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Equivalence of Different Hereditary Structures in Ordinary Differential Equations

1998
*
Journal of Differential Equations
*

We prove that different formulations of

doi:10.1006/jdeq.1998.3461
fatcat:ow6mixacnffndccvut7mqecwua
*hereditary*settings for ordinary*differential*systems, which appeared not comparable, are actually equivalent. ... Academic Press This formulation was extended to different directions; we recall, for example, the following*hereditary**structures*, where g(t, x) t [11]; x$(t)= f \ t, | E t h(s, x(s)) ds + (b) article ... (P 2 ) As the authors remark*in*[3] , this abstract formulation includes and unifies many classes of*hereditary**differential**equations*which are applied*in*various fields (see, e.g., [11, 17, 12, 10] ...##
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The Lie Algebra Structure of Nonlinear Evolution Equations Admitting Infinite Dimensional Abelian Symmetry Groups

1981
*
Progress of theoretical physics
*

861

doi:10.1143/ptp.65.861
fatcat:s53xaxqvb5hz5cesgrphjzig7e
*Hereditary*operators*in*Lie algebras are investigated. ...*In*order to construct new*hereditary*operators out of given ones we study the permanence properties of these operators; this study of permanence properties leads*in*a natural way to a notion of compatibility ... Here the linear dependence*in*A is rather special. And, of course, there is a more general*structure*having linear deformations as tangential*structure*. ...##
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Computer-algebra methods for investigation of hereditary operators of higher order soliton equations

1987
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Computer Physics Communications
*

The

doi:10.1016/0010-4655(87)90015-4
fatcat:gvbgflm3djbctj27oo52roytge
*hereditariness*of recursion operators is discussed for some 5th order nonlinear partial*differential**equations*as well as for several coupled systems. ... Consequences of the*hereditary*property are surveyed. An outline of the corresponding computer algebra proofs (based on the formula manipulation systems MAPLE and MACSYMA) is given. ...*differential**equation**in*infinitely many independent variables). ...##
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Page 5654 of Mathematical Reviews Vol. , Issue 97I
[page]

1997
*
Mathematical Reviews
*

He starts his considerations by defining

*hereditary**structures**in*more or less arbitrary algebraic*structures*such that the crucial re- sults about generating abelian substructures out of one or several ... The author wants to show that, under suitable modification, no- tions such as compatible,*hereditary*, invariance and Virasoro alge- bra, which play a crucial role*in*the*structure*theory of integrable ...##
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Vibration analysis of airfoil on hereditary deformable suspensions

2019
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E3S Web of Conferences
*

The model is based on two-degree-of-freedom

doi:10.1051/e3sconf/20199706006
fatcat:evsl7pzhrrbc7d6f4qks7462fq
*structure**in*geometrically nonlinear statements. ... With a combination of the Galerkin and the presented method, problems of nonlinear vibrations and dynamic stability*in*viscoelastic two-degree-of-freedom*structure*have been solved. ... The general procedure of solution of the nonlinear integro-*differential**equations*for an airfoil with*hereditary*-deformable suspensions is formulated and analyzed. ...##
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Tensor Equations of Discrete Dynamically Defined and Undefined Systems with Hereditary and Creep Light Elements

2010
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Annals of the Alexandru Ioan Cuza University - Mathematics
*

*In*this paper we shall present basic

*structures*of a series hybrid systems as well as tensor

*equations*of discrete dynamically defined and undefined discrete systems with

*hereditary*and creep light elements ...

*Equations*of dynamics of a discrete

*hereditary*system with finite number of the constraints and standard creep elements

*in*covariant form are composed. ...

*In*the tensor covariant form for discrete

*hereditary*system expressed by generalized coordinates, these

*differential*

*equations*are not possible to obtain

*in*every case. ...

