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31.
Andrei Korobeinikov John Norbury Graeme C. Wake 《Nonlinear Analysis: Real World Applications》2009,10(1):93-103
Spatial distribution of interacting chemical or biological species is usually described by a system of reaction–diffusion equations. In this work we consider a system of two reaction–diffusion equations with spatially varying diffusion coefficients which are different for different species and with forcing terms which are the gradient of a spatially varying potential. Such a system describes two competing biological species. We are interested in the possibility of long-term coexistence of the species in a bounded domain. Such long-term coexistence may be associated either with a periodic in time solution (usually associated with a Hopf bifurcation), or with time-independent solutions. We prove that no periodic solution exists for the system. We also consider some steady states (the time-independent solutions) and examine their stability and bifurcations. 相似文献
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Paul Norbury 《数学学报(英文版)》2017,33(9):1163-1183
We represent stationary descendant Gromov–Witten invariants of projective space, up to explicit combinatorial factors, by polynomials. One application gives the asymptotic behaviour of the large degree behaviour of stationary descendant Gromov–Witten invariants in terms of intersection numbers over the moduli space of curves. We also show that primary Gromov–Witten invariants are"virtual" stationary descendants and hence the string and divisor equations can be understood purely in terms of stationary invariants. 相似文献
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The moduli spaces of hyperbolic surfaces of genus g with n geodesic boundary components are naturally symplectic manifolds. Mirzakhani proved that their volumes are polynomials in
the lengths of the boundaries by computing the volumes recursively. In this paper, we give new recursion relations between
the volume polynomials.
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It is shown that many hyperbolic monopoles can be distinguishedfrom each other via their asymptotic values in contrast to thecase of Euclidean monopoles. 相似文献
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We present a simple application of the three-dimensional harmonic oscillator which should provide a very nice particle physics example to be presented in introductory undergraduate quantum mechanics course. The idea is to use the nonrelativistic quark model to calculate the spin-averaged mass levels of the charmonium and bottomonium spectra. 相似文献
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