...f a quadratic differential are called critical points of it. The zeros and simple poles are called finite critical points and their totality is denoted by $
...nt for each choice of the sign of the integrand; furthermore, each maximal arc of a trajectory (or orthogonal trajectory) of $ U $
7 KB (1,091 words) - 19:19, 20 January 2022
...images/r/r082/r082150/r08215077.png" /> is a parameter proportional to the arc length, takes the form
...mplete (geodesically complete) if it is complete as a metric space (if any arc of a geodesic can be extended indefinitely on both sides). A Riemannian spa
55 KB (7,564 words) - 16:56, 7 February 2011
...mid 0 \leq s \leq S \} $, $ x = (x_{1},\ldots,x_{n}) $, where $ s $ is the arc-length; let $ F = F(x(s)) $ be a function defined on $ \gamma $. The curvil
...'line integral of the first kind''', or a '''line integral with respect to arc-length'''. It is the limit of suitable integral sums, which can be describe
9 KB (1,447 words) - 06:40, 1 December 2016
...of them is also finite, then such a curve can be split into finitely many simple arcs having no common points except their end points.
...an curve|Jordan curve]] (a space homeomorphic to the circle, also called a simple closed curve).
19 KB (2,971 words) - 19:30, 26 March 2023
onto the $ w $-plane with slit along an arc of the circle $ | w- \beta _ {0} | = | \zeta _ {0} | $
The estimates (3)–(5) are simple consequences of results on the ranges of the functionals
11 KB (1,524 words) - 02:42, 14 September 2022
...l stems from the fact that they appeared first in the rectification of the arc of an ellipse and other second-order curves in work by Jacob and Johann Ber
...d kind and third kinds have a pole-type singularity with residue zero or a simple pole, respectively. Regarded as functions of the upper limit of integration
11 KB (1,593 words) - 19:37, 5 June 2020
is the arc element.
...ecessary for the solution of each problem; hence there arises a method, as simple as it is general, for solving problems concerning the motions of bodies" (
5 KB (820 words) - 08:00, 6 June 2020
Some very simple solutions are given below.
...it circle $\gamma = \{ z _ { 1 } : | z _ { 1 } | = 1 \}$ and a smooth open arc $\Gamma$ connecting two points of $\gamma$ and lying inside $\gamma$. Let $
6 KB (978 words) - 17:44, 1 July 2020
...ch functions. At that time one basically studied three, geometrically most simple, cases in the theory of cluster sets: a) $ z _ {0} $
of the second category and metrically dense on some arc $ \gamma \subset \Gamma $,
25 KB (3,728 words) - 09:43, 26 March 2023
...) \subseteq \mathbf C$, bounded by an arc of the unit circle and a smooth simple curve $\Gamma \subseteq B ( 0,1 )$ and assume that $f \in C ( \Gamma )$. Th
6 KB (961 words) - 16:45, 1 July 2020
...{C} \backslash K$. In $\mathbf{C} ^ { n }$, $n > 1$, there is no such a simple topological description.
...slash K$ (cf. also [[Analytic set|Analytic set]]). If $K$ is a rectifiable arc, $K$ is polynomially convex and $P ( K ) = C ( K )$.
20 KB (3,071 words) - 17:45, 1 July 2020
If all the roots are simple, then the functions
are real and equation (8) has a complex root, for example a simple root $ q _ {k} = \rho ( \cos \phi + i \sin \phi ) $,
14 KB (1,916 words) - 19:59, 12 January 2024
...ic features of more general random walks. In particular, even in this very simple scheme there appear properties of "randomness" which are intuitively para
\mathop{\rm arc} \sin \sqrt \alpha .
9 KB (1,462 words) - 07:50, 26 March 2023
...y classes, since it is a Hilbert space with a reproducing kernel and has a simple description in terms of the Taylor coefficients:
...igher-dimensional case becomes manifest, first of all, in the absence of a simple characterization of the zero sets and of a factorization of functions in th
37 KB (5,073 words) - 18:20, 1 December 2014
being the arc $ t ^ \prime tt ^ {\prime\prime} $
...plex-valued continuous function that does not vanish on an oriented closed simple smooth contour $ \Gamma $,
27 KB (3,955 words) - 10:05, 8 May 2022
bounded by a simple Jordan curve $ \sigma $
be a simply-connected mixed domain bounded by a simple Jordan curve $ \sigma $
19 KB (2,773 words) - 06:19, 24 February 2022
...okhotskii formulas (2) and (3) remain valid for the interior points of the arc $ \Gamma $.
The idea of representing a function on a simple closed curve as the jump of an analytic function across that curve has been
9 KB (1,249 words) - 14:55, 7 June 2020
is a simple parametric arc (the homeomorphic image of a closed interval); 3) $ \overline{S}\; \setmi
11 KB (1,688 words) - 08:12, 6 June 2020
be the length of the arc $ PQ $
The torsion and the curvature, as functions of the arc length, determine the curve up to its position in space.
16 KB (2,421 words) - 14:56, 7 June 2020
denotes the arc length reckoned from some fixed point, let $ \zeta _ {0} = \zeta (s _ {0}
regarded as a function of the arc length $ s $,
26 KB (3,804 words) - 08:11, 13 February 2022