-
34 bytes (4 words) - 19:22, 7 January 2016
...principal [[ultrafilter]]. The [[Fréchet filter]] is an example of a non-principal filter.
454 bytes (69 words) - 12:00, 23 November 2023
$#C+1 = 9 : ~/encyclopedia/old_files/data/P074/P.0704750 Principal normal
is the parametric equation of the curve and the value $ t _ {0} $
1 KB (159 words) - 08:07, 6 June 2020
...of the indicatrix of the curvature (cf. [[Dupin indicatrix]]). If $t$ is a principal direction, the relation (Rodrigues' formula)
...l direction. The normal curvature in a principal direction is known as a [[principal curvature]].
1 KB (180 words) - 16:49, 12 October 2017
$#C+1 = 45 : ~/encyclopedia/old_files/data/P074/P.0704660 Principal curvature
...direction, i.e. in a direction in which it assumes an extremal value. The principal curvatures $ k _ {1} $
4 KB (610 words) - 14:54, 7 June 2020
The left principal ideal $L(\alpha)$ of a ring $A$ contains, in addition to the element $\alph
the right principal ideal $R(\alpha)$ contains all the elements
3 KB (484 words) - 20:54, 28 November 2014
''Dirichlet principal character''
where $D$ is a given natural number. Principal characters serve to define the concepts of primitive and imprimitive charac
340 bytes (45 words) - 20:04, 9 January 2015
...scending chains of normal subgroups have finite length. If a group has two principal series, then they are isomorphic, i.e. they have the same length and there
The terminology "principal series" is almost never used in the West. Instead one uses chief series. T
2 KB (254 words) - 16:51, 30 December 2018
-
557 bytes (88 words) - 16:59, 23 November 2023
...ity $A^2=A$ is valid. All [[regular semi-group]]s are semi-simple. If each principal factor of a semi-group is either completely $0$-simple or completely simple
Any semi-group consists, as it were, of its principal factors. This explains, in particular, the important role played by ideally
2 KB (362 words) - 19:18, 16 January 2018
...th boundary, then they can be extended to the entire space $E^n$ so that a principal fundamental solution will exist for the extended operator.
1 KB (190 words) - 08:35, 31 October 2014
#REDIRECT [[Principal ideal ring]]
34 bytes (4 words) - 20:26, 7 February 2017
A [[Principal G-object|principal $ G $-
then a principal $ G $-
5 KB (854 words) - 10:51, 20 December 2019
$#C+1 = 75 : ~/encyclopedia/old_files/data/P074/P.0704690 Principal fibre bundle
The significance of principal fibre bundles lies in the fact that they make it possible to construct asso
6 KB (847 words) - 20:45, 12 January 2024
...ure Lie group acts simply transitively and analytically. In other words, a principal analytic fibration is a quadruple $ (P,\ B,\ G,\ \pi ) $
dimensional fibre determines a principal analytic fibration with base $ B $
7 KB (1,096 words) - 09:58, 20 December 2019
$#C+1 = 81 : ~/encyclopedia/old_files/data/P074/P.0704740 Principal ideal ring
...[[Associative rings and algebras]]) in which all right and left ideals are principal, i.e. have the form $ aR $
5 KB (880 words) - 19:00, 9 January 2024
$#C+1 = 99 : ~/encyclopedia/old_files/data/P074/P.0704710 Principal \BMI G\EMI\AAhobject
...ndle|principal fibre bundle]] in topology, a [[Principal homogeneous space|principal homogeneous space]] in algebraic geometry, etc. Let $ G $
6 KB (908 words) - 16:33, 7 June 2020
...ves as the base of two different deformations $F'$ and $F''$, then it is a principal base of deformation.
...normal curvature of $F$ in the direction of one of the two families of the principal base $\sigma$ at an arbitrary point $M\in F$, while $\kappa'$, $\kappa''$,
5 KB (766 words) - 12:40, 2 November 2014
$#C+1 = 14 : ~/encyclopedia/old_files/data/M062/M.0602310 Mapping, principal net of a,
The directions tangential to the lines of the principal net of the mapping at the point $ x \in G $
1 KB (229 words) - 07:59, 6 June 2020
$#C+1 = 26 : ~/encyclopedia/old_files/data/P074/P.0704790 Principal type, partial differential operator of,
whose principal part $ P( D) $(
2 KB (356 words) - 08:07, 6 June 2020
...the normal curvature of a surface in a given direction $l$ in terms of the principal curvatures $k_1$ and $k_2$:
...between the direction $l$ and the principal direction corresponding to the principal curvature $k_1$.
