Current Topics on Mathematics and Computer Science Vol. 1

The updated Operating System is from the secure and safe way to inputting, processing and output the data, to get the safest results of smooth operation and flexible working The applications and desktop programs are also have big relationship to the operating system, in case of both updated. There ae two king of OS in Windows for instance which are: 32 bit OS and 64 bit OS beside nowdays128 bit operating system. 32-bit system and 64-bit system still used in computers. Differences in processing and I/O data in case of either 64-bit or both 32-bit also is differing through that if Operating System (32- bit or 64-bit) updated or none updated or applications (32- bit or 64-bit). By using 32-bit, system could deduce implications and issued of updated, none updated 64-bit applications through inputting/outputting and processing data updated methodology. That method appear troubles in updating between OS and Apps. That be clear by scoring, appearing of the implications and errors/issues of updated, and none updated 32-bit OS which using updated and none updated 64-bit applications.

In this study we will find the relation between the fractional integral operator \(I^af\)(z),and  a special case of the integral operator\(J_{{\eta}{\lambda}}f\)(z) introduced recently by Salah And Darus [1], then we illustrate some subordination and superordination properties of \(J_{{\eta}{\lambda}}f\)(z) in the special case where \(\eta\)=0.

Indian Space Research Organization (ISRO) developed and designed the Indian Regional Navigation Satellite System (IRNSS), an indigenous navigation system.It is named as NavIC, Navigation with Indian Constellation by Indian Prime Minister. NavIC is a seven-satellite constellation that will offer India with accurate positioning, navigation, and timing services. The focal modules of NavIC receiver are acquisition, tracking and navigation unit. The data processing unit for recognising satellite signals and their related code phase and carrier frequency is called acquisition. Various acquisition strategies, such as Serial search and Parallel Code Phase search algorithms, are explored and contrasted with Cooley-Tukey FFT and sub-sampled Fast Fourier transform techniques in this chapter (ssFFT). The acquisition computation time for a ssFFT based NavIC receiver is faster than parallel FFT acquisition, and the Cooley-Tukey FFT IRNSS acquisition algorithm is faster and offers better code phase and carrier frequency values than the serial search acquisition approach, according to the results obtained in MATLAB. Reduction in the acquisition time and computation complexity is observed by the exploitation of properties of sparse FFT, Fourier transform and decimator and by the use of sub sampled FFT.

We show that systems of two different bases of the cone associated with an integer linear programming problem under a b-complementary Multisemigroup are equivalent. We also present the decomposition and the algorithm of Benders for the dual problem of the a b-Complementary Multisemigroup.

In this survey, we review some results on the behavior of the resolvent of weighted shift operator. In particular, the relation between the coefficients of the mentioned operators, the behavior of the Cesaro averages and the behavior of the resolvent were considered.

The objective of this paper is to propose a mathematical interpretation of the continuous geometric proportion (Timaeus, 32a) with which Plato accomplishes the goal to unify, harmonically and symmetrically, the Two Opposite Elements of Timaeus Cosmos—Fire and Earth—through the Mean Ratio. As we know, from the algebraic point of view, it is possible to compose a continuous geometric proportion just starting from two different quantities a (Fire) and b (Earth); their sum would be the third term, so that we would obtain the continuous geometric proportion par excellence, which carries out the agreement of opposites most perfectly: (a + b)/a = a/b. This equal proportion, applied to linear geometry, corresponds to what Euclid called the Division into Extreme and Mean Ratio (DEMR) or The Golden Proportion. In fact, according to my mathematical interpretation, in the Timaeus 32b and in the Epinomis 991 a–b, Plato uses Pingala’s Matrameru or The First Analogy of the Double to mould the body of the Cosmos as a whole, to the point of identifying the two supreme principles of the Cosmos—the One (1) and the Indefinite Dyad (\(\phi\) and1/\(\phi\))—with the DEMR. In effect, Fire and Earth are joined not by a single Mean Ratio but by two (namely, Air and Water). Moreover, using the Platonic approach to analyse the geometric properties of the shape of the Cosmos as a whole, I think that Timaeus constructed the 12 pentagonal faces of Dodecahedron by means of elementary Golden Triangles (a/b = \(\phi\)) and the Matrameru sequence. And, this would prove that my mathematical interpretation of the platonic texts is at least plausible. It is probable that Plato refers to the paradigm of the Line of the Horizon in his Republic when he speaks of the Divided Line to explain his cosmological doctrine of ideas.

Software project scope verification is an essential aspect in project scope management that must be completed correctly to prevent project rework and improve project scope control. A software project scope is defined as the work that needs to be carried out to create the required product with its necessary functions and features. Moreover, software scope verification is crucial in the process of delivering exactly what the customer requested and minimizing project scope changes. Well-defined software scope eases the process of scope verification and contributes to project success. A deliverable-oriented WBS often serves as a roadmap to a well-defined software scope of work. This chapter expands the use of deliverable-oriented WBS to the scope verification process on the basis of this. A deliverable-oriented WBS, according to this article, is a method for software scope verification.

