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Thinnest Covering of the Euclidean Plane with Incongruent Circles

100%

Dorninger D.

Analysis and Geometry in Metric Spaces

2017

tom 5

nr 1

40-46

In 1958 L. Fejes Tóth and J. Molnar proposed a conjecture about a lower bound for the thinnest covering of the plane by circles with arbitrary radii from a given interval of the reals. If only two kinds of radii can occur this conjecture was in essence proven by A. Florian in 1962, leaving the general case unanswered till now. The goal of this paper is to analytically describe the general case in such a way that the conjecture can easily be numerically verified and upper and lower limits for the asserted bound can be gained.

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Ring-like structures with unique symmetric difference related to quantum logic

51%

Dorninger D., Länger H., Maczyński M.

Discussiones Mathematicae - General Algebra and Applications

2001

tom 21

nr 2

239-253

Ring-like quantum structures generalizing Boolean rings and having the property that the terms corresponding to the two normal forms of the symmetric difference in Boolean algebras coincide are investigated. Subclasses of these structures are algebraically characterized and related to quantum logic. In particular, a physical interpretation of the proposed model following Mackey's approach to axiomatic quantum mechanics is given.

Ograniczanie wyników

1 Analysis and Geometry in Metric Spaces

1 Discussiones Mathematicae - General Algebra and Applications

2 Dorninger D.

1 Länger H.

1 Maczyński M.

1 2017

1 2001

Wyniki wyszukiwania

Thinnest Covering of the Euclidean Plane with Incongruent Circles

Ring-like structures with unique symmetric difference related to quantum logic