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

Electronic version posted on August 26, 2008.

Printed version appeared on August 26, 2008.

Vasilij Petrovich Ermakov (1845–1922): SECOND-ORDER DIFFERENTIAL EQUATIONS: CONDITIONS OF COMPLETE INTEGRABILITY

2000 Mathematical Subject Classification: 34A05, 34A34
Key words and phrases: Ermakov, integral, complete integrability.

doi:10.2298/AADM0802123E

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P. G. L. Leach, K. Andriopoulos: THE ERMAKOV EQUATION: A COMMENTARY

2000 Mathematical Subject Classification: 34A05, 01A75, 70F05, 22E70
Key words and phrases: Ermakov, Pinney, Lewis, sl(2,R), invariant.

doi:10.2298/AADM0802146L

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Qianqiao Guo, Pengcheng Niu, Jingbo Dou: MULTIPLICITY OF SOLUTIONS FOR SINGULAR SEMILINEAR ELLIPTIC EQUATIONS WITH CRITICAL HARDY-SOBOLEV EXPONENTS

2000 Mathematical Subject Classification: 35J20, 47J30
Key words and phrases: Critical Hardy-Sobolev exponents, Hardy potential, variational method.

doi:10.2298/AADM0802158G

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Mirjana Pavlović: JENSEN’S FUNCTIONAL AND POLYNOMIALS

2000 Mathematical Subject Classification: 30C10
Key words and phrases: Jensen’s functional, concentration, polynomials.

doi:10.2298/AADM0802175P

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Zhi-Gang Wang, Neng Xu: A NEW CRITERION FOR MULTIVALENT STARLIKE FUNCTIONS

2000 Mathematical Subject Classification: 30C45
Key words and phrases: Analytic functions, multivalent functions, starlike functions, Jack’s lemma.

doi:10.2298/AADM0802183W

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S. Sedghi, I. Altun, N. Shobe: A FIXED POINT THEOREM FOR MULTI-MAPS SATISFYING AN IMPLICIT RELATION ON METRIC SPACES

2000 Mathematical Subject Classification: 54H25, 47H10
Key words and phrases: Fixed point, weakly compatible maps, multi-maps, implicit relation.

doi:10.2298/AADM0802189S

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Yu Miao, Junfen Li: WEAK AND STRONG CONVERGENCE OF AN ITERATIVE METHOD FOR NONEXPANSIVE MAPPINGS IN HILBERT SPACES

2000 Mathematical Subject Classification: 47H09, 47H10
Key words and phrases: Nonexpansive mapping, iterative process, weak convergence, strong convergence.

doi:10.2298/AADM0802197M

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Živorad Tomovski: NEW INTEGRAL AND SERIES REPRESENTATIONS OF THE GENERALIZED MATHIEU SERIES

2000 Mathematical Subject Classification: Primary 33E20, 40A10. Secondary 33C10, 33C20, 44A20
Key words and phrases: Integral representations, Mathieu series, alternating Mathieu series, Fourier sine transforms, Bessel function, Gauss hypergeometric function, generalized hypergeometric function.

doi:10.2298/AADM0802205T

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E. Minguzzi: AN EQUIVALENT FORM OF YOUNG’S INEQUALITY WITH UPPER BOUND

2000 Mathematical Subject Classification: 26D10, 44A15
Key words and phrases: Young’s inequality, Legendre transform.

doi:10.2298/AADM0802213M

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Vlad Copil, Laurent¸iu Panaitopol: SOME PROPERTIES OF THE SEQUENCE OF PRIME NUMBERS

2000 Mathematical Subject Classification: 11N05, 11A41
Key words and phrases: Prime numbers, sequences, series.

doi:10.2298/AADM0802217C

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Joel Ratsaby: ESTIMATE OF THE NUMBER OF RESTRICTED INTEGER-PARTITIONS

2000 Mathematical Subject Classification: 68R05, 05A17, 11P82
Key words and phrases: Analytic combinatorics.

doi:10.2298/AADM0802222R

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Helmut Prodinger: RECORDS IN GEOMETRICALLY DISTRIBUTED WORDS: SUM OF POSITIONS

2000 Mathematical Subject Classification: 60C05 (primary), 05A30 (secondary)
Key words and phrases: Words, geometric probabilities, records, Rice’s method.

doi:10.2298/AADM0802234P

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E. Bendito, A. Carmona, A. M. Encinas, J. M. Gesto: THE CURL OF A WEIGHTED NETWORK

2000 Mathematical Subject Classification: 39A12
Key words and phrases: Networks, Laplacian, curl, Hodge’s decomposition, Helmholtz’s decomposition.

doi:10.2298/AADM0802241B

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Lihua Feng, Guihai Yu, Zhengtao Jiang, Lingzhi Ren: SHARP UPPER BOUNDS FOR THE NUMBER OF SPANNING TREES OF A GRAPH

2000 Mathematical Subject Classification: 05C05
Key words and phrases: Graph, spanning trees, Laplacian eigenvalues.

doi:10.2298/AADM0802255F

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Yi-Zheng Fan, Shuang-Dong Li, Dong Liang: SPECTRAL PROPERTY OF CERTAIN CLASS OF GRAPHS ASSOCIATED WITH GENERALIZED BETHE TREES AND TRANSITIVE GRAPHS

2000 Mathematical Subject Classification: 05C50, 15A18
Key words and phrases: Bethe tree, transitive graph, Laplacian matrix, adjacency matrix, Perron vector, Fiedler vector.

doi:10.2298/AADM0802260F

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Pavel Hìc, Milan Pokorný, Pavol Černek: NEW SUFFICIENT CONDITIONS FOR INTEGRAL COMPLETE 3-PARTITE GRAPHS

2000 Mathematical Subject Classification: 05C50
Key words and phrases: Integral graph, divisor, characteristic polynomial, graph spectrum, Diophantine equation.

doi:10.2298/AADM0802276H

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Mehdi Eliasi, Bijan Taeri: SCHULTZ POLYNOMIALS OF COMPOSITE GRAPHS

2000 Mathematical Subject Classification: Primary 05C12; Secondary 05A15.
Key words and phrases: Schultz index, Schultz polynomial, Wiener index, distance.

doi:10.2298/AADM0802285E

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