...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
of algebraic systems of the same signature''
...plica for any algebraic system of the same signature. A class of algebraic systems of a fixed signature is replica full if and only if it contains a one-eleme
2 KB (359 words) - 08:11, 6 June 2020
...projective or affine geometry. Another characteristic example of incidence systems is that of [[block design]]s: for example, [[balanced incomplete block desi
Two incidence systems $S = (A,\mathfrak{B},I)$ and $S' = (A',\mathfrak{B'},I')$ are called isomor
3 KB (488 words) - 19:37, 7 November 2023
...s or rational numbers). The study of such equations forms the topic of the theory of [[Diophantine equations|Diophantine equations]].
608 bytes (91 words) - 17:19, 7 February 2011
...ing]]s, tertiary ideals are the same as [[primary ideal]]s (cf. [[Additive theory of ideals]]; [[Primary decomposition]]).
...ions (of ideals of a ring, of submodules of a module, and others) leads to systems with fractions in which the general notions of $S$-primarity and $S$-primar
2 KB (297 words) - 19:23, 5 October 2017
...objects are arbitrary mathematical proofs is called a [[Proof theory|proof theory]] or a meta-mathematics. An example of the application of a meta-mathematic
...ot be proved by the tools of the relevant theory itself (provided that the theory is in fact consistent).
3 KB (544 words) - 15:41, 30 December 2018
A shift dynamical system is used in the theory of dynamical systems mainly to construct examples (here $ S $
...is everywhere dense, and others), and also in the theory of non-autonomous systems of ordinary differential equations, where $ S $
6 KB (862 words) - 08:13, 6 June 2020
...ätzer, "General lattice theory" , Birkhäuser (1978) (Original: Lattice theory. First concepts and distributive lattices. Freeman, 1978)</TD></TR></table>
...are, e.g., investigations concerning the structural stability of dynamical systems up to some tolerance, the Zeeman tolerance stability conjecture, [[#Referen
3 KB (402 words) - 21:38, 12 October 2014
...nalogy is not possible; this gave rise to the development of the theory of systems of hypercomplex numbers.
...lude [[Double and dual numbers|double and dual numbers]], and hypercomplex systems of the form
3 KB (484 words) - 19:37, 28 December 2020
...rem is true: Systems with fixed critical points can only be constituted by systems (1) which, after the introduction of a suitable parameter $ \epsilon $,
...l systems (1) without moving critical singular points, and in the study of systems belonging to these classes (cf. [[Singular point|Singular point]] of a diff
5 KB (748 words) - 08:05, 6 June 2020
...lastic and elastic-plastic systems; often the term stability of deformable systems is used.
...ov stability]]. The central question in the theory of stability of elastic systems is to find a region in the parameter space of the system with its external
9 KB (1,405 words) - 18:22, 30 May 2024