Some homogenization and corrector results for nonlinear monotone operators

This paper deals with the limit behaviour of the solutions of quasi-linear equations of the form \ \ds -\limfunc{div}\left(a\left(x, x/{\varepsilon _h},Du_h\right)\right)=f_h on $\Omega$ with Dirichlet boundary conditions. The sequence $(\varepsilon _h)$ tends to $0$ and the map $a(x,y,\xi )$ is periodic in $y$, monotone in $\xi$ and satisfies suitable continuity conditions. It is proved that $u_h\rightarrow u$ weakly in $H_0^{1,2}(\Omega )$, where $u$ is the solution of a homogenized problem \ -\limfunc{div}(b(x,Du))=f on $\Omega$. We also prove some corrector results, i.e. we find $(P_h)$ such that $Du_h-P_h(Du)\rightarrow 0$ in $L^2(\Omega ,R^n)$

Correctors for some nonlinear monotone operators

In this paper we study homogenization of quasi-linear partial differential equations of the form -\mbox{div}\left( a\left( x,x/\varepsilon _h,Du_h\right) \right) =f_h on $\Omega$ with Dirichlet boundary conditions. Here the sequence $\left( \varepsilon _h\right)$ tends to $0$ as $h\rightarrow \infty$ and the map $a\left( x,y,\xi \right)$ is periodic in $y,$ monotone in $\xi$ and satisfies suitable continuity conditions. We prove that $u_h\rightarrow u$ weakly in $W_0^{1,p}\left( \Omega \right)$ as $h\rightarrow \infty ,$ where $u$ is the solution of a homogenized problem of the form -\mbox{div}\left( b\left( x,Du\right) \right) =f on $\Omega .$ We also derive an explicit expression for the homogenized operator $b$ and prove some corrector results, i.e. we find $\left( P_h\right)$ such that $Du_h-P_h\left( Du\right) \rightarrow 0$ in $L^p\left( \Omega, \mathbf{R}^n\right)$

Properties of HxTaS2

The preparation of Hx TaS2 (0 \u3c x \u3c 0.87) is described. The compounds are only marginally stable at room temperature, slowly evolving H2S and H2 (and possibly Hp in air). Magnetic susceptibility data show that a low temperature transformation in 2H ... TaS2 (at so•K) is suppressed with the addition of hydrogen, and· at the same time the superconducting transition temperature T c rises from 0.8 to ~4.2•K at x = 0.11. Heat capacity measurements near this concentration show the superconductivity to be a bulk effect. Finally, by correlation of this data with susceptibility and T c measurements in other intercalation compounds, we suggest that the rise of T c (at low electron transfer) is due to suppression of the low temperature transformation and not due to an excitonic mechanism of superconductivity

Transient x-ray diffraction used to diagnose shock compressed Si crystals on the Nova laser

Transient x-ray diffraction is used to record time-resolved information about the shock compression of materials. This technique has been applied on Nova shock experiments driven using a hohlraum x-ray drive. Data were recorded from the shock release at the free surface of a Si crystal, as well as from Si at an embedded ablator/Si interface. Modeling has been done to simulate the diffraction data incorporating the strained crystal rocking curves and Bragg diffraction efficiencies. Examples of the data and post-processed simulations are presented

[Phe4]somatostatin: a potent, selective inhibitor of growth hormone release.

