Fw: new_abstracts 23 260

[Maria Odete Madeira]

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Subject: new_abstracts 23 260

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NEW ABSTRACTS (Aug 31 to Sep 7)

==================== 23-51 ====================

C sar R. de Oliveira, Vin cius L. Rocha

Effective quantum graph models of some nonequilateral graphyne materials

(808K, .pdf)

ABSTRACT.  It is shown that it is possible to adapt the quantum graph model of graphene to some types of nonequilateral graphynes considered in the literature; we also discuss the corresponding nanotubes. The proposed models are, in fact, effective models and are obtained through selected boundary conditions and an ad hoc prescription. We analytically recover some results from the literature, in particular the presence of Dirac cones for α-, β- and (6, 6, 12)-graphynes; for γ-graphyne our model presents a band gap (in according to the literature), but only for a range of parameters, with a transition at certain point with quadratic touch and then the presence of Dirac cones.

http://www.ma.utexas.edu/mp_arc-bin/mpa?yn=23-51

http://www.maia.ub.es/mp_arc-bin/mpa?yn=23-51

http://kleine.mat.uniroma3.it/mp_arc-bin/mpa?yn=23-51

==================== 23-53 ====================

Jason Holt, and Oleg Safronov

On the number of eigenvalues of the Dirac operator in a bounded interval

(420K, pdf)

ABSTRACT.  Let $H_0$ be the free Dirac operator and $V\geq 0$ be a positive potential.

We study the discrete spectrum of $H( )=H_0- V$ in the interval $(-1,1)$ for large values of the coupling constant $ >0$.

In particular, we obtain an asymptotic formula for the number of eigenvalues of $H( )$ situated

in a bounded interval $[\l,\mu)$ as $     o\infty$.

http://www.ma.utexas.edu/mp_arc-bin/mpa?yn=23-53

http://www.maia.ub.es/mp_arc-bin/mpa?yn=23-53

http://kleine.mat.uniroma3.it/mp_arc-bin/mpa?yn=23-53

==================== 23-54 ====================

Messoud Efendiev, Vitali Vougalter

On the solvability in the sense of sequences for some nonlinear Fredholm operators with the logarithmic Laplacian

(128K, pdf)

ABSTRACT.  We address the solvability of certain nonlinear nonhomogeneous systems of

equations in one dimension containing the logarithmic Laplacian and the drift terms. We establish that, under the reasonable technical conditions,

the convergence in L^1(R) of the integral kernels yields the existence and the convergence in L^2(R, R^N) of the solutions. We emphasize that the study of the systems is more difficult than of the scalar case and requires to overcome more cumbersome technicalities.

http://www.ma.utexas.edu/mp_arc-bin/mpa?yn=23-54

http://www.maia.ub.es/mp_arc-bin/mpa?yn=23-54

http://kleine.mat.uniroma3.it/mp_arc-bin/mpa?yn=23-54

==================== 23-55 ====================

Hans Koch

Attracting invariant tori and analytic conjugacies

(532K, pdf)

ABSTRACT.  We consider the problem of conjugating a flow on T^d x R

to an "integrable" flow q'=w and p'=cp, if possible, with c nonzero.

Our emphasis is on a constructive approach,

using a KAM type iteration and analyticity.

An application to the periodically forced Van der Pol oscillator is given.

http://www.ma.utexas.edu/mp_arc-bin/mpa?yn=23-55

http://www.maia.ub.es/mp_arc-bin/mpa?yn=23-55

http://kleine.mat.uniroma3.it/mp_arc-bin/mpa?yn=23-55