...gruence with respect to the variety $\mathfrak{M}$ generated by the factor system $\mathbf{F}/\eta$.
1 KB (167 words) - 19:23, 12 December 2015
...[[Affine coordinate system|affine coordinate system]] is determined by the factor $x_i$ such that $x_iv_i$ is the parallel projection of the position vector
595 bytes (104 words) - 21:12, 14 April 2014
...r system. Then the cross product of $G$ and $K$ with respect to the factor system $\rho$ and the mapping $\sigma$ is the set of all formal finite sums of the
In the defining relations for a factor system above $\rho^{\sigma(g_1)}_{g_2,g_3}$, e.g., of course stands for the result
4 KB (702 words) - 08:53, 2 June 2016
$#C+1 = 51 : ~/encyclopedia/old_files/data/S090/S.0900890 Subgroup system
...respect to union and intersection is called complete. A complete subgroup system is called subnormal if for any jump $ A $
4 KB (599 words) - 08:24, 6 June 2020
...t in an expression for the density (or for the density matrix in a quantum system) in a canonical Gibbs ensemble (cf. [[Gibbs statistical aggregate|Gibbs sta
1) In a classical system, the density of the Gibbs distribution $ p( \omega ) $,
5 KB (650 words) - 14:34, 13 January 2024
...nding sequence of subgroups (see [[Subgroup series|Subgroup series]]) each factor of which is isomorphic to an infinite cyclic group.
2 KB (253 words) - 17:28, 7 February 2011
root system and a certain sublattice in the weight lattice that
out that the system $\Sigma\subset X(T)$ of all roots of $E$ is a
4 KB (632 words) - 19:22, 12 December 2023
...ng physical (observable) quantities related to this system. In a classical system with phase space $ \Omega $,
In a quantum system described by vectors in a Hilbert space $ {\mathcal H} $,
8 KB (1,180 words) - 05:07, 23 February 2022
...stability zones. A Mathieu function is even or odd, and is unique up to a factor; the second linearly-independent solution grows linearly in $ z $
these functions reduce to the [[Trigonometric system|trigonometric system]]
3 KB (379 words) - 16:31, 6 January 2024
.... In many cases the principle can be derived as a corollary from a certain system of axioms which represents properties that are natural to demand of any "r
a factor not controllable by the consumer. The choice of concrete values $ x \in X
9 KB (1,423 words) - 08:07, 6 June 2020
...that if $( X , \mathcal{F} , \mu , T )$ is a [[Dynamical system|dynamical system]], then given $f \in L ^ { 1 } ( \mu )$ one can find a set of full [[Measur
==Uniform Wiener–Wintner theorem and Kronecker factor.==
9 KB (1,431 words) - 17:03, 1 July 2020
A relation that connects the [[Wronskian|Wronskian]] of a system of solutions and the coefficients of an ordinary linear differential equati
be an arbitrary system of $ n $
6 KB (913 words) - 08:58, 13 January 2024
...se in statistical physics in defining a Gibbs quantum state. Let a quantum system occupying a finite volume $ V $
A Gibbs state for such a system is a state on $ \mathfrak A( {\mathcal H} _ {V} ) $
4 KB (615 words) - 07:51, 14 January 2024
A system of multi-parameter identities giving a connection between different charact
...in the lower half-plane. Such a representation is unique up to a constant factor (cf. [[Wiener–Hopf method|Wiener–Hopf method]]), which allows one to id
2 KB (347 words) - 11:27, 1 August 2014
uniquely up to a constant factor and itself uniquely determines $ X $.
