### Sheaves and $\U0001d517a$-bicompactifications of mappings.

Ulyanov, V.M. (2007)

Sibirskie Ehlektronnye Matematicheskie Izvestiya [electronic only]

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Ulyanov, V.M. (2007)

Sibirskie Ehlektronnye Matematicheskie Izvestiya [electronic only]

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Dharmanand Baboolal (2011)

Czechoslovak Mathematical Journal

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Perfect compactifications of frames are introduced. It is shown that the Stone-Čech compactification is an example of such a compactification. We also introduce rim-compact frames and for such frames we define its Freudenthal compactification, another example of a perfect compactification. The remainder of a rim-compact frame in its Freudenthal compactification is shown to be zero-dimensional. It is shown that with the assumption of the Boolean Ultrafilter Theorem the Freudenthal compactification...

Fon-Der-Flaass, D.G. (2007)

Sibirskie Ehlektronnye Matematicheskie Izvestiya [electronic only]

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Kazarina, V.I. (2006)

Sibirskie Ehlektronnye Matematicheskie Izvestiya [electronic only]

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Righi, Céline (2007)

Séminaire Lotharingien de Combinatoire [electronic only]

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Hahlomaa, Immo (2007)

Annales Academiae Scientiarum Fennicae. Mathematica

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Lepsveridze, G. (1998)

Georgian Mathematical Journal

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Alexandre Eremenko, Dmitry Jakobson, Nikolai Nadirashvili (2007)

Annales de l’institut Fourier

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We discuss possible topological configurations of nodal sets, in particular the number of their components, for spherical harmonics on ${S}^{2}$. We also construct a solution of the equation $\Delta u=u$ in ${\mathbb{R}}^{2}$ that has only two nodal domains. This equation arises in the study of high energy eigenfunctions.

Akimov, A.A. (2006)

Sibirskie Ehlektronnye Matematicheskie Izvestiya [electronic only]

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Stepanov, V.N. (2005)

Sibirskie Ehlektronnye Matematicheskie Izvestiya [electronic only]

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Kulpeshov, B.Sh. (2006)

Sibirskie Ehlektronnye Matematicheskie Izvestiya [electronic only]

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Agarwal, Ravi P., O'Regan, Donal (2001)

Georgian Mathematical Journal

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Tomáš Hejda, Zuzana Masáková, Edita Pelantová (2013)

Kybernetika

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We consider positional numeration systems with negative real base $-\beta $, where $\beta >1$, and study the extremal representations in these systems, called here the greedy and lazy representations. We give algorithms for determination of minimal and maximal $(-\beta )$-representation with respect to the alternate order. We also show that both extremal representations can be obtained as representations in the positive base ${\beta}^{2}$ with a non-integer alphabet. This enables us to characterize digit sequences admissible...