

VOLUME 16, NUMBER 1, MARCH 1999

Proceedings of the 10th National Conference
on Finsler, Lagrange and Hamilton Geometry
held in Craicova, Romania
February 1998
R.Miron and M. Anastasiei
Editors

FOREWORD, III

ON THE NONLINEAR CONNECTION OF A SECOND
ORDER FINSLER SPACE,1
Mihai Anastasiei
Faculty of Mathematics
University ³Al.I.Cuza² Iasi
6600, Iasi, Romania
Hideo Shimada and Sorin Sabau
Department of Mathematics
Hokkaido Tokai University
Minami-ku, Minami-sawa, 5-1

A COMPARISON BETWEEN THE INDUCED AND
THE INTRINSIC FINSLER CONNECTIONS ON A FINSLER SUBMANIFOLD, 11
Aurel Bejancu
Department of Mathematics
Technical University ³Gh. Asachi² of Iasi
C.P. 17, Iasi 1, 6600-Iasi Romania and

Hani Reda Farran
Department of Mathematics
and Computer Science, Kuwait University
P.O. Box 5969, Safat 13060, Kuwait

THE DEFORMATION OF THE ANGLES BY QUASICONFORMAL MAPPINGS, 23
V.T. Borcea and A. Neagu
Technical University ³Gh. Asachi²
Department of Mathematics
Iasi 1, 6600-Iasi, Romania

SEMISPRAYS AND VERTICAL PROJECTORS IN THE HIGHER ORDER GEOMETRY, 31
Ioan Bucataru
³Octav Mayer² Institute of Mathematics
Iasi Branch of the Romanian Academy
B-dul Copou, no. 8
Iasi, Romania 6600

ON SOME PROPERTIES OF A QUASI-SASAKIAN MANIFOLD, 39
Constantin Calin
Department of Mathematics
Technical University of Iasi
6600-Iasi, Romania

ON ALMOST PARA-HERMITIAN MANIFOLDS, 47
Vasile Cruceanu
³Al. I Cuza² University
6600 Iasi, Romania
Fernando Etayo
Fac. de Ciencias. Univ. Cantabria
Avda. de los Castros, s/n,
39071 Santander, Spain

THE LARGE SCALE PATHOLOGY IN AN EXACT
CLASS OF SOLUTIONS WITH cosh (a z), 63
I. Astefanoaei , C. Dariescu and M.A. Dariescu
³Al. I. Cuza² University, Department of Physics
Blvd. Copou no. 11, 6600, Romania

GENERALIZED FINSLER SPACES ADMITTING
A PARALLEL FINSLER VECTOR FIELD, 73
Masashi Kitayama
Department of Mathematics
Kushiro Campus
Hokkaido University of Education
Kushiro, Hokkaido 085, Japan

FINSLER SPACES, 83
Radu Miron
Univ. ³Al. I. Cuza²
Faculty of Mathematics
6600, Iasi, Romania, and
Vasile Sorin Sabau
Univ. ³Transilvania²
Department of Mathematics
Brasov, Romania

ON HIGH ORDER STRUCTURES ON VECTOR BUNDLES, 91
Marcela Popescu and Paul Popescu
Department of Mathematics, University of Craiova,
13, Al. I. Cuza st., Craiova, 1100, Romania

SOME REMARKS ON DIFFERENTIABLE MAPS, 103
Silviu Sburlan
Department of Mathematics
³Ovidius² University
Constantza, Romania

ON THE INTEGRABILITY OF THE
STRUCTURES .... , 107
Petre Stavre
Department of Mathematics,
University of Craiova,
13, Al. I. Cuza st., Craiova, 1100, Romania

ON GENERALISED RANDERS MANIFOLDS, 115
Aly A. Tamim
Nabil L. Youssef
Department of Mathematics,
Faculty of Science,
Cairo University, Giza, Egypt.

