DSpace Collection: Volume 22 Number 4
http://hdl.handle.net/10525/526
Serdica Mathematical Journal Volume 22, Number 4, 1996The Collection's search engineSearch the Channelsearch
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Nikola Obreshkoff - Bibliography
http://hdl.handle.net/10525/624
Title: Nikola Obreshkoff - Bibliography<br/><br/>Authors: Russev, P.<br/><br/>Abstract: This year marks the centennial of the birth of Academician Nikola Obreshkoff,a distinguished Bulgarian mathematician of world recognition.<br/><br/>Description: Biographical dataTriples of Positive Integers with the same Sum and the same Product
http://hdl.handle.net/10525/623
Title: Triples of Positive Integers with the same Sum and the same Product<br/><br/>Authors: Schinzel, A.<br/><br/>Abstract: It is proved that for every k there exist k triples of positive integers with the same sum and the same product.Backlund-Darboux Transformations in Sato's Grassmannian
http://hdl.handle.net/10525/622
Title: Backlund-Darboux Transformations in Sato's Grassmannian<br/><br/>Authors: Bakalov, B.; Horozov, E.; Yakimov, M.<br/><br/>Abstract: We define Bäcklund–Darboux transformations in Sato’s Grassmannian.They can be regarded as Darboux transformations on maximal algebrasof commuting ordinary differential operators. We describe the action of thesetransformations on related objects: wave functions, tau-functions and spectralalgebras.Weakly Increasing Zero-Diminishing Sequences
http://hdl.handle.net/10525/621
Title: Weakly Increasing Zero-Diminishing Sequences<br/><br/>Authors: Bakan, Andrew; Craven, Thomas; Csordas, George; Golub, Anatoly<br/><br/>Abstract: The following problem, suggested by Laguerre’s Theorem (1884),remains open: Characterize all real sequences {μk} k=0...∞ which have the zero-diminishing property; that is, if k=0...n, p(x) = ∑(ak x^k) is any P real polynomial, then k=0...n, p(x) = ∑(μk ak x^k) has no more real zeros than p(x).In this paper this problem is solved under the additional assumption of a weakgrowth condition on the sequence {μk} k=0...∞, namely lim n→∞ | μn |^(1/n) < ∞. More precisely, it is established that the real sequence {μk} k≥0 is a weakly increasing zerodiminishingsequence if and only if there exists σ ∈ {+1,−1} and an entire functionn≥1, Φ(z)= be^(az) ∏(1+ x/αn), a, b ∈ R^1, b =0, αn > 0 ∀n ≥ 1, ∑(1/αn) < ∞, such that µk = (σ^k)/Φ(k), ∀k ≥ 0.Calculation of Reliability Characteristics for Regenerative Models
http://hdl.handle.net/10525/620
Title: Calculation of Reliability Characteristics for Regenerative Models<br/><br/>Authors: Kalashnikov, Vladimir<br/><br/>Abstract: If a regenerative process is represented as semi-regenerative, we deriveformulae enabling us to calculate basic characteristics associated with the first occurrencetime starting from corresponding characteristics for the semi-regenerativeprocess. Recursive equations, integral equations, and Monte-Carlo algorithms areproposed for practical solving of the problem.Problems and Theorems in the Theory of Multiplier Sequences
http://hdl.handle.net/10525/619
Title: Problems and Theorems in the Theory of Multiplier Sequences<br/><br/>Authors: Craven, Thomas; Csordas, George<br/><br/>Abstract: The purpose of this paper is (1) to highlight some recent and heretoforeunpublished results in the theory of multiplier sequences and (2) to surveysome open problems in this area of research. For the sake of clarity of exposition,we have grouped the problems in three subsections, although several of the problemsare interrelated. For the reader’s convenience, we have included the pertinentdefinitions, cited references and related results, and in several instances, elucidatedthe problems by examples.Quadratic Mean Radius of a Polynomial in C(Z)
http://hdl.handle.net/10525/618
Title: Quadratic Mean Radius of a Polynomial in C(Z)<br/><br/>Authors: Ivanov, K.; Sharma, A.<br/><br/>Abstract: A Schoenberg conjecture connecting quadratic mean radii of a polynomial and its derivative is verified for some kinds of polynomials, including fourth degree ones.<br/><br/>Description: * Dedicated to the memory of Prof. N. ObreshkoffSums of a Random Number of Random Variables and their Approximations with ν- Accompanying Infinitely Divisible Laws
http://hdl.handle.net/10525/617
Title: Sums of a Random Number of Random Variables and their Approximations with ν- Accompanying Infinitely Divisible Laws<br/><br/>Authors: Klebanov, Lev; Rachev, Svetlozar<br/><br/>Abstract: In this paper a general theory of a random number of random variablesis constructed. A description of all random variables ν admitting an analogof the Gaussian distribution under ν-summation, that is, the summation of a randomnumber ν of random terms, is given. The v-infinitely divisible distributionsare described for these ν-summations and finite estimates of the approximation ofν-sum distributions with the help of v-accompanying infinitely divisible distributionsare given. The results include, in particular, the description of geometricallyinfinitely divisible and geometrically stable distributions as well as their domainsof attraction.<br/><br/>Description: * Research supported by NATO GRANT CRG 900 798 and by Humboldt Award for U.S. Scientists.