th coordinate system is the coordinate system of the $ i $-
7 KB (1,079 words) - 16:43, 4 June 2020
...tant speed on a rectangular table with a convex obstacle. The state of the system (the position and velocity of the ball), at one instant of time, can be des
...em: Any flow <math>f_t</math> that is not completely predictable, has as a factor <math>B_{ct}</math> for some <math>c>0</math> (the numbers <math>c</math> i
8 KB (1,391 words) - 13:02, 12 December 2013
...n solved (see [[#References|[1]]]) for approximately-finite factors (cf. [[Factor]]) of type $\mathrm{II}$ and type $\mathrm{III}_\lambda$, $0 < \lambda < 1$
...[[#References|[6]]] that generalizes the [[entropy]] of a metric dynamical system. The entropy of automorphisms of an arbitrary $W^*$-algebra with respect to
3 KB (481 words) - 21:35, 15 December 2014
under the projection onto the second factor is a hypersurface in $ ( \widetilde{P} {} ^ {n} ) ^ {r+} 1 $
in each system of variables. The form $ F _ {X} $
5 KB (782 words) - 16:44, 4 June 2020
In accordance with the decimal system, the most commonly used are decimal logarithms $(a=10)$, denoted by $\lg N$
...se to another is carried out by the formula $\log_bN=\log_aN/\log_ab$; the factor $1/\log_ab$ is called the modulus of transition from the base $a$ to the ba
3 KB (453 words) - 15:11, 19 August 2014
...f functions|Complete system of functions]]; [[Orthogonal system|Orthogonal system]]). In spectral methods, [[Trigonometric functions|trigonometric functions]
...hod. With other types of conditions, an extra equation may be added to the system to satisfy it, or the basis functions may be modified to automatically sati
9 KB (1,381 words) - 16:55, 1 July 2020
''loss system''
However, in contrast to a system with an infinite number of channels here $ q _ {n} \leq m $,
10 KB (1,560 words) - 08:02, 14 January 2024
''natural system, homotopic resolution, $P$-decomposition of general type''
...–MacLane space]]), where $\pi_n$ is some group (Abelian for $n > 1$). This system was introduced by M.M. Postnikov
11 KB (1,963 words) - 07:35, 8 August 2018
...vertex corresponds a system of equations, chosen in a special way from the system of inequalities \eqref{eq:2}, \eqref{eq:3}, so the computational procedure
...trices. At the heart of many of them lies the idea of decomposition of the system of restrictions into subsystems for each of which it is necessary to solve
12 KB (1,882 words) - 22:25, 1 September 2016
...tions, then the product $\prod_{i\in I} X_i$ can be made into an algebraic system of the same signature: For functions $f_1,\ldots,f_k : I \rightarrow X$ and
For an arbitrary factor of a direct product $X = \prod_{i\in I} X_i$ there exists a natural project
4 KB (769 words) - 20:29, 7 February 2017
...gcd } ( a ^ { ( q ^ { i } - 1 ) / 2 } - 1 , f _ { i } )$ is a non-trivial factor of $f_i$. To describe the cost of these methods, one uses fast arithmetic,
...mbinations of the irreducible factors modulo $p ^ { k }$ to recover a true factor in $\mathbf{Q} [ x ]$. This works quite well in practice, at least for poly
12 KB (1,739 words) - 13:11, 26 March 2023
...for investigating the singular points of an [[Autonomous system|autonomous system]] of second-order ordinary differential equations
is a singular point of the system (1), that is, $ f ( O) = 0 $,
8 KB (1,224 words) - 01:42, 23 June 2022
...e types|Voronoi lattice types]]) is non-trivial if and only if the scaling factor of the tiling is a Pisot number [[#References|[a4]]].
5 KB (723 words) - 19:03, 23 January 2024
The construction of cross products with the aid of [[factor system]]s {{Cite|Ch}} results in a cohomological interpretation of Brauer groups.
...t]]; [[Extension of a group]]. The latter article contains the notion of a system of factors.
7 KB (1,232 words) - 12:12, 30 December 2015
such that any factor of $ \mathfrak A _{i} $
one of which contains some variable as factor, while the other contains the negation of this variable (under the conditio
27 KB (3,984 words) - 15:58, 22 December 2019
onto the factor $ X $,
Having chosen a coordinate system (Cartesian, polar or any other coordinates), the numerical points $ ( x,
3 KB (568 words) - 19:42, 5 June 2020
and the volumes of two similar bodies are proportional to the cube of the factor of the corresponding similarity.
and let an affine coordinate system $ ( x ^ {1} \dots x ^ {n} ) $
8 KB (1,344 words) - 08:28, 6 June 2020
define the same (quantum mechanical) state if they differ by a phase factor: $ \psi _ {2} = \mathop{\rm exp} ( ia) \psi _ {1} $.