VOLUME 15, NUMBER 2, JUNE 1999

ADMISSIBLE CONGRUENCE PAIRS ON
QUASIREGULAR SEMIGROUPS, 127
K.P. Shum
Department of Mathematics
The Chinese University of Hong Kong
Hong Kong, SAR, China
Yuqi Guo
Institute of Pure Mathematics
Yunnan University
Kunming, China
and
Xueming Ren
Department of Mathematics
Xi¹an University of Architecture & Technology
Xian, China

LOCALLY VOLUME-MINIMIZING CODIMENSION-ONE
FOLIATIONS OF ... , 145
I. Kocayusufoglu
Osmangazi Universitesi
Fen-Ed. Fakultesi
Matematik Bolumu
Eskisehir-Turkiye, and
D.L. Johnson
Dept. of Mathematics
Christmas-Saucon Hall
14 E. Packer Avenue
Lehigh University
Bethlehem, PA 18015-3174

ON THE COHOMOLOGY OF NILPOTENT
LIE ALGEBRAS OF SIMPLE TYPE, 165
X. Agrafiotou
School of Technology
Division of Mathematics
University of Thessaloniki
Thessaloniki , Greece

CHARACTERIZATION OF CROSSED CORNER, 173
M. Alp
Dumlupinar Universitesi
Fen-Edebiyat Fakultesi
Matematik, Bolumu
Kutahya, Turkey

A CHARACTERIZATION OF DIVISIBLE AND TORSION
ABELIAN GROUPS BY THEIR ENDOMORPHISM SEMIGROUPS, 183
P. Puusemp
Institute of Mathematics
Tallinn Technical University
Ehitajate tee 5
EE0026 Tallinn, Estonia

ON THE MINIMAL POLYNOMIAL OF AN ALGEBRAIC OPERATOR, 195
S. Karanasios and J. Maroulas
National Technical University of Athens
Department of Mathematics
Zografou Campus
GR 157 80 Zografou, Athens , Greece

ON CASIMIR ELEMENTS OF SIMPLE LIE ALGEBRAS, 203
M. El Houhari
Istituto de Matema~tica e Estati~stica - USP
Departamento de Matema~tica
Rua de Mataýo, 1010 , Cidade Universitaria
05315-970 Sao Paulo-SP, Brasil

ALGEBRES DE RANG 3 EN CARACTERISTIQUE 2, 223
C. Burgueno et C. Mallol
Departamento de Matema~ticas y Estadi~stica
Universidad de La Frontera
Casilla 54-D
Temuco, Chile
and
A. Walkhoff
Gunterstrasse 2
D-53179 Bonn, Germany

COMPLEX SUPERMANIFOLDS WITH BOUNDARY
AND THEIR PARAMETRIZATION, 233
S.Versaie
Department of Mathematics
University of Teheran
Teheran, Iran
'and
M.M. Rezaii
Department of Mathematics
Amir-Kabir University
Teheran, Ira

THEOREMES DE STRUCTURE D¹ALGEBRES DE JORDAN
TOPOLOGIQUES OU BORNOLOGIQUES, 245
N. El. Yacoubi
Departement de Mathematiques et d¹Informatique
Universite Mohamed V. Faculte des Sciences de Rabat
Maroc. B.P. 1014

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ALGEBRAS, GROUPS AND GEOMETRIES

VOLUME 15, 1998

UNIVERSAL CENTRAL EXTENSIONS OF KAC-MOODY
ALGEBRAS EXTENDED BY A COMMUTATIVE ALGEBRA, 1
E. M. Souidi
Universiteº Mohammed V
Faculteº des Sciences
Department de Mathematiques et Informatique
B.P. 1014 Rabat­Morocco

ON K­CHEN SUBMANIFOLDS OF
PSEUDO­RIEMANNIAN MANIFOLDS, 13
U. Dursun
Istanbul Teknik Universitesi
Fen-Edebiyat Fakultesi, Matematik
80626 Maslak, Istanbul, Turkey

JACOBI FIELDS AND ODULAR
STRUCTURE OF AFFINE MANIFOLDS, 25
A. I. Nesterov
Departamento de Fisica
Universidad de Guadalajara Department of Theoretical Physics
Krasnoyarsk State University
Krasnoyarsk, Russian Federation

IDEMPOTENTS IN THE C*­ALGEBRAS OF FREE
PRODUCTS OF GROUPS WITH AMALGAMATION, 33
B. O. Balogun
International Centre for Theoretical Physics
I 34100 Trieste
Italy

A NEW CONSTRUCTION OF
LEBESGUE­STIELTJES MEASURE, 41
M. Bodnariu
University Politehnica of Bucharest
Department of Mathematics I
Splaiul Independentei 313
77206 Bucharest, Romania

