DSpace Community: 1996
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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.Nontrivial Solutions of Quasilinear Equations In BV
http://hdl.handle.net/10525/616
Title: Nontrivial Solutions of Quasilinear Equations In BV<br/><br/>Authors: Marzocchi, Marco<br/><br/>Abstract: The existence of a nontrivial critical point is proved for a functionalcontaining an area-type term. Techniques of nonsmooth critical point theory are applied.Perturbations of Critical Values in Nonsmooth Critical Point Theory
http://hdl.handle.net/10525/615
Title: Perturbations of Critical Values in Nonsmooth Critical Point Theory<br/><br/>Authors: Degiovanni, M.; Lancelotti, S.<br/><br/>Abstract: The perturbation of critical values for continuous functionals is studied.An application to eigenvalue problems for variational inequalities is provided.<br/><br/>Description: * Supported by Ministero dell’Università e della Ricerca Scientifica e Tecnologica (40% – 1993).** Supported by Ministero dell’Università e della Ricerca Scientifica e Tecnologica (40% – 1993).On a Variational Approach to some Quasilinear Problems
http://hdl.handle.net/10525/614
Title: On a Variational Approach to some Quasilinear Problems<br/><br/>Authors: Canino, Annamaria<br/><br/>Abstract: We prove some multiplicity results concerning quasilinear ellipticequations with natural growth conditions. Techniques of nonsmooth critical pointtheory are employed.Uniform Convergence of the Newton Method for Aubin Continuous Maps
http://hdl.handle.net/10525/613
Title: Uniform Convergence of the Newton Method for Aubin Continuous Maps<br/><br/>Authors: Dontchev, Asen<br/><br/>Abstract: In this paper we prove that the Newton method applied to thegeneralized equation y ∈ f(x) + F(x) with a C^1 function f and a set-valued mapF acting in Banach spaces, is locally convergent uniformly in the parameter y ifand only if the map (f +F)^(−1) is Aubin continuous at the reference point. We alsoshow that the Aubin continuity actually implies uniform Q-quadratic convergenceprovided that the derivative of f is Lipschitz continuous. As an application, we givea characterization of the uniform local Q-quadratic convergence of the sequentialquadratic programming method applied to a perturbed nonlinear program.<br/><br/>Description: * This work was supported by National Science Foundation grant DMS 9404431.Subdifferentials of Performance Functions and Calculus of Coderivatives of Set-Valued Mappings
http://hdl.handle.net/10525/612
Title: Subdifferentials of Performance Functions and Calculus of Coderivatives of Set-Valued Mappings<br/><br/>Authors: Ioffe, Alexander; Penot, Jean-Paul<br/><br/>Abstract: The paper contains calculus rules for coderivatives of compositions,sums and intersections of set-valued mappings. The types of coderivatives considered correspond to Dini-Hadamard and limiting Dini-Hadamard subdifferentialsin Gˆateaux differentiable spaces, Fréchet and limiting Fréchet subdifferentials inAsplund spaces and approximate subdifferentials in arbitrary Banach spaces. Thekey element of the unified approach to obtaining various calculus rules for varioustypes of derivatives presented in the paper are simple formulas for subdifferentialsof marginal, or performance functions.Speculating About Mountains
http://hdl.handle.net/10525/611
Title: Speculating About Mountains<br/><br/>Authors: Ribarska, N.; Tsachev, Ts.; Krastanov, M.<br/><br/>Abstract: The definition of the weak slope of continuous functions introduced byDegiovanni and Marzocchi (cf. [8]) and its interrelation with the notion “steepness”of locally Lipschitz functions are discussed. A deformation lemma and a mountainpass theorem for usco mappings are proved. The relation between these resultsand the respective ones for lower semicontinuous functions (cf. [7]) is considered.<br/><br/>Description: ∗Partially supported by Grant MM 409/94 of the Mininstry of Education, Science and Technology,Bulgaria.∗∗Partially supported by Grants MM 521/95, MM 442/94 of the Mininstry of Education, Scienceand Technology, Bulgaria.Stability of the Iteration Method for non Expansive Mappings
http://hdl.handle.net/10525/610
Title: Stability of the Iteration Method for non Expansive Mappings<br/><br/>Authors: Lemaire, B.<br/><br/>Abstract: The general iteration method for nonexpansive mappings on a Banachspace is considered. Under some assumption of fast enough convergence on thesequence of (“almost” nonexpansive) perturbed iteration mappings, if the basicmethod is τ−convergent for a suitable topology τ weaker than the norm topology,then the perturbed method is also τ−convergent. Application is presented to thegradient-prox method for monotone inclusions in Hilbert spaces.Stability of Supporting and Exposing Elements of Convex Sets in Banach Spaces
http://hdl.handle.net/10525/609
Title: Stability of Supporting and Exposing Elements of Convex Sets in Banach Spaces<br/><br/>Authors: Azé, D.; Lucchetti, R.<br/><br/>Abstract: To a convex set in a Banach space we associate a convex function(the separating function), whose subdifferential provides useful information on thenature of the supporting and exposed points of the convex set. These points areshown to be also connected to the solutions of a minimization problem involving theseparating function. We investigate some relevant properties of this function and ofits conjugate in the sense of Legendre-Fenchel. Then we highlight the connectionsbetween set convergence, with respect to the slice and Attouch-Wets topologies,and convergence, in the same sense, of the associated functions. Finally, by usingknown results on the behaviour of the subdifferential of a convex function underthe former epigraphical perturbations, we are able to derive stability results forthe set of supported points and of supporting and exposing functionals of a closedconvex subset of a Banach space.<br/><br/>Description: * This work was supported by the CNR while the author was visiting the University of Milan.