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11.
The main goal of this paper is to prove analytically the existence of strange attractors in a family of vector fields consisting of two Brusselators linearly coupled by diffusion. We will show that such a family contains a generic unfolding of a 4-dimensional nilpotent singularity of codimension 4. On the other hand, we will prove that in any generic unfolding Xμ of an n-dimensional nilpotent singularity of codimension n there are bifurcation curves of (n−1)-dimensional nilpotent singularities of codimension n−1 which are in turn generically unfolded by Xμ. Arguments conclude recalling that any generic unfolding of the 3-dimensional nilpotent singularity of codimension 3 exhibits strange attractors. 相似文献
12.
13.
In this paper, the authors study the multiplicity of solutions to the weighted p-Laplacian with isolated singularity and di?usion suppressed by convection ?div(|x|α|?u|p?2?u) + λ 1/|x|β |?u|p?2?u · x = |x|γg(|x|) in B \ {0} subject to nonlinear Robin boundary value condition |x|α|?u|p?2?u · ?n = A ? ρu on ?B,where λ > 0, B ? RN(N ≥ 2) is the unit ball centered at the origin, α > 0, p > 1, β ∈ R, γ > ?N, g ∈ C([0,1]) with g(0) > 0, A ∈ R, ρ > 0 and ?n is the unit outward normal. The same problem with di?usion promoted by convection, namely λ ≤ 0, has already been discussed by the last two authors (Song-Yin (2012)), where the existence, nonexistence and classi?cation of singularities for solutions are presented. Completely di?erent from [Song, H. J. and Yin, J. X., Removable isolated singularities of solutions to the weighted p-Laplacian with singular convection, Math. Meth. Appl. Sci., 35, 2012, 1089–1100], in the present case λ > 0, namely the di?usion is suppressed by the convection, non-singular solutions are not only existent but also may be in?nite which vary according only to the values of solutions at the isolated singular point. At the same time, the singular solutions may exist only if the di?usion dominates the convection. 相似文献
14.
Shigeru Arimoto 《Journal of mathematical chemistry》2007,41(3):231-269
The present article is the first part of a series devoted to extending the Repeat Space Theory (RST) to apply to carbon nanotubes
and related molecular networks. Four key problems are formulated whose affirmative solutions imply the formation of the initial
investigative bridge between the research field of nanotubes and that of the additivity and other network problems studied
and solved by using the RST. All of these four problems are solved affirmatively by using tools from the RST. The Piecewise
Monotone Lemmas (PMLs) are cornerstones of the proof of the Fukui conjecture concerning the additivity problems of hydrocarbons.
The solution of the fourth problem gives a generalized analytical formula of the pi-electron energy band curves of nanotube
(a, b), with two new complex parameters c and d. These two parameters bring forth a broad class of analytic curves to which the PMLs and associated theoretical devices apply.
Based on the above affirmative solutions of the problems, a central theorem in the RST, called the asymptotic linearity theorem
(ALT) has been applied to nanotubes and monocyclic polyenes. Analytical formulae derived in this application of the ALT illuminate
in a new global context (i) the conductivity of nanotubes and (ii) the aromaticity of monocyclic polyenes; moreover an analytical
formula obtained by using the ALT provides a fresh insight into Hückel’s (4n+2) rule. The present article forms a foundation of the forthcoming articles in this series.
The present series of articles is closely associated with the series of articles entitled ‘Proof of the Fukui conjecture via
resolution of singularities and related methods’ published in the JOMC. 相似文献
15.
Shigeru?ArimotoEmail author Mark?Spivakovsky Keith?F.?Taylor Paul?G.?Mezey 《Journal of mathematical chemistry》2005,37(2):171-189
The present article is a direct continuation of the first part of this series. We reduce a proof of the Fukui conjecture (concerning the additivity problem of the zero-point vibrational energies of hydrocarbons) to that of a proposition related to the theory of algebraic curves, so that we can focus on the key mechanism of the additivity phenomena. Namely, by establishing what is called the Basic Piecewise Monotone Theorem (BPMT), we reduce a proof of the Fukui conjecture to that of a proposition, called the Local Analyticity Proposition, Version 1 (LAP1), which admits a proof via resolution of singularities. By LAP1, the essential part of the mechanism of the asymptotic linearity phenomena is extracted and is elucidated by using tools from the mathematical theory of algebraic curves, whose language is of vital importance in analyzing the crux of the additivity mechanism.
Dedicated to the memory of Prof. Kenichi Fukui (1918–1998). 相似文献
16.
Beatriz Pascual-Escudero 《Journal of Pure and Applied Algebra》2019,223(6):2598-2614
Let X be an algebraic variety defined over a field of characteristic zero, and let be a point in the closed subset of maximum multiplicity of X. We provide a criterion, given in terms of arcs, to determine whether ξ is isolated in . More precisely, we use invariants of arcs derived from the Nash multiplicity sequence to characterize when ξ is an isolated point in . 相似文献
17.
In this paper, we prove controllability results for a two-dimensional semilinear heat equation with mixed boundary conditions. It is well-known that mixed boundary conditions can present a singular behaviour of the solution. First, we will prove global Carleman estimates then we will use these inequalities to obtain controllability results. 相似文献
18.
We present here a fine singularity analysis of solutions to the Laplace equation in special polygonal domains in the plane. We assume piecewise constant Neumann data on one component of the boundary. Our motivation is to study the so‐called Berg effect, which is explained in the introduction. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
19.
The phenomenon of a topological monodromy in integrable Hamiltonian and nonholonomic systems is discussed. An efficient method for computing and visualizing the monodromy is developed. The comparative analysis of the topological monodromy is given for the rolling ellipsoid of revolution problem in two cases, namely, on a smooth and on a rough plane. The first of these systems is Hamiltonian, the second is nonholonomic. We show that, from the viewpoint of monodromy, there is no difference between the two systems, and thus disprove the conjecture by Cushman and Duistermaat stating that the topological monodromy gives a topological obstruction for Hamiltonization of the rolling ellipsoid of revolution on a rough plane. 相似文献
20.