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101.
Rink 《Journal of Nonlinear Science》2008,12(5):479-504
Summary. This paper considers the famous Fermi-Pasta-Ulam (FPU) lattice with periodic boundary conditions and quartic nonlinearities.
Due to special resonances and discrete symmetries, the Birkhoff normal form of this Hamiltonian system is Liouville integrable.
The normal form equations can easily be solved if the number of particles in the lattice is odd, but if the number of particles
is even, several nontrivial phenomena occur. In the latter case we observe that the phase space of the normal form is decomposed
in invariant subspaces that describe the interaction between the Fourier modes with wave number j and the Fourier modes with wave number n / 2-j . We study how the level sets of the integrals of the normal form foliate these invariant subspaces. The integrable foliations
turn out to be singular and the method of singular reduction shows that the normal form has invariant pinched tori and monodromy.
Monodromy is an obstruction to the existence of global action-angle variables. The pinched tori are interpreted as homoclinic
and heteroclinic connections between traveling waves. Thus we discover a class of solutions of the normal form which can be
described as direction-reversing traveling waves. The relation between the FPU lattice and its Birkhoff normal form can be
understood from KAM theory and approximation theory. This explains why we observe the impact of the direction-reversing traveling
waves numerically as a relaxation oscillation in the original FPU system. 相似文献
102.
We consider the constrained vector optimization problem min C f(x), g(x) ∈ ?K, where f:? n →? m and g:? n →? p are C 1,1 functions, and C ? m and K ? p are closed convex cones with nonempty interiors. Two type of solutions are important for our considerations, namely w-minimizers (weakly efficient points) and i-minimizers (isolated minimizers). We formulate and prove in terms of the Dini directional derivative second-order necessary conditions for a point x 0 to be a w-minimizer and second-order sufficient conditions for x 0 to be an i-minimizer of order two. We discuss the reversal of the sufficient conditions under suitable constraint qualifications of Kuhn-Tucker type. The obtained results improve the ones in Liu, Neittaanmäki, K?í?ek [21]. 相似文献
103.
L. Dorikens-Vanpraet D. Segers M. Dorikens 《Applied Physics A: Materials Science & Processing》1980,23(2):149-152
A detailed study of the prompt resolution curve of a positron annihilation lifetime spectrometer shows that the geometry of
the source-detector set-up has great influence on its shape. 相似文献
104.
Dongho Byeon 《manuscripta mathematica》2006,120(2):211-215
We shall show that the number of real quadratic fields whose absolute discriminant is ≤ x and whose class number is divisible by 5 or 7 is
29_2006_2_Article_IEq3.gif" alt="$$\gg x^{1/2}$$" align="middle" border="0"> improving the existing best known bound 29_2006_2_Article_IEq1.gif" alt="$$\gg x^{(1/5)-\epsilon}$$" align="middle" border="0"> for g = 5 and29_2006_2_Article_IEq2.gif" alt="$$\gg x^{(1/7)-\epsilon}$$" align="middle" border="0"> for g = 7 of Yu (J Number Theory 97:35–44, 2002).This work was supported by KRF-R08-2003-000-10243-0 and partially by KRF-2005-070-C00004. 相似文献
105.
Precoloring extension on unit interval graphs 总被引:1,自引:0,他引:1
Dániel Marx 《Discrete Applied Mathematics》2006,154(6):995-1002
In the precoloring extension problem a graph is given with some of the vertices having preassigned colors and it has to be decided whether this coloring can be extended to a proper k-coloring of the graph. Answering an open question of Hujter and Tuza [Precoloring extension. III. Classes of perfect graphs, Combin. Probab. Comput. 5 (1) (1996) 35-56], we show that the precoloring extension problem is NP-complete on unit interval graphs. 相似文献
106.
《Mathematische Nachrichten》2018,291(2-3):264-283
Let C be a smooth projective curve and G be a finite subgroup of whose action is mixed, i.e. there are elements in G exchanging the two isotrivial fibrations of . Let be the index two subgroup . If G0 acts freely, then is smooth and we call it semi‐isogenous mixed surface. In this paper we give an algorithm to determine semi‐isogenous mixed surfaces with given geometric genus, irregularity and self‐intersection of the canonical class. As an application we classify irregular semi‐isogenous mixed surfaces with and geometric genus equal to the irregularity; the regular case is subjected to some computational restrictions. In this way we construct new examples of surfaces of general type with . We provide an example of a minimal surface of general type with and . 相似文献
107.
Siman Wong 《Journal of Number Theory》2010,130(10):2332-2340
Let M?5. For any odd prime power q and any prime ??q, we show that there are at least pairwise coprime D∈Fq[T] which are square-free and of odd degree ?M, such that ? does not divide the class number of the complex quadratic functions fields . 相似文献
108.
Evgenia Minko Petr Sysel Michal Hauf Jiří Brus Libor Kobera 《Macromolecular Symposia》2010,295(1):88-93
Summary: The novel hyperbranched polyimide - silica hybrid materials containing theoretically 16 wt% of an inorganic phase were prepared via a sol-gel process. An amine terminated polyimide precursor (hyperbranched polyamic acid) was prepared from commercially available monomers 4,4′,4″-triaminotriphenylmethane and 4,4′-oxydiphthalic anhydride in molar ratio 1:1. Tetramethoxysilane and/or 3-glycidoxypropyltrimethoxysilane (also used as a coupling agent) were used as silica precursors. During thermal exposition the polyimide precursor was transformed to hyperbranched polyimide and hydrolyzed alkoxy groups reacted mutually to form silica. The final products were self-standing films, whose structure was characterized by using IR and 13C and 29Si solid state NMR spectroscopy. The influence of the amount of silica and/or coupling agent on their structure and thermal properties was described. 相似文献
109.
Michel Grabisch 《Discrete Applied Mathematics》2010,158(5):479-488
In cooperative game theory, games in partition function form are real-valued function on the set of the so-called embedded coalitions, that is, pairs (S,π) where S is a subset (coalition) of the set N of players, and π is a partition of N containing S. Despite the fact that many studies have been devoted to such games, surprisingly nobody clearly defined a structure (i.e., an order) on embedded coalitions, resulting in scattered and divergent works, lacking unification and proper analysis. The aim of the paper is to fill this gap, thus to study the structure of embedded coalitions (called here embedded subsets), and the properties of games in partition function form. 相似文献
110.
We characterize all the quadratic polynomial differential systems having a polynomial inverse integrating factor and provide explicit normal forms for such systems and for their associated first integrals. We also prove that these families of quadratic systems have no limit cycles. 相似文献