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Quintic function
About: Quintic function is a research topic. Over the lifetime, 1677 publications have been published within this topic receiving 26780 citations.
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TL;DR: In this paper, the authors extend the global existence result for all non-trapping obstacles and for nonlinearities with power strictly greater than quartic for a class of almost star-shaped obstacles.
Abstract: Global existence and scattering for the nonlinear defocusing Schrodinger equation in 2 dimensions are known for domains exterior to star-shaped obstacles and for nonlinearities that grow at least as the quintic power. In this paper, we extend the global existence result for all non-trapping obstacles and for nonlinearities with power strictly greater than quartic. For such nonlinearities, we also prove scattering for a class of so-called almost star-shaped obstacles.
5 citations
01 Jun 1983
TL;DR: Artin's conjecture for simultaneous equations of additive typewhere the coefficients aij are integers was studied in this paper, where it was shown that the equations (1) have a non-trivial solution in integers x 1, N, N provided that k is odd.
Abstract: We consider R simultaneous equations of additive typewhere the coefficients aij are integers. Artin's conjecture, for additive forms, is that the equations (1) have a non-trivial solution in integers x1,…,xN provided that they have a non-trivial real solution, which is clearly satisfied when k is odd, and
5 citations
TL;DR: In this article, the number and distribution of limit cycles in a Z 2-equivariant quintic vector field with a special planar polynomial system were investigated. And the results obtained are useful to study the weakened 16th Hilbert problem.
Abstract: This paper concerns the number and distributions of limit cycles in a Z
2-equivariant quintic planar vector field 25 limit cycles are found in this special planar polynomial system and four different configurations of these limit cycles are also given by using the methods of the bifurcation theory and the qualitative analysis of the differential equation It can be concluded that H(5) ⩾ 25 = 52, where H(5) is the Hilbert number for quintic polynomial systems The results obtained are useful to study the weakened 16th Hilbert problem
5 citations
TL;DR: In this article, the canonical model C of C is the base locus of a net of quadric hypersurfaces in P£ and the discriminant curve of such a net is a plane quintic which is the union of a non-singular quartic F and a line L.
Abstract: , then the canonical model C of C isthe base locus of a net of quadric hypersurfaces in P£. The discriminant curve of sucha net is a plane quintic which is the union of a non-singular quartic F and a line L.Moreover, F is endowed (in a natural way) with a non-effective theta characteristicn (that is, an invertibl rje shea on F sucf h that rj
5 citations
5 citations