Related papers: An application of Kapteyn series to a problem from…
We study the relation between the coefficients of Taylor series and Kapteyn series representing the same function. We compute explicit formulas for expressing one in terms of the other and give examples to illustrate our method.
Retrial phenomenon naturally arises in various systems such as call centers, cellular networks and random access protocols in local area networks. This paper gives a comprehensive survey on theory and applications of retrial queues in these…
Time series of counts arise in a variety of forecasting applications, for which traditional models are generally inappropriate. This paper introduces a hierarchical Bayesian formulation applicable to count time series that can easily…
An overview of the recursive equations based models and their applications in simulation based analysis and optimization of queueing systems is given. These models provide a variety of systems with a convenient and unified representation in…
The exact solution of the Cauchy problem of the linear theory of elasticity is given in the paper, when the initial data belong to a specific class of functions.
We study the Kapteyn series $% %TCIMACRO{\dsum \limits_{n=1}^{\infty}}% %BeginExpansion {\displaystyle\sum\limits_{n=1}^{\infty}} %EndExpansion t^{n}\mathrm{J}_{n}(nz) $. We find a series representation in powers of $z$ and analyze its…
Based on the technique of derivation of a theory, presented in our recent paper, we investigate the properties of the derived quantum system. We show that the derived quantum system possesses the (nonanomalous) symmetries of the original…
Networks based on entangled quantum systems enable interesting applications in quantum information processing and the understanding of the resulting quantum correlations is essential for advancing the technology. We show that the theory of…
The application of the methods of quantum mechanics to game theory provides us with the ability to achieve results not otherwise possible. Both linear superpositions of actions and entanglement between the players' moves can be exploited.…
In this work, we illustrate and explore the use of Taylor series as solutions of differential equations. For a large a number of classes of differential equations in the literature, there are plenty of sources where the well known Taylor…
Queueing-inventory systems are integrated systems consisting of two emerging fields in applied probability, namely "Queues" and "Inventory". In this paper, we present a comprehensive review of the theory and applications of…
Quantum compiling addresses the problem of approximating an arbitrary quantum gate with a string of gates drawn from a particular finite set. It has been shown that this is possible for almost all choices of base sets and furthermore that…
We obtain sufficient conditions for the uniqueness of solutions to the Cauchy problem for the continuity equation in classes of measures that need not be absolutely continuous.
Since more than three centuries Kepler's equation continues to represents an important benchmark for testing new computational techniques. In the present paper, the classical Kapteyn series solution of Kepler's equation originally conceived…
In this paper, we analyze how well a machine can solve a general problem in queueing theory. To answer this question, we use a deep learning model to predict the stationary queue-length distribution of an $M/G/1$ queue (Poisson arrivals,…
In this paper we develop the first perfect sampling algorithm for queues with Hawkes input, i.e. single-server queues with Hawkes arrivals and i.i.d. service times of general distribution. In addition to the stability condition, we also…
The results of difference sequences theory are applied to analytic function theory and Diophantine equations. As a result we have the equation which connects the $n$-th derivative of a function with the difference sequence for the values of…
We examine the convergence properties of sequences of nonnegative real numbers that satisfy a particular class of recursive inequalities, from the perspective of proof theory and computability theory. We first establish a number of results…
Convergent sequences of real numbers play a fundamental role in many different problems in system theory, e.g., in Lyapunov stability analysis, as well as in optimization theory and computational game theory. In this survey, we provide an…
We analyze a boarding solution for a transport system in which the number of passengers allowed to enter a transport cabin is automatically controlled. Expressions charac- terizing the stochastic properties of the passenger queue length,…