...[#References|[a14]]]. Let $f$ be a bounded continuous function on the open unit disc $U$ in $\mathbf{R} ^ { 2 }$. Suppose that for each point in $U$ there
...ns integrable with respect to the (normalized) Lebesgue measure $m$ on the unit ball $B$ in $\mathbf{C} ^ { n }$. If $f$ is harmonic with respect to the in
17 KB (2,607 words) - 16:38, 2 February 2024
...$\mathbf{C}$) is rational, analytic within a circle containing the closed unit disc, $\operatorname { det } k ( z ) \neq 0$, $| z | < 1$, $k ( 0 ) = I$ (a
9 KB (1,297 words) - 09:30, 3 February 2024
These ideas have been applied as well to circle diffeomorphisms [[#References|[a10]]],
..., M.L. Stein, P.R. Stein, "On finite limit sets for transformations on the unit interval" ''J. Comb. Theory'' , '''15A''' (1973) pp. 25–44 {{MR|0316636}}
12 KB (1,685 words) - 08:27, 6 June 2020
be the end point of the arc on the unit circle $ x ^ {2} + y ^ {2} = 1 $(
12 KB (1,667 words) - 08:26, 6 June 2020
...while the statement "the ratio of the length of the circumference of the circle to its diameter is greater than three and ten seventy-firsts and less than
...$\bar{\eta}=8$, $\bar{\epsilon}=5$ and $\mu^0\bar{\alpha}$ means that the unit $\bar{\alpha}$ is not to be multiplied by a power of the unknown).
18 KB (2,697 words) - 13:11, 13 December 2013
Owing to the widespread use of electronic computers the circle of customers keeps increasing; hence the tendency to establish automatizati
...se considerably simplified the programming and substantially increased the circle of customers.
13 KB (1,892 words) - 20:11, 31 December 2018
5) Fix a pairing $P$. Consider the knot $K$ as an oriented circle and connect the points $( z _ { j } , t _ { j } )$ and $( z _ { j } ^ { \pr
...urther chords attached to their points, while on the solid portions of the circle all the endpoints are explicitly shown); and
10 KB (1,481 words) - 19:05, 23 January 2024
then this reduces to the unit circle $ | \lambda | = 1 $.
7 KB (1,085 words) - 08:13, 6 June 2020
...such as the real line $\mathbf{R}$, the unit interval $\mathbf{I}$ and the circle $S ^ { 1 }$ are absolute (neighbourhood) extensors. An absolute (neighbourh
8 KB (1,172 words) - 19:57, 15 March 2023
...-known tool for computing numerically the [[conformal mapping]] $g$ of the unit disc $D$ onto a star-like region $\Delta$ given by the polar coordinates $\
...wing cross-section into the exterior of a Jordan curve that is close to a circle; see [[#References|[a6]]], Chapt. 10. Moreover, for this application, the e
7 KB (1,076 words) - 07:40, 7 February 2024
dimensional unit matrix). For the absolute stability of the system (1) with respect to the o
The frequency criterion (12) (circle criterion) means that the frequency characteristic $ W ( i \omega ) $,
16 KB (2,300 words) - 08:22, 6 June 2020
...ue to the transition of a pair of its complex eigenvalues through the unit circle.
9 KB (1,234 words) - 22:11, 5 June 2020
lies in the unit sphere $ S ^ {N- 1} = \{ {z \in \mathbf R ^ {N} } : {| z | = 1 } \} $,
manifold and bundle of unit normal vectors for $ m \in M $
24 KB (3,546 words) - 19:41, 1 May 2023
...rve has been extensively generalized. Thus, every distribution on the unit circle and every tempered distribution on $ \mathbf R $
9 KB (1,249 words) - 14:55, 7 June 2020
...the points of a straight line are cyclically ordered, like the points on a circle. In addition, in Euclidean and hyperbolic geometries every straight line in
is a constant that depends on the specific unit chosen for the measurement of areas. In elliptic geometry, as well as in [[
17 KB (2,582 words) - 08:02, 6 June 2020
is the volume of the unit $ n $-sphere. Equality holds only for a sphere. The classical isoperimetr
is the radius of the largest inscribed circle, and its generalization (see [[#References|[11]]]) for convex bodies in $
9 KB (1,287 words) - 08:14, 13 January 2024
The unit disc is naturally identified with the space of maximal ideals of $ A $.
is non-Euclidean, and the one-point sets on the circle and in the interior of the disc serve as the Gleason parts. Gleason parts d
11 KB (1,877 words) - 16:10, 1 April 2020
is the unit disc or, in general, a Jordan domain, and $ z _ {0} $
holomorphic in the unit disc $ D = \{ {z } : {| z | < 1 } \} $
25 KB (3,728 words) - 09:43, 26 March 2023
...ts, the integral invariant is the unit, for a set of lines it is again the unit if one selects for the parameters of the lines the parameters $ p $
For sets of points, the integral invariant is again equal to the unit. If a set of straight lines is given by the set of their equations in two p
28 KB (4,292 words) - 08:45, 1 July 2022
and some unit vector $ \mathbf l $
...point are zero, the point is said to be flat. If the Dupin indicatrix is a circle it is called an umbilical (or spherical) point.
26 KB (4,098 words) - 17:31, 5 June 2020