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
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...s or rational numbers). The study of such equations forms the topic of the theory of [[Diophantine equations|Diophantine equations]].
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...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).
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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 $
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...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
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...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
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...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
...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
A notion imported from group theory (cf. also [[Group|Group]]), where the [[Frattini-subgroup(2)|Frattini subgr
Related concepts are being studied in very general algebraic systems [[#References|[a2]]].
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...series]] using [[Summation methods|summation methods]]. The best developed theory of the summation of Fourier series is that which uses the trigonometric sys
Apart from these, the most important in the theory of one-dimensional trigonometric series are the [[Cesàro summation methods
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...ies of the system itself (see also [[Oscillations, theory of|Oscillations, theory of]]). The term "auto-oscillation" was introduced by A.A. Andronov (see [[#
...mous auto-oscillating systems with one degree of freedom may be defined as systems whose equations of motion have one or more limit cycles in the phase plane
9 KB (1,404 words) - 16:55, 15 April 2012
...) is a solution of the other system (equation), and conversely, where both systems (equations) are considered in one and the same domain.
...o-called elimination of the unknowns (cf. [[Elimination theory|Elimination theory]]).
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Every link has a closed braid presentation (cf. also [[Braid theory|Braid theory]]; [[Link|Link]]).
...ng the theory of braids, [[#References|[a1]]] (cf. also [[Knot theory|Knot theory]]). Alexander's theorem has its roots in Brunn's result (1897) that every k
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$#C+1 = 101 : ~/encyclopedia/old_files/data/E035/E.0305360 Elementary theory
...llection of closed formulas of first-order predicate logic. The elementary theory $ \mathop{\rm Th} ( K) $
9 KB (1,436 words) - 19:37, 5 June 2020
$#C+1 = 115 : ~/encyclopedia/old_files/data/A011/A.0101690 Algebraic systems, variety of
A class of algebraic systems (cf. [[Algebraic systems, class of|Algebraic systems, class of]]) of a fixed signature $ \Omega $,
10 KB (1,438 words) - 16:10, 1 April 2020
...attention to the more detailed internal properties. Therefore, two control systems, having in some sense identical behaviour and identical purposes, are not r
...Buslenko [[#References|[3]]] and others. A complete definition of control systems was established in [[#References|[1]]]. This definition includes all known
12 KB (1,844 words) - 16:56, 15 April 2012
...ajectory for which only one Floquet multiplier has modulus one. In certain systems the whole phase space is a hyperbolic set (cf. [[Y-system| $ Y $-
...and have since played an important role in the theory of smooth dynamical systems, both as objects of studies and as a part in many examples [[#References|[3
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When describing pure logical systems (propositional and predicate calculus), the terms "constructive" , "intui
...n to belong to constructive logic. The general manner in which most of the systems of constructive logic reflect the specific constructive understanding of th
10 KB (1,524 words) - 20:25, 4 June 2020