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181.
182.
183.
Let ? be a bounded and connected open subset of R~N with a Lipschitzcontinuous boundary,the set ? being locally on the same side of ??.A vector version of a fundamental lemma of J.L.Lions,due to C.Amrouche,the first author,L.Gratie and S.Kesavan,asserts that any vector field v =(vi) ∈(D′(?))~N,such that all the components 1/2(?_jv_i + ?_iv_j),1 ≤ i,j ≤ N,of its symmetrized gradient matrix field are in the space H~(-1)(?),is in effect in the space(L~2(?))~N.The objective of this paper is to show that this vector version of J.L.Lions lemma is equivalent to a certain number of other properties of interest by themselves.These include in particular a vector version of a well-known inequality due to J.Neˇcas,weak versions of the classical Donati and Saint-Venant compatibility conditions for a matrix field to be the symmetrized gradient matrix field of a vector field,or a natural vector version of a fundamental surjectivity property of the divergence operator. 相似文献
184.
In this paper we study multilinear isometries defined on certain subspaces of vector-valued continuous functions. We provide conditions under which such maps can be properly represented. Our results contain all known results concerning linear and bilinear isometries defined between spaces of continuous functions. The key result is a vector-valued version of the additive Bishop’s Lemma, which we think has interest in itself. 相似文献
185.
《Journal of Graph Theory》2018,89(3):266-287
The Erdős–Hajnal conjecture states that for every given undirected graph H there exists a constant such that every graph G that does not contain H as an induced subgraph contains a clique or a stable set of size at least . The conjecture is still open. Its equivalent directed version states that for every given tournament H there exists a constant such that every H‐free tournament T contains a transitive subtournament of order at least . In this article, we prove that for several pairs of tournaments, H1 and H2, there exists a constant such that every ‐free tournament T contains a transitive subtournament of size at least . In particular, we prove that for several tournaments H, there exists a constant such that every ‐free tournament T, where stands for the complement of H, has a transitive subtournament of size at least . To the best of our knowledge these are first nontrivial results of this type. 相似文献
186.
187.
This paper considers some random processes of the form X
n+1=T
X
n
+B
n
(mod p) where B
n
and X
n
are random variables over (ℤ/pℤ)
d
and T is a fixed d×d integer matrix which is invertible over the complex numbers. For a particular distribution for B
n
, this paper improves results of Asci to show that if T has no complex eigenvalues of length 1, then for integers p relatively prime to det (T), order (log p)2 steps suffice to make X
n
close to uniformly distributed where X
0 is the zero vector. This paper also shows that if T has a complex eigenvalue which is a root of unity, then order p
b
steps are needed for X
n
to get close to uniformly distributed for some positive value b≤2 which may depend on T and X
0 is the zero vector. 相似文献
188.
Slobodanka S. Mitrović 《Annali dell'Universita di Ferrara》2008,54(2):269-275
In this paper we estimate the upper boundary of the number of trees in the selection stand determined for harvesting in a
future. At the same time we showed that the present resource of the number of trees in selection stand is sustained. This
is achieved by stochastic modeling of the number of trees and the number of felled trees and by solving the partial differential
equation. The same problem is solved in the papers, Mitrović (Stochastic modeling of the number of trees and the number of
felled trees in selection stands, YUJOR, vol 14(1), pp 57–64, 2004; Stochastic modeling of the number of felled trees in selection
stands, Computational and Applied Mathematics, vol 24(2), pp 285–292, 2005). In this paper the modified mathematical model
is represented.
相似文献
189.
D. S. Lubinsky 《Proceedings of the American Mathematical Society》1999,127(2):529-536
For a polynomial of degree , normalized by the condition
we show that has at most , where is explicitly given and sharp for each . Similar estimates are given for other normalizations, such as , and for planar measure, and for generalized polynomials and potentials, thereby extending work of Cuyt, Driver and the author for . The relation to Remez inequalities is briefly discussed.
190.
George E. Andrews Anne Schilling S. Ole Warnaar 《Journal of the American Mathematical Society》1999,12(3):677-702
Using new -functions recently introduced by Hatayama et al. and by (two of) the authors, we obtain an A version of the classical Bailey lemma. We apply our result, which is distinct from the A Bailey lemma of Milne and Lilly, to derive Rogers-Ramanujan-type identities for characters of the W algebra.