منابع مشابه
Some polynomial extremal problems which emerged in the twentieth century
Most of the “extremal problems” of Harmonic (or Fourier) Analysis which emerged before the year 2000 were actually born in the twentieth century, and their emergences were scattered throughout that century, including the two world war periods. A great many of these problems pertain to polynomials, trigonometric polynomials and (finite) exponential sums. Writing a reasonably complete monograph o...
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Let G be a finite simple directed graph on n vertices. Say G is m-free if it has no directed cycles of length at most m. In 1978, Caccetta and Häggkvist [3] conjectured that if G has minimum out-degree at least r, then G is not dn/re-free. Finding upper bounds on the minimum out-degree in 3-free digraphs has been of particular interest in recent research. In this thesis, we present new results ...
متن کاملAn Extremal Nonnegative Sine Polynomial
For any positive integer n, the sine polynomials that are nonnegative in [0, π] and which have the maximal derivative at the origin are determined in an explicit form. Associated cosine polynomials Kn(θ) are constructed in such a way that {Kn(θ)} is a summability kernel. Thus, for each p, 1 ≤ p ≤ ∞ and for any 2π-periodic function f ∈ Lp[−π, π], the sequence of convolutions Kn ∗ f is proved to ...
متن کاملExtremal sequences of polynomial complexity
The joint spectral radius of a bounded set of d × d real matrices is defined to be the maximum possible exponential growth rate of products of matrices drawn from that set. For a fixed set of matrices, a sequence of matrices drawn from that set is called extremal if the associated sequence of partial products achieves this maximal rate of growth. An influential conjecture of J. Lagarias and Y. ...
متن کاملExtremal Problems for Geometric Hypergraphs 1 Extremal Problems for Geometric
A geometric hypergraph H is a collection of i-dimensional simplices, called hyperedges or, simply, edges, induced by some (i + 1)-tuples of a vertex set V in general position in d-space. The topological structure of geometric graphs, i.e., the case d = 2; i = 1, has been studied extensively, and it proved to be instrumental for the solution of a wide range of problems in combinatorial and compu...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1971
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1971-0281884-9