Chebyshev points are often chosen as "solutions" of incompatible linear systems of equations and inequalities.
...><TD valign="top">[3]</TD> <TD valign="top"> I.I. Eremin, "Incompatible systems of linear inequalities" ''Dokl. Akad. Nauk SSSR'' , '''138''' : 6 (1961)
2 KB (296 words) - 16:59, 22 November 2018
...of the principles of the elementary constructive theory of numbers. These systems were originally conceived as formalizations of parts of intuitionistic logi
...us) are obtained from the ordinary versions of the corresponding classical systems with a full set ( $ \wedge , \lor , \supset , \neg , \forall , \exists $)
9 KB (1,350 words) - 22:10, 5 June 2020
...op">[1]</TD> <TD valign="top"> V.V. Nemytskii, V.V. Stepanov, "Qualitative theory of differential equations" , Princeton Univ. Press (1960) (Translated from
In arbitrary dynamical systems (where the phase space is not necessarily metric) the periodic points are c
5 KB (770 words) - 18:12, 16 December 2020
A concept in the theory of orthogonal systems (cf. [[Orthonormal system|Orthonormal system]]). Let a [[Complete system of
..., therefore one has to single out the special class of Riesz systems, i.e. systems $\{\psi_n\}$ satisfying
4 KB (643 words) - 19:53, 27 February 2021
...al analysis which is known as the [[Riemann sphere|Riemann sphere]] in the theory of functions of a complex variable.
be coordinate systems in $ \sigma $
2 KB (322 words) - 10:58, 29 May 2020
...properties of a given system. For this reason, in the theory of dynamical systems one speaks of a continuous spectrum whenever $U_T$ or $A$ have no eigenfunc
...to a [[Metric isomorphism|metric isomorphism]] {{Cite|CFS}}. An analogous theory has also been developed for transformation groups more general than $\mathb
5 KB (710 words) - 12:58, 16 July 2014
...ideration of difference schemes for integrating one-dimensional hyperbolic systems. If $\tau$ is the grid spacing with respect to $t$, $h$ the grid spacing wi
...="top">[1]</TD> <TD valign="top"> S.K. Godunov, V.S. Ryaben'kii, "The theory of difference schemes" , North-Holland (1964) (Translated from Russian)</
729 bytes (103 words) - 10:39, 10 August 2014
...bers; as written notations of numerical symbols began to appear, so number systems began to vary in the character of their numerical signs and in the principl
...numbers are formed by grouping nodal numbers together are called additive systems. Thus, in ancient Egyptian (hieroglyphic) notation, the numbers 1, 2, 3, 4,
8 KB (1,143 words) - 08:03, 6 June 2020
...inear mapping]] $V \times V \times V \rightarrow V$, is mainly used in the theory of non-associative algebras and appears in the construction of Lie algebras
...d> <td valign="top"> W. Hein, "A construction of Lie algebras by triple systems" ''Trans. Amer. Math. Soc.'' , '''205''' (1975) pp. 79–95</td></tr>
3 KB (498 words) - 19:51, 27 February 2021
There are systems of other types, where each request must necessarily be served, such as, for
==I. Systems with waiting (systems with a queue, queueing systems).==
15 KB (2,349 words) - 09:05, 21 January 2024
...rmational processes in [[#References|[a11]]], and in networks of cognitive systems in [[#References|[a15]]] and [[#References|[a16]]].
...o be used in more complex social processes, involving many self-organizing systems.
9 KB (1,251 words) - 18:24, 14 January 2021
...there is also an analogue of Mikhailov's criterion for non-linear control systems (see [[#References|[6]]]).
...i, L.E. El'sgol'ts, "Mathematical foundations of the theory of control systems" , Moscow (1969) (In Russian)</td></tr><tr><td valign="top">[6]</td> <td
5 KB (692 words) - 15:30, 1 July 2020
...equations may be employed to find approximate solutions of the non-linear systems.
which is typical in the theory of quasi-linear oscillations, the harmonic balance method consists in repla
4 KB (613 words) - 19:43, 5 June 2020
...ion of the initial elements are such that the operation of complex control systems can be described with the aid of Boolean functions. Boolean functions are a
...cube (cf. [[Boolean functions, metric theory of|Boolean functions, metric theory of]]), as well as of the various algebras of Boolean functions (cf. [[Many-
5 KB (836 words) - 12:39, 14 February 2020
...ties: positive entropy (cf. [[Entropy theory of a dynamical system|Entropy theory of a dynamical system]]) and [[Ergodicity|ergodicity]]; [[Mixing|mixing]] o
systems are sometimes called Kolmogorov systems (flows, etc.), after their originator (see ), who used the term "quasi-reg
7 KB (1,037 words) - 16:58, 1 July 2020
...ary to consider statistical states of systems; for classical (non-quantum) systems they are described by probability distributions on the phase space. The rul
...ferentiable [[Dynamical system|dynamical system]] (which includes the main systems considered in analytical mechanics and classical statistical physics), the
6 KB (906 words) - 21:49, 30 April 2014
...ent or a more general type, including the case of non-ideal and quantified systems.
The theory was presented by L. Boltzmann in 1872.
2 KB (326 words) - 17:14, 30 December 2018
...of motion (understood in the same wide form). Thus, stability theory is a theory in the widest sense of this word. Among the different concepts of the stabi
...]]) and having a large intersection with the theory of linear systems, the theory of Lyapunov characteristic exponents (cf. [[Lyapunov characteristic exponen
9 KB (1,252 words) - 10:41, 15 April 2014
...I.I. Gordon, A.G. Maier, "Qualitative theory of second-order dynamic systems" , Wiley (1973) (Translated from Russian)</TD></TR></table>
698 bytes (110 words) - 15:19, 17 July 2014
...of Chetaev functions have been suggested, in particular for non-autonomous systems (cf. [[#References|[3]]]).
...bility of motion. Applications of Lyapunov's second method to differential systems and equations with delay" , Stanford Univ. Press (1963) (Translated from
2 KB (299 words) - 15:31, 14 February 2020