[Phe4]Somatostatin was twice as active as somatostatin (SS) in suppressing rat growth hormone release in vitro but had only weak activity toward inhibition of insulin and glucagon release in vivo. The ability of this analogue to inhibit growth hormone release more actively than SS was confirmed in vivo by two separately designed bioassays. Further structure/activity studies of position 4 were carried out with [Glu4]SS, [Thr4]SS, and des-Lys4-SS, all of which had negligible inhibiting activity in the pituitary and pancreas. In this context the strikingly selective activity of [Phe4]SS suggests a fundamental difference in the SS receptors of pituitary and pancreas and the normal side-chain basicity of position 4 appears to be more important for action in pancreas than in pituitary. [Phe4]SS has properties that may be useful in the development of agents for the treatment of acromegaly or other disorders associated with increased growth hormone levels

A Calibration of NICMOS Camera 2 for Low Count-Rates

NICMOS 2 observations are crucial for constraining distances to most of the existing sample of z > 1 SNe Ia. Unlike the conventional calibration programs, these observations involve long exposure times and low count rates. Reciprocity failure is known to exist in HgCdTe devices and a correction for this effect has already been implemented for high and medium count-rates. However observations at faint count-rates rely on extrapolations. Here instead, we provide a new zeropoint calibration directly applicable to faint sources. This is obtained via inter-calibration of NIC2 F110W/F160W with WFC3 in the low count-rate regime using z ~ 1 elliptical galaxies as tertiary calibrators. These objects have relatively simple near-IR SEDs, uniform colors, and their extended nature gives superior signal-to-noise at the same count rate than would stars. The use of extended objects also allows greater tolerances on PSF profiles. We find ST magnitude zeropoints (after the installation of the NICMOS cooling system, NCS) of 25.296 +- 0.022 for F110W and 25.803 +- 0.023 for F160W, both in agreement with the calibration extrapolated from count-rates 1,000 times larger (25.262 and 25.799). Before the installation of the NCS, we find 24.843 +- 0.025 for F110W and 25.498 +- 0.021 for F160W, also in agreement with the high-count-rate calibration (24.815 and 25.470). We also check the standard bandpasses of WFC3 and NICMOS 2 using a range of stars and galaxies at different colors and find mild tension for WFC3, limiting the accuracy of the zeropoints. To avoid human bias, our cross-calibration was "blinded" in that the fitted zeropoint differences were hidden until the analysis was finalized.Comment: Accepted for Publication in the Astronomical Journal. New version contains added referenc

Sustaining remission of psychotic depression: rationale, design and methodology of STOP-PD II

BACKGROUND: Psychotic depression (PD) is a severe disabling disorder with considerable morbidity and mortality. Electroconvulsive therapy and pharmacotherapy are each efficacious in the treatment of PD. Expert guidelines recommend the combination of antidepressant and antipsychotic medications in the acute pharmacologic treatment of PD. However, little is known about the continuation treatment of PD. Of particular concern, it is not known whether antipsychotic medication needs to be continued once an episode of PD responds to pharmacotherapy. This issue has profound clinical importance. On the one hand, the unnecessary continuation of antipsychotic medication exposes a patient to adverse effects, such as weight gain and metabolic disturbance. On the other hand, premature discontinuation of antipsychotic medication has the potential risk of early relapse of a severe disorder. METHODS/DESIGN: The primary goal of this multicenter randomized placebo-controlled trial is to assess the risks and benefits of continuing antipsychotic medication in persons with PD once the episode of depression has responded to treatment with an antidepressant and an antipsychotic. Secondary goals are to examine age and genetic polymorphisms as predictors or moderators of treatment variability, potentially leading to more personalized treatment of PD. Individuals aged 18-85 years with unipolar psychotic depression receive up to 12 weeks of open-label treatment with sertraline and olanzapine. Participants who achieve remission of psychosis and remission/near-remission of depressive symptoms continue with 8 weeks of open-label treatment to ensure stability of remission. Participants with stability of remission are then randomized to 36 weeks of double-blind treatment with either sertraline and olanzapine or sertraline and placebo. Relapse is the primary outcome. Metabolic changes are a secondary outcome. DISCUSSION: This trial will provide clinicians with much-needed evidence to guide the continuation and maintenance treatment of one of the most disabling and lethal of psychiatric disorders. TRIAL REGISTRATION AND URL: NCT: NCT01427608

