204 research outputs found
Small divisors and large multipliers
We study germs of singular holomorphic vector fields at the origin of of which the linear part is 1-resonant and which have a polynomial normal
form. The formal normalizing diffeomorphism is usually divergent at the origin
but there exists holomorphic diffeomorphisms in some "sectorial domains" which
transform these vector fields into their normal form. In this article, we study
the interplay between the small divisors phenomenon and the Gevrey character of
the sectorial normalizing diffeomorphisms. We show that the Gevrey ordrer of
the latter is linked to the diophantine type of the small divisors.Comment: 22 pages, to appear in Annales de l'Institut Fourie
Extension of formal conjugations between diffeomorphisms
We study the formal conjugacy properties of germs of complex analytic
diffeomorphisms defined in the neighborhood of the origin of .
More precisely, we are interested on the nature of formal conjugations along
the fixed points set. We prove that there are formally conjugated local
diffeomorphisms such that every formal conjugation
(i.e. ) does not extend to
the fixed points set of , meaning that it is not
transversally formal (or semi-convergent) along .
We focus on unfoldings of 1-dimensional tangent to the identity
diffeomorphisms. We identify the geometrical configurations preventing formal
conjugations to extend to the fixed points set: roughly speaking, either the
unperturbed fiber is singular or generic fibers contain multiple fixed points.Comment: 34 page
Tunneling in Fractional Quantum Mechanics
We study the tunneling through delta and double delta potentials in
fractional quantum mechanics. After solving the fractional Schr\"odinger
equation for these potentials, we calculate the corresponding reflection and
transmission coefficients. These coefficients have a very interesting
behaviour. In particular, we can have zero energy tunneling when the order of
the Riesz fractional derivative is different from 2. For both potentials, the
zero energy limit of the transmission coefficient is given by , where is the order of the derivative ().Comment: 21 pages, 3 figures. Revised version; accepted for publication in
Journal of Physics A: Mathematical and Theoretica
Are critical finite-size scaling functions calculable from knowledge of an appropriate critical exponent?
Critical finite-size scaling functions for the order parameter distribution
of the two and three dimensional Ising model are investigated. Within a
recently introduced classification theory of phase transitions, the universal
part of the critical finite-size scaling functions has been derived by
employing a scaling limit that differs from the traditional finite-size scaling
limit. In this paper the analytical predictions are compared with Monte Carlo
simulations. We find good agreement between the analytical expression and the
simulation results. The agreement is consistent with the possibility that the
functional form of the critical finite-size scaling function for the order
parameter distribution is determined uniquely by only a few universal
parameters, most notably the equation of state exponent.Comment: 11 pages postscript, plus 2 separate postscript figures, all as
uuencoded gzipped tar file. To appear in J. Phys. A
Annotated bibliography of research in the teaching of English
The committee reviews important research works in the teaching of English that have been published in the last year. Committee members include Richard Beach, Martha Bigelow, Martine Braaksma, Deborah Dillon, Jessie Dockter, Lee Galda, Lori Helman, Tanja Janssen, Karen Jorgensen, Richa Kapoor, Lauren Liang, Bic Ngo, David O’Brien, Mistilina Sato, and Cassie Scharber
Beyond series expansions: mathematical structures for the susceptibility of the square lattice Ising model
We first study the properties of the Fuchsian ordinary differential equations
for the three and four-particle contributions and
of the square lattice Ising model susceptibility. An analysis of some
mathematical properties of these Fuchsian differential equations is sketched.
For instance, we study the factorization properties of the corresponding linear
differential operators, and consider the singularities of the three and
four-particle contributions and , versus the
singularities of the associated Fuchsian ordinary differential equations, which
actually exhibit new ``Landau-like'' singularities. We sketch the analysis of
the corresponding differential Galois groups. In particular we provide a
simple, but efficient, method to calculate the so-called ``connection
matrices'' (between two neighboring singularities) and deduce the singular
behaviors of and . We provide a set of comments and
speculations on the Fuchsian ordinary differential equations associated with
the -particle contributions and address the problem of the
apparent discrepancy between such a holonomic approach and some scaling results
deduced from a Painlev\'e oriented approach.Comment: 21 pages Proceedings of the Counting Complexity conferenc
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