Displaying similar documents to “On some properties of squares of Sierpiński sets”

Some results on magic squares based on generating magic vectors and R-C similar transformations

Xiaoyang Ma, Kai-tai Fang, Yu hui Deng (2017)

Special Matrices

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In this paper we propose a new method, based on R-C similar transformation method, to study classification for the magic squares of order 5. The R-C similar transformation is defined by exchanging two rows and related two columns of a magic square. Many new results for classification of the magic squares of order 5 are obtained by the R-C similar transformation method. Relationships between basic forms and R-C similar magic squares are discussed. We also propose a so called GMV (generating...

On the sum of two squares and two powers of k

Roger Clement Crocker (2008)

Colloquium Mathematicae

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It can be shown that the positive integers representable as the sum of two squares and one power of k (k any fixed integer ≥ 2) have positive density, from which it follows that those integers representable as the sum of two squares and (at most) two powers of k also have positive density. The purpose of this paper is to show that there is an infinity of positive integers not representable as the sum of two squares and two (or fewer) powers of k, k again any fixed integer ≥ 2. ...

On melancholic magic squares

Götz Trenkler, Dietrich Trenkler (2013)

Discussiones Mathematicae Probability and Statistics

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Starting with Dürer's magic square which appears in the well-known copper plate engraving Melencolia we consider the class of melancholic magic squares. Each member of this class exhibits the same 86 patterns of Dürer's magic square and is magic again. Special attention is paid to the eigenstructure of melancholic magic squares, their group inverse and their Moore-Penrose inverse. It is seen how the patterns of the original Dürer square to a large extent are passed down also to the inverses...

Latin squares of order 10.

McKay, Brendan D., Rogoyski, Eric (1995)

The Electronic Journal of Combinatorics [electronic only]

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Kriging and masurement errors

István Fazekas, Alexander G. Kukush (2005)

Discussiones Mathematicae Probability and Statistics

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A linear geostatistical model is considered. Properties of a universal kriging are studied when the locations of observations aremeasured with errors. Alternative prediction procedures are introduced and their least squares errors are analyzed.