A parabolic free boundary problem with Bernoulli type condition on the free boundary

Consider the parabolic free boundary problem $$\Delta u - \partial_t u = 0 \textrm{in} \{u>0\}, |\nabla u|=1 \textrm{on} \partial\{u>0\} .$$ For a realistic class of solutions, containing for example {\em all} limits of the singular perturbation problem $$\Delta u_\epsilon - \partial_t u_\epsilon = \beta_\epsilon(u_\epsilon) \textrm{as} \epsilon\to 0,$$ we prove that one-sided flatness of the free boundary implies regularity. In particular, we show that the topological free boundary $\partial\{u>0\}$ can be decomposed into an {\em open} regular set (relative to $\partial\{u>0\}$) which is locally a surface with H\"older-continuous space normal, and a closed singular set. Our result extends the main theorem in the paper by H.W. Alt-L.A. Caffarelli (1981) to more general solutions as well as the time-dependent case. Our proof uses methods developed in H.W. Alt-L.A. Caffarelli (1981), however we replace the core of that paper, which relies on non-positive mean curvature at singular points, by an argument based on scaling discrepancies, which promises to be applicable to more general free boundary or free discontinuity problems

Ca2+ Permeable AMPA Channels in Diseases of the Nervous System

Since the discovery and molecular characterization of Ca2+-permeable AMPA channels just over two decades ago, a large body of evidence has accumulated implicating contributions of these unusual glutamate activated channels to selective neurodegeneration in certain conditions, including ischemia and amyotrophic lateral sclerosis. Factors likely involved in their contributions to disease include their distinct patterns of expression in certain neuronal populations, their upregulation via various mechanisms in response to disease associated stresses, and their high permeability to Zn2+ as well as to Ca2+. However, full characterization of their contributions to certain diseases as well as development of therapeutics has been limited by the lack of selective and bioavailable blockers of these channels that can be employed in animals or humans. This review summarizes some of the clues that have emerged over recent years to the contributions of these channels in disease

Presence of an expressed 13-tubulin gene (TUBB) in the HLA class I region may provide the genetic basis for HLA-linked microtubule dysfunction

An expressed beta-tubulin gene (TUBB) has previously been localized to chromosome region 6pter-p21 in man. By using a panel of deletion mutant cell lines and radiation-reduced hybrids containing fragments of chromosome 6, the TUBB locus could be mapped to the HLA class I region at 6p21.3. A long range restriction map including TUBB and several HLA class I genes was then generated by rotating field gel electrophoresis. The results show that TUBB maps to a segment 170-370 kb telomeric of HLA-C. This location suggests that a mutation at the TUBB locus could be the cause for certain forms of HLAlinked microtubule dysfunction, including immotile cilia syndrome

A Safe, Stable Place to Call Home Supports Young Children's Health in Arkansas

Families should be able to afford a roof over their heads and still have enough money to pay for food, utilities, and healthcare. Unfortunately, for many Arkansans, wages are not keeping up with housing costs. Presently, fair market rent for a two-bedroom apartment is $216 more a month than a full-time minimum wage employee earning$7.25/hour can afford. Children's HealthWatch research shows families are forced to sacrifice basic necessities when they confront the gap between the cost of housing and their ability to pay for it

Glycogen synthase kinases 3α and 3β in cardiac myocytes: regulation and consequences of their inhibition

Inhibition of glycogen synthase kinase 3β (GSK3β) as a consequence of its phosphorylation by protein kinase B/Akt (PKB/Akt) has been implicated in cardiac myocyte hypertrophy in response to endothelin-1 or phenylephrine. We examined the regulation of GSK3α (which we show to constitute a significant proportion of the myocyte GSK3 pool) and GSK3β in cardiac myocytes. Although endothelin increases phosphorylation of GSK3 and decreases its activity, the response is less than that induced by insulin (which does not promote cardiac myocyte hypertrophy). GSK3 phosphorylation induced by endothelin requires signalling through the extracellular signal-regulated kinase 1/2 (ERK1/2) cascade and not the PKB/Akt pathway, whereas the reverse is true for insulin. Cardiac myocyte hypertrophy involves changes in morphology, and in gene and protein expression. The potent GSK3 inhibitor 1-azakenpaullone increases myocyte area as a consequence of increased cell length whereas phenylephrine increases both length and width. Azakenpaullone or insulin promotes AP1 transcription factor binding to an AP1 consensus oligonucleotide, but this was significantly less than that induced by endothelin and derived principally from increased binding of JunB protein, the expression of which was increased. Azakenpaullone promotes significant changes in gene expression (assessed by Affymetrix microarrays), but the overall response is less than with endothelin and there is little overlap between the genes identified. Thus, although GSK3 may contribute to cardiac myocyte hypertrophy in some respects (and presumably plays an important role in myocyte metabolism), it does not appear to contribute as significantly to the response induced by endothelin as has been maintained

