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161.
Whenever the defining sequence of a Carleman ultraholomorphic class (in the sense of H. Komatsu) is strongly regular and associated with a proximate order, flat functions are constructed in the class on sectors of optimal opening. As consequences, we obtain analogues of both Borel–Ritt–Gevrey theorem and Watson's lemma in this general situation. 相似文献
162.
163.
A. Wöstehoff 《Applicable analysis》2013,92(8):1561-1593
We consider Cauchy’s equation of motion for hyperelastic materials. The solution of this nonlinear initial-boundary value problem is the vector field which discribes the displacement which a particle of this material perceives when exposed to stress and external forces. This equation is of greatest relevance when investigating the behavior of elastic, anisotropic composites and for the detection of defects in such materials from boundary measurements. This is why results on unique solvability and continuous dependence from the initial values are of large interest in materials’ research and structural health monitoring. In this article we present such a result, provided that reasonable smoothness assumptions for the displacement field and the boundary of the domain are satisfied for a certain class of hyperelastic materials where the first Piola–Kirchhoff tensor is written as a conic combination of finitely many, given tensors. 相似文献
164.
Fei Fang 《Journal of Mathematical Analysis and Applications》2009,351(1):138-795
We consider p-Laplacian equations on a bounded domain, where the nonlinearity is superlinear but dose not satisfy the usual Ambrosetti-Rabinowitz condition near infinity, or its dual version near zero. Nontrivial solutions are obtained by computing the critical groups and Morse theory. 相似文献
165.
Michael Ruzhansky 《Functional Analysis and Its Applications》2009,43(1):75-77
A multidimensional version of the well-known van der Corput lemma is presented. A class of phase functions is described for which the corresponding oscillatory integrals satisfy a multidimensional decay estimate. The obtained estimates are uniform with respect to parameters on which the phases and amplitudes may depend. 相似文献
166.
Let G be a graph with n vertices and e≥4n edges, drawn in the plane in such a way that if two or more edges (arcs) share an interior point p, then they properly cross one another at p. It is shown that the number of crossing points, counted without multiplicity, is at least constant times e and that the order of magnitude of this bound cannot be improved. If, in addition, two edges are allowed to cross only at
most once, then the number of crossing points must exceed constant times (e/n)4.
The research of J. Pach was supported by NSF grant CCF-05-14079 and by grants from NSA, PSC-CUNY, BSF, and OTKA-K-60427.
The research of G. Tóth was supported by OTKA-K-60427. 相似文献
167.
The partial sums of basic hypergeometric series are investigated by means of the modified Abel lemma on summation by parts.
Several transformation and summation formulae for well-poised, quadratic, cubic and quartic q-series are established.
This work was partially supported by National Natural Science Foundation for the Youth (Grant No. 10801026) 相似文献
168.
Oliver Dragi
evi Stefanie Petermichl Alexander Volberg 《Journal de Mathématiques Pures et Appliquées》2006,86(6):492-509
In [O. Dragičević, A. Volberg, Sharp estimate of the Ahlfors–Beurling operator via averaging martingale transforms, Michigan Math. J. 51 (2) (2003) 415–435] the Ahlfors–Beurling operator T was represented as an average of two-dimensional martingale transforms. The same result can be proven for powers Tn. Motivated by [T. Iwaniec, G. Martin, Riesz transforms and related singular integrals, J. Reine Angew. Math. 473 (1996) 25–57], we deduce from here that Tnp are bounded from above by Cnp*, . We further improve this estimate to obtain the optimal behaviour of the Lp norms in question. 相似文献
169.
A graph G is loosely-c-connected, or ?-c-connected, if there exists a number d depending on G such that the deletion of fewer than c vertices from G leaves precisely one infinite component and a graph containing at most d vertices. In this paper, we give the structure of a set of ?-c-connected infinite graphs that form an unavoidable set among the topological minors of ?-c-connected infinite graphs. Corresponding results for minors and parallel minors are also obtained. 相似文献
170.
Francisco J. Fernández-Polo 《Journal of Functional Analysis》2010,259(2):343-358
We establish several generalisations of Urysohn's lemma in the setting of JB∗-triples which provide full answers to Problems 1.12 and 1.13 in Fernández-Polo and Peralta (2007) [22]. These results extend the previous generalisations obtained by C.A. Akemann, G.K. Pedersen and L.G. Brown in the setting of C∗-algebras. A generalised Kadison's transitivity theorem is established for finite sums of pairwise orthogonal compact tripotents in JBW∗-triples. We introduce the notion of positively open tripotent in the bidual of a JB∗-triple as an extension of a concept which was already considered in the setting of ternary rings of operators. We investigate the connections appearing between positively open tripotents and hereditary inner ideals. 相似文献