ON HV ­ GROUP RINGS, 47
S. Spartalis, A. Dramalides
and T. Vougiouklis
Department of Mathematics
Democritus University of Thrace
67100 Xanthis, Greece

RIEMANNIAN GEODESIC ORBIT
METRICS ON FIBER BUNDLES, 55
H. Tamaru
Department of Mathematics
Sophia University
Tokyo 102, Japan

SMOOTH EXACT FILLINGS, 69
H. R. Farran,
Department of Mathematics
P.O. Box 5969
Kuwait University
13060 Safat, Kuwait
and
S. A. Robertson
Faculty of Mathematical Studies
University of Southampton
Southampton S017 1 BJ, U.K.

COASSOCIATIVITY, COHOMOLOGY AND
GERSTENHABER ALGEBRAS, 85
E. Paal
Department of Mathematics
Tallinn Technical University
Ehitajate tee 5
EE026 Tallinn, Estonia

INFLATING A SYMMETRIC HYPERSPHERE, 95
H. R. Farran
Department of Mathematics
Kuwait University
P.O. Box 5969
13060 Safat, Kuwait
and
S. A. Robertson
Faculty of Mathematical Studies
University of Southampton
Southampton S017 1 BJ, U.K.

Z-FILTERS AND A FAMILY OF
COMPACT HAUSDORFF SPACES, 107
M. Kocak and Z. Arvasi
Department of Mathematics
Faculty of Arts and Science
University of Osmangazi
26480, Eskisehir, Turkiye

SOME SERIES CONTAINING THE
GENERALIZED HYPERGEOMETRIC
FUNCTIONS OF THE GAUSS TYPE, 115
L. Galue'
Centro de Investigacion
de Matematica Aplicada (C.I.M.A)
Facultad de Ingenieria
La Universidad del Zulia
Apartado 10482
Maracaibo, Venezuela

SMOOTH LOOPS I, 127
L. V. Sabinin
Department of Mathematics
Friendship of Nations University
M. Maklaya 6
Moscow 117198 Russia
and
Department of Mathematics
Michoacan University
Morelia, Michoacan, Mexico

HARMONIC MORPHISMS FROM THREE­DIMENSIONAL
EUCLIDEAN AND SPHERICAL SPACE FORMS, 155
M. T. Mustafa
Faculty of Engineering Sciences
GIK Institute of Engineering Sciences and Technology
Topi, Distt. Swabi, NWFP, Pakistan
and
J. C. Wood
Department of Pure Mathematics
University of Leeds
Leeds LS2 9JT, U.K.

A CLASSIFICATION OF IMMERSIONS
OF MANIFOLDS, 173
M. R. Adhikari
Department of Mathematics
Burdwan University
Golapbag, Burdwan 713 104
West Bengal, India
and
U.C. De
Department of Mathematics
University of Kalyani
Kalyani 741 235
West Bengal, India
and
B. K. De
Calcutta Mathematical Society
AE­374, Sector I, Salt Lake City
West Bengal, India

SOME CONJUGACY CLASSES IN GROUPS
ASSOCIATED WITH THE GENERAL
LINEAR GROUPS, 183
M. R. Darafsheh
Institute for Studies in Theoretical
Physics and Mathematics
P.O. Box 19395-1795
Tehran, Iran

INTEGRALS INVOLVING JACOBI¹S GENERALIZED
FUNCTIONS AND MEIJER¹S FUNCTIONS, 201
S. Salinas and B. Gonzalez
Centro de Investigation
de Matematica Aplicada (C.I.M.A.)
Research Center of Applied Mathematics
P. O. Box 10482
Maracaibo, Venezuela

SOLUTION OF A CLASS OF INTEGRO-
DIFFERENTIAL EQUATIONS BY FRACTIONAL
CALCULUS, 213
I. Ali and S. Kalla
Department of Mathematics and Computer Science
P.O. Box 5969 Safat
13060 Kuwait

PRIME FILTERS ON LATTICES AND A
FAMILY OF COMPACT HAUSDORFF SPACES, 229
M. Kocak
Department of Mathematics
Faculty of Arts and Science
University of Osmangazi
26480 Eskisehir, Turkiye

