Browsing by Author "Ostrovska, Sofiya"
Now showing 1 - 20 of 103
- Results Per Page
- Sort Options
Article Citation - WoS: 5Citation - Scopus: 5Analytical Properties of the Lupas q-transform(Academic Press inc Elsevier Science, 2012) Ostrovska, Sofiya; MathematicsThe Lupas q-transform emerges in the study of the limit q-Lupas operator. The latter comes out naturally as a limit for a sequence of the Lupas q-analogues of the Bernstein operator. Given q is an element of (0, 1), f is an element of C left perpendicular0, 1right perpendicular, the q-Lupas transform off is defined by (Lambda(q)f) (z) := 1/(-z; q)(infinity) . Sigma(infinity)(k=0) f(1 - q(k))q(k(k -1)/2)/(q; q)(k)z(k). The transform is closely related to both the q-deformed Poisson probability distribution, which is used widely in the q-boson operator calculus, and to Valiron's method of summation for divergent series. In general, Lambda(q)f is a meromorphic function whose poles are contained in the set J(q) := {-q(-j)}(j=0)(infinity). In this paper, we study the connection between the behaviour of f on leftperpendicular0, 1right perpendicular and the decay of Lambda(q)f as z -> infinity. (C) 2012 Elsevier Inc. All rights reserved.Article Citation - WoS: 17Citation - Scopus: 16The Approximation by q-bernstein Polynomials in the Case q ↓ 1(Springer Basel Ag, 2006) Ostrovska, S; MathematicsLet B-n (f, q; x), n = 1, 2, ... , 0 < q < infinity, be the q-Bernstein polynomials of a function f, B-n (f, 1; x) being the classical Bernstein polynomials. It is proved that, in general, {B-n (f, q(n); x)} with q(n) down arrow 1 is not an approximating sequence for f is an element of C[0, 1], in contrast to the standard case q(n) up arrow 1. At the same time, there exists a sequence 0 < delta(n) down arrow 0 such that the condition 1 <= q(n) <= delta(n) implies the approximation of f by {B-n(f, qn; x)} for all f is an element of C[0, 1].Article Citation - WoS: 3Citation - Scopus: 2The Approximation of All Continuous Functions on [0,1] by q-bernstein Polynomials in the Case q → 1+(Springer Basel Ag, 2008) Ostrovska, Sofiya; MathematicsSince for q > 1, the q-Bernstein polynomials B-n,B-q(f;.) are not positive linear operators on C[0, 1], their convergence properties are not similar to those in the case 0 < q = 1. It has been known that, in general, B-n,B-qn(f;.) does not approximate f is an element of C[0, 1] if q(n) -> 1(+), n ->infinity, unlike in the case q(n) -> 1(-). In this paper, it is shown that if 0 <= q(n) - 1 = o(n(-1)3(-n)), n -> infinity, then for any f is an element of C[0, 1], we have: B-n,B-qn(f; x) -> f(x) as n -> infinity, uniformly on [ 0,1].Book Part Citation - WoS: 0Citation - Scopus: 0Approximation of Discontinuous Functions by q-bernstein Polynomials(Springer international Publishing Ag, 2016) Ostrovska, Sofia; Ozban, Ahmet Yasar; MathematicsThis chapter presents an overview of the results related to the q-Bernstein polynomials with q > 1 attached to discontinuous functions on [0, 1]. It is emphasized that the singularities of such functions located on the set Jq : = {0} boolean OR {q-l}(l=0, infinity), q > 1 are definitive for the investigation of the convergence properties of their q-Bernstein polynomials.Article Citation - WoS: 9Citation - Scopus: 9The Approximation of Logarithmic Function by q-bernstein Polynomials in the Case q > 1(Springer, 2007) Ostrovska, Sofiya; MathematicsSince in the case q > 1, q-Bernstein polynomials are not positive linear operators on C[ 0, 1], the study of their approximation properties is essentially more difficult than that for 0 < q < 1. Despite the intensive research conducted in the area lately, the problem of describing the class of functions in C[ 0, 1] uniformly approximated by their q-Bernstein polynomials ( q > 1) remains open. It is known that the approximation occurs for functions admitting an analytic continuation into a disc {z : | z| < R}, R > 1. For functions without such an assumption, no general results on approximation are available. In this paper, it is shown that the function f ( x) = ln( x + a), a > 0, is uniformly approximated by its q-Bernstein polynomials ( q > 1) on the interval [ 0, 1] if and only if a >= 1.Article Citation - WoS: 2The Approximation of Power Function by the q-bernstein Polynomials in the Case q > 1(Element, 2008) Ostrovska, Sofiya; MathematicsSince for q > 1. q-Bernstein polynomials are not positive linear operators on C[0, 1] the investigation of their