Displaying similar documents to “Cyclic permutations of sequences and uniform partitions.”

Cyclic derangements.

Assaf, Sami H. (2010)

The Electronic Journal of Combinatorics [electronic only]

Similarity:

Sets of determination for solutions of the Helmholtz equation

Jarmila Ranošová (1997)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

Let α > 0 , λ = ( 2 α ) - 1 / 2 , S n - 1 be the ( n - 1 ) -dimensional unit sphere, σ be the surface measure on S n - 1 and h ( x ) = ∫ S n - 1 e λ 〈 x , y 〉 d σ ( y ) . We characterize all subsets M of ℝ n such that inf x ∈ ℝ n u ( x ) h ( x ) = inf x ∈ M u ( x ) h ( x ) for every positive solution u of the Helmholtz equation on ℝ n . A closely related problem of representing functions of L 1 ( S n - 1 ) as sums of blocks of the form e λ 〈 x k , . 〉 / h ( x k ) corresponding to points of M is also considered. The results provide a counterpart to results for classical harmonic functions in a ball, and for parabolic functions on a slab, see References.