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In this short paper I report on a paper published in Nonlinear Analysis: Real World Applications in 2004. There is a major mistake early in that paper which makes most of its claims false. The class of reaction–diffusion systems considered in the paper has been the object of a renewed investigation in the past few years, by myself and others, and recent discoveries provide explicit counter-examples. 相似文献
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《Physics letters. A》2020,384(7):126152
Derived from quantum waves immersed in an Abelian gauge potential, the quasiperiodic Aubry-André-Harper (AAH) model is a simple yet powerful Hamiltonian to study the Anderson localization of ultracold atoms. Here, we investigate the localization properties of ultracold atoms in quasiperiodic optical lattices subject to a non-Abelian gauge potential, which are depicted by non-Abelian AAH models. We identify that the non-Abelian AAH models can bear the self-duality. We analyze the localization of such non-Abelian self-dual optical lattices, revealing a rich phase diagram driven by the non-Abelian gauge potential involved: a transition from a pure delocalization phase, then to coexistence phases, and finally to a pure localization phase. This is in stark contrast to the Abelian counterpart that does not support the coexistence phases. Our results establish the connection between localization and gauge symmetry, and thus comprise a new insight on the fundamental aspects of localization in quasiperiodic systems, from the perspective of non-Abelian gauge potential. 相似文献
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The existence of a solitary wave for the shallow water model in convecting circumstance was established in previous works. It is still unknown that whether there exist periodic waves. In this paper, we prove that the models possess periodic waves with a fixed range of wave speed. The amplitude and wave speed are explicitly given. Moreover, the coexistence of the solitary wave and one periodic wave is established. 相似文献
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In this paper, we investigate a two-cooperative species model with reaction cross-diffusion under the Dirichlet boundary value condition. By applying Lyapunov–Schmidt reduction method and some important formulas, we obtain the existence of coexistence solutions under some given conditions. 相似文献
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Abstract The top part of the coexistence curve of methyl fluoride in the critical region has been determined first by direct observation of the disappearance of the meniscus of the fluid situated in a high-pressure light scattering cell and subsequently from the measured maximum depolarization ratio of an appreciable number of isochores close to the critical point. The experimental data obtained from direct observations yield a coexistence curve which nearly coincides with that found recently from pVT measurements. However, the data obtained from light scattering experiments describe a gravity induced coexistence curve which lies above the previous one and which shows a minimum at the critical point. The complete experimental data have been used to evaluate the critical parameters pc, ρc and Tc and the critical exponent β. 相似文献
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This paper deals with a predator–prey model with specialist harvesting, representing a two predators (Zooplankton) and one resource (Phytoplankton) system. First, the existence and stability of equilibria is analyzed both from local and global point of view. Our results indicate that a specialist harvesting which is discriminate may mediate the coexistence of the two zooplankton species which competitively exclude each other in absence harvesting. Although in most cases increasing harvesting reduces the two zooplankton species numbers, when harvesting leads to coexistence, it may also lead to increase the two zooplankton species numbers. Furthermore, to protect fish population from over exploitation a control instrument tax is imposed. The problem of optimal taxation policy is then solved by using Pontryagin’s maximal principle. It is established that the zero discounting leads to the maximization of the net economic revenue to the society and an infinite discount rate leads to complete dissipation of the net economic revenue to the society. Finally, the impact of harvesting is mentioned along with numerical results to provide some support to the analytical findings. 相似文献
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8.
M. A. Van Hove 《Progress in Surface Science》2000,64(3-8):157-162
Attention is drawn to challenges facing the structure determination of compound surfaces of growing complexity. Besides the questions of large unit cells and disorder, and of many independent atoms in the unit cells, one must address the determination of composition, compositional disorder and simultaneously coexisting structures. Of special concern is the issue of stability of complex and compound surfaces, and the resulting concerns about experimental surface preparation and reproducibility. 相似文献
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We describe two new methods for locating the dew/bubble curves of fluids. One is a numerical method and the other an analytical method based on the use of series expansions. The utility of these two methods is illustrated by application to a simple one-component fluid model and to several model polydisperse fluids. The numerical method is based on a new geometric representation of the equilibrium conditions-similar in spirit to the geometric representations often used for solving the equilibrium conditions of pure fluids. Our calculations show that the series-expansion technique can be quite effective at producing accurate representations of the phase boundaries. 相似文献
10.
Coexistence states for systems of mutualist species 总被引:1,自引:0,他引:1
Zongming Guo 《Journal of Mathematical Analysis and Applications》2005,303(1):61-80
Coexistence states for a class of systems of mutualist species are obtained via bifurcation theory and monotone techniques. 相似文献