convergence properties turns out to be much more difficult than that in the case 0 < q < 1. It is known that, in the case q > 1. the q-Bernstein polynomials approximate the entire functions and, in particular, polynomials uniformly on any compact set in C. In this paper. the possibility of the approximation for the function (z + a)(alpha), a >= 0. with a non-integer alpha > -1 is studied. It is proved that for a > 0, the function is uniformly approximated on any compact set in {z : vertical bar z vertical bar < a}, while on any Jordan arc in {z : vertical bar z vertical bar > a}. the uniform approximation is impossible, In the case a = 0(1) the results of the paper reveal the following interesting phenomenon: the power function z(alpha), alpha > 0: is approximated by its, q-Bernstein polynomials either on any (when alpha is an element of N) or no (when alpha is not an element of N) Jordan arc in C.Article Citation - Scopus: 2The Approximation of Power Function by the Q-Bernstein Polynomials in the Case Q > 1(Element D.O.O., 2008) Ostrovska,S.; MathematicsSince for q > 1, q-Bernstein polynomials are not positive linear operators on C[0, 1], the investigation of their convergence properties turns out to be much more difficult than that in the case 0 < q < 1. It is known that, in the case q > 1, the q-Bernstein polynomials approximate the entire functions and, in particular, polynomials uniformly on any compact set in ℂ. In this paper, the possibility of the approximation for the function (z + a)α, a ≥ 0, with a non-integer α > -1 is studied. It is proved that for a > 0, the function is uniformly approximated on any compact set in {z: \z| < a}, while on any Jordan arc in {z: \z\ > a}, the uniform approximation is impossible. In the case a = 0, the results of the paper reveal the following interesting phenomenon: the power function zα, α > 0, is approximated by its q-Bernstein polynomials either on any (when α ∈ ℕ) or no (when α ∉ ℕ) Jordan arc in ℂ.Editorial Citation - Scopus: 1Approximation Theory and Numerical Analysis(Hindawi Publishing Corporation, 2014) Ostrovska,S.; Berdysheva,E.; Nowak,G.; Özban,A.Y.; Mathematics[No abstract available]Article Citation - WoS: 3Citation - Scopus: 8Assessing Software Quality Using the Markov Decision Processes(Wiley-blackwell, 2014) Korkmaz, Omer; Akman, Ibrahim; Ostrovska, Sofiya; Mathematics; Computer EngineeringQuality of software is one of the most critical concerns in software system development, and many products fail to meet the quality objectives when constructed initially. Software quality is highly affected by the development process's actual dynamics. This article proposes the use of the Markov decision process (MDP) for the assessment of software quality because MDP is a useful technique to abstract the model of dynamics of the development process and to test its impact on quality. Additionally, the MDP modeling of the dynamics leads to early prediction of the quality, from the design phases all the way through the different stages of development. The proposed approach is based on the stochastic nature of the software development process, including project architecture, construction strategy of Software Quality Assurance system, its qualification actions, and team assignment strategy. It accepts these factors as inputs, generating a relative quality degree as an output. The proposed approach has been demonstrated for the design phase with a case study taken from the literature. The results prove its robustness and capability to identify appropriate policies in terms of quality, cost, and time. (c) 2011 Wiley Periodicals, Inc.Article Citation - WoS: 11Citation - Scopus: 12Assessing Team Work in Engineering Projects(Tempus Publications, 2015) Mishra, Deepti; Ostrovska, Sofiya; Hacaloglu, Tuna; Mathematics; Computer Engineering; Information Systems Engineering; Mathematics; Computer Engineering; Information Systems EngineeringTeam work is considered a valuable teaching technique in higher education. However, the assessment of an individual's work in teams has proved to be a challenging task. Consequently, self-and peer-evaluations are becoming increasingly popular for the assessment of individuals in a team work, though it is essential to determine whether students can judge their own as well as their peer's performance effectively. Self-and peer-evaluations have been applied in different disciplines and their authenticity with regard to teacher's