...inear mapping]] $V \times V \times V \rightarrow V$. They are used in the theory of [[Non-associative rings and algebras|non-associative algebras]] and appe
678 bytes (104 words) - 18:13, 19 March 2018
...aces all intuitive notions of complex systems. Typical examples of complex systems are: the nervous system, the brain, a computer, a control system in human s
...ir names, such as systems analysis, system-technology, and general systems theory, among others.
4 KB (532 words) - 17:22, 7 February 2011
...etween Post production systems and Post canonical systems. Post production systems were used by Post and A.A. Markov (1947) to construct the first examples of
...</TD></TR><TR><TD valign="top">[2]</TD> <TD valign="top"> A.A. Markov, "Theory of algorithms" , Israel Program Sci. Transl. (1961) (Translated from Russ
1 KB (172 words) - 16:25, 1 May 2014
...eneral relativity theory, such reference systems are called local Galilean systems (Galilean frames). The existence of a local Galilean system implies that th
...ems are a corollary of the principles of relativity. In special relativity theory an inertial system is usually defined as a [[Galilean coordinate system|Gal
3 KB (381 words) - 17:51, 13 August 2023
...2]</TD> <TD valign="top"> V.V. Nemytskii, V.V. Stepanov, "Qualitative theory of differential equations" , Princeton Univ. Press (1960) (Translated fro
...valign="top"> N.P. Bhatia, G.P. Szegö, "Stability theory of dynamical systems" , Springer (1970) pp. 30–36</TD></TR></table>
1 KB (231 words) - 10:45, 15 April 2014
...of the language with free variables $x_1,\dotsc,x_n$ is equivalent in the theory $T$ to one of the formulas of $F_n$. The collection of axioms:
...\aleph_0$. The following general theorem holds: If a first-order countable theory $T$ is categorical in some uncountable cardinality, then it is categorical
4 KB (681 words) - 13:30, 14 February 2020
...ties of algebraic systems are defined by quasi-identities (cf. [[Algebraic systems, quasi-variety of]]). An identity is a special case of a quasi-identity.
...ommonly called ''Horn sentences'' or ''Horn clauses'': see [[Horn clauses, theory of]].
1 KB (193 words) - 07:40, 21 October 2016
...e cosets of a subgroup. Cf. [[#References|[a1]]] for some uses of Schreier systems, such as a proof of the Nielsen–Schreier theorem that subgroups of free g
...lign="top"> W. Magnus, A. Karrass, B. Solitar, "Combinatorial group theory: presentations in terms of generators and relations" , Wiley (Interscience)
1 KB (211 words) - 12:17, 19 August 2014
An isomorphism is a correspondence (relation) between objects or systems of objects
algebraic systems (initially, with groups) and was extended in a
3 KB (465 words) - 22:01, 5 March 2012
...tributed computing (more generally, architectures occurring in multi-agent systems).
...ation protocol on the power, the complexity, and the properties of grammar systems and of the generated languages.
5 KB (767 words) - 19:10, 5 August 2014
...ame requirement. The concept of a deducible expression in effective formal systems is, generally speaking, not effective.
...some branch of meaningful mathematics. Historically, this class of formal systems arose in connection with the program of D. Hilbert of providing a foundatio
3 KB (392 words) - 12:21, 19 August 2014
...20 : ~/encyclopedia/old_files/data/E110/E.1100090 Equivalence of dynamical systems
Two autonomous systems of ordinary differential equations (cf. [[Autonomous system|Autonomous syst
3 KB (414 words) - 19:37, 5 June 2020
...the point of view of mathematical logic, as models of logics, that is, as systems of propositions with logical operations on them; and from the point of view
...ems of many-valued logic. Among the most important problems for functional systems are those of completeness, of the complexity of expressing some functions i
7 KB (1,087 words) - 19:40, 5 June 2020
Examples of Markov function systems are:
...valign="top">[1]</TD> <TD valign="top"> N.I. [N.I. Akhiezer] Achiezer, "Theory of approximation" , F. Ungar (1956) (Translated from Russian)</TD></TR></
1 KB (202 words) - 06:03, 5 August 2014
...veloping numerical methods for some class of problems. For example, in the theory of [[Quadrature|quadrature]] the problem of calculating integrals of functi
...g of methods for the solution of the [[Cauchy problem|Cauchy problem]] for systems of ordinary differential equations historically was done by investigating t
2 KB (281 words) - 08:01, 6 June 2020
...<TD valign="top">[4]</TD> <TD valign="top"> T. Berger, "Rate distortion theory" , Prentice-Hall (1971)</TD></TR></table>
...J. Körner, "Information theory. Coding theorems for discrete memoryless systems" , Akad. Kiado (1981)</TD></TR></table>
2 KB (247 words) - 18:10, 18 September 2014
...ety of areas: to the theory of non-linear oscillations, to physics, to the theory of automatic control, to astrodynamics, and to others. Averaging methods ha
1) Standard systems in the sense of N.N. Bogolyubov
5 KB (679 words) - 03:42, 21 March 2022
<TR><TD valign="top">[1]</TD> <TD valign="top"> G. Birkhoff, "Lattice theory" , ''Colloq. Publ.'' , '''25''' , Amer. Math. Soc. (1967)</TD></TR>
..."top">[3]</TD> <TD valign="top"> L. Fuchs, "Partially ordered algebraic systems" , Pergamon (1963) {{ZBL|0137.02001}}</TD></TR>
1 KB (193 words) - 16:45, 4 September 2016
...utomatic control systems (cf. [[Automatic control theory|Automatic control theory]]) if there is a delay in the control mechanism.
1 KB (198 words) - 17:10, 7 February 2011
...y]]), and the system of the theory of types (cf. [[Types, theory of|Types, theory of]]).
407 bytes (61 words) - 17:28, 7 February 2011