Production of edible carbohydrates from formaldehyde in a spacecraft. pH variations in the calcium hydroxide catalyzed formose reaction

The study of the calcium hydroxide catalyzed condensation of formaldehyde was extended to a batch reactor system. Decreases in pH were observed, often in the acid regime, when using this basic catalyst. This observation was shown to be similar to results obtained by others using less basic catalysts in the batch mode. The relative rates of these reactions are different in a batch reactor than in a continuous stirred tank reactor. This difference in relative rates is due to the fact that at any degree of advancement in the batch system, the products have a history of previous products, pH, and dissolved catalyst. The relative rate differences can be expected to yield a different nature of product sugars for the two types of reactors

QZ Serpentis: A Dwarf Nova with a 2-Hour Orbital Period and an Anomalously Hot, Bright Secondary Star

We present spectroscopy and time-series photometry of the dwarf nova QZ Ser. The spectrum shows a rich absorption line spectrum of type K4 +- 2. K-type secondary stars are generally seen in dwarf novae with orbital periods P-orb around 6 h, but in QZ Ser the absorption radial velocities show an obvious modulation (semi-amplitude 207(5) km/s) at P-orb = 119.752(2) min, much shorter than typical for such a relatively warm and prominent secondary spectrum. The H-alpha emission-line velocity is modulated at the same period and roughly opposite phase. Time-series photometry shows flickering superposed on a modulation with two humps per orbit, consistent with ellipsoidal variation of the secondary's light. QZ Ser is a second example of a relatively short-period dwarf nova with a surprisingly warm secondary. Model calculations suggest that the secondary is strongly enhanced in helium, and had already undergone significant nuclear evolution when mass transfer began. Several sodium absorption features in the secondary spectrum are unusually strong, which may indicate that the present-day surface was the site of CNO-cycle hydrogen burning in the past.Comment: 11 pages, 3 postscript figures, 1 jpeg greyscale figure. Accepted for publication in PAS

Long-Period Giant Companions to Three Compact, Multiplanet Systems

Understanding the relationship between long-period giant planets and multiple smaller short-period planets is critical for formulating a complete picture of planet formation. This work characterizes three such systems. We present Kepler-65, a system with an eccentric (e = 0.28 ± 0.07) giant planet companion discovered via radial velocities (RVs) exterior to a compact, multiply transiting system of sub-Neptune planets. We also use precision RVs to improve mass and radius constraints on two other systems with similar architectures, Kepler-25 and Kepler-68. In Kepler-68 we propose a second exterior giant planet candidate. Finally, we consider the implications of these systems for planet formation models, particularly that the moderate eccentricity in Kepler-65\u27s exterior giant planet did not disrupt its inner system

Lindblad rate equations

In this paper we derive an extra class of non-Markovian master equations where the system state is written as a sum of auxiliary matrixes whose evolution involve Lindblad contributions with local coupling between all of them, resembling the structure of a classical rate equation. The system dynamics may develops strong non-local effects such as the dependence of the stationary properties with the system initialization. These equations are derived from alternative microscopic interactions, such as complex environments described in a generalized Born-Markov approximation and tripartite system-environment interactions, where extra unobserved degrees of freedom mediates the entanglement between the system and a Markovian reservoir. Conditions that guarantees the completely positive condition of the solution map are found. Quantum stochastic processes that recover the system dynamics in average are formulated. We exemplify our results by analyzing the dynamical action of non-trivial structured dephasing and depolarizing reservoirs over a single qubit.Comment: 12 pages, 2 figure

A reservoir for inverse power law decoherence of a qubit

The exact dynamics of a Jaynes-Cummings model for a qubit interacting with a continuous distribution of bosons, characterized by a special form of the spectral density, is evaluated analytically. The special reservoir is designed to induce anomalous decoherence, resulting in an inverse power law relaxation, of power 3/2, over an evaluated long time scale. If compared to the exponential-like relaxation obtained from the original Jaynes-Cummings model for Lorentzian-type spectral density functions, decoherence is strongly suppressed. The special reservoir exhibits an upper band edge frequency coinciding with the qubit transition frequency. Known theoretical models of photonic band gap media suitable for the realization of the designed reservoir are proposed.Comment: 5 pages, 2 figure