Recurrence relations for the number of labeled structures on a finite set

1984 ◽  
pp. 43-61 ◽  
Author(s):  
Chr. Blatter ◽  
E. Specker
Keyword(s):  
Recurrence Relations ◽  
Finite Set

On the semigroups of order-decreasing finite full transformations

1992 ◽  
Vol 120 (1-2) ◽  
pp. 129-142 ◽  
Author(s):  
Abdullahi Umar
Keyword(s):  
Recurrence Relations ◽  
Transformation Semigroup ◽  
Stirling Number ◽  
Abundant Semigroup ◽  
Full Transformation ◽  
Full Transformation Semigroup ◽  
Finite Set ◽  
Image Position

SynopsisLet Singn be the subsemigroup of singular elements of the full transformation semigroup on a totally ordered finite set with n elements. Let be the subsemigroup of all decreasing maps of Singn. In this paper it is shown that is a non-regular abundant semigroup with n − 1 -classes and . Moreover, is idempotent-generated and it is generated by the n(n − 1)/2 idempotents in J*n−1. LetandSome recurrence relations satisfied by J*(n, r) and sh (n, r) are obtained. Further, it is shown that sh (n, r) is the complementary signless (or absolute) Stirling number of the first kind.

Zeros of pseudo-ultraspherical polynomials

2014 ◽  
Vol 12 (05) ◽  
pp. 563-581 ◽  
Author(s):  
Kathy Driver ◽  
Martin E. Muldoon
Keyword(s):  
Weight Function ◽  
Explicit Expression ◽  
Comparison Theorem ◽  
Recurrence Relations ◽  
Ultraspherical Polynomial ◽  
Real Zeros ◽  
Ultraspherical Polynomials ◽  
Simple Zeros ◽  
Finite Set ◽  
Polynomial Formula

The pseudo-ultraspherical polynomial of degree n can be defined by [Formula: see text] where [Formula: see text] is the ultraspherical polynomial. It is known that when λ < -n, the finite set [Formula: see text] is orthogonal on (-∞, ∞) with respect to the weight function (1 + x2)λ-½ and when λ < 1 - n, the polynomial [Formula: see text] has exclusively real and simple zeros. Here, we undertake a deeper study of the zeros of these polynomials including bounds, numbers of real zeros, monotonicity and interlacing properties. Our methods include the Sturm comparison theorem, recurrence relations, and the explicit expression for the polynomials.

Existence of a pair of new recurrence relations for the Meixner-Pollaczek polynomials

2018 ◽  
Vol 11 (3) ◽  
pp. 29-39
Author(s):  
E. I. Jafarov ◽  
A. M. Jafarova ◽  
S. M. Nagiyev
Keyword(s):  
Recurrence Relations ◽  
Pollaczek Polynomials

COMMUNICATION OF COMMON AND MARGINAL CHARACTERISTICS OF CONDITIONS IN A TWO-CHANNEL SYSTEM WITH SIMPLE STREAMLINES OF APPLICATIONS

2017 ◽  
pp. 7-19 ◽  
Author(s):  
Georgiy Aleksandrovich Popov
Keyword(s):  
Operating Systems ◽  
Queue Length ◽  
Recurrence Relations ◽  
Queuing Systems ◽  
Channel System ◽  
Current Period ◽  
Multichannel Systems ◽  
Incoming Call ◽  
Marginal Values ◽  
Time Required

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.

New family of Whitney numbers

Filomat ◽  
2017 ◽  
Vol 31 (2) ◽  
pp. 309-320 ◽  
Author(s):  
B.S. El-Desouky ◽  
Nenad Cakic ◽  
F.A. Shiha
Keyword(s):  
Generating Functions ◽  
Recurrence Relations ◽  
Stirling Numbers ◽  
Explicit Formulas ◽  
Basic Properties ◽  
New Family ◽  
Whitney Numbers ◽  
Special Cases

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.

Non-repetitive sequences

1970 ◽  
Vol 68 (2) ◽  
pp. 267-274 ◽  
Author(s):  
P. A. B. Pleasants
Keyword(s):  
Repetitive Sequences ◽  
Finite Set ◽  
Infinite Sequences

This note is concerned with infinite sequences whose terms are chosen from a finite set of symbols. A segment of such a sequence is a set of one or more consecutive terms, and a repetition is a pair of finite segments that are adjacent and identical. A non-repetitive sequence is one that contains no repetitions.

The inverse problem of recovering the coefficients of a differential equations on a graph

2020 ◽  
Vol 28 (5) ◽  
pp. 727-738
Author(s):  
Victor Sadovnichii ◽  
Yaudat Talgatovich Sultanaev ◽  
Azamat Akhtyamov
Keyword(s):  
Inverse Problem ◽  
Inverse Problems ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Finite Number ◽  
Characteristic Equation ◽  
Arbitrary Number ◽  
New Class ◽  
Finite Set

AbstractWe consider a new class of inverse problems on the recovery of the coefficients of differential equations from a finite set of eigenvalues of a boundary value problem with unseparated boundary conditions. A finite number of eigenvalues is possible only for problems in which the roots of the characteristic equation are multiple. The article describes solutions to such a problem for equations of the second, third, and fourth orders on a graph with three, four, and five edges. The inverse problem with an arbitrary number of edges is solved similarly.

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