An element $e$ in a set $M$ is called a left (right) unit (left (right) identity) with respect to a [[binary operation]] $*$ defined
...unit is used for only one of these operations, usually multiplication. The unit with respect to addition is called the [[zero]] element.
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...m''' asks how large the values of such a polynomial must be on the [[unit circle]] in the [[complex plane]]. The answer to this would yield information ab
...= \pm 1$. Let $\Vert p \Vert$ denote the supremum of $p(z)$ on the unit circle. ''Littlewood's problem'' asks for constants $c_1$ and $c_2$ such that th
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...le has 180 degrees. Degrees are also used to measure circular arcs (a full circle has 360 degrees).
...ee of irrationality, and many more. It is also, of course, the name of the unit for temperature measurements in various scales.
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...$ radians; it is approximately $57^\circ17'44''$. A radian is taken as the unit of measurement of angles in the so-called circular, or radian, measurement
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...e real axis (the equation is stable), then the multipliers lie on the unit circle. Consider a canonical equation $\dot x = i \lambda J H(t) x$ with a real pa
...ability it is necessary and sufficient that all multipliers be on the unit circle and that there be no coincident multipliers of different kinds.
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then the circle $\lvert z\rvert=R$ is a [[natural boundary]]: all points of the cicle are s
...t sequence $p_n$, radius of convergence equal to 1, but for which the unit circle is not a natural boundary.
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Szegö quadrature formulas are the analogues on the unit circle $\bf T$ in the complex plane of the Gauss quadrature formulas on an interva
...i_n$ as nodes (as in Gaussian formulas), because these are all in the open unit disc $\mathbf D$ (cf. also [[Szegö polynomial|Szegö polynomial]]). Theref
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...ert kernel and the [[Cauchy kernel|Cauchy kernel]] in the case of the unit circle:
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...[[Multipliers|Multipliers]]) of the variational equation lies on the unit circle. There are also results about the local structural stability of certain hyp
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...nces|[4]]]). There are various generalizations of a self-perimeter for the unit sphere $S$ in a normed space of dimension greater than two (see [[#Referenc
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...al power dilation with spectrum in $\partial S$. The minimal radius of the circle which is a spectral set for every contraction in a Banach space is equal to
...> J. von Neumann, "Eine Spektraltheorie für allgemeine Operatoren eines unitären Raumes" ''Math. Nachr.'' , '''4''' (1951) pp. 258–281</TD></TR><T
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...a closed curve $L'$ with a cusp at the point $w=1$, touching an arc of the circle $L$ (the image of $K$) at that point; this image is represented in Fig. ban
The function $w=\lambda(\rho t+\alpha)$ maps the exterior of the unit circle in the $t$-plane to the exterior of $L'$. To obtain a Zhukovskii profile of
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be a bounded regular analytic function in the unit disc $ \Omega = \{ {z \in \mathbf C } : {| z | < 1 } \} $,
...s serve as Lobachevskii straight lines, these being orthogonal to the unit circle (Poincaré's model), and
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...omeomorphism of the open attainable boundary arc onto some open arc of the circle $|z| = 1$.
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...n a so-called great circle is obtained as the intersection. A unique great circle can be drawn through any two points $A$ and $B$ on the sphere (Fig. a), exc
...a straight line is the shortest curve between its ends, an arc of a great circle on a sphere is only the shortest curve when it is shorter than the compleme
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...fmath.org/legacyimages/a/a013/a013980/a0139808.png" /> lie inside the unit circle, then equation (*) has the solution
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...ally onto a standard pair $(D^n,D^m)$ or $(D^n,D_+^m)$, where $D^k$ is the unit ball of the space $\mathbf R^k$ with centre at the origin and $D_+^k$ is th
...imbedding of a circle and an arc into a plane is locally flat; however, a circle or an arc can be imbedded in $\mathbf R^k$ with $k\geq3$ in a manner that i
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...nd bijectively. The circle property: Under a fractional-linear mapping any circle in $ \overline{\mathbf C}\; $(
i.e. a circle in $ \mathbf C $
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...axis of revolution and the circle described by the centre of its rotating circle.
...f $u$ and $v$, $r$ is the radius vector of the surface $F$, and $n$ is the unit normal to $F$.
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in the open unit disc whose $ H ^ \infty $-
...hur algorithm can also be used to obtain a Routh or Jury test for the open unit disc, that is, the Schur algorithm can be used to determine whether or not
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