assessment has been evaluated in the literature but this issue has not been investigated in the field of engineering education so far. In this study, a peer-and self-assessment procedure is applied to the evaluation of a project work conducted in teams of 3 or 4 students. The participants were engineering students taking two similar courses related with database design and development. It is found that a majority of the students were unable to assess themselves as objectively as their instructor. Further, it is observed that successful students tend to under-estimate, whereas unsuccessful students tend to over-estimate, their own performance. The paper also establishes that the results of self-assessments are independent from the gender factor.Article Citation - WoS: 0Citation - Scopus: 0Complementability of Isometric Copies of L1 in Transportation Cost Spaces(Academic Press inc Elsevier Science, 2024) Ostrovska, Sofiya; Ostrovskii, Mikhail I.; MathematicsThis work aims to establish new results pertaining to the structure of transportation cost spaces. Due to the fact that those spaces were studied and applied in various contexts, they have also become known under different names such as Arens-Eells spaces, Lipschitz-free spaces, and Wasserstein spaces. The main outcome of this paper states that if a metric space X is such that the transportation cost space on X contains an isometric copy of L1, then it contains a 1-complemented isometric copy of $1. (c) 2023 Elsevier Inc. All rights reserved.Article Citation - WoS: 2Citation - Scopus: 4Constructing Stieltjes Classes for M-Indeterminate Absolutely Continuous Probability Distributions(Impa, 2014) Ostrovska, Sofiya; Mathematics; MathematicsIf P is a moment-indeterminate probability distribution, then it is desirable to present explicitly other distributions possessing the same moments as P. In this paper, a method to construct an infinite family of probability densities - called the Stieltjes class - all with the same moments is presented. The method is applicable for densities with support (0, infinity) which satisfy the lower bound: f(x) >= A exp{-ax(alpha)} for some A > 0, a > 0 and some alpha is an element of(0, 1/2):Article Citation - WoS: 2Citation - Scopus: 1The Continuity in Q of the Lupaş Q-Analogues of the Bernstein Operators(Academic Press inc Elsevier Science, 2024) Yilmaz, Ovgue Gurel; Turan, Mehmet; Ostrovska, Sofiya; Turan, Mehmet; Ostrovska, Sofiya; Turan, Mehmet; Ostrovska, Sofiya; Mathematics; MathematicsThe Lupas q-analogue Rn,q of the Bernstein operator is the first known q-version of the Bernstein polynomials. It had been proposed by A. Lupas in 1987, but gained the popularity only 20 years later, when q-analogues of classical operators pertinent to the approximation theory became an area of intensive research. In this work, the continuity of operators Rn,q with respect to parameter q in the strong operator topology and in the uniform operator topology has been investigated. The cases when n is fixed and n -> infinity have been considered. (c) 2022 Elsevier Inc. All rights reserved.Article Citation - WoS: 1Citation - Scopus: 1The Convergence of q-bernstein Polynomials (0 < q < 1) and Limit q-bernstein Operators in Complex Domains(Rocky Mt Math Consortium, 2009) Ostrovska, Sofiya; Wang, Heping; MathematicsDue to the fact that the convergence properties of q-Bernstein polynomials are not similar to those in the classical case q = 1, their study has become an area of intensive research with a wide scope of open problems and unexpected results. The present paper is focused on the convergence of q-Bernstein polynomials, 0 < q < 1, and related linear operators in complex domains. An analogue of the classical result on the simultaneous approximation is presented. The approximation of analytic functions With the help of the limit q-Bernstein operator is studied.Article Citation - WoS: 9Citation - Scopus: 11The Convergence of q-bernstein Polynomials (0 < q < 1) in the Complex Plane(Wiley-v C H verlag Gmbh, 2009) Ostrovska, Sofiya; MathematicsThe paper focuses at the estimates for the rate of convergence of the q-Bernstein polynomials (0 < q < 1) in the complex plane. In particular, a generalization of previously known results on the possibility of analytic continuation of the limit function and an elaboration of the theorem by Wang and Meng is presented. (C) 2009 WILEY-VCH Verlag GmbH & Co. KGaA, WeinheimArticle Citation - WoS: 