Numerical exploration of a bivariate lindley process via the bivariate laguerre transform

1987 ◽  
Vol 8 (1) ◽  
pp. 321-349 ◽  
Author(s):  
U. Sumita ◽  
M. Kijima
Keyword(s):  
Laguerre Transform ◽  
Numerical Exploration ◽  
Lindley Process

Evaluation of the total time in system in a preempt/resume priority queue via a modified Lindley process

1983 ◽  
Vol 15 (04) ◽  
pp. 840-856 ◽  
Author(s):  
J. Keilson ◽  
U. Sumita
Keyword(s):  
Time Distribution ◽  
Arrival Rate ◽  
Priority Queue ◽  
Service Time Distribution ◽  
Transform Method ◽  
Laguerre Transform ◽  
Poisson Stream ◽  
Lindley Process ◽  
Theoretical Results ◽  
Time Sequences

A Poisson stream of arrival rate λI and service-time distribution A I(x) has preempt/resume priority over a second stream of rate λII and distribution A II(x). Abundant theoretical results exist for this system, but severe numerical difficulties have made many descriptive distributions unavailable. Moreover, the distribution of total time in system of low-priority customers has not been discussed theoretically. It is shown that the waiting-time sequences of such customers before first entry into service is a Lindley process modified by replacement. This leads to the total time distribution needed. A variety of descriptive distributions, transient and stationary, is obtained numerically via the Laguerre transform method.

The bivariate Laguerre transform and its applications: numerical exploration of bivariate processes

1985 ◽  
Vol 17 (4) ◽  
pp. 683-708 ◽  
Author(s):  
Ushio Sumita ◽  
Masaaki Kijima
Keyword(s):  
Numerical Computation ◽  
Orthonormal Basis ◽  
Laguerre Functions ◽  
Bivariate Polynomials ◽  
Laguerre Transform ◽  
Partial Differentiation ◽  
Numerical Exploration ◽  
Shock Models ◽  
Numerical Tool

In the study of bivariate processes, one often encounters expressions involving repeated combinations of bivariate continuum operations such as multiple bivariate convolutions, marginal convolutions, tail integration, partial differentiation and multiplication by bivariate polynomials. In many cases numerical computation of such results is quite tedious and laborious. In this paper, the bivariate Laguerre transform is developed which provides a systematic numerical tool for evaluating such bivariate continuum operations. The formalism is an extension of the univariate Laguerre transform developed by Keilson and Nunn (1979), Keilson et al. (1981) and Keilson and Sumita (1981), using the product orthonormal basis generated from Laguerre functions. The power of the procedure is proven through numerical exploration of bivariate processes arising from correlated cumulative shock models.

The bivariate Laguerre transform and its applications: numerical exploration of bivariate processes

1985 ◽  
Vol 17 (04) ◽  
pp. 683-708 ◽  
Author(s):  
Ushio Sumita ◽  
Masaaki Kijima
Keyword(s):  
Numerical Computation ◽  
Orthonormal Basis ◽  
Laguerre Functions ◽  
Bivariate Polynomials ◽  
Laguerre Transform ◽  
Partial Differentiation ◽  
Numerical Exploration ◽  
Shock Models ◽  
Numerical Tool

In the study of bivariate processes, one often encounters expressions involving repeated combinations of bivariate continuum operations such as multiple bivariate convolutions, marginal convolutions, tail integration, partial differentiation and multiplication by bivariate polynomials. In many cases numerical computation of such results is quite tedious and laborious. In this paper, the bivariate Laguerre transform is developed which provides a systematic numerical tool for evaluating such bivariate continuum operations. The formalism is an extension of the univariate Laguerre transform developed by Keilson and Nunn (1979), Keilson et al. (1981) and Keilson and Sumita (1981), using the product orthonormal basis generated from Laguerre functions. The power of the procedure is proven through numerical exploration of bivariate processes arising from correlated cumulative shock models.

Evaluation of the total time in system in a preempt/resume priority queue via a modified Lindley process

1983 ◽  
Vol 15 (4) ◽  
pp. 840-856 ◽  
Author(s):  
J. Keilson ◽  
U. Sumita
Keyword(s):  
Time Distribution ◽  
Arrival Rate ◽  
Priority Queue ◽  
Service Time Distribution ◽  
Transform Method ◽  
Laguerre Transform ◽  
Poisson Stream ◽  
Lindley Process ◽  
Theoretical Results ◽  
Time Sequences

A Poisson stream of arrival rate λI and service-time distribution AI(x) has preempt/resume priority over a second stream of rate λII and distribution AII(x). Abundant theoretical results exist for this system, but severe numerical difficulties have made many descriptive distributions unavailable. Moreover, the distribution of total time in system of low-priority customers has not been discussed theoretically. It is shown that the waiting-time sequences of such customers before first entry into service is a Lindley process modified by replacement. This leads to the total time distribution needed. A variety of descriptive distributions, transient and stationary, is obtained numerically via the Laguerre transform method.

Exploiting Laguerre transform in image steganography

2021 ◽  
Vol 89 ◽  
pp. 106964
Author(s):  
Sudipta Kr Ghosal ◽  
Souradeep Mukhopadhyay ◽  
Sabbir Hossain ◽  
Ram Sarkar
Keyword(s):  
Image Steganography ◽  
Laguerre Transform

PATTERNS, DEFECTS, AND EVOLUTION OF BÉNARD–MARANGONI CELLS

1996 ◽  
Vol 06 (09) ◽  
pp. 1665-1671 ◽  
Author(s):  
J. BRAGARD ◽  
J. PONTES ◽  
M.G. VELARDE
Keyword(s):  
Fluid Layer ◽  
Ambient Air ◽  
Finite Geometry ◽  
Amplitude Equations ◽  
Ginzburg Landau ◽  
Weakly Nonlinear ◽  
Numerical Exploration ◽  
Ginzburg Landau Equations ◽  
Rigid Plane ◽  
Selection Of

We consider a thin fluid layer of infinite horizontal extent, confined below by a rigid plane and open above to the ambient air, with surface tension linearly depending on the temperature. The fluid is heated from below. First we obtain the weakly nonlinear amplitude equations in specific spatial directions. The procedure yields a set of generalized Ginzburg–Landau equations. Then we proceed to the numerical exploration of the solutions of these equations in finite geometry, hence to the selection of cells as a result of competition between the possible different modes of convection.

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