9,665 research outputs found

    Finiteness and the falsification by fellow traveler property

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    We prove that groups enjoying the falsification by fellow traveler property are of type F3F_3, and have at most an exponential second order isoperimetric function.Comment: Appeared in 2002. I am putting all my past publications on arxi

    Fundamental electrode kinetics

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    Report presents the fundamentals of electrode kinetics and the methods used in evaluating the characteristic parameters of rapid-charge transfer processes at electrode-electrolyte interfaces. The concept of electrode kinetics is outlined, followed by the principles underlying the experimental techniques for the investigation of electrode kinetics

    A non-Hopfian almost convex group

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    In this article we prove that an "isometric multiple HNN-extension" of a group satisfying the falsification by fellow traveler property is almost convex. As a corollary, Wise's example of a CAT(0) non-Hopfian group is Almost convex.Comment: Appeared in 2004. I am putting all my past papers on arxi

    On the Schr\"odinger equations with isotropic and anisotropic fourth-order dispersion

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    This paper deals with the Cauchy problem associated to the nonlinear fourth-order Schr\"odinger equation with isotropic and anisotropic mixed dispersion. This model is given by the equation i∂tu+ϵΔu+δAu+λ∣u∣αu=0,i\partial _{t}u+\epsilon \Delta u+\delta A u+\lambda|u|^\alpha u=0, x∈Rn,x\in \mathbb{R}^{n}, t∈R,t\in \mathbb{R}, where AA represents either the operator Δ2\Delta^2 (isotropic dispersion) or ∑i=1d∂xixixixi, 1≤d<n\sum_{i=1}^d\partial_{x_ix_ix_ix_i},\ 1\leq d<n (anisotropic dispersion), and α,ϵ,λ\alpha, \epsilon, \lambda are given real parameters. We obtain local and global well-posedness results in spaces of initial data with low regularity, such as weak-LpL^p spaces. Our analysis also includes the biharmonic and anisotropic biharmonic equation (ϵ=0)(\epsilon=0) for which, the existence of self-similar solutions is obtained as consequence of his scaling invariance. In a second part, we investigate the vanishing second order dispersion limit in the framework of weak-LpL^p spaces. We also analyze the convergence of the solutions for the nonlinear fourth-order Schr\"odinger equation i∂tu+ϵΔu+δΔ2u+λ∣u∣αu=0i\partial _{t}u+\epsilon \Delta u+\delta \Delta^2 u+\lambda|u|^\alpha u=0, as ϵ\epsilon goes to zero, in H2H^2-norm, to the solutions of the corresponding biharmonic equation i∂tu+δΔ2u+λ∣u∣αu=0i\partial _{t}u+\delta \Delta^2 u+\lambda|u|^\alpha u=0

    On wild ramification in quaternion extensions

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    Quaternion extensions are often the smallest extensions to exhibit special properties. In the setting of the Hasse-Arf Theorem, for instance, quaternion extensions are used to illustrate the fact that upper ramification numbers need not be integers. These extensions play a similar role in Galois module structure. To better understand these examples, we catalog the ramification filtrations that are possible in totally ramified extensions of dyadic number fields. Interestingly, we find that the catalog depends, for sharp lower bounds, upon the refined ramification filtration, which is associated with the biquatratic subfield. Moreover these examples, as counter-examples to the conclusion of Hasse-Arf, occur only when the refined filtration is, in two different ways, extreme.Comment: 19 pages. This is an extensive revision of the earlier draf

    Morphological instability, evolution, and scaling in strained epitaxial films: An amplitude equation analysis of the phase field crystal model

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    Morphological properties of strained epitaxial films are examined through a mesoscopic approach developed to incorporate both the film crystalline structure and standard continuum theory. Film surface profiles and properties, such as surface energy, liquid-solid miscibility gap and interface thickness, are determined as a function of misfit strains and film elastic modulus. We analyze the stress-driven instability of film surface morphology that leads to the formation of strained islands. We find a universal scaling relationship between the island size and misfit strain which shows a crossover from the well-known continuum elasticity result at the weak strain to a behavior governed by a "perfect" lattice relaxation condition. The strain at which the crossover occurs is shown to be a function of liquid-solid interfacial thickness, and an asymmetry between tensile and compressive strains is observed. The film instability is found to be accompanied by mode coupling of the complex amplitudes of the surface morphological profile, a factor associated with the crystalline nature of the strained film but absent in conventional continuum theory.Comment: 16 pages, 10 figures; to be published in Phys. Rev.

    Patterns theory and geodesic automatic structure for a class of groups

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    We introduce a theory of "patterns" in order to study geodesics in a certain class of group presentations. Using patterns we show that there does not exist a geodesic automatic structure for certain group presentations, and that certain group presentations are almost convex.Comment: Appeared in 2003. I am putting all my past papers on arxi
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