Results 11 to 20 of about 427,912 (276)

Smoothness Parameter of Power of Euclidean Norm. [PDF]

J Optim Theory Appl, 2020
AbstractIn this paper, we study derivatives of powers of Euclidean norm. We prove their Hölder continuity and establish explicit expressions for the corresponding constants. We show that these constants are optimal for odd derivatives and at most two times suboptimal for the even ones.
Rodomanov A, Nesterov Y.
europepmc   +7 more sources

Some generalized Euclidean and 2-stage Euclidean number fields that are not norm-Euclidean [PDF]

Mathematics of Computation, 2011
We give examples of Generalized Euclidean but not norm-Euclidean number fields of degree greater than 2. In the same way we give examples of 2-stage Euclidean but not norm-Euclidean number fields of degree greater than 2. In both cases, no such examples were known.
Jean-Paul Cerri, Cerri, Jean-Paul
core   +5 more sources

EXAMPLES OF NORM-EUCLIDEAN IDEAL CLASSES [PDF]

International Journal of Number Theory, 2012
In this paper, we study the notion of norm-Euclidean ideal class, which was defined by Lenstra [Euclidean ideal classes, Astérisque 61 (1979) 121–131]. Using a slight modification of an algorithm determining among other properties the Euclidean minimum described in [P. Lezowski, Computation of the Euclidean minimum of algebraic number fields, preprint
LEZOWSKI, Pierre
openaire   +2 more sources

Quadratic number fields that are euclidean but not norm-euclidean [PDF]

, 2009
Diese Diplomarbeit befasst sich mit quadratischen Zahlkörpern welche euklidisch aber nicht normeuklidisch sind.
Lutzmann, Bernhard
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Norm-Euclidean Galois fields [PDF]

, 2010
Let K be a Galois number field of prime degree $\ell$. Heilbronn showed that for a given $\ell$ there are only finitely many such fields that are norm-Euclidean. In the case of $\ell=2$ all such norm-Euclidean fields have been identified, but for $\ell\neq 2$, little else is known. We give the first upper bounds on the discriminants of such fields when
McGown, Kevin Joseph, Kevin Joseph Mcgown   +1 more
openaire   +3 more sources

Upper Bounds for the Euclidean Operator Radius and Applications [PDF]

, 2006
The main aim of the present paper is to establish various sharp upper bounds for the Euclidean operator radius of an n−tuple of bounded linear operators on a Hilbert space.
Dragomir, Sever S
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Norm-Euclidean cyclic fields of prime degree [PDF]

Let K be a cyclic number field of prime degree ℓ. Heilbronn showed that for a given ℓ there are only finitely many such fields that are norm-Euclidean. In the case of ℓ = 2 all such norm-Euclidean fields have been identified, but for ℓ ≠ 2, little else ...
McGown, Kevin J.
core   +6 more sources

Planar separators and the Euclidean norm [PDF]

, 1990
In this paper we show that every 2-connected embedded planar graph with faces of sizes d1.....d f has a simple cycle separator of size 1.58 \(\sqrt {d_1^2 + \cdots + d_f^2 }\)and we give an almost linear time algorithm for finding these separators, O(no(n,n)). We show that the new upper bound expressed as a function of ‖G‖=\(\sqrt {d_1^2 + \cdots + d_f^
Hillel Gazit, Gary L. Miller
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Fractional Vector Cross Product in Euclidean 3-Space

International Journal of Analysis and Applications, 2023
In this research a new definition of fractional vector cross product of two vectors in Euclidean 3-space is presented. Using this new definition the formulae for Euclidean norm, fractional triple vector cross product, curl and divergence of fractional ...
Manisha M. Kankarej, Jai P. Singh
doaj   +1 more source

On the Lq-reflector problem in ℝn with non-Euclidean norm

Advanced Nonlinear Studies, 2022
In this article, we introduce a class of geometric optics measure-the LqΣ{L}_{q}\hspace{0.33em}\Sigma -reflector measure which arises from an Lq{L}_{q} extension of the Σ\Sigma -reflector measure.
Wang Jing
doaj   +1 more source