We relate the fractional powers of the discrete Laplacian with a standard time-fractional derivative in the sense of Liouville by encoding the iterative nature of the discrete operator through a time-fractional memory term.

We consider the standard GI/G/1 queue with unlimited waiting room and the first-in first-out service discipline. We investigate the steady-state waiting-time tail probabilities P(W > x) when the service-time distribution has a long-tail distribution, i.e., when the service-time distribution fails to have a finite moment generating function. We have developed algorithms for computing the waiting...

In this paper, the authors deal with a complex network having n-identical units in series and two identical standby units for evaluation of its ability measures. The authors have been used supplementary variables technique to formulate the mathematical equations for various flow-states of fig-1(b). These mathematical equations have been solved by the application of Laplace transform. The Laplac...

1. The list below comprises a number of distributions, including in each case, the support, parameter space, and density or probability mass function. Determine whether each of the distributions belongs to the exponential dispersion family. Similarly for the two-parameter exponential family of distributions. In both cases, justify your answers. (a) Double exponential (or Laplace) distribution. ...

We present an algorithm for approximating the Laplace-Beltrami operator from an arbitrary point cloud obtained from a k-dimensional manifold embedded in the d-dimensional space. We show that this PCD Laplace (Point-Cloud Data Laplace) operator converges to the Laplace-Beltrami operator on the underlying manifold as the point cloud becomes denser. Unlike the previous work, we do not assume that ...

We construct an efficient methodology for calculating wormlike chain statistics in arbitrary D dimensions over all chain rigidities, from fully rigid to completely flexible. The structure of our exact analytical solution for the end-to-end distribution function for a wormlike chain in arbitrary D dimensions in Fourier-Laplace space (i.e., Fourier-transformed end position and Laplace-transformed...

We present an algorithm for approximating the LaplaceBeltrami operator from an arbitrary point cloud obtained from a k-dimensional manifold embedded in the ddimensional space. We show that this PCD Laplace (PointCloud Data Laplace) operator converges to the LaplaceBeltrami operator on the underlying manifold as the point cloud becomes denser. Unlike the previous work, we do not assume that the ...

In this paper, the authors deal with a complex network having n-identical units in series and two identical standby units for evaluation of its ability measures. The authors have been used supplementary variables technique to formulate the mathematical equations for various flow-states of fig-1(b). These mathematical equations have been solved by the application of Laplace transform. The Laplac...

• We present a new adaptive sampling method for statistical quality control. In this method, called LSI (Laplace sampling intervals), we use the probability distribution function of the Laplace standard distribution to obtain the sampling instants, depending on a k parameter that allows control of sampling costs. Several algebraic expressions concerning the statistical properties of the LSI met...