Distribution of points for convergent interpolatory integration rules on (??, ?)

1993 ◽  
Vol 9 (1) ◽  
pp. 59-82 ◽  
Author(s):  
T. Bloom ◽  
D. S. Lubinsky ◽  
H. Stahl
Keyword(s):  
Distribution Of Points ◽  
Integration Rules

Finite-order Integration Weights Can be Dangerous

2007 ◽  
Vol 7 (3) ◽  
pp. 239-254 ◽  
Author(s):  
I.H. Sloan
Keyword(s):  
Function Space ◽  
Finite Order ◽  
Small Subset ◽  
Worst Case ◽  
Integration Rule ◽  
Dimensional Lattice ◽  
3 Dimensional ◽  
Sum Of Functions ◽  
Integration Rules

Abstract Finite-order weights have been introduced in recent years to describe the often occurring situation that multivariate integrands can be approximated by a sum of functions each depending only on a small subset of the variables. The aim of this paper is to demonstrate the danger of relying on this structure when designing lattice integration rules, if the true integrand has components lying outside the assumed finiteorder function space. It does this by proving, for weights of order two, the existence of 3-dimensional lattice integration rules for which the worst case error is of order O(N¯½), where N is the number of points, yet for which there exists a smooth 3- dimensional integrand for which the integration rule does not converge.

scholarly journals Distribution of points on Abelian covers over finite fields

2018 ◽  
Vol 14 (05) ◽  
pp. 1375-1401 ◽  
Author(s):  
Patrick Meisner
Keyword(s):  
Finite Fields ◽  
Galois Extension ◽  
Random Variables ◽  
Families Of Curves ◽  
Abelian Covers ◽  
Distribution Of Points ◽  
Genus Formula

We determine in this paper the distribution of the number of points on the covers of [Formula: see text] such that [Formula: see text] is a Galois extension and [Formula: see text] is abelian when [Formula: see text] is fixed and the genus, [Formula: see text], tends to infinity. This generalizes the work of Kurlberg and Rudnick and Bucur, David, Feigon and Lalin who considered different families of curves over [Formula: see text]. In all cases, the distribution is given by a sum of [Formula: see text] random variables.

Properties of Minimal Integration Rules. II

1971 ◽  
Vol 8 (3) ◽  
pp. 497-508 ◽  
Author(s):  
Nira Richter-Dyn
Keyword(s):  
Integration Rules

Acute activation and inactivation of macaque frontal eye field with GABA-related drugs

1995 ◽  
Vol 74 (6) ◽  
pp. 2744-2748 ◽  
Author(s):  
E. C. Dias ◽  
M. Kiesau ◽  
M. A. Segraves
Keyword(s):  
Injection Site ◽  
Rhesus Monkeys ◽  
Frontal Eye Field ◽  
Surgical Removal ◽  
Gamma Aminobutyric Acid ◽  
Eye Field ◽  
Distribution Of Points ◽  
Direction Opposite ◽  
Voluntary Saccades

1. This project tests the behavioral effects of reversible activation and inactivation of sites within the frontal eye field of rhesus monkeys with microinjections of the gamma-aminobutyric acid (GABA)-related drugs bicuculline and muscimol. 2. Muscimol injections impaired the monkeys' ability to make both visually and memory-guided saccades to targets at the center of the area represented by the injection site. The latencies of saccades to targets in regions flanking the injection were increased. For memory-guided saccades, saccades in the direction opposite to that represented by the injection site, were made with shorter latency than controls and often occurred before the movement cue. 3. Bicuculline injections produced irrepressible saccades equivalent to the saccade vector represented by the injection site, often in a staircase of several closely spaced movements. 4. Both substances decreased the accuracy of fixation of a central light. The distribution of points of fixation on different trials was diffuse, and the angle of gaze tended to deviate towards the side of the injection. 5. The results of these acute injections are similiar to those observed in the superior colliculus and are much more substantial than the effects observed in the long term after surgical removal of the frontal eye field. The results of this study promote a central role for the frontal eye field in the generation of all voluntary saccades and in the control of fixation.

scholarly journals Revisited Optimal Error Bounds for Interpolatory Integration Rules

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
François Dubeau
Keyword(s):  
Error Bounds ◽  
Error Term ◽  
Quadrature Rules ◽  
Optimal Error ◽  
Integration By Parts ◽  
Integration Rules

We present a unified way to obtain optimal error bounds for general interpolatory integration rules. The method is based on the Peano form of the error term when we use Taylor’s expansion. These bounds depend on the regularity of the integrand. The method of integration by parts “backwards” to obtain bounds is also discussed. The analysis includes quadrature rules with nodes outside the interval of integration. Best error bounds for composite integration rules are also obtained. Some consequences of symmetry are discussed.

Towards Public Services and Process Integration

2013 ◽  
pp. 275-287
Author(s):  
Guillermo Infante Hernández ◽  
Aquilino A. Juan Fuente ◽  
Benjamín López Pérez ◽  
Edward Rolando Núñez-Valdéz
Keyword(s):  
Process Model ◽  
Public Services ◽  
Process Integration ◽  
Domain Specific ◽  
Modeling Environment ◽  
Proposed Model ◽  
Domain Specific Modeling ◽  
Hardware Platforms ◽  
Business Requirements ◽  
Integration Rules

Software platforms for e-government transactions may differ in developed functionalities, languages and technologies, hardware platforms, and operating systems that support them. Those differences can be found among public organizations that share common processes, services, and regulations. This scenario hinders interoperability between these organizations. Hence, to find a technique for integrating these platforms becomes a necessity. In this chapter, a rule-based domain-specific modeling environment for public services and process integration is suggested, which consists of common identified public service elements and a set of process integration rules. This approach provides the needed integration or interoperability pursued in this domain. Furthermore a service and process model is proposed to formalize the information needed for integration of both. A set of integration rules is also presented as part of the modeling environment. This set of integration rules completes the proposed model to meet the business requirements of this domain.

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