Current Topics on Mathematics and Computer Science Vol. 8

Spatio-temporal velocity correlation analysis of aerodynamic flow was conducted in a bid to elucidate acoustic regimes in turbulent jets. When flow characteristics are considered in Lagrangian and Eulerian modes, acoustic source regions are deemed as moving and fixed in space respectively, mindful of their peculiarities. Here space-time energy spectrum furnished correlation coefficient functions with which sound may be predicted within an acoustic region. It is observed that the autocorrelation function of a given time-bound spatial Fourier element may be found by expressing the Eulerian turbulent velocity field in the similitude of a Fourier series.  

In this chapter, ((r₁,r₂ ),m,(c₁,c₂ ) ) -regular intuitionistic fuzzy graph and totally ((r₁,r₂ ),m,(c₁,c₂ ) ) -regular intuitionistic fuzzy graphs are presented.. Intuitionistic fuzzy sets have been applied in a wide variety of fields including computer science, engineering, mathematics, medicine, chemistry and economics. On an intuitive fuzzy graph, the relationship((r₁,r₂ ),m,(c₁,c₂ ) ) -regularity and totally ((r₁,r₂ ),m,(c₁,c₂ ) ) -regularity is investigated. There is a necessary and sufficient condition for them to be comparable.Additionally,, ((r₁,r₂ ),m,(c₁,c₂ ) ) - regularity on various intuitionistic fuzzy graphs whose underlying crisp graphs is a cycle is investigated using some special membership functions.

This is a book chapter of an article published first time in the journal IMF in 2012. In section 2 of the chapter, we give evaluations of Legendre functions, which are quite general. As a consequence in section 3, we give the two complete elliptic integrals K and E in the form of Ramanujan’s type-1/ formulas. These formulas, consit of a new way, to write K and E other form the traditional one. As main application, in section 4 a formula for the constant \(\Gamma\)\((1/4)^2\) \(\pi^{-3/2}\), with accuracy about 120 digits per term is given.

This paper describes an architecture to relay on demand a real-time IP multicast audio-video stream broadcasted by a satellite on a terrestrial link. The stream is received by suitably equipped sites and then relayed to other sites that are not equipped with satellite receiving hardware but are nonetheless willing to receive the stream. By exploiting the properties of satellite transmission and adopting a hybrid satellite/terrestrial, multicast/unicast approach, the described architecture allows to overcome the restrictions suffered by multicast traffic in the global Internet, allowing it to scale easily across autonomous systems. All things considered, the proposed architecture outlines a large-scale interactive audio-video distribution system similar to those based on Content Distribution Networks (CDNs) and it compares favourably with them when performances, costs and scalability are examined.

The objective of this study is to develop, analyze, implement and compare finite-difference techniques in order to make available robust numerical approaches. An autocatalytic biochemical system in the presence of recycling enzyme is solved numerically using two numerical methods based on finite difference schemes. The first method is the well-known Euler method which is an explicit method, whereas the second method is implicit. Although the implicit method, method 2, is first order accurate in time it converges to the fixed point(s) for large time step, \(\ell\). Numerical results show the existence of hard excitation and birhythmicity.

In this paper, Bernstein Polynomials are used as a basis to solve Volterra’s model for population growth of a species within a closed system. This model is a nonlinear Integro-differential equation where the integral term represents the effect of toxin. Using the prescribed method, the solution of this problem is reducing to a system of algebraic equations. The results demonstrate the applicability and accuracy of the technique.

In this study the reasons obliging a relation to be transitive were established. Unified definitions of different symmetry and reflexivity manifests were made. It was shown that among relations’ properties only transitivity has the direct negation.

This work illustrates the required phases for the achieving of the interactive software used for the study of 3D analytic geometry software. The development of this software aimed to achieve the following goals: the presentation of theoretical notions, the interactive presentation of some important applications, and the realization of exact drawings by replacing the pencil and ruler with the mouse. The modelling of the interactive software is accomplished by specific UML diagrams representing the phases of analysis, design, and implementation. Object-oriented modelling is arduous, and reusable object-oriented design is even more complex. In the procedure of modelling a software, design represents probably the most significant factor that can influence its quality. Thus, each design pattern aims to resolve a specific design issue in case of oriented object programming paradigm. The interactive software design is optimized by using of the "Factory" creational pattern and “Observer” behavioural pattern. The implementation of the software was realised through the Java programming language. Incorporating modern methods and techniques, the presented software will lead the user to obtain experience in understanding and handling the knowledge in 3D analytic geometry field.

