...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
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...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.
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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]]
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.... 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.==
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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 $
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...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
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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