scholarly journals Lie theoretic origin of some generating functions of Fox’s H-Function

2012 ◽  
Vol 43 (2) ◽  
pp. 179-185
Author(s):  
D.K. Jain ◽  
Renu Jain
Keyword(s):  
Generating Functions ◽  
Special Functions ◽  
Addition Theorems ◽  
Matrix Elements ◽  
Powerful Technique ◽  
Group Theoretic Method ◽  
In Series ◽  
Special Case ◽  
Fox’S H Function ◽  
Basis Vectors

The group theoretic method for achieving unification of diverse mass of literature of special functions is most recent of such efforts and is definitely the most elegant one. In this method the special functions emerge as basis vectors and matrix elements of local multiplier representation of some well known groups. This dual role played by special functions affords a powerful technique for derivation of several generating functions and addition theorems for them. The present paper aims at harnessing this technique to generate, derive and interpret certain expansion of Fox's H-function in series of H-function. In the special case these expansions reduce to corresponding results for G-function.

scholarly journals On partial bilateral and improper partial bilateral generating functions involving some special functions

Filomat ◽  
2004 ◽  
pp. 41-49
Author(s):  
Asit Sarkar
Keyword(s):  
Generating Functions ◽  
General Class ◽  
Special Functions ◽  
Gegenbauer Polynomials ◽  
Theoretic Method ◽  
Group Theoretic Method ◽  
Bilateral Generating Functions

A group-theoretic method of obtaining more general class of generating functions from a given class of improper partial bilateral generating functions involving Hermite. Laguerre and Gegenbauer polynomials are discussed.

Parameter Sensitivity Analysis of a Large-Scale System With Several Components Interacting in Series

1989 ◽  
Author(s):  
H. Torab
Keyword(s):  
Sensitivity Analysis ◽  
Large Scale ◽  
Optimization Problems ◽  
Parameter Sensitivity ◽  
Engineering Optimization ◽  
Parameter Sensitivity Analysis ◽  
Large Scale Systems ◽  
In Series ◽  
Special Case ◽  
Engineering Optimization Problems

Abstract Parameter sensitivity for large-scale systems that include several components which interface in series is presented. Large-scale systems can be divided into components or sub-systems to avoid excessive calculations in determining their optimum design. Model Coordination Method of Decomposition (MCMD) is one of the most commonly used methods to solve large-scale engineering optimization problems. In the Model Coordination Method of Decomposition, the vector of coordinating variables can be partitioned into two sub-vectors for systems with several components interacting in series. The first sub-vector consists of those variables that are common among all or most of the elements. The other sub-vector consists of those variables that are common between only two components that are in series. This study focuses on a parameter sensitivity analysis for this special case using MCMD.

scholarly journals MODELING OF DISTURBANCES IN STUDY OF CONTROL SYSTEMS

2020 ◽  
Vol 2020 (4) ◽  
pp. 70-79
Author(s):  
Mikhail Vasilevich Lyakhovets ◽  
Georgiy Valentinovich Makarov ◽  
Alexandr Sergeevich Salamatin
Keyword(s):  
Control Systems ◽  
Generating Functions ◽  
Special Functions ◽  
Computer Training ◽  
Full Scale ◽  
Analytical Models ◽  
Scale Model ◽  
Data Series ◽  
Dynamic Databases ◽  
Natural Data

The article is devoted to questions of synthesis of full-scale - model realizations of data series on the basis of natural data for modeling of controllable and uncontrollable influences at research of operating and projected control systems, and also in training systems of computer training. The possibility of formation of model effects on the basis of joint use of multivariate dynamic databases and natural data simulator is shown. Dynamic databases store information that characterizes the typical representative situations of systems in the form of special functions - generating functions. Multiple variability of dynamic databases is determined by the type of the selected generating function, the methods of obtaining parameters (coefficients) of this function, as well as the selected accuracy of approximation. The situation models recovered by generating functions are used as basic components (trends) in the formation of the resulting full-scale - model implementations and are input into the natural data simulator. The data simulator allows for each variant of initial natural data to form an implementation of the perturbation signal with given statistical properties on a given simulation interval limited by the initial natural implementation. This is achieved with the help of a two-circuit structure, where the first circuit is responsible for evaluation and cor-rection of initial properties of the natural signal, and the second - for iterative correction of deviations of properties of the final implementation from the specified ones. The resulting realizations reflect the properties of their full-scale components, which are difficult to describe by analytical models, and are supplemented by model values, allowing in increments to correct the properties to the specified ones. The given approach allows to form set of variants of course of processes on the basis of one situation with different set degree of uncertainty and conditions of functioning.

scholarly journals Wear of elastic tube with nonuniform coating by rigid bush

2020 ◽  
Vol 162 ◽  
pp. 02002 ◽  
Author(s):  
Kirill E. Kazakov
Keyword(s):  
Analytical Solution ◽  
Special Form ◽  
Special Functions ◽  
Contact Stresses ◽  
Elastic Tube ◽  
Analytical Representation ◽  
Standard Methods ◽  
In Series ◽  
Separate Factor ◽  
Over Time

This article is devoted to the statement and construction of analytical solution of the wearcontact problem for a rigid bush and elastic pipe with a coating in the case when the coating is nonuniform. The presence of nonuniformity leads us to the necessity of constructing a solution in a special form over special functions, since standard methods does not allow us to effectively take into account the complex properties of the coating. Analytical representation for contact stresses under the bush is presented in series with separate factor, which connect with complex properties of coating. This allows provide effective calculation even if these properties are described by rapidly changing or discontinuous functions. It is also shown that contact stresses will be negligible over time.

