A representation of the Peano kernel for some quadrature rules and applications

2006 ◽  
Vol 462 (2073) ◽  
pp. 2817-2832 ◽  
Author(s):  
Josip Pečarić ◽  
Nenad Ujević
Keyword(s):  
Quadrature Rules ◽  
Closed Type ◽  
Interpolating Polynomials ◽  
Effective Representation ◽  
Peano Kernel

A general interpolating formula is established. From this formula all Newton–Cotes quadrature rules of the closed type can be derived. Some corrected interpolating polynomials are also derived and used for obtaining corresponding quadrature rules. A new effective representation of the Peano kernel is derived. Estimation of errors for these quadrature rules is established.

The first kind Chebyshev–Newton–Cotes quadrature rules (closed type) and its numerical improvement

2005 ◽  
Vol 168 (1) ◽  
pp. 479-495 ◽  
Author(s):  
M.R. Eslahchi ◽  
Mehdi Dehghan ◽  
M. Masjed-Jamei
Keyword(s):  
Quadrature Rules ◽  
Closed Type

Modelling Gas Processing Unit: An Inter-disciplinary Approach Based on Petri Nets

2008 ◽  
Vol 59 (7) ◽  
Author(s):  
Sanda Florentina Mihalache
Keyword(s):  
Industrial Process ◽  
Industrial Processes ◽  
Processing Unit ◽  
Industrial System ◽  
Modeling Framework ◽  
Gas Processing ◽  
Human Interactions ◽  
Modelling Method ◽  
Effective Representation ◽  
Modelling Approach

A modelling approach that will facilitate an in-depth understanding of the interactions of the different phenomena, human interactions and environmental factors constituting �real world� industrial processes is presented. An important industrial system such as Gas Processing Unit (GPU) have inter-related internal process activities coexisting with external events and requires a real time inter-disciplinary approach to model them. This modeling framework is based on identifying as modules, the part of processes that have interactions and can be considered active participants in overall behaviour. The selected initial set of modules are structured as Petri net models and made to interact iteratively to provide process states of the system. The modeling goal is accomplished by identifying the evolution of the process states as a means of effective representation of the �actual running�� of the industrial process. The paper discusses the function and the implementation of the modelling method as applicable to the industrial case of GPU.

scholarly journals Closed type families with overlapping equations

2014 ◽  
Vol 49 (1) ◽  
pp. 671-683 ◽  
Author(s):  
Richard A. Eisenberg ◽  
Dimitrios Vytiniotis ◽  
Simon Peyton Jones ◽  
Stephanie Weirich
Keyword(s):  
Closed Type

scholarly journals On Appel-Type Quadrature Rules

2002 ◽  
Vol 9 (3) ◽  
pp. 405-412
Author(s):  
C. Belingeri ◽  
B. Germano
Keyword(s):  
Remainder Term ◽  
Quadrature Rule ◽  
Bernoulli Numbers ◽  
Quadrature Rules ◽  
Rule Based ◽  
Numerical Example ◽  
The Given ◽  
Derivatives Of

Abstract The Radon technique is applied in order to recover a quadrature rule based on Appel polynomials and the so called Appel numbers. The relevant formula generalizes both the Euler-MacLaurin quadrature rule and a similar rule using Euler (instead of Bernoulli) numbers and even (instead of odd) derivatives of the given function at the endpoints of the considered interval. In the general case, the remainder term is expressed in terms of Appel numbers, and all derivatives appear. A numerical example is also included.

The role of Digitally Reconstructed Radiographs in the verification process

1999 ◽  
Vol 1 (3) ◽  
pp. 103-108 ◽  
Author(s):  
N. S. Stanley
Keyword(s):  
Digital Imaging ◽  
Digitally Reconstructed Radiographs ◽  
Verification Methods ◽  
Digital Imaging Technology ◽  
Potential Impact ◽  
Portal Images ◽  
Verification Process ◽  
Effective Representation ◽  
Radiotherapy Treatment

This article reviews the development and potential impact of Digitally Reconstructed Radiographs (DRR's) in the planning and verification of radiotherapy treatments. It explores the requirements for the creation of usable DRR's their integration into current verification methods and it highlights some of the factors that may influence the routine use of DRR's. Continuing developments in radiotherapy techniques demand increasingly accurate verification methods. DRR's provide an efficient and effective representation of planned treatments for comparison with both simulator and portal images, encompassing the digital imaging technology which is the future of radiotherapy treatment verification.

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