Counting subwords in flattened involutions and Kummer functions

2016 ◽  
Vol 22 (10) ◽  
pp. 1404-1425
Author(s):  
Toufik Mansour ◽  
Mark Shattuck
Keyword(s):  
Kummer Functions

scholarly journals Dynamic Keynesian Model of Economic Growth with Memory and Lag

Mathematics ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 178 ◽  
Author(s):  
Vasily Tarasov ◽  
Valentina Tarasova
Keyword(s):  
Differential Equation ◽  
Economic Growth ◽  
Fractional Differential Equation ◽  
Differential Operators ◽  
Continuous Distribution ◽  
National Income ◽  
Fading Memory ◽  
Kummer Functions ◽  
Distributed Lag ◽  
Fractional Differential

A mathematical model of economic growth with fading memory and continuous distribution of delay time is suggested. This model can be considered as a generalization of the standard Keynesian macroeconomic model. To take into account the memory and gamma-distributed lag we use the Abel-type integral and integro-differential operators with the confluent hypergeometric Kummer function in the kernel. These operators allow us to propose an economic accelerator, in which the memory and lag are taken into account. The fractional differential equation, which describes the dynamics of national income in this generalized model, is suggested. The solution of this fractional differential equation is obtained in the form of series of the confluent hypergeometric Kummer functions. The asymptotic behavior of national income, which is described by this solution, is considered.

The matrix M/M/∞ system: retrial models and Markov Modulated sources

1993 ◽  
Vol 25 (2) ◽  
pp. 453-471 ◽  
Author(s):  
J. Keilson ◽  
L. D. Servi
Keyword(s):  
Numerical Evaluation ◽  
Stability Conditions ◽  
Kummer Functions ◽  
The Matrix ◽  
Service Rates ◽  
System Properties ◽  
Markov Modulated ◽  
The Stability ◽  
Analytical Expressions

The matrix-geometric work of Neuts could be viewed as a matrix variant of M/M/1. A 2 × 2 matrix counterpart of Neuts for M/M/∞ is introduced, the stability conditions are identified, and the ergodic solution is solved analytically in terms of the ten parameters that define it. For several cases of interest, system properties can be found from simple analytical expressions or after easy numerical evaluation of Kummer functions. When the matrix of service rates is singular, a qualitatively different solution is derived. Applications to telecommunications include some retrial models and an M/M/∞ queue with Markov-modulated input.

scholarly journals Free Axial Vibrations of Non-Uniform Rods

2011 ◽  
Vol 2-3 ◽  
pp. 882-889
Author(s):  
Shu Qi Guo ◽  
Shao Pu Yang
Keyword(s):  
Exact Solution ◽  
Material Properties ◽  
Taylor Expansion ◽  
Series Solution ◽  
Wkb Method ◽  
Kummer Functions ◽  
Axial Vibrations ◽  
Special Case

Free axial vibrations of non-uniform rods are investigated by a proposed method, which results in a series solution. In a special case, with the proposed method an exact solution with a concise form can be obtained, which imply four types of profiles with variation in geometry or material properties. However, the WKB (Wentzel-Kramers-Brillouin) method leads to a series solution, which is a Taylor expansion of the results of the pro-posed method. For the arbitrary non-uniform rods, the comparison indicates that the WKB method is simpler, but the convergent speed of the series solution resulting from the proposed method is faster than that of the WKB method, which is also validated numerically using an exact solution of a kind of non-uniform rods with Kummer functions.

On hitting times for compound Poisson dams with exponential jumps and linear release rate

2001 ◽  
Vol 38 (3) ◽  
pp. 781-786 ◽  
Author(s):  
Offer Kella ◽  
Wolfgang Stadje
Keyword(s):  
Release Rate ◽  
Shot Noise ◽  
Hypergeometric Functions ◽  
Hitting Times ◽  
Stieltjes Transform ◽  
Compound Poisson ◽  
Confluent Hypergeometric Functions ◽  
Kummer Functions ◽  
Shot Noise Process ◽  
The Mean

For a compound Poisson dam with exponential jumps and linear release rate (shot-noise process), we compute the Laplace-Stieltjes transform (LST) and the mean of the hitting time of some positive level given that the process starts from some given positive level. The solution for the LST is in terms of confluent hypergeometric functions of the first and second kinds (Kummer functions).

scholarly journals Some multiple Gaussian hypergeometric generalizations of Buschman-Srivastava theorem

2005 ◽  
Vol 2005 (1) ◽  
pp. 143-153 ◽  
Author(s):  
M. I. Qureshi ◽  
M. Sadiq Khan ◽  
M. A. Pathan
Keyword(s):  
Hypergeometric Function ◽  
Hypergeometric Functions ◽  
Kummer Functions ◽  
Special Cases ◽  
Watson’S Theorem

Some generalizations of Bailey's theorem involving the product of two Kummer functions1F1are obtained by using Watson's theorem and Srivastava's identities. Its special cases yield various new transformations and reduction formulae involving Pathan's quadruple hypergeometric functionsFp(4), Srivastava's triple and quadruple hypergeometric functionsF(3),F(4), Lauricella's quadruple hypergeometric functionFA(4), Exton's multiple hypergeometric functionsXE:G;HA:B;D,K10,K13,X8,(k)H2(n),(k)H4(n), Erdélyi's multiple hypergeometric functionHn,k, Khan and Pathan's triple hypergeometric functionH4(P), Kampé de Fériet's double hypergeometric functionFE:G;HA:B;D, Appell's double hypergeometric function of the second kindF2, and the Srivastava-Daoust functionFD:E(1);E(2);…;E(n)A:B(1);B(2);…;B(n). Some known results of Buschman, Srivastava, and Bailey are obtained.

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