Subaru FOCAS Spectroscopic Observations of High-Redshift Supernovae

We present spectra of high-redshift supernovae (SNe) that were taken with the Subaru low resolution optical spectrograph, FOCAS. These SNe were found in SN surveys with Suprime-Cam on Subaru, the CFH12k camera on the Canada-France-Hawaii Telescope (CFHT), and the Advanced Camera for Surveys (ACS) on the Hubble Space Telescope (HST). These SN surveys specifically targeted z>1 Type Ia supernovae (SNe Ia). From the spectra of 39 candidates, we obtain redshifts for 32 candidates and spectroscopically identify 7 active candidates as probable SNe Ia, including one at z=1.35, which is the most distant SN Ia to be spectroscopically confirmed with a ground-based telescope. An additional 4 candidates are identified as likely SNe Ia from the spectrophotometric properties of their host galaxies. Seven candidates are not SNe Ia, either being SNe of another type or active galactic nuclei. When SNe Ia are observed within a week of maximum light, we find that we can spectroscopically identify most of them up to z=1.1. Beyond this redshift, very few candidates were spectroscopically identified as SNe Ia. The current generation of super red-sensitive, fringe-free CCDs will push this redshift limit higher.Comment: 19 pages, 26 figures. PASJ in press. see http://www.supernova.lbl.gov/2009ClusterSurvey/ for additional information pertaining to the HST Cluster SN Surve

The importance of major mergers in the build up of stellar mass in brightest cluster galaxies at z=1

Recent independent results from numerical simulations and observations have shown that brightest cluster galaxies (BCGs) have increased their stellar mass by a factor of almost two between z~0.9 and z~0.2. The numerical simulations further suggest that more than half this mass is accreted through major mergers. Using a sample of 18 distant galaxy clusters with over 600 spectroscopically confirmed cluster members between them, we search for observational evidence that major mergers do play a significant role. We find a major merger rate of 0.38 +/- 0.14 mergers per Gyr at z~1. While the uncertainties, which stem from the small size of our sample, are relatively large, our rate is consistent with the results that are derived from numerical simulations. If we assume that this rate continues to the present day and that half of the mass of the companion is accreted onto the BCG during these mergers, then we find that this rate can explain the growth in the stellar mass of the BCGs that is observed and predicted by simulations. Major mergers therefore appear to be playing an important role, perhaps even the dominant one, in the build up of stellar mass in these extraordinary galaxies.Comment: 15 pages, 6 figures, accepted for publication in MNRAS. Reduced data will be made available through the ESO archiv

An Evaluation of Putative Sympatric Speciation within Limnanthes (Limnanthaceae)

Limnanthes floccosa ssp. floccosa and L. floccosa ssp. grandiflora are two of five subspecies within Limnanthes floccosa endemic to vernal pools in southern Oregon and northern California. Three seasons of monitoring natural populations have quantified that L. floccosa ssp. grandiflora is always found growing sympatrically with L. floccosa ssp. floccosa and that their flowering times overlap considerably. Despite their subspecific rank within the same species crossing experiments have confirmed that their F1 hybrids are sterile. An analysis of twelve microsatellite markers, with unique alleles in each taxon, also shows exceedingly low levels of gene flow between populations of the two subspecies. Due to the lack of previous phylogenetic resolution among L. floccosa subspecies, we used Illumina next generation sequencing to identify single nucleotide polymorphisms from genomic DNA libraries of L. floccosa ssp. floccosa and L. floccosa ssp. grandiflora. These data were used to identify single nucleotide polymorphisms in the chloroplast, mitochondrial, and nuclear genomes. From these variable loci, a total of 2772 bp was obtained using Sanger sequencing of ten individuals representing all subspecies of L. floccosa and an outgroup. The resulting phylogenetic reconstruction was fully resolved. Our results indicate that although L. floccosa ssp. floccosa and L. floccosa ssp. grandiflora are closely related, they are not sister taxa and therefore likely did not diverge as a result of a sympatric speciation event