Word Sense Disambiguation has been a trending research area in Natural Language Processing. WSD is basically solution to the ambiguity which comes due to different meaning of words in different context. Major problem of WSD is that completely different algorithm might be needed for different applications. This paper presents a brief introduction to Word Sense Disambiguation and provides a structure for discovering concept drift. It works with the situation of the linguistic processing.

Interval arithmetic is a useful method for working with inequalities, estimated numbers, error bounds, and other convex and bounded sets in general.  In this part, we'll look at a few simple cases where intervals and ranges of functions over intervals naturally appear. Interval mathematics is a generalisation in which interval numbers are used instead of real numbers, interval arithmetic is used instead of real arithmetic, and interval analysis is used instead of real analysis. There are two limits to the interval: a lower bound and an upper bound. The current paper presents some of the fundamental notions and techniques from interval analysis that will be required in the future to present various applications of interval analysis in electric circuit theory.  The representation of uncertain and inaccurate information, interval arithmetic, and its application to electrical circuits are discussed in this article. Each function has a mathematical equivalent elementary interval; there is equivalent interval for all usual mathematical functions.

Project managers face a challenge in aligning project requirements with project team members’ due to the fast-paced, competitive world in which information and communication technology (ICT) projects are run, as well as ICT professionals' constant evolving requirements. A project client measures a project success by how well has a project manager been able to meet project goals, while on the other hand software project teams (SPTs) measure project success by a manager’s ability to satisfy their project associated needs. This chapter purports that if projects’ requirements are properly aligned with team members’ requirements, then this will result in a balanced decision approach. Moreover, such an alignment will result in the realization of SPTs’ needs as well as meeting project’s needs. The chapter presents a Software Project’s needs and Software Project Team’s needs (SPnSPTn) alignment model and argues that a balanced decision, which meets both software project’s requirements and team members’ requirements can be achieved through the application of the SPnSPTn alignment model.

 In this present chapter, we consider a product of quasi-differential expressions \({\tau}_1, {\tau}_2,... {\tau}_n\)  each of order n  with complex coefficients and their formal adjoints \({\tau}_1^+, {\tau}_2^+,... {\tau}_n^+\) on [0,b)  respectively.  We show in the direct sum spaces \(L_w^2 (I_p), p = 1,2, ... , N\)  of functions defined on each of the separate intervals in the case of one singular end-points and under suitable conditions on the function F that all solutions of the product integro quasi-differential equations \({\prod}_{j=1}^n {\tau}_j, - {\lambda}I]y(t)= wF\) are bounded and \(L_w^2 -\) bounded on [0,b).

The Ryan-Einot-Gabriel-Welsch and Quiot (REGWQ) test allows one to compare vast amounts of data while monitoring the likelihood of having at least one Type I or Family wise mistake. The REGWQ multiple comparisons test for qualitative data was used in this investigation. For multiple comparisons of the means, okra characterisation data was utilised and submitted to ANOVA (P_0.05) with REGWQ. When variances are heterogeneous, the findings of this study define a summary technique of following a significant ANOVA F with REGWQ test on several comparisons of means in summation of a broad entries/treatments to the small classes.

Cluster analysis could be particularly helpful for categorising qualitative treatments and should also be used in combination with REFWQ multiple generates. The research will be developed in REGWQ multiple producers in SAS alternative for distributing a large number of treatments to a small population with summering the best treatment preference.  The use of REGWQ for multiple comparisons of qualitative data typically produce overlapping group of means, unless access multiple comparison of gaulatitive data need new approaches in computer program to calculate exact studentized range values.

Jackson queuing networks have a lot of practical applications, mainly in services and technologic devices. For the first case, an example are the healthcare networks and, for the second, the computation and telecommunications networks. Evidently the time that a customer - a person, a job, a message … – spends in this kind of systems, its sojourn time[1], is an important measure of its performance, among others. In this work, the practical statistical known results about the sojourn time of a customer, in a Jackson network, distribution are collected and presented. And an emphasis is set on the numerical methods applicable to compute the distribution function and the moments.  

In this paper a simulation study of a parametric mixture model of three different distributions is considered to model heterogeneous survival data. Some properties of the proposed parametric mixture of Exponential, Gamma and Weibull are investigated. The Expectation Maximization Algorithm (EM) is implemented to estimate the maximum likelihood estimators of three different postulated parametric mixture model parameters. The simulations are performed by simulating data sampled from a population of three component parametric mixture of three different distributions, and the simulations are repeated 10, 30, 50, 100 and 500 times to investigate the consistency and stability of the EM scheme. The EM Algorithm scheme developed is able to estimate the parameters of the mixture which are very close to the parameters of the postulated model.The repetitions of the simulation give parameters closer and closer to the postulated models, as the number of repetitions increases, with relatively small standard errors. The results revealed that the EM successfully estimated the parameters of the three component mixture model.