Browsing by Author "Ostrovska, Sofiya"

Now showing 1 - 20 of 66

Citation Count: 0
Approximation of Discontinuous Functions by q-Bernstein Polynomials
(Springer international Publishing Ag, 2016) Ostrovska, Sofia; Ozban, Ahmet Yasar; Mathematics
This 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.
Citation Count: 1
Approximation theory and numerical analysis
(Hindawi Publishing Corporation, 2014) Ostrovska,S.; Berdysheva,E.; Nowak,G.; Özban,A.Y.; Mathematics
[No abstract available]
Citation Count: 3
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 Count: 11
Assessing Team Work in Engineering Projects
(Tempus Publications, 2015) Mishra, Deepti; Ostrovska, Sofiya; Hacaloglu, Tuna; 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.
Citation Count: 12
Assessing team work in engineering projects
(Tempus Publications, 2015) Mishra,D.; Ostrovska,S.; Hacaloglu,T.; 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 ownas 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. © 2015 TEMPUS Publications.
Citation Count: 0
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 Count: 0
The continuity in q of the Lupaş q-analogues of the Bernstein operators
(Academic Press inc Elsevier Science, 2024) Yilmaz, Ovgue Gurel; Ostrovska, Sofiya; Turan, Mehmet; 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 Count: 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 Count: 127
Convergence of generalized Bernstein polynomials
(Academic Press inc Elsevier Science, 2002) Il'inskii, A; Ostrovska, S; Mathematics
Let 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).
Citation Count: 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 Count: 4
DISTORTION IN THE FINITE DETERMINATION RESULT FOR EMBEDDINGS OF LOCALLY FINITE METRIC SPACES INTO BANACH SPACES
(Cambridge Univ Press, 2019) Ostrovska, S.; Ostrovskii, M. I.; Mathematics
Given 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).
Citation Count: 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.
Citation Count: 9
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.
Citation Count: 0
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 Count: 9
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.
Citation Count: 2
HOW DO SINGULARITIES OF FUNCTIONS AFFECT THE CONVERGENCE OF q-BERNSTEIN POLYNOMIALS?
(Element, 2015) Ostrovska, Sofiya; Ozban, Ahmet Yasar; Turan, Mehmet; Mathematics
In this article, the approximation of functions with a singularity at alpha is an element of (0, 1) by the q-Bernstein polynomials for q > 1 has been studied. Unlike the situation when alpha is an element of (0, 1) \ {q(-j)} j is an element of N, in the case when alpha = q(-m), m is an element of N, the type of singularity has a decisive effect on the set where a function can be approximated. In the latter event, depending on the types of singularities, three classes of functions have been examined, and it has been found that the possibility of approximation varies considerably for these classes.
Citation Count: 3
The q-Bernstein polynomials of the Cauchy kernel with a pole on [0,1] in the case q > 1
(Elsevier Science inc, 2013) Ostrovska, Sofiya; Ozban, Ahmet Yasar; Mathematics
The problem to describe the Bernstein polynomials of unbounded functions goes back to Lorentz. The aim of this paper is to investigate the convergence properties of the q-Bernstein polynomials B-n,B-q(f; x) of the Cauchy kernel 1/x-alpha with a pole alpha is an element of [0, 1] for q > 1. The previously obtained results allow one to describe these properties when a pole is different from q(-m) for some m is an element of {0, 1, 2, ...}. In this context, the focus of the paper is on the behavior of polynomials B-n,B-q(f; x) for the functions of the form f(m)(x) = 1/(x - q(-m)), x not equal q(-m) and f(m)(q(-m)) = a, a is an element of R. Here, the problem is examined both theoretically and numerically in detail. (C) 2013 Elsevier Inc. All rights reserved.
Citation Count: 3
q-Stieltjes classes for some families of q-densities
(Elsevier Science Bv, 2019) Ostrovska, Sofiya; Turan, Mehmet; Mathematics
The Stieltjes classes play a significant role in the moment problem allowing to exhibit explicitly infinite families of probability densities with the same sequence of moments. In this paper, the notion of q-moment determinacy/indeterminacy is proposed and some conditions for a distribution to be either q-moment determinate or indeterminate in terms of its q-density have been obtained. Also, a q-analogue of Stieltjes classes is defined for q-distributions and q-Stieltjes classes have been constructed for a family of q-densities of q-moment indeterminate distributions. (C) 2018 Elsevier B.V. All rights reserved.
Citation Count: 49
Impact of physical ambiance on communication, collaboration and coordination in agile software development: An empirical evaluation
(Elsevier, 2012) Mishra, Deepti; Mishra, Alok; Ostrovska, Sofiya; Mathematics; Software Engineering; Computer Engineering
Context: Communication, collaboration and coordination are key enablers of software development and even more so in agile methods. The physical environment of the workspace plays a significant role in effective communication, collaboration, and coordination among people while developing software. Objective: In this paper, we have studied and further evaluated empirically the effect of different constituents of physical environment on communication, coordination, and collaboration, respectively. The study aims to provide a guideline for prospective agile software developers. Method: A survey was conducted among software developers at a software development organization. To collect data, a survey was carried out along with observations, and interviews. Results: It has been found that half cubicles are 'very effective' for the frequency of communication. Further, half cubicles were discovered 'effective' but not 'very effective' for the quality/effectiveness of communication. It is found that half-height cubicles and status boards are 'very effective' for the coordination among team members according to the survey. Communal/discussion space is found to be 'effective' but not 'very effective' for coordination among team members. Our analysis also reveals that half-height glass barriers are 'very effective' during the individuals problem-solving activities while working together as a team. Infact, such a physically open environment appears to improve communication, coordination, and collaboration. Conclusion: According to this study, an open working environment with only half-height glass barriers and communal space plays a major role in communication among team members. The presence of status boards significantly help in reducing unnecessary communication by providing the required information to individuals and therefore, in turn reduce distractions a team member may confront in their absence. As communication plays a significant role in improving coordination and collaboration, it is not surprising to find the effect of open working environment and status boards in improving coordination and collaboration. An open working environment increases the awareness among software developers e.g. who is doing what, what is on the agenda, what is taking place, etc. That in turn, improves coordination among them. A communal/discussion space helps in collaboration immensely. (C) 2012 Elsevier B.V. All rights reserved.
Citation Count: 0
The Impact of the Limit q-Durrmeyer Operator on Continuous Functions
(Springer Heidelberg, 2024) Yilmaz, Ovgu Gurel; Ostrovska, Sofiya; Turan, Mehmet; Mathematics
The limit q-Durrmeyer operator, D-infinity,D-q, was introduced and its approximation properties were investigated by Gupta (Appl. Math. Comput. 197(1):172-178, 2008) during a study of q-analogues for the Bernstein-Durrmeyer operator. In the present work, this operator is investigated from a different perspective. More precisely, the growth estimates are derived for the entire functions comprising the range of D-infinity,D-q. The interrelation between the analytic properties of a function f and the rate of growth for D(infinity,q)f are established, and the sharpness of the obtained results are demonstrated.