DERIVATIONS DE PEIRCE ET UNE
CLASSE D¹ALGEBRES DE BERSTEIN
JORDAN D¹ORDRE, 239
C. Burgueno and C. Mallol
Departamento de Matema~tica
Universidad de La Frontera
Casilla 54-D, Temuco Chile
and
R. Varro
Universite de Montpellier III
B.P. 5043
34032 Montpellier Cedex 1, France

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ALGEBRAS, GROUPS AND GEOMETRIES

VOL. 15, SPECIAL ISSUE NO. 3, 1998

DEDICATED TO FERMAT'S LAST THEOREM

AN ALGEBRAIC PROOF OF FERMAT¹S LAST THEOREM, 247
S. N. Athanasopoulos
Dept. of Physics
Division of Theoretical Physics
University of Patras, Greece

FERMAT¹S LAST THEOREM, 289
C. Obi
Nanna Institute for Scientific Studies
P.O. Box 2128, Onitsha, Nigeria

ISOTOPIC PROOF AND RE-PROOF OF FERMAT¹S
LAST THEOREM VERIFYING BEAL¹S CONJECTURE, 299
E. Trell
Faculty of Health Sciences,
University of Linkoping,
S-581 85 Linkoping, Sweden.

ON THE FERMAT- SANTILLI ISOTHEOREM, 319
C. X. Jiang
P.O Box 3924, Beijing 100854, P.R. China

FOUNDATIONS OF SANTILLI'S ISONUMBER THEORY
PART I: ISONUMBER THEORY OF THE FIRST KIND, 351
C. X. Jiang
P.O. Box 3924, Beijing 100854, P.R. China

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ALGEBRAS, GROUPS AND GEOMETRIES

VOL. 15, SPECIAL ISSUE NO. 4, 1998
DEDICATED TO MARIUS SUPHUS LIE
ON THE CENTENNIEL OF HIS DEATH

MARIUS SOPHUS LIE¹S DOCTORAL THESIS
OVER EN CLASSE GEOMETRISKE TRANSFORMATIONER, 395
English Translation by Erik Trell,
Commentary by
Erik Trell
Faculty of Health and Sciences
University of Linkoping
S-581 85 Linkoping, Sweden
and
Ruggero Maria Santilli
Institute for Basic Research
P. O. Box 1577, Palm Harbor, FL 34682, USA

THE EIGHTFOLD EIGHTFOLD WAY:
APPLICATION OF LIE¹S TRUE
GEOMETRISKE TRANSFORMATIONER
TO ELEMENTARY PARTICLES, 447
Erik Trell
Faculty of Health and Sciences
University of Linkoping
S-581 85 Linkoping, Sweden

ISOTOPIC, GENOTOPIC AND HYPERSTRUCTURAL
LIFTINGS OF LIE'S THEORY AND THEIR ISODUALS, 473
Ruggero Maria Santilli
Institute for Basic Research
P.O.Box 1577, Palm Harbor, FL 34682, U.S.A.

COMMENTS ON A RECENT PAPER BY
MOROSI AND PIZZOCCHERO ON THE
LIE­SANTILLI ISOTHEORY, 497
J. V. Kadeisvili
Institute for Basic Research
P. O. Box. 1577, Palm Harbor, FL 34682, U. S. A.

FOUNDATIONS OF SANTILLI¹S ISONUMBER THEORY,
PART II: ISONUMBER THEORY OF
THE SECOND KIND, 509
Chun-xuan Jiang
P. O. Box 3924, Beijing 1200854, China

INFINITESIMAL MOTIONS ON
SANTILLI-SOURLAS-TSAGAS ISOMANIFOLDS, 545
Recep Aslander
Inonu Universitesi, Egitim Fakultesi
Matematik Egitimi Bolumu
44100 Malatya, Turkey
and
Sadik Keles
Inonu Universitesi, Fen-Edebiyat Fakultesi
Matematik Bolumu
44100 Malatya, Turkey

ON SANTILLI¹S ONE­DIMENSIONAL
ISODYNAMICAL SYSTEMS, 563
M. R. Molaei
Faculty of Mathematics
Shahid Bahonar University of Kerman
P. O. Box 76135­133, Kerman, Iran

