...f. [[Sector in the theory of ordinary differential equations|Sector in the theory of ordinary differential equations]]) by semi-trajectories (the separatrice
...eontovich, "Methods and means for a qualitative investigation of dynamical systems on the plane" , Moscow (1976) (In Russian)</TD></TR>
4 KB (577 words) - 09:06, 1 October 2023
...been rarely examined. The major importance of transference theorems in the theory of Diophantine approximation can be explained by a transference theorem in
[[Category:Number theory]]
2 KB (255 words) - 20:56, 25 October 2014
...of its origin. A syntactic language is used to study this aspect of formal systems.
...e [[Gödel incompleteness theorem|Gödel incompleteness theorem]] for formal systems is based on this fact.
2 KB (394 words) - 17:28, 7 February 2011
with zero initial conditions. In control theory, relation (1) is represented graphically as:
...on is one of the basic concepts in the theory of linear stationary control systems. It is independent of the control actions imposed on the system and is gove
4 KB (608 words) - 13:08, 18 June 2020
...development of the Galilean relativity principle forms part of the general theory of relativity.
...><TD valign="top">[1]</TD> <TD valign="top"> V.A. [V.A. Fok] Fock, "The theory of space, time and gravitation" , Macmillan (1964) (Translated from Russi
2 KB (272 words) - 17:21, 7 February 2011
...groups (cf. [[Kleinian group|Kleinian group]]) and the theory of dynamical systems (cf. e.g. [[Limit set of a trajectory|Limit set of a trajectory]]).
348 bytes (56 words) - 19:35, 19 October 2014
.... Let $\left\{{\psi_n}\right\}$ and $\left\{{g_n}\right\}$ be two complete systems of functions in $L_2 \! \left({a, b}\right) = L_2$ (i.e. measurable functio
1 KB (233 words) - 05:56, 14 January 2017
...cal systems'' , '''I: Ordinary differential equations and smooth dynamical systems''' , Springer (1988) pp. 159ff (Translated from Russian)</TD></TR></tabl
3 KB (535 words) - 21:47, 30 April 2014
$#C+1 = 15 : ~/encyclopedia/old_files/data/D033/D.0303160 Discrete systems in statistical mechanics
...change is considered to be independent of the others. One of the simplest systems — the Ising model (1925) — is characterized by the Hamiltonian [[#Refer
4 KB (585 words) - 11:53, 26 March 2023
...[3]</TD> <TD valign="top"> A.A. Andronov, A.A. Vitt, A.E. Khaikin, "Theory of oscillators" , Pergamon (1966) (Translated from Russian)</TD></TR></ta
...I.I. Gordon, A.G. Maier, "Qualitative theory of second-order dynamic systems" , Wiley (1973) (Translated from Russian)</TD></TR></table>
2 KB (364 words) - 15:57, 14 February 2020
...economics and cybernetics. In the framework of combinatorial mathematics, systems of distinct representatives play an important role in questions of choice a
In view of the wide use of systems of distinct representatives, algorithms for their practical determination (
6 KB (900 words) - 08:25, 6 June 2020
...investigated degenerate equilibrium positions are those of two-dimensional systems, for which several methods for studying the behaviour of trajectories in a
...valign="top"> A.A. Bryuno, "Stepwise asymptotic solutions of non-linear systems" ''Izv. Akad. Nauk SSSR Ser. Mat.'' , '''29''' (1965) pp. 329–364 (In
3 KB (453 words) - 17:32, 5 June 2020
The design, development, tuning, and operation of computer and communication systems heavily rely on mathematical techniques which are usually indicated as perf
...f the daily operation and capacity planning of computer- and communication systems also requires techniques from such areas as combinatorial optimization (sch
5 KB (732 words) - 08:05, 6 June 2020
Just as for traditional dynamical systems the phase space of a flow usually is provided with a certain structure with
In applications one usually encounters flows described by autonomous systems (cf. [[Autonomous system|Autonomous system]]) of ordinary differential equa
3 KB (541 words) - 19:39, 5 June 2020
...> <TD valign="top"> D. Ruelle, "Small random perturbations of dynamical systems and the definition of attractors" ''Comm. Math. Phys.'' , '''82''' (1981)
2 KB (382 words) - 12:08, 18 August 2014
...the channel coding problem, [[Steiner system]]s, $t$-designs, and in the theory of finite groups. The most important special case is the sphere packing in
491 bytes (69 words) - 01:32, 11 February 2012
...eorem for polynomials of best uniform approximation is valid for Chebyshev systems (see also [[Haar condition|Haar condition]]; [[Chebyshev set|Chebyshev set]
...="top">[5]</TD> <TD valign="top"> S. Karlin, V. Studden, "Tchebycheff systems with applications in analysis and statistics" , Interscience (1966)</TD></
3 KB (491 words) - 10:46, 15 August 2014
...nts; all Gentzen formal systems are sometimes treated as natural deduction systems, since they reflect to some extent the usual methods of handling logical co
Natural deduction systems comprise rules for the introduction of logical symbols and their discharge.
10 KB (1,428 words) - 19:41, 5 June 2020
An important particular case of a dissipative system are the so-called systems with convergence, for which all solutions $ x ( t ; t _ {0} , x _ {0} )
...ution on the entire axis which is asymptotically stable in the large. Such systems have been thoroughly studied (see, for example, [[#References|[1]]]).
2 KB (276 words) - 19:36, 5 June 2020
...ultitude of algebraically completely integrable systems in the 1970s. Such systems are given by a Lax-pair equation: $L=[M,L]$ with $(n\times n)$-matrices $L$
...tems for principal $G$-bundles [[#References|[a5]]]; and quantized Hitchin systems with applications to the geometric Langlands program [[#References|[a2]]].
5 KB (752 words) - 15:33, 4 October 2014