...quantum measurements [[#References|[a1]]] overcomplete subsystems of this system indexed by a lattice in $ \mathbf C $
3 KB (511 words) - 19:02, 1 May 2024
...able manifold is called a Lie pseudo-group of transformations defined by a system $ S $
that satisfy the system $ S $.
13 KB (1,866 words) - 18:13, 20 January 2022
...s not complete in $H ^ { 2 } ( \mu )$ (cf. also [[Complete system|Complete system]]).
...2 } = \mu ^ { \prime } ( \theta )$. Therefore it is also called a spectral factor of the weight function $\mu ^ { \prime }$. Other asymptotic formulas were o
7 KB (1,105 words) - 10:02, 11 November 2023
5) basic states, elementary excitations (in the case of a quantum system).
...udied. Statistical mechanics, depending on the method used to describe the system, is divided into classical and quantum mechanics.
28 KB (4,019 words) - 10:50, 5 March 2022
the [[Root system|root system]] of $ G $
induced by left-multiplication on the first factor of $ G ( K ) \times A $.
7 KB (1,021 words) - 06:29, 30 May 2020
3) a scalar factor can be taken out of the scalar product:
is called the [[Minkowski space|Minkowski space]]. In any system of $ n $
9 KB (1,270 words) - 08:54, 13 January 2024
Statistics used in a system of non-interacting particles obeying the laws of classical mechanics (a cla
must be divided by a factor $ N ! $:
5 KB (797 words) - 10:59, 29 May 2020
...take into account the effects of the influence of state degeneracy of the system.
...orresponds to a single energy level more than one independent state of the system; the average $ \langle A \rangle $
11 KB (1,490 words) - 08:09, 6 June 2020
...results of the productive activity of economic systems at various levels; factor models of productivity; systems of demand functions for groups of consumers
...solution of problems of one class, as well as the tendency to formulate a system of recommendations by means of which the hypotheses concerning the models o
14 KB (2,040 words) - 19:36, 5 June 2020
A linear dynamical input-output system
used here is uniquely determined by the discount factor $ \lambda $,
5 KB (752 words) - 08:29, 6 June 2020
$#C+1 = 106 : ~/encyclopedia/old_files/data/D110/D.1100230 Discrete event system
...t driven as opposed to time driven, i.e. the behaviour of a discrete event system is governed only by occurrences of different types of events over time rath
14 KB (2,165 words) - 19:35, 5 June 2020
are called the roots of the root system $ R $.
A root system $ R $
22 KB (3,351 words) - 19:14, 21 December 2019
The solution to the system
the error in the initial approximation can be reduced in norm by a factor $ \epsilon ^ {-1} $
6 KB (890 words) - 07:28, 9 February 2024
...g so (s)he must take into consideration such factors as the purpose of the system, the conditions under which it is to operate, and also economic factors. A
...tical models in reliability theory. Assume that the state of an industrial system is defined by a point $ x $
16 KB (2,542 words) - 08:10, 6 June 2020
...tions. This probability density can be expressed, apart from a normalizing factor, by means of a functional integral over paths of the process. The correspon
5 KB (784 words) - 16:52, 1 July 2020
...ro divisors and let $f$ be a non-degenerate sesquilinear form. Then, for a system of elements $v_1,\dots,v_n$ from $E$ to be free it is necessary and suffici
...ined invariantly, while its discriminant is defined up to a multiplicative factor which is the square of a non-zero element of $F$. The algebra $A$ is separa
16 KB (2,947 words) - 08:53, 9 December 2016
...number of places with bounded gaps. In other words, the symbolic dynamical system generated by the Thue–Morse sequence is minimal (see, for instance,
[[Dynamical system|Dynamical system]]).
10 KB (1,633 words) - 08:05, 26 November 2023
...its of measurement and has the form of a monomial. For example, in the CGS system the dimension formulas contain three arguments: the length unit $L$, the ti
In the CGS system the formula for any quantity $N$ of a mechanical, thermal or electromagneti
16 KB (2,568 words) - 20:00, 4 January 2024
...of which to the argument multiplies the value of the function by a certain factor. In other words, one has the identities (in $ z $):
is the moduli system or system of periods and quasi-periods of $ \theta ( z) $.
14 KB (1,941 words) - 05:01, 23 February 2022