共查询到20条相似文献,搜索用时 15 毫秒
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Martin Klazar 《Discrete Mathematics》1996,150(1-3):195-203
Davenport-Schinzel sequences DS(s) are finite sequences of some symbols with no immediate repetition and with no alternating subsequence (i.e. of the type ababab …) of the length s. This concept based on a geometrical motivation is due to Davenport and Schinzel in the middle of 1960s. In the late 1980s strong lower and upper (superlinear) bounds on the maximum length of the DS(s) sequences on n symbols were found. DS(s) sequences are well known to computer geometrists because of their application to the estimates of the complexity of the lower envelopes.
Here we summarize some properties of the generalization of this concept and prove that the extremal functions of aa… abb… baa… abb… b grow linearly. 相似文献
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Kai-Ching Lin 《Transactions of the American Mathematical Society》1996,348(7):2663-2671
Let be a bounded smooth domain in , and a function with compact support in . Moser's inequality states that there is a constant , depending only on the dimension , such that
where is the Lebesgue measure of , and the surface area of the unit ball in . We prove in this paper that there are extremal functions for this inequality. In other words, we show that the
is attained. Earlier results include Carleson-Chang (1986, is a ball in any dimension) and Flucher (1992, is any domain in 2-dimensions).
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In this article Turán-type problems for several triple systems arising from (k, k ? 2)-configurations [i.e. (k ? 2) triples on k vertices] are considered. It will be shown that every Steiner triple system contains a (k, k ? 2)-configuration for some k < c log n/ log log n. Moreover, the Turán numbers of (k, k ? 2)-trees are determined asymptotically to be ((k ? 3)/3).(n2) (1?o(1)). Finally, anti-Pasch hypergraphs avoiding (5, 3) -and (6, 4)-Configurations are considered. © 1993 John Wiley & Sons, Inc. 相似文献
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Aharon Atzmon 《Journal of Mathematical Analysis and Applications》1978,65(2):333-338
It is shown that the theorem of Carathéodory and Toeplitz on the characterization of the Taylor coefficients of analytic functions with positive real part can be applied to extremal problems in several classes of analytic functions. 相似文献
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Science China Mathematics - In this paper, using the blow-up analysis, we prove a singular Hardy-Morser-Trudinger inequality, and find its extremal functions. Our results extend those of Wang and... 相似文献
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We characterize the extremal measures of an indeterminate moment problem associated with a system of orthogonal polynomials defined by a three-term recurrence relation. 相似文献
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G. M. Kesel'man 《Mathematical Notes》1979,25(3):177-182
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Mathieu Mansuy 《代数通讯》2018,46(4):1397-1419
We define integrable representations of quantum toroidal algebras of type A by tensor product, using the Drinfeld “coproduct.” This allows us to recover the vector representations recently introduced by Feigin–Jimbo–Miwa–Mukhin [7] and constructed by the author [21] as a subfamily of extremal loop weight modules. In addition we get new extremal loop weight modules as subquotients of tensor powers of vector representations. As an application we obtain finite-dimensional representations of quantum toroidal algebras by specializing the quantum parameter at roots of unity. 相似文献
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Andreas Hartmann 《Journal of Functional Analysis》2003,202(2):342-362
In this paper, an extremal function of a Banach space of analytic functions in the unit disk (not all functions vanishing at 0) is a function solving the extremal problem for functions f of norm 1. We study extremal functions of kernels of Toeplitz operators on Hardy spaces Hp, 1<p<∞. Such kernels are special cases of so-called nearly invariant subspaces with respect to the backward shift, for which Hitt proved that when p=2, extremal functions act as isometric divisors. We show that the extremal function is still a contractive divisor when p<2 and an expansive divisor when p>2 (modulo p-dependent multiplicative constants). We give examples showing that the extremal function may fail to be a contractive divisor when p>2 and also fail to be an expansive divisor when p<2. We discuss to what extent these results characterize the Toeplitz operators via invariant subspaces for the backward shift. 相似文献