A Lie algebraic criterion for non-existence of finite dimensionally computable filters

1989 ◽  
pp. 197-204 ◽  
Author(s):  
Daniel Ocone ◽  
Etienne Pardoux
Keyword(s):  
Algebraic Criterion

scholarly journals An algebraic criterion for the ultraviolet finiteness of quantum field theories

2001 ◽  
Vol 34 (44) ◽  
pp. 9485-9505 ◽  
Author(s):  
V E R Lemes ◽  
M S Sarandy ◽  
S P Sorella ◽  
O S Ventura ◽  
L C Q Vilar
Keyword(s):  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Algebraic Criterion

scholarly journals An Algebraic Criterion of Zero Solutions of Some Dynamic Systems

2012 ◽  
Vol 2012 ◽  
pp. 1-13
Author(s):  
Ying Wang ◽  
Baodong Zheng ◽  
Chunrui Zhang
Keyword(s):  
Dynamic Systems ◽  
Real Coefficient ◽  
Coupled Systems ◽  
Decomposition Technique ◽  
Exponential Polynomials ◽  
Basic Theorem ◽  
Algebraic Criterion ◽  
The Stability

We establish some algebraic results on the zeros of some exponential polynomials and a real coefficient polynomial. Based on the basic theorem, we develop a decomposition technique to investigate the stability of two coupled systems and their discrete versions, that is, to find conditions under which all zeros of the exponential polynomials have negative real parts and the moduli of all roots of a real coefficient polynomial are less than 1.

An algebraic characterization of indistinguishable cardinals

1970 ◽  
Vol 35 (1) ◽  
pp. 97-104
Author(s):  
A. B. Slomson
Keyword(s):  
Second Order ◽  
Order Logic ◽  
Algebraic Characterization ◽  
Algebraic Criterion ◽  
Characterizable Cardinals ◽  
Second Order Logic ◽  
Interesting Theorem ◽  
Straightforward Proof

Two cardinals are said to beindistinguishableif there is no sentence of second order logic which discriminates between them. This notion, which is defined precisely below, is closely related to that ofcharacterizablecardinals, introduced and studied by Garland in [3]. In this paper we give an algebraic criterion for two cardinals to be indistinguishable. As a consequence we obtain a straightforward proof of an interesting theorem about characterizable cardinals due to Zykov [6].

Determination of Nonchaotic Behavior for Some Classes of Polynomial Jerk Equations

2020 ◽  
Vol 30 (08) ◽  
pp. 2050117
Author(s):  
Marcelo Messias ◽  
Rafael Paulino Silva
Keyword(s):  
Mathematical Model ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Simple Form ◽  
Chaotic Dynamics ◽  
Third Order ◽  
Algebraic Criterion

In this work, by using an algebraic criterion presented by us in an earlier paper, we determine the conditions on the parameters in order to guarantee the nonchaotic behavior for some classes of nonlinear third-order ordinary differential equations of the form [Formula: see text] called jerk equations, where [Formula: see text] is a polynomial of degree [Formula: see text]. This kind of equation is often used in literature to study chaotic dynamics, due to its simple form and because it appears as mathematical model in several applied problems. Hence, it is an important matter to determine when it is chaotic and also nonchaotic. The results stated here, which are proved using the mentioned algebraic criterion, corroborate and extend some results already presented in literature, providing simpler proofs for the nonchaotic behavior of certain jerk equations. The algebraic criterion proved by us is quite general and can be used to study nonchaotic behavior of other types of ordinary differential equations.

On the Distribution of Limit Cycles in a Liénard System with a Nilpotent Center and a Nilpotent Saddle

2016 ◽  
Vol 26 (02) ◽  
pp. 1650025 ◽  
Author(s):  
R. Asheghi ◽  
A. Bakhshalizadeh
Keyword(s):  
Limit Cycles ◽  
Upper Bound ◽  
Integral Formula ◽  
Abelian Integral ◽  
Liénard System ◽  
Algebraic Criterion ◽  
Period Annulus ◽  
Lienard System ◽  
Nilpotent Center ◽  
Nilpotent Saddle

In this work, we study the Abelian integral [Formula: see text] corresponding to the following Liénard system, [Formula: see text] where [Formula: see text], [Formula: see text] and [Formula: see text] are real bounded parameters. By using the expansion of [Formula: see text] and a new algebraic criterion developed in [Grau et al., 2011], it will be shown that the sharp upper bound of the maximal number of isolated zeros of [Formula: see text] is 4. Hence, the above system can have at most four limit cycles bifurcating from the corresponding period annulus. Moreover, the configuration (distribution) of the limit cycles is also determined. The results obtained are new for this kind of Liénard system.

scholarly journals Sharp Bound of the Number of Zeros for a Liénard System with a Heteroclinic Loop

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Junning Cai ◽  
Minzhi Wei ◽  
Guoping Pang
Keyword(s):  
Limit Cycles ◽  
Upper Bound ◽  
Sharp Bound ◽  
Abelian Integral ◽  
Heteroclinic Loop ◽  
Liénard System ◽  
Algebraic Criterion ◽  
Number Of Zeros ◽  
Lienard System ◽  
Nilpotent Saddle

In the presented paper, the Abelian integral I h of a Liénard system is investigated, with a heteroclinic loop passing through a nilpotent saddle. By using a new algebraic criterion, we try to find the least upper bound of the number of limit cycles bifurcating from periodic annulus.

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