DSpace Collection: Volume 33, Number 1
http://hdl.handle.net/10525/2549
Serdica Mathematical Journal Volume 33, Number 1, 2007The Collection's search engineSearch the Channelsearch
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On some Extremal Problems of Landau
http://hdl.handle.net/10525/2556
Title: On some Extremal Problems of Landau<br/><br/>Authors: Révész, Szilárd<br/><br/>Abstract: The prime number theorem with error term presents itself as &pi'(x) = ∫2x [dt/ logt] + O ( x e- K logL x). In 1909, Edmund Landau provided a systematic analysis of the proof seeking better values of L and K. At a key point of his 1899 proof de la Vallée Poussin made use of the nonnegative trigonometric polynomial 2/3 (1+cos x)2 = 1+4/3 cosx +1/3 cos2x. Landau considered more general positive definite nonnegative cosine polynomials 1+a1cos x+… + ancos nx ≥ 0, with a1> 1,ak ≥ 0 (k = 1,…,n), and deduced the above error term with L = 1/2 and any K< 1/(2V(a))½, where V(a): = (a1+a2+…+ an)/(( (a1)½-1)2). Thus the extremal problem of finding V: = minV(a) over all admissible coefficients, i.e. polynomials, arises.The question was further studied by Landau and later on by many other eminent mathematicians. The present work surveys these works as well as current questions and ramifications of the theme, starting with a long unnoticed, but rather valuable Bulgarian publication of Lubomir Chakalov.<br/><br/>Description: 2000 Mathematics Subject Classification: Primary: 42A05. Secondary: 42A82, 11N05.A New Characterization of Weighted Peetre K-Functionals (II)
http://hdl.handle.net/10525/2555
Title: A New Characterization of Weighted Peetre K-Functionals (II)<br/><br/>Authors: Draganov, Borislav; Ivanov, Kamen<br/><br/>Abstract: Certain types of weighted Peetre K-functionals are characterized by means of the classical moduli of smoothness taken on a proper lineartransforms of the function. The weights with power-type asymptotic at theends of the interval with arbitrary real exponents are considered. This paperextends the method and results presented in [3].<br/><br/>Description: 2000 Mathematics Subject Classification: 46B70, 41A25, 41A17, 26D10.∗Part of the results were reported at the Conference “Pioneers of Bulgarian Mathematics”,Sofia, 2006.The Asymptotic Behaviour of the First Eigenvalue of Linear Second-Order Elliptic Equations in Divergente Form
http://hdl.handle.net/10525/2554
Title: The Asymptotic Behaviour of the First Eigenvalue of Linear Second-Order Elliptic Equations in Divergente Form<br/><br/>Authors: Fabricant, Alexander; Kutev, Nikolai; Rangelov, Tsviatko<br/><br/>Abstract: The asymptotic of the first eigenvalue for linear second orderelliptic equations in divergence form with large drift is studied. A necessaryand a sufficient condition for the maximum possible rate of the first eigenvalueis proved.<br/><br/>Description: 2000 Mathematics Subject Classification: 35J70, 35P15.Oligopoly Model of a Debit Card Network
http://hdl.handle.net/10525/2553
Title: Oligopoly Model of a Debit Card Network<br/><br/>Authors: Manchev, Peter<br/><br/>Abstract: The paper builds an oligopoly model of a debit card network.It examines the competition between debit card issuers. We show thatthere is an optimal pricing for the debit card network, which maximizesall issuer’s revenues. The paper also shows that establishing a link betweendebit card networks averages the costs provided that there is no growth inthe customer’s usage of the networks, resulting from the link.<br/><br/>Description: JEL Classification: G21, L13.Groups of Order 32 as Galois Groups
http://hdl.handle.net/10525/2552
Title: Groups of Order 32 as Galois Groups<br/><br/>Authors: Michailov, Ivo<br/><br/>Abstract: We find the obstructions to realizability of groups of order 32 asGalois groups over arbitrary field of characteristic not 2. We discuss explicitextensions and automatic realizations as well.<br/><br/>Description: 2000 Mathematics Subject Classification: 12F12.