Representation of an infinitely diff erentiable function as a sum of functions belonging to quasianalytic classes

1980 ◽  
Vol 31 (3) ◽  
pp. 227-233
Author(s):  
V. G. Khryptun
Keyword(s):  
Erentiable Function ◽  
Sum Of Functions

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.

When a Sum of Functions Is Increasing: 10768

2001 ◽  
Vol 108 (1) ◽  
pp. 82
Author(s):  
Sung Soo Kim ◽  
Mark D. Meyerson
Keyword(s):  
Sum Of Functions

scholarly journals Different type parameterized inequalities via generalized integral operators with applications

2021 ◽  
Vol 66 (3) ◽  
pp. 423-440
Author(s):  
Artion Kashuri ◽  
Rozana Liko
Keyword(s):  
Integral Operator ◽  
Integral Operators ◽  
Integral Inequalities ◽  
Fractional Integrals ◽  
Recent Past ◽  
Special Means ◽  
Special Cases ◽  
Type Integral ◽  
Erentiable Function ◽  
Almost All

"The authors have proved an identity for a generalized integral operator via di erentiable function with parameters. By applying the established identity, the generalized trapezium, midpoint and Simpson type integral inequalities have been discovered. It is pointed out that the results of this research provide integral inequalities for almost all fractional integrals discovered in recent past decades. Various special cases have been identi ed. Some applications of presented results to special means and new error estimates for the trapezium and midpoint quadrature formula have been analyzed. The ideas and techniques of this paper may stimulate further research in the eld of integral inequalities."

Accelerated Gradient Sliding for Minimizing a Sum of Functions

2020 ◽  
Vol 101 (3) ◽  
pp. 244-246
Author(s):  
D. M. Dvinskikh ◽  
S. S. Omelchenko ◽  
A. V. Gasnikov ◽  
A. I. Tyurin
Keyword(s):  
Accelerated Gradient ◽  
Sum Of Functions

Static Friction in a Robot Joint—Modeling and Identification of Load and Temperature Effects

2012 ◽  
Vol 134 (5) ◽  
Author(s):  
André Carvalho Bittencourt ◽  
Svante Gunnarsson
Keyword(s):  
Static Friction ◽  
Joint Modeling ◽  
Friction Model ◽  
Load Torque ◽  
Complex Interactions ◽  
Proposed Model ◽  
Friction Models ◽  
Interacting Surfaces ◽  
Sum Of Functions ◽  
Wide Operating

Friction is the result of complex interactions between contacting surfaces in down to a nanoscale perspective. Depending on the application, the different models available are more or less suitable. Static friction models are typically considered to be dependent only on relative speed of interacting surfaces. However, it is known that friction can be affected by other factors than speed. In this paper, the typical friction phenomena and models used in robotics are reviewed. It is shown how such models can be represented as a sum of functions of relevant states which are linear and nonlinear in the parameters, and how the identification method described in Ref. [1] can be used to identify them when all states are measured. The discussion follows with a detailed experimental study of friction in a robot joint under changes of joint angle, load torque, and temperature. Justified by their significance, load torque and temperature are included in an extended static friction model. The proposed model is validated in a wide operating range, considerably improving the prediction performance compared to a standard model.

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