Current work and open problems in the numerical analysis of Volterra functional equations with vanishing delays

2009 ◽  
Vol 4 (1) ◽  
pp. 3-22 ◽  
Author(s):  
Hermann Brunner
Keyword(s):  
Numerical Analysis ◽  
Functional Equations ◽  
Current Work ◽  
Open Problems

Iteration Theory: Dynamical Systems and Functional Equations

2003 ◽  
Vol 13 (07) ◽  
pp. 1627-1647 ◽  
Author(s):  
F. Balibrea ◽  
L. Reich ◽  
J. Smítal
Keyword(s):  
Dynamical Systems ◽  
Functional Equations ◽  
Discrete Dynamical Systems ◽  
Iteration Theory ◽  
Open Problems ◽  
Research Directions ◽  
The Past ◽  
New Research

The aim of this paper is to give an account of some problems considered in the past years in the setting of Discrete Dynamical Systems and Iterative Functional Equations, some new research directions and also state some open problems.

scholarly journals Some functional equations characterizing polynomials

2009 ◽  
Vol 44 (1) ◽  
pp. 27-40
Author(s):  
Barbara Koclęga-Kulpa ◽  
Tomasz Szostok ◽  
Szymon Wąsowicz
Keyword(s):  
Numerical Analysis ◽  
Functional Equations ◽  
Integral Domain ◽  
Quadrature Rule ◽  
All Solutions

Abstract We present a method of solving functional equations of the type where f, F: P → P are unknown functions acting on an integral domain P and parameteres are given. We prove that under some assumptions on the parameters involved, all solutions to such kind of equations are polynomials. We use this method to solve some concrete equations of this type. For example, the equation (1) for f, F: ℝ → ℝ is solved without any regularity assumptions. It is worth noting that (1) stems from a well-known quadrature rule used in numerical analysis.

Functional equations stemming from numerical analysis

2015 ◽  
Vol 508 ◽  
pp. 1-57 ◽  
Author(s):  
Tomasz Szostok
Keyword(s):  
Numerical Analysis ◽  
Functional Equations

Three Open Problems in Functional Equations

1995 ◽  
Vol 102 (8) ◽  
pp. 741-742 ◽  
Author(s):  
P. K. Sahoo
Keyword(s):  
Functional Equations ◽  
Open Problems

Three Open Problems in Functional Equations

1995 ◽  
Vol 102 (8) ◽  
pp. 741 ◽  
Author(s):  
P. K. Sahoo
Keyword(s):  
Functional Equations ◽  
Open Problems

Impairment Tutorial: Rating Facial Disfigurement After an Injury

1998 ◽  
Vol 3 (4) ◽  
pp. 6-6
Author(s):  
Marc T. Taylor
Keyword(s):  
Current Work ◽  
Workers Compensation ◽  
Loss Of Function ◽  
Facial Disfigurement ◽  
Work Related ◽  
Work Related Injury ◽  
Compensation Claim ◽  
Impairment Ratings

Abstract This article discusses two important cases that involve the AMA Guides to the Evaluation of Permanent Impairment (AMA Guides). First, in Vargas v Industrial Com’n of Arizona, a claimant had a pre-existing non–work-related injury to his right knee as well as a work-related injury, and the issue was apportionment of the pre-existing injury. The court held that, under Arizona's statute, the impairment from the pre-existing injury should be subtracted from the current work-related impairment. In the second case, Colorado courts addressed the issue of apportionment in a workers’ compensation claim in which the pre-existing injury was asymptomatic at the time of the work-related injury (Askey v Industrial Claim Appeals Office). In this case, the court held that the worker's benefits should not be reduced to account for an asymptomatic pre-existing condition that could not be rated accurately using the AMA Guides. The AMA Guides bases impairment ratings on anatomic or physiologic loss of function, and if an examinee presents with two or more sequential injuries and calculable impairments, the AMA Guides can be used to apportion between pre-existing and subsequent impairments. Courts often use the AMA Guides to decide statutorily determined benefits and are subject to interpretation by courts and administrative bodies whose interpretations may vary from state to state.

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