Displaying similar documents to “Sheaves and 𝔗 a -bicompactifications of mappings.”

Speculating About Mountains

Ribarska, N., Tsachev, Ts., Krastanov, M. (1996)

Serdica Mathematical Journal

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∗Partially supported by Grant MM 409/94 of the Mininstry of Education, Science and Technology, Bulgaria. ∗∗Partially supported by Grants MM 521/95, MM 442/94 of the Mininstry of Education, Science and Technology, Bulgaria. The definition of the weak slope of continuous functions introduced by Degiovanni and Marzocchi (cf. [8]) and its interrelation with the notion “steepness” of locally Lipschitz functions are discussed. A deformation lemma and a mountain pass theorem for...

Greedy and lazy representations in negative base systems

Tomáš Hejda, Zuzana Masáková, Edita Pelantová (2013)

Kybernetika

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We consider positional numeration systems with negative real base - β , where β > 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 ( - β ) -representation with respect to the alternate order. We also show that both extremal representations can be obtained as representations in the positive base β 2 with a non-integer alphabet. This enables us to characterize digit sequences admissible...

On nodal sets and nodal domains on S 2 and ℝ 2

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 Δ u = u in ℝ 2 that has only two nodal domains. This equation arises in the study of high energy eigenfunctions.