Current Issue : January - March Volume : 2019 Issue Number : 1 Articles : 6 Articles
This paper discusses the Bayesian approach to estimation and prediction of the\nreliability of software systems during the testing process. A Non-Homogeneous\nPoisson Process (NHPP) arising from the Musa-Okumoto (1984) software reliability\nmodel is proposed for the software failures. The Musa-Okumoto\nNHPP reliability model consists of two componentsâ??the execution time\ncomponent and the calendar time component, and is a popular model in\nsoftware reliability analysis. The predictive analyses of software reliability\nmodel are of great importance for modifying, debugging and determining\nwhen to terminate software development testing process. However, Bayesian\nand Classical predictive analyses on the Musa-Okumoto (1984) NHPP model\nis missing on the literature. This paper addresses four software reliability issues\nin single-sample prediction associated closely with development testing\nprogram. Bayesian approach based on non-informative prior was adopted to\ndevelop explicit solutions to these problems. Examples based on both real and\nsimulated data are presented to illustrate the developed theoretical prediction\nresults....
In this paper, we have investigated and introduced some new definitions of\ntransitivity on the set of all continuous maps, denoted by....., called\nthe point-wise convergence transitive, the compact-open transitive and point\nwise convergence topological transitive sets. Relationship between these new\ndefinitions is studied. Finally, we have introduced a number of very important\ntopological concepts and shown that every compact-open convergence\ntransitive map implies point wise transitive maps but the converse not necessarily\ntrue....
A topological index is a number related to the atomic index that allows quantitative\nstructureâ??action/property/toxicity connections. All the more vital topological indices correspond to\ncertain physico-concoction properties like breaking point, solidness, strain vitality, and so forth,\nof synthetic mixes. The idea of the hyper Zagreb index, multiple Zagreb indices and Zagreb\npolynomials was set up in the substance diagram hypothesis in light of vertex degrees. These indices\nare valuable in the investigation of calming exercises of certain compound systems. In this paper,\nwe computed the first and second Zagreb index, the hyper Zagreb index, multiple Zagreb indices and\nZagreb polynomials of the line graph of wheel and ladder graphs by utilizing the idea of subdivision....
The concept of quasi-periodic property of a function has been introduced by\nHarald Bohr in 1921 and it roughly means that the function comes (quasi)-\nperiodically as close as we want on every vertical line to the value taken by\nit at any point belonging to that line and a bounded domain... He proved\nthat the functions defined by ordinary Dirichlet series are quasi-periodic in\ntheir half plane of uniform convergence. We realized that the existence of the\ndomain... is not necessary and that the quasi-periodicity is related to the\ndenseness property of those functions which we have studied in a previous\npaper. Hence, the purpose of our research was to prove these two facts. We\nsucceeded to fulfill this task and more. Namely, we dealt with the quasi-\nperiodicity of general Dirichlet series by using geometric tools perfected by\nus in a series of previous projects. The concept has been applied to the whole\ncomplex plane (not only to the half plane of uniform convergence) for series\nwhich can be continued to meromorphic functions in that plane. The question\narise: in what conditions such a continuation is possible? There are\nknown examples of Dirichlet series which cannot be continued across the\nconvergence line, yet there are no simple conditions under which such a continuation\nis possible. We succeeded to find a very natural one....
The article proves several inequalities derived from nodal multiplication on\nT3\ntree. The proved inequalities are helpful to estimate certain quantities related\nwith the T\n3 tree as well as examples of proving an inequality embedded\nwith the floor functions....
In this work, we study the completely integrable sixth-order nonlinear Ramani equation.\nBy applying the Lie symmetry analysis technique, the Lie point symmetries and the optimal system\nof one-dimensional sub-algebras of the equation are derived. The optimal system is further used\nto derive the symmetry reductions and exact solutions. In conjunction with the Riccati Bernoulli\nsub-ODE (RBSO), we construct the travelling wave solutions of the equation by solving the ordinary\ndifferential equations (ODEs) obtained from the symmetry reduction. We show that the equation is\nnonlinearly self-adjoint and construct the conservation laws (CL) associated with the Lie symmetries\nby invoking the conservation theorem due to Ibragimov. Some figures are shown to show the physical\ninterpretations of the acquired results....
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