803 bytes (112 words) - 17:23, 30 July 2014
...l space of a [[bundle]], transforming the latter into a [[Bundle#principal|principal $G$-bundle]].
174 bytes (28 words) - 08:59, 12 December 2013
...of the indicatrix of the curvature (cf. [[Dupin indicatrix]]). If $t$ is a principal direction, the relation (Rodrigues' formula)
...l direction. The normal curvature in a principal direction is known as a [[principal curvature]].
1 KB (180 words) - 16:49, 12 October 2017
...principal [[ultrafilter]]. The [[Fréchet filter]] is an example of a non-principal filter.
454 bytes (69 words) - 12:00, 23 November 2023
...discarding all the terms not containing derivatives of maximal order. The principal part of the differential operator
...differentiations with respect to the various arguments. For instance, the principal part of the differential operator $D_1-D_2^2+\alpha D_2$ is sometimes defin
2 KB (249 words) - 14:26, 8 August 2014
...by K.M. Peterson as examples of surfaces allowing of a deformation over a principal base.
827 bytes (119 words) - 17:12, 7 February 2011
...onversely (Finikov's theorem), the only surface with an infinite number of principal bases is a right helicoid [[#References|[2]]].
1 KB (170 words) - 17:32, 5 June 2020
''Dirichlet principal character''
where $D$ is a given natural number. Principal characters serve to define the concepts of primitive and imprimitive charac
340 bytes (45 words) - 20:04, 9 January 2015
#REDIRECT [[Principal translation]]
35 bytes (3 words) - 20:38, 1 September 2017
#REDIRECT [[Principal ideal ring]]
34 bytes (4 words) - 20:26, 7 February 2017
...ly for principal ideals) which is Bezout is a principal ideal ring. As for principal ideal rings, a module of finite type over a Bezout ring is a direct sum of
1 KB (190 words) - 19:52, 2 November 2014
...equal to zero, one of the principal curvatures (cf. [[Principal curvature|Principal curvature]]) vanishes, and the coefficients of the [[Second fundamental for
924 bytes (123 words) - 19:11, 12 April 2014
...that generates a prime ideal). An atomic [[Bezout ring|Bezout ring]] is a principal ideal ring.
...one simply speaks of rings which satisfy the ascending chain condition for principal ideals or the divisor chain condition.
1 KB (177 words) - 17:14, 7 February 2011
$#C+1 = 14 : ~/encyclopedia/old_files/data/M062/M.0602310 Mapping, principal net of a,
The directions tangential to the lines of the principal net of the mapping at the point $ x \in G $
1 KB (229 words) - 07:59, 6 June 2020
...states that $b^G$ is the principal block of $RG$ if and only if $b$ is the principal block of $RH$.
1 KB (249 words) - 09:15, 27 June 2014
$#C+1 = 26 : ~/encyclopedia/old_files/data/P074/P.0704790 Principal type, partial differential operator of,
whose principal part $ P( D) $(
2 KB (356 words) - 08:07, 6 June 2020
...ity $A^2=A$ is valid. All [[regular semi-group]]s are semi-simple. If each principal factor of a semi-group is either completely $0$-simple or completely simple
Any semi-group consists, as it were, of its principal factors. This explains, in particular, the important role played by ideally
2 KB (362 words) - 19:18, 16 January 2018
...and vice versa. If $\sigma$ is a principal base for a [[Deformation over a principal base|deformation]] of $X$, then $Y$ is a [[Bianchi surface]].
468 bytes (76 words) - 19:44, 24 April 2016
...f it is closed with respect to all translations (or with respect to merely principal translations).
759 bytes (110 words) - 16:59, 23 November 2023
...ase|deformation over a principal base]] and to classify them. Thus, if the principal base contains two families of geodesic lines, the functions $U$ and $V$ are
...ss $B_1$ is characterized by the fact that only one family of lines of the principal base are geodesics (one of the functions $U,V$ is constant); conoids may se
2 KB (294 words) - 14:19, 29 April 2014