125Citation - Scopus: 134Convergence of Generalized Bernstein Polynomials(Academic Press inc Elsevier Science, 2002) Il'inskii, A; Ostrovska, S; MathematicsLet f is an element of C[0, 1], q is an element of (0, 1), and B-n(f, q; x) be generalized Bernstein polynomials based on the q-integers. These polynomials were introduced by G. M. Phillips in 1997. We study convergence properties of the sequence {B-n(f, q; x)}(n=1)(infinity). It is shown that in general these properties are essentially different from those in the classical case q = 1. (C) 2002 Elsevier Science (USA).Article Citation - WoS: 1Citation - Scopus: 1The Distance Between Two Limit q-bernstein Operators(Rocky Mt Math Consortium, 2020) Ostrovska, Sofiya; Turan, Mehmet; MathematicsFor q is an element of (0, 1), let B-q denote the limit q-Bernstein operator. The distance between B-q and B-r for distinct q and r in the operator norm on C[0, 1] is estimated, and it is proved that 1 <= parallel to B-q - B-r parallel to <= 2, where both of the equalities can be attained. Furthermore, the distance depends on whether or not r and q are rational powers of each other. For example, if r(j) not equal q(m) for all j, m is an element of N, then parallel to B-q - B-r parallel to = 2, and if r = q(m) for some m is an element of N, then parallel to B-q - B-r parallel to = 2(m - 1)/m.Article Citation - WoS: 5Citation - Scopus: 4Distortion in the Finite Determination Result for Embeddings of Locally Finite Metric Spaces Into Banach Spaces(Cambridge Univ Press, 2019) Ostrovska, S.; Ostrovskii, M. I.; MathematicsGiven a Banach space X and a real number alpha >= 1, we write: (1) D(X) <= alpha if, for any locally finite metric space A, all finite subsets of which admit bilipschitz embeddings into X with distortions <= C, the space A itself admits a bilipschitz embedding into X with distortion <= alpha . C; (2) D(X) = alpha(+) if, for every epsilon > 0, the condition D(X) <= alpha + epsilon holds, while D(X) <= alpha does not; (3) D(X) <= alpha(+) if D(X) = alpha(+) or D(X) <= alpha. It is known that D(X) is bounded by a universal constant, but the available estimates for this constant are rather large. The following results have been proved in this work: (1) D((circle plus(infinity)(n= 1) X-n)(p)) <= 1(+) for every nested family of finite-dimensional Banach spaces {X-n}(n=1)(infinity) and every 1 <= p <= 8 infinity. (2) D((circle plus 8(n=1)(infinity)l(infinity)(n) )(p)) = 1(+) for 1 < p < infinity. (3) D(X) <= 4(+) for every Banach space X with no nontrivial cotype. Statement (3) is a strengthening of the Baudier-Lancien result (2008).Article Citation - WoS: 1Distortion in the Metric Characterization of Superreflexivity in Terms of the Infinite Binary Tree(Element, 2022) Ostrovska, Sofiya; MathematicsThe article presents a quantitative refinement of the result of Baudier (Archiv Math., 89 (2007), no. 5, 419-429): the infinite binary tree admits a bilipschitz embedding into an arbitrary non-superreflexive Banach space. According to the results of this paper, we can additionally require that, for an arbitrary epsilon > 0 and an arbitrary non-superreflexive Banach space X, there is an embedding of the infinite binary tree into X whose distortion does not exceed 4 + epsilon .Article Citation - WoS: 2Citation - Scopus: 2Distortion of Embeddings of Binary Trees Into Diamond Graphs(Amer Mathematical Soc, 2018) Leung, Siu Lam; Nelson, Sarah; Ostrovska, Sofiya; Ostrovskii, Mikhail; MathematicsDiamond graphs and binary trees are important examples in the theory of metric embeddings and also in the theory of metric characterizations of Banach spaces. Some results for these families of graphs are parallel to each other; for example superreflexivity of Banach spaces can be characterized both in terms of binary trees (Bourgain, 1986) and diamond graphs (Johnson-Schechtman, 2009). In this connection, it is natural to ask whether one of these families admits uniformly bilipschitz embeddings into the other. This question was answered in the negative by Ostrovskii (2014), who left it open to determine the order of growth of the distortions. The main purpose of this paper is to get a sharp up-to-a-logarithmic-factor estimate for the distortions of embeddings of binary trees into diamond graphs and, more generally, into diamond graphs of any finite branching k >= 2. Estimates for distortions of embeddings of diamonds into infinitely branching diamonds are also obtained.
