Serdica Mathematical Journal

Volume 41, Number 4, 2015





C O N T E N T S

Preface (pp. i-ii)
Lukarevski, M. Evolution equations for the Stefan problem (pp. 333−342)
Iliev, A., C. Madonna. EPW sextics and Hilbert squares of K3 surfaces (pp. 343−354)
Küçük, N., O. Duman. Summability methods in weighted approximation to derivatives of functions (pp. 335−368)
Matsuoka, T. Koszul duality for locally constant factorization algebras (pp. 369−414)
Bazhlekova, E. Convolutional calculus of Dimovski and QR-regularization of the backward heat problem (pp. 415−430)
Sekiguchi, Y. Notes on optimality conditions using Newton diagrams and sums of squares (pp. 431−456)
Özmen, N., E. Erkuş-Duman. On the Poisson-Charlier polynomials (pp. 457−470)
Markov, L. Mean value theorems for analytic functions (pp. 471−480)
Kutev, N., N. Kolkovska, M. Dimova. Finite time blow up of the solutions to nonlinear Klein-Gordon equation with arbitrary high positive initial energy (pp. 481−492)
Fabricant, A., N. Kutev, Ts. Rangelov. Hardy-type inequalities with weights (pp. 493−512)
Boyadzhiev, G. Bi-characteristic curves of body and surface waves and application in geophysics (pp. 513−526)

A B S T R A C T S


EVOLUTION EQUATIONS FOR THE STEFAN PROBLEM
Martin Lukarevski martin.lukarevski@ugd.edu.mk

2010 Mathematics Subject Classification: 35R35, 35B65, 35J70.
Key words: Stefan problem, evoulution equation, free boundary problem.


EPW SEXTICS AND HILBERT SQUARES OF K3 SURFACES
Atanas Iliev ailiev@snu.ac.kr,
Carlo Madonna carlo.madonna@uam.es

2010 Mathematics Subject Classification: 14J35, 14F05.
Key words: K3 surface, EPW sextic, Eisenbud-Popescu-Walter sextic.


SUMMABILITY METHODS IN WEIGHTED APPROXIMATION TO DERIVATIVES OF FUNCTIONS
Nisa Küçük nkucuk@etu.edu.tr,
Oktay Duman oduman@etu.edu.tr

2010 Mathematics Subject Classification: 41A30, 42B08, 47B38.
Key words: Summability process, weighted approximation, almost convergence, Cesàro method.


KOSZUL DUALITY FOR LOCALLY CONSTANT FACTORIZATION ALGEBRAS
Takuo Matsuoka motogeomtop@gmail.com

2010 Mathematics Subject Classification: 55M05, 16E40, 57R56, 16D90.
Key words: Koszul duality, factorization algebra, topological chiral homology, topological quantum field theory, higher Morita category.


CONVOLUTIONAL CALCULUS OF DIMOVSKI AND QR-REGULARIZATION OF THE BACKWARD HEAT PROBLEM
Emilia Bazhlekova e.bazhlekova@math.bas.bg

2010 Mathematics Subject Classification: 35C10, 35R30, 44A35, 44A40.
Key words: convolutional calculus, non-classical convolution, Duhamel principle, ill-posed problem, quasi-reversibility.


NOTES ON OPTIMALITY CONDITIONS USING NEWTON DIAGRAMS AND SUMS OF SQUARES
Yoshiyuki Sekiguchi yoshi-s@kaiyodai.ac.jp

2010 Mathematics Subject Classification: 90C46, 13J30, 14M25.
Key words: Polynomial optimization, Newton diagram, optimality conditions, sums of squares.


ON THE POISSON-CHARLIER POLYNOMIALS
Nejla Özmen nejlaozmen06@gmail.com,
Esra Erkuş-Duman eduman@gazi.edu.tr

2010 Mathematics Subject Classification: 33C45.
Key words: Poisson-Charlier polynomials, recurrence relation, generating function, hypergeometric function, Lauricella functions.


MEAN VALUE THEOREMS FOR ANALYTIC FUNCTIONS
Lubomir Markov lmarkov@barry.edu

2010 Mathematics Subject Classification: 30C15.
Key words: Complex Rolle's Theorem, Mean Value Theorem, Evard-Jafari Theorem, Flett's Mean Value Theorem, Davitt-Powers-Riedel-Sahoo Theorem.


FINITE TIME BLOW UP OF THE SOLUTIONS TO NONLINEAR KLEIN-GORDON EQUATION WITH ARBITRARY HIGH POSITIVE INITIAL ENERGY
N. Kutev,
N. Kolkovska natali@math.bas.bg,
M. Dimova mkoleva@math.bas.bg

2010 Mathematics Subject Classification: 35L05, 35L15.
Key words: Klein-Gordon equation, Blow up, Arbitrary high positive initial energy.


HARDY-TYPE INEQUALITIES WITH WEIGHTS
Alexander Fabricant,
Nikolai Kutev,
Tsviatko Rangelov rangelov@math.bas.bg

2010 Mathematics Subject Classification: 26D10.
Key words: Hardy inequality, weights, sharp estimates.


BI-CHARACTERISTIC CURVES OF BODY AND SURFACE WAVES AND APPLICATION IN GEOPHYSICS
Georgi Boyadzhiev gpb@math.bas.bg

2010 Mathematics Subject Classification: 35L53, 35Q86, 86A15.
Key words: Strongly coupled linear hyperbolic systems, modelling of multi-layered solid body, applications in Geophysics.


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