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Page 6110 of Mathematical Reviews Vol. , Issue 99i
[page]

1999
*
Mathematical Reviews
*

The authors consider three different abstract notions of ordinary

*differential**equations*with a*hereditary**structure*that have ap- peared*in*the literature. ... Hausrath (1-BOISE; Boise, ID) 99i:34102 34K15 34C99 34K25 Mareelli, Cristina (I-PERG; Perugia) ; Salvadori, Anna (I-PERG; Perugia) Equivalence of different*hereditary**structures**in*ordinary*differential*...##
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MULTIPERIODIC SOLUTIONS OF LINEAR SYSTEMS INTEGRO-DIFFERENTIAL EQUATIONS WITH cD -OPERATOR AND -PERIOD OF HEREDITARY

2020
*
Izvestiâ Nacionalʹnoj akademii nauk Respubliki Kazahstan. Seriâ fiziko-matematičeskaâ
*

Integro-

doi:10.32014/2020.2518-1726.3
fatcat:j7kiwy3apfapfmzqawd4tn5joy
*differential**equations*describing phenomena with such*hereditary*effects are considered*in*[3] . ...*equations*with a special D c operator*in*partial*differential*, *hereditary*effect and the linear integral operator. ...*In*order for the system of integro-*differential**equations*(3.1) has no multiperiodic solutions, except for the zero one under the conditions of theorem 3.4, the fulfillment of condition (3.17 Linear ...##
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Page 433 of Mathematical Reviews Vol. , Issue 90A
[page]

1990
*
Mathematical Reviews
*

This

*structure*seems somewhat insufficient to handle the problems by itself, since the author uses the (stronger) concept of a “*hereditary*symmetry” [B. ... which arise*in**differential*geometry rather than*in*physics. ...##
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Analysis of Numerical Solutions of a Hereditary Deformable System

2018
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International Journal of Mechanical and Production Engineering Research and Development
*

The pure vertical motion of an air-cushion

doi:10.24247/ijmperdaug201842
fatcat:65u6s2t4v5hfhnhbo6sal4yxky
*structure*is investigated using a non-linear mathematical model; this incorporates a simple model to account the*hereditary*deformable characteristic of the material ... A numerical investigation was conducted to determine the vertical response characteristic of an open plenum aircushion*structure*. ... The constitutive relation (stress-strain) was used*in*form of a*hereditary*law with the relation kernel represented by Abelian type function. ...##
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Fractional order state equations for the control of viscoelasticallydamped structures

1991
*
Journal of Guidance Control and Dynamics
*

The

doi:10.2514/3.20641
fatcat:ejzyna67rja6rketvtsujd5tqa
*hereditary*nature of the*structural**equations*suppresses the existence of homogeneous solutions found*in*the state*equations*. ... This is necessary for heavily damped*structures*.*In*lightly damped*structures*the*hereditary*effects are much smaller, and the pseudoforces may be ignored. ...##
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Page 4455 of Mathematical Reviews Vol. , Issue 92h
[page]

1992
*
Mathematical Reviews
*

The author discusses relations between

*structures*appearing*in*conformal field theory and hierarchies of integrable*differential**equations*. ... Lie theory,*differential**equations*and representation theory (Montreal, PQ, 1989), 309-320, Univ. Montréal, Montreal, PQ, 1990. ...##
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Page 226 of Mathematical Reviews Vol. , Issue 2002A
[page]

2002
*
Mathematical Reviews
*

.,
Providence, RI, 2001

*In*this paper, the authors study a class of functional-*differential**equations*whose*hereditary**structure*is induced by a Volterra-type property. ... Explicit tests for convergence of all its solutions (for f — +00) are proved.” 2002a:34097 34K05 Ceppitelli, Rita (I-PERG; Perugia); Faina, Loris (I-PERG; Perugia*Differential**equations*with*hereditary*...##
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Page 329 of Mathematical Reviews Vol. 27, Issue 2
[page]

1964
*
Mathematical Reviews
*

The

*structure*of these examples is such that one or more periodic solutions is possible. No attempt has been made to present a general theory of periodic solutions*in*irreducible*hereditary*systems. ... Schaffer (Montevideo) Hale, Jack K. 1670 On*differential**equations*containing a small parameter. Contributions to*Differential**Equations*1 (1963), 215- 250. ...##
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Page 326 of Mathematical Reviews Vol. 37, Issue 2
[page]

1969
*
Mathematical Reviews
*

Stephen 1739

*Hereditary**structure**in**differential**equations*. Math. Systems Theory 1 (1967), 263-278. Let Q denote the set of all closed subsets of R which are bounded above. ... A general*differential**equation*of*hereditary*type may be expressed*in*the form #(t)= F(t, x(a,(z(t)))), where F is a suitably defined n-vector functional. ...
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