Browsing by Author "Ostrovska, Sofiya"

Now showing 1 - 20 of 85

Citation - WoS: 5
Citation - Scopus: 5
Analytical Properties of the Lupas q-transform
(Academic Press inc Elsevier Science, 2012) Ostrovska, Sofiya; Mathematics
The 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.
Citation - WoS: 3
Citation - Scopus: 2
The Approximation of All Continuous Functions on [0,1] by q-bernstein Polynomials in the Case q → 1⁺
(Springer Basel Ag, 2008) Ostrovska, Sofiya; Mathematics
Since 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].
Citation - WoS: 9
Citation - Scopus: 9
The Approximation of Logarithmic Function by q-bernstein Polynomials in the Case q > 1
(Springer, 2007) Ostrovska, Sofiya; Mathematics
Since 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.
Citation - WoS: 2
The Approximation of Power Function by the q-bernstein Polynomials in the Case q > 1
(Element, 2008) Ostrovska, Sofiya; Mathematics
Since 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.
Citation - WoS: 3
Citation - Scopus: 8
Assessing Software Quality Using the Markov Decision Processes
(Wiley-blackwell, 2014) Korkmaz, Omer; Akman, Ibrahim; Ostrovska, Sofiya; Mathematics; Computer Engineering
Quality 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.
Citation - WoS: 11
Citation - Scopus: 12
Assessing 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 Engineering
Team 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.
Complementability of Isometric Copies of L1 in Transportation Cost Spaces
(Academic Press inc Elsevier Science, 2024) Ostrovska, Sofiya; Ostrovskii, Mikhail I.; Mathematics
This 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.
Citation - WoS: 2
Citation - Scopus: 4
Constructing Stieltjes Classes for M-Indeterminate Absolutely Continuous Probability Distributions
(Impa, 2014) Ostrovska, Sofiya; Mathematics; Mathematics
If 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):
Citation - WoS: 2
Citation - Scopus: 1
The 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; Mathematics
The 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.
Citation - WoS: 1
Citation - Scopus: 1
The 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; Mathematics
Due 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.
Citation - WoS: 9
Citation - Scopus: 11
The Convergence of q-bernstein Polynomials (0 < q < 1) in the Complex Plane
(Wiley-v C H verlag Gmbh, 2009) Ostrovska, Sofiya; Mathematics
The 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, Weinheim
Citation - WoS: 1
Citation - Scopus: 1
The Distance Between Two Limit q-bernstein Operators
(Rocky Mt Math Consortium, 2020) Ostrovska, Sofiya; Turan, Mehmet; Mathematics
For 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.
Citation - WoS: 1
Distortion in the Metric Characterization of Superreflexivity in Terms of the Infinite Binary Tree
(Element, 2022) Ostrovska, Sofiya; Mathematics
The 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 .
Citation - WoS: 2
Citation - Scopus: 2
Distortion of Embeddings of Binary Trees Into Diamond Graphs
(Amer Mathematical Soc, 2018) Leung, Siu Lam; Nelson, Sarah; Ostrovska, Sofiya; Ostrovskii, Mikhail; Mathematics
Diamond 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.
An Elaboration of the Cai-Xu Result on (p, q)-integers
(Springer Heidelberg, 2020) Ostrovska, Sofiya; Mathematics
The investigation of the (p, q)-Bernstein operators put forth the problem of finding the conditions when a sequence of (p, q)-integers tends to infinity. This is crucial for justifying the convergence results pertaining to the (p, q)-operators. Recently, Cai and Xu found a necessary and sufficient condition on sequences {p(n)} and {q(n)}, where 0 < q(n) < p(n) <= 1, to guarantee that a sequence of (p(n), q(n))-integers tends to infinity. This article presents an elaborated version of their result.
Citation - WoS: 11
Citation - Scopus: 12
Exploring and Expanding Students' Success in Software Testing
(Emerald Group Publishing Ltd, 2017) Mishra, Deepti; Ostrovska, Sofiya; Hacaloglu, Tuna; Mathematics; Information Systems Engineering; Computer Engineering
Purpose - Testing is one of the indispensable activities in software development and is being adopted as an independent course by software engineering (SE) departments at universities worldwide. The purpose of this paper is to carry out an investigation of the performance of learners about testing, given the tendencies in the industry and motivation caused by the unavailability of similar studies in software testing field. Design/methodology/approach - This study is based on the data collected over three years (between 2012 and 2014) from students taking the software testing course. The course is included in the second year of undergraduate curriculum for the bachelor of engineering (SE). Findings - It has been observed that, from the performance perspective, automated testing outperforms structural and functional testing techniques, and that a strong correlation exists among these three approaches. Moreover, a strong programming background does help toward further success in structural and automated testing, but has no effect on functional testing. The results of different teaching styles within the course are also presented together with an analysis exploring the relationship between students' gender and success in the software testing course, revealing that there is no difference in terms of performance between male and female students in the course. Moreover, it is advisable to introduce teaching concepts one at a time because students find it difficult to grasp the ideas otherwise. Research limitations/implications - These findings are based on the analysis conducted using three years of data collected while teaching a course in testing. Obviously, there are some limitations to this study. For example, student's strength in programming is calculated using the score of C programming courses taken in previous year/semester. Such scores may not reflect their current level of programming knowledge. Furthermore, attempt was made to ensure that the exercises given for different testing techniques have similar difficulty level to guarantee that the difference in success between these testing techniques is due to the inherent complexity of the technique itself and not because of different exercises. Still, there is small probability that a certain degree of change in success may be due to the difference in the difficulty levels of the exercises. As such, it is obviously premature to consider the present results as final since there is a lack of similar type of studies, with which the authors can compare the results. Therefore, more work needs to be done in different settings to draw sound conclusions in this respect. Originality/value - Although there are few studies (see e.g. Chan et al., 2005; Garousi and Zhi, 2013; Ng et al., 2004) exploring the preference of testers over distinct software testing techniques in the industry, there appears to be no paper comparing the preferences and performances of learners in terms of different testing techniques.
