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Analysis of an M/M/1 Queue With Working Vacation and Vacation Interruption
Get PDFIn this paper, an M/M/1 queue with working vacation and vacation interruption is investigated. The server is supposed to interrupt the vacation and return back to the normal working period, if there are at least N customers waiting in the system at a service completion instant during the working vacation period. Otherwise, the server continues the vacation until the system is nonempty after a vacation ends or there are at least N customers after a service ends. In terms of the quasi birth and death process and matrix-geometric solution method, we obtain the distributions for the stationary queue length. Moreover, we demonstrate stochastic decomposition structures of the queue length and waiting time, and obtain the distributions of the additional queue length and additional delay for the case N = 2 . Finally, numerical examples are presented
A Study of Transversely Isotropic Thermoelastic Beam with Green-Naghdi Type-II and Type-III Theories of Thermoelasticity
Get PDFThe present research deals with the study of transversely isotropic thermoelastic beam in the context of Green-Naghdi (GN) theory of thermoelasticity of Type-II and Type-III. The mathematical model is prepared for the thin beam in a closed form with the application of Euler Bernoulli beam theory. The Laplace Transform technique has been used to find the expressions for displacement component, lateral thermal moment, deflection and axial stress in transformed domain. The general algorithm of the inverse Laplace Transform is developed to compute the results numerically in physical domain. The effect of two theories of thermoelasticity Green-Naghdi-II and Green-Naghdi-III has been depicted on the various quantities. Some particular cases have also been deduced
Chlodowsky Szász-Kantorovich operators via Dunkl analogue
No full textThe main objective of the present article is to design a sequence of Chlodowsky Szasz-Kantorovich operators based on Dunkl analogue for the purpose to achieve faster rate of convergence in terms of two positive and unbounded real number sequences and the basic results are estimated. Further, the uniform approximation by means of Korovkin theorem using test functions ei(t) = ti ; i = 0; 1; 2 is investigated. Moreover, the local and global approximation results are discussed for these sequences of linear positive operators
Understanding the Fundamental Molecular Mechanism of Osteogenic Differentiation from Mesenchymal Stem Cells
Get PDFA mathematical model is presented to study the regulatory effects of growth factors in osteoblastogenesis. The model incorporates the interactions among mesenchymal stem cells, osteoblasts, and growth factors. The resulting system of nonlinear ordinary differential equations is studied analytically and numerically. Mathematical conditions for successful osteogenic differentiation and optimal osteoblasts population are formulated, which can be used in practice to accelerate bone formation. Numerical simulations are also presented to support the theoretical results and to explore different medical interventions to enhance osteoblastogenesis
A Certain Class of Statistical Deferred Weighted A-summability Based on (p; q)-integers and Associated Approximation Theorems
Get PDFStatistical summability has recently enhanced researchers’ substantial awareness since it is more broad than the traditional (ordinary) convergence. The basic concept of statistical weighted A- summability was introduced by Mohiuddine (2016). In this investigation, we introduce the (presumably new) concept of statistical deferred weighted A-summability and deferred weighted A- statistical convergence with respect to the difference sequence of order r involving (p; q)-integers and establish an inclusion relation between them. Furthermore, based upon the proposed methods, we intend to approximate the rate of convergence and to demonstrate a Korovkin type approximation theorem for functions of two variables defined on a Banach space CB(D). Finally, several illustrative examples are presented in light of our definitions and outcomes established in this paper
New Notions From (r; s)-Generalized Fuzzy e-open Sets
Get PDFThe present article discuss (r; s)-generalized fuzzy e-border, (r; s)-generalized fuzzy e-exterior and (r; s)-generalized fuzzy e-frontier in double fuzzy topologies. Furthermore, some characterizations of generalized double fuzzy e-continuous, generalized double fuzzy e-open, generalized double fuzzy e-closed and generalized double fuzzy e-closure-irresolute functions are studied and investigated. Moreover, the interrelations among the new concepts are discussed with some necessary examples
A New Method to Solve Fractional Differential Equations: Inverse Fractional Shehu Transform Method
Get PDFIn this paper, we propose a new method called the inverse fractional Shehu transform method to solve homogenous and non-homogenous linear fractional differential equations. Fractional derivatives are described in the sense of Riemann-Liouville and Caputo. Illustrative examples are given to demonstrate the validity, efficiency and applicability of the presented method. The solutions obtained by the proposed method are in complete agreement with the solutions available in the literature
Blow up of Solutions for a Coupled Kirchhoff-type Equations with Degenerate Damping Terms
Get PDFIn this paper, we investigate a system of coupled Kirchhoff-type equations with degenerate damping terms. We prove a nonexistence of global solutions with positive initial energy. Later, we give some estimates for lower bound of the blow up time
Inverse Spectral Problems for Spectral Data and Two Spectra of N by N Tridiagonal Almost-Symmetric Matrices
Get PDFOne way to study the spectral properties of Sturm-Liouville operators is difference equations. The coefficients of the second order difference equation which is equivalent Sturm-Liouville equation can be written as a tridiagonal matrix. One investigation area for tridiagonal matrix is finding eigenvalues, eigenvectors and normalized numbers. To determine these datas, we use the solutions of the second order difference equation and this investigation is called direct spectral problem. Furthermore, reconstruction of matrix according to some arguments is called inverse spectral problem. There are many methods to solve inverse spectral problems according to selecting the datas which are generalized spectral function, spectral data of the matrix and two spectra of the matrix. In this article, we study discrete form the Sturm-Liouville equation with generalized function potential and we will focus on the inverse spectral problems of second order difference equation for spectral data and two spectra. The examined difference equation is equivalent Sturm-Liouville equation which has a discontinuity in an interior point. First, we have written the investigated Sturm-Liouville equation in difference equation form and then constructed N by N tridiagonal matrix from the coefficients of this difference equation system. The inverse spectral problems for spectral data and two-spectra of N by N tridiagonal matrices which are need not to be symmetric are studied. Here, the matrix comes from the investigated discrete Sturm-Liouville equation is not symmetric, but almost symmetric. Almost symmetric means that the entries above and below the main diagonal are the same except two entries
A Comparison of Original and Inverse Motion in Minkowski Plane
Get PDFIn this paper, we investigate the inflection circle, circling-point curve, and center-point curve for the original and inverse motion of Minkowski planes, and we also deal with their degenerate cases individually. For this purpose, we consider the trajectory of origin with respect to the instantaneous invariants of Bottema in Minkowski plane by using hyperbolic numbers. Finally, we give the geometric interpretation of the circling-point and center-point curves by comparing the original and inverse motion in Minkowski planes