Recurrence relations in the theory of Hecke operators

1984 ◽  
Vol 26 (6) ◽  
pp. 2342-2348 ◽  
Author(s):  
V. A. Gritsenko
2018 ◽  
Vol 11 (3) ◽  
pp. 29-39
Author(s):  
E. I. Jafarov ◽  
A. M. Jafarova ◽  
S. M. Nagiyev

Author(s):  
Georgiy Aleksandrovich Popov

The article deals with a two-channel queuing system with a Poisson incoming call flow, in which the application processing time on each of the devices is different. Such models are used, in particular, when describing the operation of the system for selecting service requests in a number of operating systems. A complex system characteristic was introduced at the time of service endings on at least one of the devices, including the queue length, the remaining service time on the occupied device, and the time since the beginning of the current period of employment. This characteristic determines the state of the system at any time. Recurrence relations are obtained that connect this characteristic with its marginal values when there is no queue in the system. The method of introducing additional events was chosen as one of the main methods for analyzing the model. The relationships presented in this article can be used for analysis of the average characteristics of this system, as well as in the process of its simulation. Summarizing the results of work on multichannel systems with an arbitrary number of servicing devices will significantly reduce the time required for simulating complex systems described by sets of multichannel queuing systems.


Filomat ◽  
2017 ◽  
Vol 31 (2) ◽  
pp. 309-320 ◽  
Author(s):  
B.S. El-Desouky ◽  
Nenad Cakic ◽  
F.A. Shiha

In this paper we give a new family of numbers, called ??-Whitney numbers, which gives generalization of many types of Whitney numbers and Stirling numbers. Some basic properties of these numbers such as recurrence relations, explicit formulas and generating functions are given. Finally many interesting special cases are derived.


Author(s):  
Antonio Sánchez Herguedas ◽  
Adolfo Crespo Márquez ◽  
Francisco Rodrigo Muñoz

Abstract This paper describes the optimization of preventive maintenance (PM) over a finite planning horizon in a semi-Markov framework. In this framework, the asset may be operating, and providing income for the asset owner, or not operating and undergoing PM, or not operating and undergoing corrective maintenance following failure. PM is triggered when the asset has been operating for τ time units. A number m of transitions specifies the finite horizon. This system is described with a set of recurrence relations, and their z-transform is used to determine the value of τ that maximizes the average accumulated reward over the horizon. We study under what conditions a solution can be found, and for those specific cases the solution τ* is calculated. Despite the complexity of the mathematical solution, the result obtained allows the analyst to provide a quick and easy-to-use tool for practical application in many real-world cases. To demonstrate this, the method has been implemented for a case study, and its accuracy and practical implementation were tested using Monte Carlo simulation and direct calculation.


1999 ◽  
Vol 42 (2) ◽  
pp. 129-138 ◽  
Author(s):  
Andrew Baker

AbstractHecke operators are used to investigate part of the E2-term of the Adams spectral sequence based on elliptic homology. The main result is a derivation of Ext1 which combines use of classical Hecke operators and p-adic Hecke operators due to Serre.


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