Differential equations for p, q-Touchard polynomials

We discuss c≤3 topological Landau-Ginzburg models. In particular we give the potential for the three exceptional models E6,7,8 in the constant metric coordinates of coupling constant space and derive the generating function F for correlation functions. For the c=3 torus cases with one marginal deformation and relevant perturbations, we derive and solve the differential equation resulting from flatness of coupling constant space. We perform the transformation to constant metric coordinates and calculate the generating function F. Comparing the three-point correlation functions with those of orbifold superconformal field theory, we find agreement. We finally demonstrate that the differential equations derived from flatness of coupling constant space are the same as the ones satisfied by the periods of the tori.

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PROBABILISTIC SPACE FOR CALCULATION OF PROBABILISTIC CHARACTERISTICS OF A THREE-PARAMETER QUEUEING SYSTEM MODEL

Science Evolution ◽

10.21603/2500-1418-2017-2-1-100-109 ◽

2017 ◽

pp. 100-109

Author(s):

Valery Pavsky ◽

Kirill Pavsky ◽

Svetlana Ivanova ◽

...

Keyword(s):

Differential Equation ◽

Partial Differential Equation ◽

Probability Distribution ◽

Differential Equations ◽

Ordinary Differential Equations ◽

Generating Function ◽

Queueing Theory ◽

Probability Space ◽

Queueing System ◽

Probabilistic Space

A model of queueing theory is proposed that describes a queueing system with three parameters, which has important practical applications. The model is based on the continuous time Markov process with a discrete number of states. The model is formalized by a probabilistic space in which the space of elementary events is a set of inconsistent states of the queueing system; and the probabilistic measure is a probability distribution corresponding to a set of elementary events, that is, each elementary event is associated with the probability of the system staying in this state, for each fixed time moment. The model is represented by a system of ordinary differential equations, compiled by methods of queueing theory (Kolmogorov equations). To find the solution of the system of equations, the method of generating functions is used. For the generating function, a partial differential equation is obtained. Finding the generating function completes the construction of a probability space. The latter means that for any random variables and functions defined on the resulting probability space, one can find their probabilistic characteristics. In particular, analytical expressions of the moments (mathematical expectations and variances) of random functions that depend on time are obtained. The peculiarity of finding a solution is that it is obtained not from the probability distribution, but directly from the partial differential equation, which represents a system of ordinary differential equations. For the probability distribution, the solution was found by a combinatorial method, which made it possible to significantly reduce the computations. To apply the formulas in engineering calculations, we consider the stationary case, to which a considerable simplification of the calculations corresponds. A relationship between a system of differential equations and a polynomial distribution known in probability theory is shown. The results are used in the analysis of the reliability of the operation of scalable computing systems; graphical implementation is shown

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Enumeration of Generalized $BCI$ Lambda-terms

The Electronic Journal of Combinatorics ◽

10.37236/3051 ◽

2013 ◽

Vol 20 (4) ◽

Cited By ~ 3

Author(s):

Olivier Bodini ◽

Danièle Gardy ◽

Bernhard Gittenberger ◽

Alice Jacquot

Keyword(s):

Differential Equation ◽

Differential Equations ◽

Recurrence Relation ◽

Generating Function ◽

Generating Functions ◽

Combinatory Logic ◽

Efficient Computation ◽

Asymptotic Number ◽

Axiom Systems

We investigate the asymptotic number of elements of size $n$ in a particular class of closed lambda-terms (so-called $BCI(p)$-terms) which are related to axiom systems of combinatory logic. By deriving a differential equation for the generating function of the counting sequence we obtain a recurrence relation which can be solved asymptotically. We derive differential equations for the generating functions of the counting sequences of other more general classes of terms as well: the class of $BCK(p)$-terms and that of closed lambda-terms. Using elementary arguments we obtain upper and lower estimates for the number of closed lambda-terms of size $n$. Moreover, a recurrence relation is derived which allows an efficient computation of the counting sequence. $BCK(p)$-terms are discussed briefly.

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Explicit Identities for 3-Variable Degenerate Hermite Kampé de Fériet Polynomials and Differential Equation Derived from Generating Function

Symmetry ◽

10.3390/sym13010007 ◽

2020 ◽

Vol 13 (1) ◽

pp. 7

Author(s):

Kyung-Won Hwang ◽

Young-Soo Seol ◽

Cheon-Seoung Ryoo

Keyword(s):

Differential Equation ◽

Differential Equations ◽

Generating Function ◽

Generating Functions ◽

Symmetric Identities

We get the 3-variable degenerate Hermite Kampé de Fériet polynomials and get symmetric identities for 3-variable degenerate Hermite Kampé de Fériet polynomials. We make differential equations coming from the generating functions of degenerate Hermite Kampé de Fériet polynomials to get some identities for 3-variable degenerate Hermite Kampé de Fériet polynomials,. Finally, we study the structure and symmetry of pattern about the zeros of the 3-variable degenerate Hermite Kampé de Fériet equations.

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Normalization Bernstein Basis For Solving Fractional Fredholm-Integro Differential Equation

Ibn AL- Haitham Journal For Pure and Applied Science ◽

10.30526/2017.ihsciconf.1821 ◽

2018 ◽

pp. 491

Author(s):

Abdul Khaleq O. Al-Jubory ◽

Shaymaa Hussain Salih

Keyword(s):

Differential Equation ◽

Approximate Solution ◽

Linear System ◽

Differential Equations ◽

Bernstein Basis ◽

Traditional Methods ◽

Integro Differential Equation

In this work, we employ a new normalization Bernstein basis for solving linear Freadholm of fractional integro-differential equations nonhomogeneous of the second type (LFFIDEs). We adopt Petrov-Galerkian method (PGM) to approximate solution of the (LFFIDEs) via normalization Bernstein basis that yields linear system. Some examples are given and their results are shown in tables and figures, the Petrov-Galerkian method (PGM) is very effective and convenient and overcome the difficulty of traditional methods. We solve this problem (LFFIDEs) by the assistance of Matlab10.

