Displaying similar documents to “On the geometric concomitants”

Basic concepts of the theory of geometric objects

M. Kucharzewski, M. Kuczma

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ContentsIntroduction............................................................................................................................................................................... 3§ 1. Historical development of the concept of a geometric object..................................................................................4§ 2. Manifold, coordinate system, transformations of the coordinate system............................................................. 7§ 3. Group,...

Integral formula for secantoptics and its application

Witold Mozgawa, Magdalena Skrzypiec (2012)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

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Some properties of secantoptics of ovals defined by Skrzypiec in 2008 were proved by Mozgawa and Skrzypiec in 2009. In this paper we generalize to this case results obtained by Cieslak, Miernowski and Mozgawa in 1996 and derive an integral formula for an annulus bounded by a given oval and its secantoptic. We describe the change of the area bounded by a secantoptic and find the differential equation for this function. We finish with some examples illustrating the above results. ...

PROBLEMS

M. Chrobak, M. Habib, P. John, H. Sachs, H. Zernitz, J. R. Reay, G. Sierksma, M. M. Sysło, T. Traczyk, W. Wessel (1987)

Applicationes Mathematicae

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Integral formula for secantoptics and its application

Witold Mozgawa, Magdalena Skrzypiec (2012)

Annales UMCS, Mathematica

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Some properties of secantoptics of ovals defined by Skrzypiec in 2008 were proved by Mozgawa and Skrzypiec in 2009. In this paper we generalize to this case results obtained by Cieślak, Miernowski and Mozgawa in 1996 and derive an integral formula for an annulus bounded by a given oval and its secantoptic. We describe the change of the area bounded by a secantoptic and find the differential equation for this function. We finish with some examples illustrating the above results. ...

Estimation of the noncentrality matrix of a noncentral Wishart distribution with unit scale matrix. A matrix generalization of Leung's domination result.

Heinz Neudecker (2004)

SORT

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The main aim is to estimate the noncentrality matrix of a noncentral Wishart distribution. The method used is Leung's but generalized to a matrix loss function. Parallelly Leung's scalar noncentral Wishart identity is generalized to become a matrix identity. The concept of Löwner partial ordering of symmetric matrices is used.

A proof of the birationality of certain BHK-mirrors

Patrick Clarke (2014)

Complex Manifolds

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We generalize and give an elementary proof of Kelly’s refinement [9] of Shoemaker’s result [11] on the birationality of certain BHK-mirrors. Our approach uses a construction that is equivalent to the Krawitz generalization [10] of the duality in Berglund-Hübsch [2].