The moment problem in statistical mechanics: Correlation functions of purely dissipative systems

The present work deals with optimization in kinematics, generalizing previous results of the author. A second theme is maximizing the constrained gain linear function and minimizing the constrained cost function. Elementary notions of optimal control are considered as well. Finally, polynomial approximation results on unbounded subsets in several variables are applied to the moment problem. The existence of the solution of a two dimensional moment problem is characterized in terms of quadratic forms.

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An analysis of steady-state distribution in M/M/1 queueing system with balking based on concept of statistical mechanics

RAIRO - Operations Research ◽

10.1051/ro/2019064 ◽

2019 ◽

Cited By ~ 1

Author(s):

IKUO ARIZONO ◽

Yasuhiko Takemoto

Keyword(s):

Steady State ◽

Statistical Mechanics ◽

Queue Length ◽

Queueing System ◽

Analysis Model ◽

Steady State Distribution ◽

Steady State Analysis ◽

Extended Analysis ◽

The Moment ◽

State Analysis

The phenomenon of balking has been considered frequently in the steady-state analysis of the M/M/1 queueing system. Balking means the phenomenon that a customer who arrives at a queueing system leaves without joining a queue, since he/she is disgusted with the waiting queue length at the moment of his/her arrival. In the traditional studies for the steady-state analysis of the M/M/1 queueing system with balking, it has been typically assumed that the arrival rates obey an inverse proportional function for the waiting queue length. In this study, based on the concept of the statistical mechanics, we have a challenge to extend the traditional steady-state analysis model for the M/M/1 queueing system with balking. As the result, we have defined an extended analysis model for the M/M/1 queueing system under the consideration of the change in the directivity strength of balking. In addition, the procedure for estimating the strength of balking in this analysis model using the observed data in the M/M/1 queueing system has been also constructed.

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Orthogonal polynomials and the moment problem

Translations of Mathematical Monographs - Lectures on Integral Transforms ◽

10.1090/mmono/070/10 ◽

1988 ◽

pp. 64-71

Keyword(s):

Orthogonal Polynomials ◽

Moment Problem ◽

The Moment

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Solutions of the Al-Salam–Chihara and allied moment problems

Analysis and Applications ◽

10.1142/s0219530519500088 ◽

2019 ◽

Vol 18 (02) ◽

pp. 185-210 ◽

Cited By ~ 1

Author(s):

Mourad E. H. Ismail

Keyword(s):

Moment Problem ◽

Sufficient Conditions ◽

Infinite Family ◽

Weight Functions ◽

Moment Problems ◽

Order Operator ◽

Absolutely Continuous ◽

Rodrigues Formula ◽

Wilson Operator ◽

The Moment

We study the moment problem associated with the Al-Salam–Chihara polynomials in some detail providing raising (creation) and lowering (annihilation) operators, Rodrigues formula, and a second-order operator equation involving the Askey–Wilson operator. A new infinite family of weight functions is also given. Sufficient conditions for functions to be weight functions for the [Formula: see text]-Hermite, [Formula: see text]-Laguerre and Stieltjes–Wigert polynomials are established and used to give new infinite families of absolutely continuous orthogonality measures for each of these polynomials.

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