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Equivalence of Different Hereditary Structures in Ordinary Differential Equations

Cristina Marcelli, Anna Salvadori
1998 Journal of Differential Equations  
We prove that different formulations of 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]  ... 
doi:10.1006/jdeq.1998.3461 fatcat:ow6mixacnffndccvut7mqecwua

The Lie Algebra Structure of Nonlinear Evolution Equations Admitting Infinite Dimensional Abelian Symmetry Groups

B. Fuchssteiner
1981 Progress of theoretical physics  
861 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.  ... 
doi:10.1143/ptp.65.861 fatcat:s53xaxqvb5hz5cesgrphjzig7e

Computer-algebra methods for investigation of hereditary operators of higher order soliton equations

Benno Fuchssteiner, Walter Oevel, Waldemar Wiwianka
1987 Computer Physics Communications  
The 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).  ... 
doi:10.1016/0010-4655(87)90015-4 fatcat:gvbgflm3djbctj27oo52roytge

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  ... 

Vibration analysis of airfoil on hereditary deformable suspensions

Botir Usmonov, Quvvatali Rakhimov, A. Volkov, A. Pustovgar, T. Sultanov, A. Adamtsevich
2019 E3S Web of Conferences  
The model is based on two-degree-of-freedom 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.  ... 
doi:10.1051/e3sconf/20199706006 fatcat:evsl7pzhrrbc7d6f4qks7462fq

Tensor Equations of Discrete Dynamically Defined and Undefined Systems with Hereditary and Creep Light Elements

Katica Hedrih
2010 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.  ... 
doi:10.2478/v10157-010-0009-5 fatcat:vljb3tcuhvfunocjk3hurnqw6a

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  ... 

MULTIPERIODIC SOLUTIONS OF LINEAR SYSTEMS INTEGRO-DIFFERENTIAL EQUATIONS WITH cD -OPERATOR AND  -PERIOD OF HEREDITARY

Zh.А. Sartabanov, K. Zhubanov Aktobe Regional State University, Doctor of Physical and Mathematical Sciences, Professor, sartabanov42@mail.ru, https://orcid.org/0000-0003-2601-2678, G.M.Aitenova, K.Zhubanov Aktobe Regional State University, PhD-student, gulsezim-88@mail.ru, https://orcid.org/0000-0002-4572-8252
2020 Izvestiâ Nacionalʹnoj akademii nauk Respubliki Kazahstan. Seriâ fiziko-matematičeskaâ  
Integro-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  ... 
doi:10.32014/2020.2518-1726.3 fatcat:j7kiwy3apfapfmzqawd4tn5joy

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.  ... 

Analysis of Numerical Solutions of a Hereditary Deformable System

Botir Usmonov et al., Botir Usmonov et al.,
2018 International Journal of Mechanical and Production Engineering Research and Development  
The pure vertical motion of an air-cushion 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.  ... 
doi:10.24247/ijmperdaug201842 fatcat:65u6s2t4v5hfhnhbo6sal4yxky

Fractional order state equations for the control of viscoelasticallydamped structures

R. L. BAGLEY, R. A. CALICO
1991 Journal of Guidance Control and Dynamics  
The 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.  ... 
doi:10.2514/3.20641 fatcat:ejzyna67rja6rketvtsujd5tqa

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.  ... 

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  ... 

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.  ... 

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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