ALGEBRAS, GROUPS AND GEOMETRIES


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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 Ana~sta~siei
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 Saýýýýýýo Paulo-SP, Brasil

ALGEBRES DE RANG 3 EN CARACTERISTIQUE 2, 223
C. Burguenýo 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 Mathe~matiques et d¹Informatique
Universite~ Mohamed V. Faculte~ des Sciences de Rabat
Maroc. B.P. 1014

****************************************

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
Deºpartment de Matheºmatiques et Informatique
B.P. 1014 Rabat­Morocco

ON K­CHEN SUBMANIFOLDS OF
PSEUDO­RIEMANNIAN MANIFOLDS, 13
U. Dursun
IŽstanbul Teknik U¤niversitesi
Fen-Edebiyat Fakultesi, Matematik Bolumu
80626 Maslak, IŽstanbul, Turkey

JACOBI FIELDS AND ODULAR
STRUCTURE OF AFFINE MANIFOLDS, 25
A. I. Nesterov
Departamento de Fisica
Universidad de Guadalajara
Guadalajara, Jalisco, Meºxico
and
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 Investigacioºn
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. Gonzaºlez
Centro de Investigatioºn
de Matemaºtica 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

------------------------

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

-------------------------------------------

ALGEBRAS, GROUPS AND GEOMETRIES
VOL. 15, SPECIAL ISSUE NO. 4, 1998
DEDICATED TO MARIUS SUPHUS LIE
on the centennial 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 Linkoping
S-581 85 Linkoping, 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
Contents

THE GEOMETRY OF SPACE­TIME WITH SUPERLUMINAL PHENOMENA, 1


SOLVABILITY OF Z2­GRADED (-1, 1) ALGEBRAS, 17
DERIVATIONS IN SOME BERNSTEIN ALGEBRAS OF ORDER 2, 31
EXTENSIONS PONDE~RKE~ES D¹ALGE`BRES, 41
THE GENERATING FUNCTIONS FOR Enl(®) POLYNOMIALS, 49
FREE GROUPS AND FREE PRODUCTS IN SL2(Z), 57
ON A NEW GENERALIZATION OF FAMILIES OF
ELLIPTIC­TYPE INTEGRALS, 83
THE DYNKIN DIAGRAM AND THE OTHER ELEMENTS OF A
CLASS OF NILPOTENT LIE-ALGEBRAS OF DIMENSION NINE, 107 >
ON MODULAR LOOP ALGEBRAS OF RA2 LOOPS, 163
SIMPLE CALCULATION OF THE ADELIC ZETA
FUNCTION ASSOCIATED WITH THE SPACE OF
BINARY CUBIC FORMS OVER A FUNCTION FIELD, 183 STUDIES ON SANTILLI¹S LOCALLY ANISOTROPIC
AND INHOMOGENEOUS ISOGEOMETRIES, I:
ISOBUNDLES AND GENERALIZED ISOFINSLER GRAVITY, 211
GROUP DISTRIBUTIVE QUASIGROUP ALGEBRAS, 259
CHARACTERIZATION OF THE EVEN PRINCIPAL
SERIES REPRESENTATIONS OF SL2(R) ON THE
POINCARE´ HALF-PLANE, 271
CARTAN¹S STRUCTURE EQUATIONS ON SANTILLI­
SOURLAS­TSAGAS ISOMANIFOLDS, 283
AUTOMORPHISMES ET DERIVATIONS DANS LES
ALGEBRES DE JORDAN DE RANG 3, 297
ON Cn­COMPLEMENTED NORMED ALGEBRAS, I, 313
LOW DIMENSIONAL 2-STEP NILPOTENT LIE
GROUPS IN RESONANCE, 321
OPTIMIZATION METHODS ON RIEMANNIAN MANIFOLDS, 339
LIE¹S THIRD THEOREM IN SUPERGEOMETRY, 359
ON THE TORSION SUBGROUPS AND ENDOMORPHISM
SEMIGROUPS OF ABELIAN GROUPS, 407
TENSOR INVARIANTS ASSOCIATED WITH CLASSICAL
LIE ALGEBRAS: A NEW CLASSIFICATION OF
SIMPLE LIE ALGEBRAS, 423
STARLIKENESS AND CONVEXITY OF CERTAIN
LINEAR OPERATORS, 447
THE CYLINDER LIE GROUP IN E5 AND
ITS ACTION AS LIE TRANSFORMATION GROUP, 453
BOOK REVIEW: INDEX TRANSFORMS, 453
********************************************

