of algebraic systems (cf. [[Algebraic system|Algebraic system]]) $ A _ {i} $
is non-empty and is a subsystem of each of the systems $ A _ {i} , A _ {j} $.
4 KB (674 words) - 16:10, 1 April 2020
...quivalent (cf. [[Equivalence of dynamical systems|Equivalence of dynamical systems]]) near the origin to the normal form
...quivalent (cf. [[Equivalence of dynamical systems|Equivalence of dynamical systems]]) near the origin to the suspension of the normal form (a3) by the standar
6 KB (872 words) - 08:12, 6 June 2020
...cal systems, provided with the $C^1$-topology [[#References|[1]]], . Thus, systems whose trajectories display a behaviour which is more complex and more sensi
...<TR><TD valign="top">[4b]</TD> <TD valign="top"> A.B. Katok, "Dynamical systems with hyperbolic structure" ''Transl. Amer. Math. Soc.'' , '''116''' (1981
8 KB (1,203 words) - 17:01, 23 March 2023
...= 12 : ~/encyclopedia/old_files/data/K110/K.1100100 Kharitonov polynomial theory
...motivation for this theory derives from the issue of robust stability for systems of linear time-invariant differential equations. For a system of linear dif
5 KB (695 words) - 22:14, 5 June 2020
In 1844 W. Woolhouse stated the existence problem for Steiner
systems, and P. Kirkman solved it in 1847 for <img align="absmiddle" border="0" src
...diaofmath.org/legacyimages/s/s087/s087670/s08767034.png" /> (using Steiner
systems).
32 KB (4,451 words) - 15:16, 19 March 2018
The theory of eliminating unknowns from systems of algebraic equations. More precisely, suppose one is given a system of eq
...$x_1,\dots,x_k$, one also consider the homogeneous problem in elimination theory (the inhomogeneous problem is trivial in this case): Find the projection on
8 KB (1,363 words) - 16:04, 13 January 2021
...yclopedia/old_files/data/P071/P.0701560 Parametric resonance, mathematical theory of
The branch of the theory of ordinary differential equations that studies the phenomenon of parametri
10 KB (1,385 words) - 09:16, 13 May 2022
...orks), which is oriented to the qualitative analysis and synthesis of such systems (discovering deadlocks or conflict situations and bottlenecks, computer-aid
...ine is the use of Petri nets as the basis of models for discrete dynamical systems in information technology, economics, digital engineering, etc.
6 KB (897 words) - 19:23, 16 August 2016
...e concept of local coordinates. This, for example, is the situation in the theory of manifolds.
...coordinates "from without" , preserving as it were the "purity" of the theory, have not justified themselves (e.g. the synthetic constructions of [[Proje
7 KB (980 words) - 17:09, 11 April 2014
...group]]) are a special case of BCI-algebras. One may take different axiom systems for BCI-algebras, and one such system says that a BCI-algebra is a non-empt
...top"> C.S. Hoo, "Fuzzy ideals of BCI and MV-algebras" ''Fuzzy Sets and Systems'' , '''62''' (1994) pp. 111–114</TD></TR>
5 KB (790 words) - 02:33, 15 February 2024
...o another is called local Lorentz invariance. Some branches of the general theory of relativity also examine quantities determined by giving a [[congruence]]
<TR><TD valign="top">[1]</TD> <TD valign="top"> V.A. Fok, "Einstein's theory and physical relativity" , Moscow (1967) (In Russian)</TD></TR>
1 KB (179 words) - 08:28, 29 April 2016
...D.V. Anosov (see , [[#References|[2]]]), and they are often called Anosov systems.
...f a $Y$-system of period at most $T$ increases exponentially with $T$. $Y$-systems possess strong ergodic properties with respect to the wide class of so-call
9 KB (1,321 words) - 07:59, 21 June 2014
...space of the representation). Frequently, representation theory means the theory of linear representations. If $V$ is finite-dimensional, then its dimension
...to abstract (or algebraic) representation theory there is a representation theory of topological objects, e.g., topological groups or Banach algebras (cf. [[
4 KB (513 words) - 11:58, 9 November 2014
Problems of finding solutions of (systems of) partial differential equations of hyperbolic type that satisfy specific
...and systems|Mixed and boundary value problems for parabolic equations and systems]]).
31 KB (4,290 words) - 01:21, 14 February 2013
...eorems for loss systems are completely analogous to stability theorems for systems with an infinite number of channels. Suppose sequences $ \{ \tau _ {j} ^
...ds of investigation of loss systems may also be effective for the study of systems with heavy traffic or with a large number of service channels.
10 KB (1,560 words) - 08:02, 14 January 2024
...is as follows: The laws of physics take an identical form in all inertial systems.
...the light source, form the basis of special [[Relativity theory|relativity theory]].
1 KB (221 words) - 17:11, 7 February 2011
...such systems plays an important role in the physical interpretation of the theory.
4 KB (532 words) - 19:41, 5 June 2020
...braic geometry|algebraic geometry]] (commutative algebra, polynomial ideal theory) can be reduced by structurally easy algorithms to the construction of Grö
...Gröbner bases are routinely available in all modern mathematical software systems, as for example Mathematica and Maple.
6 KB (1,000 words) - 17:05, 7 July 2014
...ne to establish whether or not any pair of recursively-presented algebraic systems (cf. [[Algebraic system|Algebraic system]]) in a given class are isomorphic
...isomorphism problem is unsolvable for many important classes of algebraic systems. The unsolvability of the partial isomorphism problem for a finitely-presen
3 KB (386 words) - 22:13, 5 June 2020
...which — the simple theory of types — is described below. The terminology "theory of types" has no rigidly fixed meaning. It denotes formal theories which a
...ble $ y ^ \rho $ must belong (this is the main point of type-theoretic systems) to a higher level in the hierarchy of types than the types $ \sigma _{1}
8 KB (1,261 words) - 20:30, 13 December 2019