Results 221 to 230 of about 71,302 (258)

On semialgebraic tangent cones

1998
Summary: The paper deals with the following question: Which semialgebraic subsets of \(\mathbb{R}^n\) can be realized as tangent cones to real algebraic subsets of \(\mathbb{R}^n\)? At first we prove that the answer is positive for every closed semialgebraic cone in \(\mathbb{R}^n\) of dimension \(\leq 2\). Then, for closed semialgebraic cones \(A\) in
FERRAROTTI M, FORTUNA, ELISABETTA
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Tangent cones and Dini derivatives

Journal of Optimization Theory and Applications, 1991
Characterizations of the Bouligand contingent cone to the epigraph and graph of a locally Lipschitz function are given. It is proved that, if f:H\(\mapsto {\mathbb{R}}\) is a locally Lipschitz function on a Hilbert space H, then \(T_{Epi(f)}(x,f(x))=\{(x',y')| \quad \exists \{a_ n\}^{\infty}_{n=1},\quad \{y_ n\}^{\infty}_{n=1}\subset {\mathbb{R}},\quad
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Singular Points and Tangent Cones

1992
The Zariski tangent space to a variety X ⊂ 𝔸n at a point p is described by taking the linear part of the expansion around p of all the functions on 𝔸n vanishing on X. In case p is a singular point of X, however, this does not give us a very refined picture of the local geometry of X; for example, if X ⊂ 𝔸2 is a plane curve, the Zariski tangent space to
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STABLE MINIMAL HYPERSURFACES AND TANGENT CONE SINGULARITIES

International Journal of Mathematics, 1999
In this paper, I give an estimate on the dimension of the singular set of a tangent cone at infinity of a stable minimal hypersurface. Namely, let Mn ⊂ ℝn+1, n ≥ 2, be a complete orientable stable minimal immersion with bounded volume growth. Then n < 7 implies T∞(M) is smooth, and n ≥ 7 implies the singular set of T∞(M) has codimension at least ...
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Tangent Cones and Intersection Theory

1989
Let E be an arbitrary set in ℝ N . A vector ν ∈ ℝ N is called tangent to E at a point a ∈ Ē if there exist a sequence of points a j ∈ E and numbers t j > 0 such that a j → a and t j (a j − a) → ν as j→ ∞. The set of all such tangent vectors is denoted by C(E, a) and is called the tangent cone to E at a.
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Tangent Cones

2008
Jean-Pierre Aubin, Hèléne Frankowska
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Dirac cone, flat band and saddle point in kagome magnet YMn6Sn6

Nature Communications, 2021
Man Li, Rui Lou, Zhengtai Liu
exaly  

Tangent cones and analytic branches

1986
Let X be an algebraic variety over an algebraically closed field. Let Y be an irreducible subvariety of X of codimension 1 with generic point y. The structure of the tangent cone \(T_{X,x}\) of X at almost all closed points x in Y is compared to that of \(T_{x,y}\). This is done by using the theory of branches as developed by \textit{S. Greco} in Proc.
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A fully automatic AI system for tooth and alveolar bone segmentation from cone-beam CT images

Nature Communications, 2022
Zhiming Cui, Yu Fang, Lanzhuju Mei
exaly  

Tangent Cones, Tangent Spaces, Tangent Stars: Secant, Tangent, Tangent Star and Dual Varieties of an Algebraic Variety

2016
We recall the definitions of tangent cone, tangent space, tangent star to a variety at a fixed point, define the secant variety SX, the higher secant varieties S k X, the tangent variety TX and the variety of tangent stars T∗X of a variety \(X \subset \mathbb{P}^{N}\). We consider the join of a variety \(X \subset \mathbb{P}^{N}\) with another variety \
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