The shift equivalence problem

1999 ◽  
Vol 21 (4) ◽  
pp. 18-29 ◽  
Author(s):  
K. H. Kim ◽  
F. W. Roush ◽  
J. B. Wagoner
Keyword(s):  
Equivalence Problem ◽  
Shift Equivalence

scholarly journals Shift Equivalence of P-finite Sequences

10.37236/1126 ◽  
2006 ◽  
Vol 13 (1) ◽  
Author(s):  
Manuel Kauers
Keyword(s):  
Equivalence Problem ◽  
Recurrence Equation ◽  
The Other ◽  
Linear Recurrence ◽  
Initial Values ◽  
Polynomial Coefficients ◽  
Shift Equivalence ◽  
Finite Sequences ◽  
Homogeneous Linear

We present an algorithm which decides the shift equivalence problem for P-finite sequences. A sequence is called P-finite if it satisfies a homogeneous linear recurrence equation with polynomial coefficients. Two sequences are called shift equivalent if shifting one of the sequences $s$ times makes it identical to the other, for some integer $s$. Our algorithm computes, for any two P-finite sequences, given via recurrence equation and initial values, all integers $s$ such that shifting the first sequence $s$ times yields the second.

Equivalence problem of Mann and Ishikawa Iterations in Banach Spaces

2011 ◽  
Vol 12 (3) ◽  
pp. 279-288
Author(s):  
Shuang WANG ◽  
Guoqing CHAI ◽  
Changsong HU
Keyword(s):  
Banach Spaces ◽  
Equivalence Problem

Multiple Regularity and Binary ETOL-Systems1

1981 ◽  
Vol 4 (1) ◽  
pp. 19-34
Author(s):  
Ryszard Danecki
Keyword(s):  
Equivalence Problem ◽  
Tree Automata ◽  
Closure Properties ◽  
Multiple Tree

Closure properties of binary ETOL-languages are investigated by means of multiple tree automata. Decidability of the equivalence problem of deterministic binary ETOL-systems is proved.

scholarly journals Equivalence problem for the orthogonal webs on the 3-sphere

2011 ◽  
Vol 52 (5) ◽  
pp. 053509 ◽  
Author(s):  
Caroline M. Cochran ◽  
Raymond G. McLenaghan ◽  
Roman G. Smirnov
Keyword(s):  
Equivalence Problem

The Geometry of d2y1/dt2 = f (y, ẏ, t) and d2y2/dt2 = g(y, ẏ, t), and Euclidean Spaces

2006 ◽  
Vol 49 (2) ◽  
pp. 170-184
Author(s):  
Richard Atkins
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Shortest Paths ◽  
Equivalence Problem ◽  
Second Order ◽  
System Of Differential Equations ◽  
Lagrange Equations ◽  
Invariant Functions ◽  
Underlying Geometry ◽  
The Relationship

AbstractThis paper investigates the relationship between a system of differential equations and the underlying geometry associated with it. The geometry of a surface determines shortest paths, or geodesics connecting nearby points, which are defined as the solutions to a pair of second-order differential equations: the Euler–Lagrange equations of the metric. We ask when the converse holds, that is, when solutions to a system of differential equations reveals an underlying geometry. Specifically, when may the solutions to a given pair of second order ordinary differential equations d2y1/dt2 = f (y, ẏ, t) and d2y2/dt2 = g(y, ẏ, t) be reparameterized by t → T(y, t) so as to give locally the geodesics of a Euclidean space? Our approach is based upon Cartan's method of equivalence. In the second part of the paper, the equivalence problem is solved for a generic pair of second order ordinary differential equations of the above form revealing the existence of 24 invariant functions.

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