Quantum algebras and parity-dependent spectra

2007 ◽  
Vol 463 (2086) ◽  
pp. 2415-2427 ◽  
Author(s):  
C.V Sukumar ◽  
Andrew Hodges
Keyword(s):  
Quantum Optics ◽  
Harmonic Oscillator ◽  
Combinatorial Theory ◽  
Squeezed States ◽  
Quantum Algebras ◽  
Matrix Elements ◽  
Euler Numbers ◽  
Simple Harmonic Oscillator ◽  
Non Gaussian ◽  
Special Case

We study the structure of a quantum algebra in which a parity-violating term modifies the standard commutation relation between the creation and annihilation operators of the simple harmonic oscillator. We discuss several useful applications of the modified algebra. We show that the Bernoulli and Euler numbers arise naturally in a special case. We also show a connection with Gaussian and non-Gaussian squeezed states of the simple harmonic oscillator. Such states have been considered in quantum optics. The combinatorial theory of Bernoulli and Euler numbers is developed and used to calculate matrix elements for squeezed states.

Bounds on the extinction time distribution of a branching process

1974 ◽  
Vol 6 (2) ◽  
pp. 322-335 ◽  
Author(s):  
Alan Agresti
Keyword(s):  
Generating Function ◽  
Generating Functions ◽  
Time Distribution ◽  
Branching Process ◽  
Probability Generating Function ◽  
Extinction Time ◽  
Expected Time ◽  
Time To Extinction ◽  
Special Case ◽  
Better Than

The class of fractional linear generating functions, one of the few known classes of probability generating functions whose iterates can be explicitly stated, is examined. The method of bounding a probability generating function g (satisfying g″(1) < ∞) by two fractional linear generating functions is used to derive bounds for the extinction time distribution of the Galton-Watson branching process with offspring probability distribution represented by g. For the special case of the Poisson probability generating function, the best possible bounding fractional linear generating functions are obtained, and the bounds for the expected time to extinction of the corresponding Poisson branching process are better than any previously published.

scholarly journals ON ITERATED TRANSLATED POINTS FOR CONTACTOMORPHISMS OF ℝ2n+1 AND ℝ2n × S1

2012 ◽  
Vol 23 (02) ◽  
pp. 1250042 ◽  
Author(s):  
SHEILA SANDON
Keyword(s):  
Fixed Points ◽  
Critical Points ◽  
Generating Functions ◽  
Contact Manifold ◽  
Contact Form ◽  
Compactly Supported ◽  
Partial Contact ◽  
Legendrian Submanifolds ◽  
Special Case

A point q in a contact manifold is called a translated point for a contactomorphism ϕ with respect to some fixed contact form if ϕ(q) and q belong to the same Reeb orbit and the contact form is preserved at q. The problem of existence of translated points has an interpretation in terms of Reeb chords between Legendrian submanifolds, and can be seen as a special case of the problem of leafwise coisotropic intersections. For a compactly supported contactomorphism ϕ of ℝ2n+1 or ℝ2n × S1 contact isotopic to the identity, existence of translated points follows immediately from Chekanov's theorem on critical points of quasi-functions and Bhupal's graph construction. In this article we prove that if ϕ is positive then there are infinitely many nontrivial geometrically distinct iterated translated points, i.e. translated points of some iteration ϕk. This result can be seen as a (partial) contact analog of the result of Viterbo on existence of infinitely many iterated fixed points for compactly supported Hamiltonian symplectomorphisms of ℝ2n, and is obtained with generating functions techniques.

XIII.—Some Integrals, with respect to their Degrees, of Associated Legendre Functions

1935 ◽  
Vol 54 ◽  
pp. 135-144 ◽  
Author(s):  
T. M. MacRobert
Keyword(s):  
Type A ◽  
Fourier Integral ◽  
Contour Integration ◽  
Legendre Functions ◽  
Integral Type ◽  
Integral Theorem ◽  
Associated Legendre Functions ◽  
In Series ◽  
Special Case

Little is known regarding the integration of Legendre Functions with respect to their degrees. In this paper several such integrals are evaluated, three different methods being employed. In § 2 proofs are given of a number of formulae which are required later. In § 3 an example is given of the evaluation of an integral by contour integration. The following section contains the proof of a formula of the Fourier Integral type, a special case of which was given in a previous paper (Proc. Roy. Soc. Edin., vol. li, 1931, p. 123). In § 5 an integral is evaluated by employing Fourier's Integral Theorem; while in § 6 other integrals are evaluated by. means of expansions in series.

Sign in / Sign up

Export Citation Format

Share Document