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For an arbitrary triangle ABC and an integer n we define points Dn, En, Fn on the sides BC, CA, AB respectively, in such a manner that |AC|n|AB|n=|CDn||BDn|,|AB|n|BC|n=|AEn||CEn|,|BC|n|AC|n=|BFn||AFn|. $\frac{{|A C|}^{n}}{{|A B|}^{n}} = \frac{|C D_{n}|}{|B D_{n}|}, \frac{{|A B|}^{n}}{{|B C|}^{n}} = \frac{|A E_{n}|}{|C E_{n}|}, \frac{{|B C|}^{n}}{{|A C|}^{n}} = \frac{|B F_{n}|}{|A F_{n}|} .$ Cevians ADn, BEn, CFn are said to be the Maneeals of order n. In this paper we discuss some properties of the Maneeals and related objects.

Shape tiling.

Keating, Kevin, King, Jonathan L. (1997)

The Electronic Journal of Combinatorics [electronic only]

Sharpening on Mircea's inequality.

Wu, Yu-Dong, Zhang, Zhi-Hua, Lokesha, V. (2007)

JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]

Sharply 2-transitive sets of permutations and groups of affine projectivities.

Grundhöfer, Theo, Müller, Peter (2009)

Beiträge zur Algebra und Geometrie

Shells of monotone curves

Josef Mikeš, Karl Strambach (2015)

Czechoslovak Mathematical Journal

We determine in $ℝ^{n}$ the form of curves $C$ corresponding to strictly monotone functions as well as the components of affine connections $\nabla$ for which any image of $C$ under a compact-free group $Ω$ of affinities containing the translation group is a geodesic with respect to $\nabla$ . Special attention is paid to the case that $Ω$ contains many dilatations or that $C$ is a curve in $ℝ^{3}$ . If $C$ is a curve in $ℝ^{3}$ and $Ω$ is the translation group then we calculate not only the components of the curvature and the Weyl tensor but...

Shodná zobrazení v prostoru

František Kuřina (1966)

Pokroky matematiky, fyziky a astronomie

Sigma models with non-commuting complex structures and extended supersymmetry

M. Göteman, Ulf Lindström (2010)

Archivum Mathematicum

We discuss additional supersymmetries for $𝒩 = (2, 2)$ supersymmetric non-linear sigma models described by left and right semichiral superfields.

Similarity motions in $E_{3}$ with plane trajectories

Adolf Karger (1981)

Aplikace matematiky

In this paper the author finds and describes all similarity space motions, which have only plane trajectories of points. All such motions are explicitly expressed. They are of 5 types, all of them cylindrical. Trajectories are conic sections (3 types) or arbitrary plane curves (2 types).

Simple counter examples for the unsolvability of the Fermat- and Steiner-Weber-problem by compass and ruler.

Mehlhos, St. (2000)

Beiträge zur Algebra und Geometrie

Simple Groups and Möbius Planes of Even Order.

Judita Cofman (1971)

Mathematische Zeitschrift

Simplicial finite elements in higher dimensions

Jan Brandts, Sergey Korotov, Michal Křížek (2007)

Applications of Mathematics

Over the past fifty years, finite element methods for the approximation of solutions of partial differential equations (PDEs) have become a powerful and reliable tool. Theoretically, these methods are not restricted to PDEs formulated on physical domains up to dimension three. Although at present there does not seem to be a very high practical demand for finite element methods that use higher dimensional simplicial partitions, there are some advantages in studying the methods independent of the...

Simplicial maps from the 3-sphere to the 2-sphere.

Madahar, Keerti Vardhan (2002)

Advances in Geometry

Skewsquares in quadratical quasigroups

Vladimír Volenec, Ružica Kolar-Šuper (2008)

Commentationes Mathematicae Universitatis Carolinae

The concept of pseudosquare in a general quadratical quasigroup is introduced and connections to some other geometrical concepts are studied. The geometrical presentations of some proved statements are given in the quadratical quasigroup $ℂ (\frac{1 + i}{2})$ .

Sliding subspace design based on linear matrix inequalities

Alán Tapia, Raymundo Márquez, Miguel Bernal, Joaquín Cortez (2014)

Kybernetika

In this work, an alternative for sliding surface design based on linear and bilinear matrix inequalities is proposed. The methodology applies for reduced and integral sliding mode control, both continuous- and discrete-time; it takes advantage of the Finsler's lemma to provide a greater degree of freedom than existing approaches for sliding subspace design. The sliding surfaces thus constructed are systematically found via convex optimization techniques, which are efficiently implemented in commercially...

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