572 research outputs found
Zero Entropy Interval Maps And MMLS-MMA Property
We prove that the flow generated by any interval map with zero topological
entropy is minimally mean-attractable (MMA) and minimally mean-L-stable (MMLS).
One of the consequences is that any oscillating sequence is linearly disjoint
with all flows generated by interval maps with zero topological entropy. In
particular, the M\"obius function is orthogonal to all flows generated by
interval maps with zero topological entropy (Sarnak's conjecture for interval
maps). Another consequence is a non-trivial example of a flow having the
discrete spectrum.Comment: 12 page
Homogenization of Maxwell's equations in periodic composites
We consider the problem of homogenizing the Maxwell equations for periodic
composites. The analysis is based on Bloch-Floquet theory. We calculate
explicitly the reflection coefficient for a half-space, and derive and
implement a computationally-efficient continued-fraction expansion for the
effective permittivity. Our results are illustrated by numerical computations
for the case of two-dimensional systems. The homogenization theory of this
paper is designed to predict various physically-measurable quantities rather
than to simply approximate certain coefficients in a PDE.Comment: Significantly expanded compared to v1. Accepted to Phys.Rev.E. Some
color figures in this preprint may be easier to read because here we utilize
solid color lines, which are indistinguishable in black-and-white printin
Interpolation of Hilbert and Sobolev Spaces: Quantitative Estimates and Counterexamples
This paper provides an overview of interpolation of Banach and Hilbert
spaces, with a focus on establishing when equivalence of norms is in fact
equality of norms in the key results of the theory. (In brief, our conclusion
for the Hilbert space case is that, with the right normalisations, all the key
results hold with equality of norms.) In the final section we apply the Hilbert
space results to the Sobolev spaces and
, for and an open . We exhibit examples in one and two dimensions of sets
for which these scales of Sobolev spaces are not interpolation scales. In the
cases when they are interpolation scales (in particular, if is
Lipschitz) we exhibit examples that show that, in general, the interpolation
norm does not coincide with the intrinsic Sobolev norm and, in fact, the ratio
of these two norms can be arbitrarily large
Bladder perforations in children
Context: Bladder perforations in children occur due to several different reasons.Aim: In this clinical series study, we focused on bladder perforations due to the pelvic injury, and our aim also was to create awareness for a rare type of bladder injuries.Setting and Design: This was a retrospective study of the patients who were treated in our clinic for bladder perforation between 2006 and 2011.Subjects and Methods: We reviewed the documents of childhood bladder perforations, and demographic and clinical characteristics of the patients were obtained. No statistical analyses were used because of the limited number of cases.Results: There were ten patients who suffered from bladder perforation in 5‑year period; 5 were male, and 5 were female. The mean age of the patients was 4.35 years. Four patients (40%) experienced iatrogenic perforation and six patients (60%) experienced perforation due to the accident. Common symptoms were hematuria, abdominal tenderness, and inability to urinate. Three patients were diagnosed via emergency laparotomy, without any radiological examinations performed before surgery. Four patients suffered from the intraperitoneal perforation, three patients suffered from extraperitoneal injury and three of them both of intraperitoneal and extraperitoneal injuries. Mean recovery time for patients was 15 days. One patient developed a urinary tract infection and one newborn died due to accompanying morbidities. Nine patients were discharged from the hospital.Conclusion: If the patients had a pelvic injury, surgeons must pay attention for the bladder perforation. Isolated bladder perforations are rare, and they are generally associated with iatrogenic injuries. Clinicians should pay attention to findings such as anuria, inability to insert a urinary catheter, and free fluid in the abdomen in order to diagnose the bladder perforation in newborns. Novice surgeons should pay more attention to avoid causing iatrogenic bladder perforation during inguinal hernia repair.Keywords: Bladder, child, iatrogenic, perforation, traum
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Pink verrucous plaque in a man with systemic mastocytosis
Porokeratosis ptychotropica is a rare and commonly misdiagnosed subtype of porokeratosis involving the body folds. We present a 53-year-old man with systemic mastocytosis who presented with a pruritic, verrucous plaque in the gluteal fold that showed multiple cornoid lamellae on histopathologic evaluation, diagnostic of porokeratosis ptychotropica. Various treatments have been reported, including topical corticosteroids, retinoids, vitamin D analogs, calcineurin inhibitors, imiquimod, phototherapy, cryotherapy, or ablative laser therapy, but recurrences are common
The nonlinear diffusion limit for generalized Carleman models: the initial-boundary value problem
Consider the initial-boundary value problem for the 2-speed Carleman model of
the Boltzmann equation of the kinetic theory of gases set in some bounded
interval with boundary conditions prescribing the density of particles entering
the interval. Under the usual parabolic scaling, a nonlinear diffusion limit is
established for this problem. In fact, the techniques presented here allow
treating generalizations of the Carleman system where the collision frequency
is proportional to some power of the macroscopic density, with exponent in
[-1,1]
Bounds on strong field magneto-transport in three-dimensional composites
This paper deals with bounds satisfied by the effective non-symmetric
conductivity of three-dimensional composites in the presence of a strong
magnetic field. On the one hand, it is shown that for general composites the
antisymmetric part of the effective conductivity cannot be bounded solely in
terms of the antisymmetric part of the local conductivity, contrary to the
columnar case. So, a suitable rank-two laminate the conductivity of which has a
bounded antisymmetric part together with a high-contrast symmetric part, may
generate an arbitrarily large antisymmetric part of the effective conductivity.
On the other hand, bounds are provided which show that the antisymmetric part
of the effective conductivity must go to zero if the upper bound on the
antisymmetric part of the local conductivity goes to zero, and the symmetric
part of the local conductivity remains bounded below and above. Elementary
bounds on the effective moduli are derived assuming the local conductivity and
effective conductivity have transverse isotropy in the plane orthogonal to the
magnetic field. New Hashin-Shtrikman type bounds for two-phase
three-dimensional composites with a non-symmetric conductivity are provided
under geometric isotropy of the microstructure. The derivation of the bounds is
based on a particular variational principle symmetrizing the problem, and the
use of Y-tensors involving the averages of the fields in each phase.Comment: 21 page
Realizability of metamaterials with prescribed electric permittivity and magnetic permeability tensors
We show that any pair of real symmetric tensors \BGve and \BGm can be
realized as the effective electric permittivity and effective magnetic
permeability of a metamaterial at a given fixed frequency. The construction
starts with two extremely low loss metamaterials, with arbitrarily small
microstructure, whose existence is ensured by the work of Bouchitt{\'e} and
Bourel and Bouchitt\'e and Schweizer, one having at the given frequency a
permittivity tensor with exactly one negative eigenvalue, and a positive
permeability tensor, and the other having a positive permittivity tensor, and a
permeability tensor having exactly one negative eigenvalue. To achieve the
desired effective properties these materials are laminated together in a
hierarchical multiple rank laminate structure, with widely separated length
scales, and varying directions of lamination, but with the largest length scale
still much shorter than the wavelengths and attenuation lengths in the
macroscopic effective medium.Comment: 12 pages, no figure
Anomalous diffusion for a class of systems with two conserved quantities
We introduce a class of one dimensional deterministic models of energy-volume
conserving interfaces. Numerical simulations show that these dynamics are
genuinely super-diffusive. We then modify the dynamics by adding a conservative
stochastic noise so that it becomes ergodic. System of conservation laws are
derived as hydrodynamic limits of the modified dynamics. Numerical evidence
shows these models are still super-diffusive. This is proven rigorously for
harmonic potentials
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