Applicable Analysis and Discrete Mathematics Vol. 2, No 2 (October, 2008)

Online version (ISSN 2406-100X) posted on August 26, 2008.

Printed version (ISSN 1452-8630) appeared on August 26, 2008.

• Title:

  SECOND-ORDER DIFFERENTIAL EQUATIONS: CONDITIONS OF COMPLETE INTEGRABILITY

  Authors:

  Vasilij Petrovich Ermakov (1845-1922)

  Classification:

  2000 Mathematical Subject Classification: 34A05, 34A34

  Keywords:

  Keywords and phrases: Ermakov, integral, complete integrability

  Doi:

  DOI: 10.2298/AADM0802123E

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• Title:

  THE ERMAKOV EQUATION: A COMMENTARY

  Authors:

  P. G. L. Leach, K. Andriopoulos

  Classification:

  2000 Mathematical Subject Classification: 34A05, 01A75, 70F05, 22E70

  Keywords:

  Keywords and phrases: Ermakov, Pinney, Lewis, sl(2,R), invariant

  Doi:

  DOI: 10.2298/AADM0802146L

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• Title:

  MULTIPLICITY OF SOLUTIONS FOR SINGULAR SEMILINEAR ELLIPTIC EQUATIONS WITH CRITICAL HARDY-SOBOLEV EXPONENTS

  Authors:

  Qianqiao Guo, Pengcheng Niu, Jingbo Dou

  Classification:

  2000 Mathematical Subject Classification: 35J20, 47J30

  Keywords:

  Keywords and phrases: Critical Hardy-Sobolev exponents, Hardy potential, variational method

  Doi:

  DOI: 10.2298/AADM0802158G

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• Title:

  JENSEN'S FUNCTIONAL AND POLYNOMIALS

  Authors:

  Mirjana Pavlović

  Classification:

  2000 Mathematical Subject Classification: 30C10

  Keywords:

  Keywords and phrases: Jensen's functional, concentration, polynomials

  Doi:

  DOI: 10.2298/AADM0802175P

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• Title:

  A NEW CRITERION FOR MULTIVALENT STARLIKE FUNCTIONS

  Authors:

  Zhi-Gang Wang, Neng Xu

  Classification:

  2000 Mathematical Subject Classification: 30C45

  Keywords:

  Keywords and phrases: Analytic functions, multivalent functions, starlike functions, Jack's lemma

  Doi:

  DOI: 10.2298/AADM0802183W

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• Title:

  A FIXED POINT THEOREM FOR MULTI-MAPS SATISFYING AN IMPLICIT RELATION ON METRIC SPACES

  Authors:

  S. Sedghi, I. Altun, N. Shobe

  Classification:

  2000 Mathematical Subject Classification: 54H25, 47H10

  Keywords:

  Keywords and phrases: Fixed point, weakly compatible maps, multi-maps, implicit relation

  Doi:

  DOI: 10.2298/AADM0802189S

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• Title:

  WEAK AND STRONG CONVERGENCE OF AN ITERATIVE METHOD FOR NONEXPANSIVE MAPPINGS IN HILBERT SPACES

  Authors:

  Yu Miao, Junfen Li

  Classification:

  2000 Mathematical Subject Classification: 47H09, 47H10

  Keywords:

  Keywords and phrases: Nonexpansive mapping, iterative process, weak convergence, strong convergence

  Doi:

  DOI: 10.2298/AADM0802197M

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• Title:

  NEW INTEGRAL AND SERIES REPRESENTATIONS OF THE GENERALIZED MATHIEU SERIES

  Authors:

  Živorad Tomovski

  Classification:

  2000 Mathematical Subject Classification: Primary 33E20, 40A10. Secondary 33C10, 33C20, 44A20

  Keywords:

  Keywords and phrases: Integral representations, Mathieu series, alternating Mathieu series, Fourier sine transforms, Bessel function, Gauss hypergeometric function, generalized hypergeometric function

  Doi:

  DOI: 10.2298/AADM0802205T

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• Title:

  AN EQUIVALENT FORM OF YOUNG'S INEQUALITY WITH UPPER BOUND

  Authors:

  E. Minguzzi

  Classification:

  2000 Mathematical Subject Classification: 26D10, 44A15

  Keywords:

  Keywords and phrases: Young's inequality, Legendre transform

  Doi:

  DOI: 10.2298/AADM0802213M

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• Title:

  SOME PROPERTIES OF THE SEQUENCE OF PRIME NUMBERS

  Authors:

  Vlad Copil, Laurenţiu Panaitopol

  Classification:

  2000 Mathematical Subject Classification: 11N05, 11A41

  Keywords:

  Keywords and phrases: Prime numbers, sequences, series

  Doi:

  DOI: 10.2298/AADM0802217C

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• Title:

  ESTIMATE OF THE NUMBER OF RESTRICTED INTEGER-PARTITIONS

  Authors:

  Joel Ratsaby

  Classification:

  2000 Mathematical Subject Classification: 68R05, 05A17, 11P82

  Keywords:

  Keywords and phrases: Analytic combinatorics

  Doi:

  DOI: 10.2298/AADM0802222R

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• Title:

  RECORDS IN GEOMETRICALLY DISTRIBUTED WORDS: SUM OF POSITIONS

  Authors:

  Helmut Prodinger

  Classification:

  2000 Mathematical Subject Classification: 60C05 (primary), 05A30 (secondary)

  Keywords:

  Keywords and phrases: Words, geometric probabilities, records, Rice's method

  Doi:

  DOI: 10.2298/AADM0802234P

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• Title:

  THE CURL OF A WEIGHTED NETWORK

  Authors:

  E. Bendito, A. Carmona, A. M. Encinas, J. M. Gesto

  Classification:

  2000 Mathematical Subject Classification: 39A12

  Keywords:

  Keywords and phrases: Networks, Laplacian, curl, Hodge's decomposition, Helmholtz's decomposition

  Doi:

  DOI: 10.2298/AADM0802241B

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• Title:

  SHARP UPPER BOUNDS FOR THE NUMBER OF SPANNING TREES OF A GRAPH

  Authors:

  Lihua Feng, Guihai Yu, Zhengtao Jiang, Lingzhi Ren

  Classification:

  2000 Mathematical Subject Classification: 05C05

  Keywords:

  Keywords and phrases: Graph, spanning trees, Laplacian eigenvalues

  Doi:

  DOI: 10.2298/AADM0802255F

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• Title:

  SPECTRAL PROPERTY OF CERTAIN CLASS OF GRAPHS ASSOCIATED WITH GENERALIZED BETHE TREES AND TRANSITIVE GRAPHS

  Authors:

  Yi-Zheng Fan, Shuang-Dong Li, Dong Liang

  Classification:

  2000 Mathematical Subject Classification: 05C50, 15A18

  Keywords:

  Keywords and phrases: Bethe tree, transitive graph, Laplacian matrix, adjacency matrix, Perron vector, Fiedler vector

  Doi:

  DOI: 10.2298/AADM0802260F

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• Title:

  NEW SUFFICIENT CONDITIONS FOR INTEGRAL COMPLETE 3-PARTITE GRAPHS

  Authors:

  Pavel Hic, Milan Pokorný, Pavol Černek

  Classification:

  2000 Mathematical Subject Classification: 05C50

  Keywords:

  Keywords and phrases: Integral graph, divisor, characteristic polynomial, graph spectrum, Diophantine equation

  Doi:

  DOI: 10.2298/AADM0802276H

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• Title:

  SCHULTZ POLYNOMIALS OF COMPOSITE GRAPHS

  Authors:

  Mehdi Eliasi, Bijan Taeri

  Classification:

  2000 Mathematical Subject Classification: Primary 05C12; Secondary 05A15.

  Keywords:

  Keywords and phrases: Schultz index, Schultz polynomial, Wiener index, distance

  Doi:

  DOI: 10.2298/AADM0802285E

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