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

Rank-(n – 1) convexity and quasiconvexity for divergence free fields

No description supplie

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 $H^s(\Omega)$ and $\widetilde{H}^s(\Omega)$, for $s\in \mathbb{R}$ and an open $\Omega\subset \mathbb{R}^n$. We exhibit examples in one and two dimensions of sets $\Omega$ for which these scales of Sobolev spaces are not interpolation scales. In the cases when they are interpolation scales (in particular, if $\Omega$ 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

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