Fedja’s Proof of Deepti’s Inequality
(Tubitak Scientific & Technological Research Council Turkey, 2018) Ostrovska, Sofiya; Turan, Mehmet; Mathematics
The paper aims to present, in a systematic way, an elegant proof of Deepti’s inequality. Both the inequalityand various ideas concerning the issue were discussed on the Mathoverflow website by a number of users, but none haveappeared in the literature thus far. In this work, suggestions pertaining to users ‘Deepti’ and ‘fedja’ are traced, whencethe title. The results or the paper are new, and the proof is divided into a series of statements, many of which are ofinterest in themselves.
Citation - WoS: 1
Citation - Scopus: 2
The Functional-Analytic Properties of the Limit q-bernstein Operator
(Hindawi Ltd, 2012) Ostrovska, Sofiya; Mathematics
The limit q-Bernstein operator B-q, 0 < q < 1, emerges naturally as a modification of the Szasz-Mirakyan operator related to the Euler distribution. The latter is used in the q-boson theory to describe the energy distribution in a q-analogue of the coherent state. Lately, the limit q-Bernstein operator has been widely under scrutiny, and it has been shown that B-q is a positive shape-preserving linear operator on C[0, 1] with parallel to B-q parallel to = 1. Its approximation properties, probabilistic interpretation, eigenstructure, and impact on the smoothness of a function have been examined. In this paper, the functional-analytic properties of B-q are studied. Our main result states that there exists an infinite-dimensional subspace M of C[0, 1] such that the restriction B-q vertical bar(M) is an isomorphic embedding. Also we show that each such subspace M contains an isomorphic copy of the Banach space c(0).
Citation - WoS: 1
Citation - Scopus: 2
Functions Whose Smoothness Is Not Improved Under the Limit q-bernstein Operator
(Springer, 2012) Ostrovska, Sofiya; Mathematics
The limit q-Bernstein operator B-q emerges naturally as a modification of the Szasz-Mirakyan operator related to the Euler probability distribution. At the same time, this operator serves as the limit for a sequence of the q-Bernstein polynomials with 0 < q < 1. Over the past years, the limit q-Bernstein operator has been studied widely from different perspectives. Its approximation, spectral, and functional-analytic properties, probabilistic interpretation, the behavior of iterates, and the impact on the analytic characteristics of functions have been examined. It has been proved that under a certain regularity condition, B-q improves the smoothness of a function which does not satisfy the Holder condition. The purpose of this paper is to exhibit 'exceptional' functions whose smoothness is not improved under the limit q-Bernstein operator. MSC: 26A15; 26A16; 41A36
Citation - WoS: 12
Citation - Scopus: 11
Generalized Transportation Cost Spaces
(Springer Basel Ag, 2019) Ostrovska, Sofiya; Ostrovskii, Mikhail I.; Mathematics
The paper is devoted to the geometry of transportation cost spaces and their generalizations introduced by Melleray et al. (Fundam Math 199(2):177-194, 2008). Transportation cost spaces are also known as Arens-Eells, Lipschitz-free, or Wasserstein 1 spaces. In this work, the existence of metric spaces with the following properties is proved: (1) uniformly discrete metric spaces such that transportation cost spaces on them do not contain isometric copies of l(1), this result answers a question raised by Cuth and Johanis (Proc Am Math Soc 145(8):3409-3421, 2017); (2) locally finite metric spaces which admit isometric embeddings only into Banach spaces containing isometric copies of l(1); (3) metric spaces for which the double-point norm is not a norm. In addition, it is proved that the double-point norm spaces corresponding to trees are close to l(infinity)(d) of the corresponding dimension, and that for all finite metric spaces M, except a very special class, the infimum of all seminorms for which the embedding of M into the corresponding seminormed space is isometric, is not a seminorm.