[[Category:Dynamical systems and ergodic theory]]
1,020 bytes (154 words) - 19:16, 25 October 2014
The modern theory of linear inequalities has been constructed on the basis of this generaliza
...onomic technology and economic planning reduce to the solution of specific systems of linear inequalities; this has significantly determined the modern trend
14 KB (2,052 words) - 10:49, 21 March 2022
...t is hard to say whether field theory, the theory of finite groups and the theory of finite-dimensional Lie algebras should be regarded as general algebra.
...n 1916. Initially this reorientation concerned group theory, and then ring theory. The results of this reorientation are reflected in the monograph of B.L. v
5 KB (725 words) - 21:52, 30 March 2012
...s governing the structure, composition, dynamics, and evolution of stellar systems.
...acteristic problem in stellar kinematics is the solution of overdetermined systems of conditional equations, each equation being derived for an individual sta
9 KB (1,236 words) - 08:23, 6 June 2020
...concerning the qualitative behaviour of linear equations and second-order systems (see [[#References|[3]]], [[#References|[4]]]).
...ontrol|optimal control]], filtration, stabilization of controllable linear systems, etc. (see [[Control system|Control system]], and [[#References|[6]]], [[#R
8 KB (1,202 words) - 14:55, 7 June 2020
..., expressing the most general conditions for the equilibrium of mechanical systems interconnected by ideal constraints.
Condition (*) contains all the equations and equilibrium laws of systems with ideal constraints; it is therefore justifiable to say that the entire
5 KB (805 words) - 08:28, 6 June 2020
...ding of rules a derivation is defined in the Post canonical system. In the theory of calculi one uses the following definition of an enumerable set of words
...t specializations of the notion of a Post canonical system: 1) Post normal systems (all rules have the form
4 KB (601 words) - 14:35, 17 March 2023
Triorthogonal systems of surfaces are given by the systems of coordinate surfaces in an orthogonal curvilinear coordinate system of sp
...an ellipsoid. Spherical transformations are automorphisms of triorthogonal systems of surfaces in Euclidean space.
3 KB (517 words) - 19:56, 12 July 2014
...ced as an algebraic system which is a generalization both of the algebraic systems appearing in the metasymplectic geometry developed by H. Freudenthal and of
...tem]], it is useful in obtaining all Lie algebras, without the use of root systems and Cartan matrices.
8 KB (1,154 words) - 19:44, 27 February 2021
[[Category:Ergodic theory]]
In ergodic theory, properties related to mixing are considered: multiple mixing and weak mixi
5 KB (696 words) - 08:01, 6 June 2020
...of dynamical processes with memory requires the further development of the theory of functional equations with abstract Volterra operators. Numerous applicat
...equations involving classical integral operators of Volterra type when the theory is framed in abstract spaces, see [[#References|[a2]]], [[#References|[a7]]
5 KB (745 words) - 15:29, 13 July 2014
...valign="top"> A.M. Krall, "$M(\lambda)$ theory for singular Hamiltonian systems with one singular point" ''SIAM J. Math. Anal.'' , '''20''' (1989) pp. 6
3 KB (586 words) - 10:02, 15 June 2015
The theory of $ L $-
...the work of A. Lindenmayer, [[#References|[a1]]]. The original aim of this theory was to provide mathematical models for the development of simple filamentou
13 KB (1,968 words) - 18:43, 26 March 2023
...$ is a metric space, then $k\in\N$). The quotient spaces of many dynamical systems do not satisfy any of the separation axioms, even if $S$ does. For example,
...ion in topological dynamics" , ''Sem. Differential Equations and Dynamical Systems II'' , ''Lect. notes in math.'' , '''144''' , Springer (1970) pp. 79–89
4 KB (578 words) - 06:37, 22 April 2012
...i for any fixed $t\in\mathbf R$. These manifolds are widely encountered in systems of type \eqref{*} describing oscillatory processes.
...5]</TD> <TD valign="top"> Yu.A. Mitropol'skii, "Problems of the asymptotic theory of nonstationary vibrations" , D. Davey (1965) (Translated from Russian)</T
4 KB (624 words) - 17:09, 14 February 2020
...g five codimension-two bifurcations of equilibria in ordinary differential
systems [[#References|[a1]]], [[#References|[a5]]]:<table border="0" cellpadding="0
...olds in the parameter space of (a1). For example, in generic two-parameter
systems, codimension-two bifurcations happen at isolated points in the parameter pl
12 KB (1,485 words) - 13:18, 8 February 2020
...cal models of hysteresis and is convenient for the analysis of closed-loop systems with hysteresis non-linearities is presently (1996) under construction [[#R
In this theory, a hysteresis non-linearity is treated as a transducer, with an input, an o
4 KB (584 words) - 22:11, 5 June 2020
...fficient conditions for imbeddability, formulated in the language of graph theory (cf., for example, [[#References|[5]]]), are known.
...>[1]</TD> <TD valign="top"> A.I. Mal'tsev, "On inclusion of associative systems in a group" ''Mat. Sb.'' , '''6 (48)''' : 2 (1939) pp. 331–336 (In R
3 KB (457 words) - 12:04, 7 July 2024
...duction, $L$-systems constituted a significant part of [[formal language]] theory, allowing one to compare parallel rewriting to a more classical sequential
...d with these notions, in particular with D$0$L-sequences, which made D$0$L-systems mathematically very fruitful. The most famous problem is the D$0$L-sequence
10 KB (1,542 words) - 11:21, 26 March 2023
...edback system ensures stabilization of any process belonging to a class of systems. However, a precise and universal definition of adaptive control is still e
...1970s and early 1980s, when rigorous proofs for the stability of adaptive systems were presented. However, very soon a drawback was discovered. The existing
6 KB (870 words) - 06:53, 26 March 2023