ALGEBRAS, GROUPS AND GEOMETRIES
VOLUME 13, 1996
Contents


THE THEORY OF SMOOTH HYPOREDUCTIVE
AND PSEUDOREDUCTIVE LOOPS, 1


ON THE NEW VERSION OF THE HAHN–BANACH THEOREM, 25
ON THE CLASSIFICATION OF QUADRATIC
HARMONIC MORPHISMS BETWEEN EUCLIDEAN SPACES, 41
STUDY OF TWO INVARIANTS IN COMPLEX
FILIFORM LIE ALGEBRAS, 55
A LOCAL ERGODIC THEOREM IN SEMIFINITE
ON NEUMANN ALGEBRAS, 71
HYPERSURFACES IN IR1N SATISFYING Îx = Ax + B, 81
INVARIANT CONNECTIONS ON COMPACT SIMPLE LIE GROUPS, 93
CALCULATION OF THE ADELIC ZETA FUNCTION
ASSOCIATED WITH P.V.(GL(2),M(2)) OVER
A FUNCTION FIELD, 105
STUDIES ON THE CLASSIFICATION OF
LIE-SANTILLI ALGEBRAS, 129
ISOAFFINE CONNECTIONS AND SANTILLI'S ISORIEMANNIAN
METRICS ON AN ISOMANIFOLD, 149
AN INTRODUCTION TO THE LIE–SANTILLI ISOTHEORY, 171
A CHARACTERIZATION OF PSEUDOISOFIELDS, 283

ON POWER ASSOCIATIVE BERNSTEIN ALGEBRAS
OF ARBITRARY ORDER, 295
ON THE GEOMETRY OF THE LAGRANGIAN–GRASSMANNIAN BUNDLES, 323
FINITELY GENERATED BERNSTEIN ALGEBRAS, 343
INVARIANTS DANS LES ALGEBRES DE BERNSTEIN, 349
ROTATIONAL SURFACES OF FINITE TYPE IN
3-DIMENSIONAL DE SITTER SPACE, 369
SEMISYMMETRIC CURVATURE OPERATORS AND
RIEMANNIAN 4–SPACES ELEMENTARILY CLASSIFIED, 371
ON QUASI–CYCLIC NILPOTENT LIE ALGEBRAS, 389
PIERCE TRANSFORMATION, AUTHOMOSPHISMS AND
DERIVATIONS IN TRAIN ALGEBRAS OF RANK 3, 401
NONCOMMUTATIVE JORDAN LOCALLY PSEUDOCONVEX Q–ALGEBRAS, 413
REALIZATION OF THE EXCEPTIONAL SIMPLE GRADED
LIE ALGEBRAS OF THE SECOND KIND, 431
LOCAL DIFFERENTIABLE LOOPS AND BRST–LIKE COHOMOLOGY, 465
LINEAR REPRESENTATIONS OF ANALYTICMOUFANG LOOPS, 471
LEFT QUASIGROUPS AND REDUCTIVE SPACES, 479
PARTIAL ISOMETRIES AND EXTREME POINTS
OF CERTAIN OPERATOR ALGEBRAS, 489
EXAMPLES OF HYPOSPECIAL LOOPS, 499
BOOK REVIEW, 515

Last updated January 10, 1999


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