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Boundary-Value Problems for Third-Order Lipschitz Ordinary Differential Equations

Proceedings of the Edinburgh Mathematical Society ◽

10.1017/s0013091514000042 ◽

2014 ◽

Vol 58 (1) ◽

pp. 183-197 ◽

Cited By ~ 2

Author(s):

John R. Graef ◽

Johnny Henderson ◽

Rodrica Luca ◽

Yu Tian

Keyword(s):

Differential Equation ◽

Differential Equations ◽

Ordinary Differential Equations ◽

Boundary Value Problems ◽

Order Differential Equation ◽

Boundary Value ◽

Point Boundary ◽

Third Order ◽

Optimal Length ◽

The Third

AbstractFor the third-order differential equationy′″ = ƒ(t, y, y′, y″), where, questions involving ‘uniqueness implies uniqueness’, ‘uniqueness implies existence’ and ‘optimal length subintervals of (a, b) on which solutions are unique’ are studied for a class of two-point boundary-value problems.

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Asymptotic behavior of solutions of half-linear differential equations and generalized Karamata functions

Georgian Mathematical Journal ◽

10.1515/gmj-2020-2070 ◽

2020 ◽

Vol 0 (0) ◽

Author(s):

Kusano Takaŝi ◽

Jelena V. Manojlović

Keyword(s):

Differential Equation ◽

Asymptotic Behavior ◽

Continuous Function ◽

Differential Equations ◽

Linear Differential Equation ◽

Regular Variation ◽

Asymptotic Formulas ◽

Asymptotic Behavior Of Solutions ◽

Positive Continuous Function ◽

Linear Differential

AbstractWe study the asymptotic behavior of eventually positive solutions of the second-order half-linear differential equation(p(t)\lvert x^{\prime}\rvert^{\alpha}\operatorname{sgn}x^{\prime})^{\prime}+q(% t)\lvert x\rvert^{\alpha}\operatorname{sgn}x=0,where q is a continuous function which may take both positive and negative values in any neighborhood of infinity and p is a positive continuous function satisfying one of the conditions\int_{a}^{\infty}\frac{ds}{p(s)^{1/\alpha}}=\infty\quad\text{or}\quad\int_{a}^% {\infty}\frac{ds}{p(s)^{1/\alpha}}<\infty.The asymptotic formulas for generalized regularly varying solutions are established using the Karamata theory of regular variation.

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Oscillation and non-oscillation of some neutral differential equations of odd order

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/s0161171292000668 ◽

1992 ◽

Vol 15 (3) ◽

pp. 509-515 ◽

Cited By ~ 2

Author(s):

B. S. Lalli ◽

B. G. Zhang

Keyword(s):

Differential Equation ◽

Differential Equations ◽

Sufficient Conditions ◽

Nonoscillatory Solution ◽

Neutral Differential Equation ◽

Neutral Differential Equations ◽

Neutral Term ◽

Odd Order ◽

Existence Criterion ◽

Oscillation Of Solutions

An existence criterion for nonoscillatory solution for an odd order neutral differential equation is provided. Some sufficient conditions are also given for the oscillation of solutions of somenth order equations with nonlinearity in the neutral term.

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The number of meetings in free Poisson traffic

Journal of Applied Probability ◽

10.2307/3212753 ◽

1974 ◽

Vol 11 (2) ◽

pp. 320-331

Author(s):

Hans D. Unkelbach ◽

Helmut Wegmann

Keyword(s):

Differential Equation ◽

Generating Function ◽

Practical Interest ◽

Time Interval ◽

Integro Differential Equation

Using Rényi's model of free Poisson traffic the distribution of the number of meetings of vehicles on a highway section during a given time interval is investigated. An integro-differential equation for the generating function of that variable is deduced and the first moments are calculated. The generating function is given explicitly in simple cases and approximately in cases of practical interest.

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Enhancing Accuracy of Runge–Kutta-Type Collocation Methods for Solving ODEs

Mathematics ◽

10.3390/math9020174 ◽

2021 ◽

Vol 9 (2) ◽

pp. 174

Author(s):

Janez Urevc ◽

Miroslav Halilovič

Keyword(s):

Differential Equation ◽

Differential Equations ◽

Ordinary Differential Equations ◽

Numerical Integration ◽

Integral Form ◽

Collocation Methods ◽

Nonlinear Odes ◽

New Class ◽

New Methods ◽

Runge Kutta

In this paper, a new class of Runge–Kutta-type collocation methods for the numerical integration of ordinary differential equations (ODEs) is presented. Its derivation is based on the integral form of the differential equation. The approach enables enhancing the accuracy of the established collocation Runge–Kutta methods while retaining the same number of stages. We demonstrate that, with the proposed approach, the Gauss–Legendre and Lobatto IIIA methods can be derived and that their accuracy can be improved for the same number of method coefficients. We expressed the methods in the form of tables similar to Butcher tableaus. The performance of the new methods is investigated on some well-known stiff, oscillatory, and nonlinear ODEs from the literature.

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