In this paper a strong convergence theorem is established for a three-step iterative scheme for the class of Zamfirescu operators in normed linear spaces. The result obtained in this paper extends and improves upon, among others, the corresponding result of V.Berinde [1].

Universally prestarlike functions of order \(\alpha\)\(\le\)1 in the slit domain \(\Lambda\) = \(\mathit{C}\)\[1,\(\infty\)) have been recently introduced by S. Ruscheweyh. This notion generalizes the corresponding one for functions in the unit disk \(\Delta\)( and other circular domains in C).In this paper, we introduce Universally prestarlike functions of complex order. The main objective is to give the Fekete-Szegö inequality and fractional derivative for such functions.

Several general mathematical properties of the new family of distributions are examined in a consistent manner by using the power series distributions (PSD) class. A new cumulative distribution function and probability density are obtained for the continuous type random variables which represent the maximum or the minimum in a sequence of independent and identically distributed random variables, in a random number with a power series distribution. An asymptotic result characterized by the Poisson Limit Theorem is formulated and analyzed.

In this chapter, the simulation s algorithms for these family distributions are proposed. This study is intended as a completion of the research by Balkema and de Haan (1974), Bryson (1974), Ahsanullah (1991), Balakrishnan and Ahsanullah (1994), Childs and others (2001), Al Awadhi and Ghitany (2001, 2007), Zahrani and Harbi (2013), Leahu, Munteanu and Cataranciuc (2013), Al-Zahrani and Sagor (2014), MH Tahir, GM Cordeiro (2016), AS Hassan, AM Abd-Elfattah (2016). The above mentioned algorithm was implemented by means of the Eclipse SDK programming environment.  

In this paper, a mathematical model describing the dynamics of Chlamydia trachomatis infection in a human carrier is presented. It has been suggested that cell-mediated immunity, not humoral immunity, plays the dominant role in protective immunity against Chlamydia. The model incorporated relevant feature such as recovery through drug administration. The existence and uniqueness of solutions of the model were examined by actual solution. We conduct local and global stability analysis for the model. The results show that it is stable under certain conditions. The system of equations were solved analytically using parameter-expanding method coupled with direct integration. The results are presented graphically and discussed. It is discovered that the influence of burst size per infected cell, rate of cell infection and recovery rate due to drug administration is quite significant.

Mobile Ad-hoc networks in the form of cellular networks, IoT devices, Wireless Hotspots, Vehicular Networks, etc. have gained considerable popularity in the past few decades as these networks facilitate secured, integrated, and cost-effective wireless communication. Recently, various studies and practical deployments have established that these mobile ad-hoc networks may commendably support the growth of cloud-based services, as the operations of both networks significantly complement each other. This manuscript will assist in identifying the role and performance of mobile ad-hoc networks in the growth of cloud-based services, while recognizing different issues and challenges. Mobile ad-hoc performance limitation and challenges may play a major role in affecting the performance and growth of cloud-based services. In this regard, different techniques and methods will also be analyzed and encapsulated in the current study to assure the reliability of cloud-based services’ operations.

This research provides a new hybrid algorithm for supplier selection and assessment in supply chain management, taking into account both quantitative and qualitative aspects.

Supplier selection and evaluation are formulated by combining multi-criteria decision-making approaches such as Analytic hierarchy process (AHP) improved by Rough set theory and Technique for order performance by similarity to ideal solution (TOPSIS) to rank suppliers based on their overall performances. The decision makers employ rough set theory to screen providers. The relative weights of evaluation criteria were determined using AHP.TOPSIS was used to assign a rank to suppliers based on their overall performance. This strategy assists the decision maker in selecting the best supplier who meets all supply chain management needs.

A case study is conducted in a high technology company called Multi-Flex Lami-Print Ltd, which makes Flexible Packaging materials in India, to evaluate the algorithm.