Displaying similar documents to “Integral formula for secantoptics and its application”

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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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 matrix derivation of a representation theorem for (tr A).

Heinz Neudecker (1989)

Qüestiió

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A matrix derivation of a well-known representation theorem for (tr A) is given, which is the solution of a restricted maximization problem. The paper further gives a solution of the corresponding restricted minimization problem.

The Lvov years of Wacław Sierpiński

Andrzej Schinzel (2009)

Banach Center Publications

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An account is given of Sierpiński's activity in Lvov (1908-1918) interrupted by World War I.

A note on the scalar Haffian.

Heinz Neudecker (2000)

Qüestiió

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In this note a uniform transparent presentation of the scalar Haffian will be given. Some well-known results will be generalized. A link will be established between the scalar Haffian and the derivative matrix as developed by Magnus and Neudecker.