**************************************************** ALGEBRAS, GROUPS AND GEOMETRIES

VOLUME 14, 1997

THE GEOMETRY OF SPACE­TIME WITH SUPERLUMINAL PHENOMENA, 1

T. Matolcsi
Department of Applied Analysis
Eotvos Lorand University
Budapest, Hungary
and
W. A. Rodrigues, Jr
Instituto de Matematica, Estatistica
e Computacao Cientifica
Universidade Estadual de Campinas
C.P. 6065, 13081-970 Campinas, SP, Brasil

ALGEBRAS, GROUPS AND GEOMETRIES

VOLUME 13, 1996

THE THEORY OF SMOOTH HYPOREDUCTIVE
AND PSEUDOREDUCTIVE LOOPS, 1

L. V. Sabinin
Department of Mathematics
Russia Friendship of Nations University
Mikluho Maklaya, 6, Moscow 117198, Russia

Aboubakr Bayoumi
Department of Mathematics, College of Science
King Saud University, P. O. Box 2455
Riyadh 11451, Saudi Arabia

Ye–Lin Ou
Department of Mathematics,
Guangxi University for Nationalities
Nanning 530006, P. R., China

John C. Wood
Department of Pure Mathematics, br> School of Mathematics
University of Leeds, Leeds LS2 9JT, U. K.

F. J. Echarte Reula, br> J. Nunez Valdes and F. Ramirez Lopez
Dept. Algebra, Computacion, br> Geometria y Topologia
Universidad de Sevilla, Aptdo 1160
41080 Sevilla, Spain

E. Castrandas
National Technical University of Athens
Department of Mathematics, Athens, Greece

S. M. B. Kashani
Institute for Studies in br> Theoretical Physics and Mathematics
P. O. Box 19395– 1795, Tehran, Iran

Osamu Ikawa
Department of Mathematics
Fukushima National College of Technology
Iwaki, Fukushima 970, Japan

Takeyoshi Kogiso
Institute of Mathematics, University of Tsukuba
Ibaraki 305, Japan

Grigorios Tsagas
Aristotle University of Thessaloniki
School of Technology, Division of Mathematics
Thessaloniki 54006, Greece

Grigorios Tsagas
Aristotle University of Thessaloniki
School of Technology, Division of Mathematics
Thessaloniki 54006, Greece

J. V. Kadeisvili
Institute for Basic Research
P.O.Box 1577, Palm Harbor, FL 34682, USA

Noriaki Kamiya
Department of Mathematics, Shimane University
Matsue 690, Japan

Ruggero Maria Santilli
Institute for Basic Research
P.O.Box 1577, Palm Harbor, FL 34682

D. A. Towers
Department of Mathematics and Statistics
Lancaster University, Lancaster LA1 4YF, England

K. Bowman
Department of Mathematics and Statistics
University of Central Lancashire, Preston PR1 2HE, England

Izu Vaisman
Department of Mathematics and Computer Science
University of Haifa, Haifa 31905, Israel

Ivan Correa
Departamente de Matematica, Facultad de Ciencias
Benavente 980, La Serena, Chile

Cesar Burguenýo and Cristian Mallol
Departamento de Matematica y Estadistica
Universidad de la Frontera, Casilla 54-D, Temuco, Chile

Huili Liu
Technische Universitat, FB-Mathematik, MA-8-3
Strae des 17. Juni, 136, 10623 Berlin, Germany

Ulo Lumiste
Institute of Pure Mathematics, Tartu University
Vanemuise 46, EE2400 Tartu, Estonia

A. Kobotis
Department of Business Administration
University of Macedonia, 156 Egnatia Str.
54006 Thessaloniki, Greece

R.Benavides and C. Mallol
Departamento de Matematica y Estadistica
Universidad de la Frontera,
Casilla 54-D, Temuco, Chile

Mati Abel
Institute of Pure Mathematics, University of Tartu
EE2400 Tartu, Estonia

Satoshi Gomyo
Department of Mathematical Sciences
Yokohama City University, 22–2 Seto, Kanazawa–ku
Yokohama 236, Japan

Piret Kuusk
Institute of Physics, Riia 142
Tartu EE2400, Estonia

Eugen Paal
Department of Mathematics, Tallinn Technical University
Ehitajate tee 5, Tallinn EE2400, Estonia

E. K. Loginov
Department of Mathematics, Ivanovo State Energy University