On The Properties Of qq-Bernstein-Type Polynomials

The aim of this paper is to give a new approach to modified $q$-Bernstein polynomials for functions of several variables. By using these polynomials, the recurrence formulas and some new interesting identities related to the second Stirling numbers and generalized Bernoulli polynomials are derived. Moreover, the generating function, interpolation function of these polynomials of several variables and also the derivatives of these polynomials and their generating function are given. Finally, we get new interesting identities of modified $q$-Bernoulli numbers and $q$-Euler numbers applying $p$-adic $q$-integral representation on $\mathbb {Z}_p$ and $p$-adic fermionic $q$-invariant integral on $\mathbb {Z}_p$, respectively, to the inverse of $q$-Bernstein polynomials.Comment: 17 pages, some theorems added to new versio

Some new identities on the Apostol-Bernoulli polynomials of higher order derived from Bernoulli basis

In the present paper, we obtain new interesting relations and identities of the Apostol-Bernoulli polynomials of higher order, which are derived using a Bernoulli polynomial basis. Finally, by utilizing our method, we also derive formulas for the convolutions of Bernoulli and Euler polynomials, expressed via Apostol-Bernoulli polynomials of higher order.Comment: 8 pages, submitte

Some New Identities of Genocchi Numbers and Polynomials involving Bernoulli and Euler polynomials

In this paper, we will deal with some new formulae for two product Genocchi polynomials together with both Euler polynomials and Bernoulli polynomials. We get some applications for Genocchi polynomials. Our applications possess a number of interesting properties to study in Theory of Analytic numbers which we express in the present paper.Comment: 10 pages, submitte

A Comprehensive X-ray Absorption Model for Atomic Oxygen

An analytical formula is developed to represent accurately the photoabsorption cross section of O I for all energies of interest in X-ray spectral modeling. In the vicinity of the Kedge, a Rydberg series expression is used to fit R-matrix results, including important orbital relaxation effects, that accurately predict the absorption oscillator strengths below threshold and merge consistently and continuously to the above-threshold cross section. Further minor adjustments are made to the threshold energies in order to reliably align the atomic Rydberg resonances after consideration of both experimental and observed line positions. At energies far below or above the K-edge region, the formulation is based on both outer- and inner-shell direct photoionization, including significant shake-up and shake-off processes that result in photoionization-excitation and double photoionization contributions to the total cross section. The ultimate purpose for developing a definitive model for oxygen absorption is to resolve standing discrepancies between the astronomically observed and laboratory measured line positions, and between the inferred atomic and molecular oxygen abundances in the interstellar medium from XSTAR and SPEX spectral models

Radiation Damping in the Photoionization of Fe^{14+}

A theoretical investigation of photoabsorption and photoionization of Fe^{14+} extending beyond an earlier frame transformation R-matrix implementation is performed using a fully-correlated, Breit-Pauli R-matrix formulation including both fine-structure splitting of strongly-bound resonances and radiation damping. The radiation damping of $2p\rightarrow nd$ resonances gives rise to a resonant photoionization cross section that is significantly lower than the total photoabsorption cross section. Furthermore, the radiation-damped photoionization cross section is found to be in good agreement with recent experimental results once a global shift in energy of $\approx -3.5$ eV is applied. These findings have important implications. Firstly, the presently available synchrotron experimental data are applicable only to photoionization processes and not to photoabsorption; the latter is required in opacity calculations. Secondly, our computed cross section, for which the L-shell ionization threshold is aligned with the NIST value, shows a series of $2p \rightarrow nd$ Rydberg resonances that are uniformly 3-4 eV higher in energy than the corresponding experimental profiles, indicating that the L-shell threshold energy values currently recommended by NIST are likely in error.Comment: 4 pages, 1 figures, and 2 table

Some New Symmetric Identities for the q-Zeta Type Functions

The main object of this paper is to obtain several symmetric properties of the q-Zeta type functions. As applications of these properties, we give some new interesting identities for the modified q-Genocchi polynomials. Finally, our applications are shown to lead to a number of interesting results which we state in the present paper.Comment: 8 pages; submitte

A note on the values of the weighted q-Bernstein polynomials and modified q-Genocchi numbers with weight alpha and beta via the p-adic q-integral on Zp

The rapid development of q-calculus has led to the discovery of new generalizations of Bernstein polynomials and Genocchi polynomials involving q-integers. The present paper deals with weighted q-Bernstein polynomials and q-Genocchi numbers with weight alpha and beta. We apply the method of generating function and p-adic q-integral representation on Zp, which are exploited to derive further classes of Bernstein polynomials and q-Genocchi numbers and polynomials. To be more precise we summarize our results as follows, we obtain some combinatorial relations between q-Genocchi numbers and polynomials with weight alpha and beta. Furthermore, we derive an integral representation of weighted q-Bernstein polynomials of degree n on Zp. Also we deduce a fermionic p-adic q-integral representation of product weighted q-Bernstein polynomials of different degrees n1,n2,...on Zp and show that it can be written with q-Genocchi numbers with weight alpha and beta which yields a deeper insight into the effectiveness of this type of generalizations. Our new generating function possess a number of interesting properties which we state in this paper.Comment: 10 page

CENGO: a web-based serious game to increase the programming knowledge levels of computer engineering students

In recent years, games are used to increase the level of knowledge and experience of individuals working in different domains. Especially in the education field, there are several different serious games to teach the subjects of the lectures or other educational materials to students in an enjoyable way. Hence, this study proposes a quantitative research approach to increase the programming knowledge levels of the first-year undergraduate students at computer engineering departments. For this aim, a responsive web platform was developed to teach the syntax and logic of C programming language by using some game elements. Therefore, the students have a chance to repeat the topics related to C programming language continuously since the platform is always accessible. To figure out the efficiency of the designed environment, 10 first-year computer engineering students were selected. According to the results obtained from the user tests, this game can be used as an educational tool, which supports the traditional training methods, to increase the knowledge levels of students about the syntax and logic of C programming language

Interoperability specification development for integrated BIM use in performance based design

Interoperability in BIM is low and the focus is on 3D coordination. Despite the available standards including IFC and IDM, there is still no clear guidance how such standards can be effectively used for performance based design. Thus, early collaboration is discouraged and performance analysis is conducted as late as possible to minimize the number of information exchanges, leading to difficulties and costly changes in design that is almost completed. The aim is to propose an interoperability specification development approach for performance based design through the Design4Energy case study project. Findings show that the design process had increased flexibility, shared understanding between stakeholders about what information nuggets should be provided from whom to whom, at what stage, using which tool and data model. It can guide for the integrated BIM practice and help developing BIM execution plans for Level 2 BIM while paving the way for Level 3 BIM

The changing role of the software engineer

In this paper we will discuss the changing role of a software engineer. We will examine this from four major standpoints, the software development life cycle, the influence of open source software, testing and deployment and the emergence of new technologies. We will first analyze what the role of a software engineer was in the past. We will examine limitations associated with software development life cycle models, and software failures that catalyzed increased importance for quality assurance. We then outline the current role of a software engineer. We discuss the impact of agile software development and automation on the software development cycle, the influence of open source software and how new technologies such as Function-as-a-Service and machine learning may impacted the role. Based on our research, we analyze why the software engineer role has changed and postulate prospective changes to the role of software engineer, and in particular how new responsibilities may affect the day to day work of future software engineers. We ultimately find that the role of a “software engineer” is nowadays widely varied and very broad, and it only generally indicates the type of work that the software engineer may undertake