Low frequency resolvent estimates for long range perturbations of the Euclidean Laplacian

Using Mourre theory, we obtain low frequency resolvent estimates with sharp weights for long range metric perturbations of the flat Laplacian

Well-posedness of the Viscous Boussinesq System in Besov Spaces of Negative Order Near Index s=−1s=-1

This paper is concerned with well-posedness of the Boussinesq system. We prove that the $n$ ($n\ge2$) dimensional Boussinesq system is well-psoed for small initial data $(\vec{u}_0,\theta_0)$ ($\nabla\cdot\vec{u}_0=0$) either in $({B}^{-1}_{\infty,1}\cap{B^{-1,1}_{\infty,\infty}})\times{B}^{-1}_{p,r}$ or in ${B^{-1,1}_{\infty,\infty}}\times{B}^{-1,\epsilon}_{p,\infty}$ if $r\in[1,\infty]$, $\epsilon>0$ and $p\in(\frac{n}{2},\infty)$, where $B^{s,\epsilon}_{p,q}$ ($s\in\mathbb{R}$, $1\leq p,q\leq\infty$, $\epsilon>0$) is the logarithmically modified Besov space to the standard Besov space $B^{s}_{p,q}$. We also prove that this system is well-posed for small initial data in $({B}^{-1}_{\infty,1}\cap{B^{-1,1}_{\infty,\infty}})\times({B}^{-1}_{\frac{n}{2},1}\cap{B^{-1,1}_{\frac{n}{2},\infty}})$.Comment: 18 page

Observed relationships between cloud vertical structure and convective aggregation over tropical ocean

Using the satellite-infrared-based Simple Convective Aggregation Index (SCAI) to determine the degree of aggregation, 5 years of CloudSat-CALIPSO cloud profiles are composited at a spatial scale of 10 degrees to study the relationship between cloud vertical structure and aggregation. For a given large-scale vertical motion and domain-averaged precipitation rate, there is a large decrease in anvil cloud (and in cloudiness as a whole) and an increase in clear sky and low cloud as aggregation increases. The changes in thick anvil cloud are proportional to the changes in total areal cover of brightness temperatures below 240 K (cold cloud area, CCA), which is negatively correlated with SCAI. Optically thin anvil cover decreases significantly when aggregation increases, even for a fixed CCA, supporting previous findings of a higher precipitation efficiency for aggregated convection. Cirrus, congestus, and mid-level clouds do not display a consistent relationship with the degree of aggregation. We present the lidar-observed low-level cloud cover (where the lidar is not attenuated) as our best estimate of the true low-level cloud cover and show that it increases as aggregation increases. Qualitatively, the relationships between cloud distribution and SCAI do not change with sea-surface temperature, while cirrus clouds are more abundant and low-level clouds less at higher sea-surface temperatures. For the observed regimes, the vertical cloud profile varies more evidently with SCAI than with mean precipitation rate. These results confirm that convective scenes with similar vertical motion and rainfall can be associated with vastly different cloudiness (both high and low cloud) and humidity depending on the degree of convective aggregation

The Effect of Structured Counseling Towards Knowledge, Attitude, and Participation of Modern Contraceptive Among Unmet Need Couples

The number of unmet need for family planning remains high in developing countries, including in Indonesia. Structured contraceptive counseling potentially increases contraceptive use effectively maintain its continuity and enhances client's satisfaction. Contraceptive counseling had not been properly performed, therefore this study aimed to analyze structured counseling influence toward knowledge improvement, attitude and participation at modern contraceptive among unmet need reproductive-aged couples. This study was conducted on March - June 2015 by using a randomized pretestposttest measurement with control group design. The subjects were recruited through stratified random sampling method. Inclusion subjects were further classified into 48 persons for the intervention group and other 48 persons for the control group. The increase of knowledge and attitude between intervention and control group was then compared by using Mann-Whitney U test, and the effect of structured counseling toward participation of modern contraceptive was analyzed by using multiple logistic regression. Results showed that there was a significant difference of test score for knowledge and attitude between the intervention and the control group (p value < 0.05). Reproductive-aged women are more likely to participate at modern contraceptive with odds ratio = 6.167 (95% CI= 2,427 - 15,67). Inconclusion, structured counseling can increase knowledge, attitude, and participation at modern contraceptive among reproductive-aged couples

Should We Assess Pituitary Function in Children After a Mild Traumatic Brain Injury? A Prospective Study

The aim of this study was to evaluate the frequency of hypopituitarism following TBI in a cohort of children who had been hospitalized for mild TBI and to identify the predictive factors for this deficiency. A prospective study was conducted on children between 2 and 16 years of age who had been hospitalized for mild TBI according to the Glasgow Coma Scale between September 2009 and June 2013. Clinical parameters, basal pituitary hormone assessment at 0, 6, and 12 months, as well as a dynamic testing (insulin tolerance test) 12 months after TBI were performed. The study included 109 children, the median age was 8.5 years. Patients were examined 6 months ( = 99) and 12 months ( = 96) after TBI. Somatotropic deficiency (defined by a GH peak &lt;20 mUI/l in two tests, an IGF-1 &lt;-1SDS and a delta height &lt;0SDS) were confirmed in 2 cases. One case of gonadotrophic deficiency occurred 1 year after TBI among 13 pubertal children. No cases of precocious puberty, 5 cases of low prolactin level, no cases of corticotropic insufficiency (cortisol peak &lt;500 nmol/l) and no cases diabetes insipidus were recorded. Pituitary insufficiency was present 1year after mild TBI in about 7% of children. Based on our results, we suggest testing children after mild TBI in case of clinical abnormalities. i.e., for GH axis, IGF-1, which should be assessed in children with a delta height &lt;0 SDS, 6 to 12 months after TBI, and a dynamic GH testing (preferentially by an ITT) should be performed in case of IGF-1 &lt;-1SDS, with a GH threshold at 20 mUI/L. However, if a systematic pituitary assessment is not required for mild TBI, physicians should monitor children 1 year after mild TBI with particular attention to growth and weight gain

Global well-posedness for a Smoluchowski equation coupled with Navier-Stokes equations in 2D

We prove global existence for a nonlinear Smoluchowski equation (a nonlinear Fokker-Planck equation) coupled with Navier-Stokes equations in two dimensions. The proof uses a deteriorating regularity estimate and the tensorial structure of the main nonlinear terms

Laplacian Growth, Elliptic Growth, and Singularities of the Schwarz Potential

The Schwarz function has played an elegant role in understanding and in generating new examples of exact solutions to the Laplacian growth (or "Hele- Shaw") problem in the plane. The guiding principle in this connection is the fact that "non-physical" singularities in the "oil domain" of the Schwarz function are stationary, and the "physical" singularities obey simple dynamics. We give an elementary proof that the same holds in any number of dimensions for the Schwarz potential, introduced by D. Khavinson and H. S. Shapiro [17] (1989). A generalization is also given for the so-called "elliptic growth" problem by defining a generalized Schwarz potential. New exact solutions are constructed, and we solve inverse problems of describing the driving singularities of a given flow. We demonstrate, by example, how \mathbb{C}^n - techniques can be used to locate the singularity set of the Schwarz potential. One of our methods is to prolong available local extension theorems by constructing "globalizing families". We make three conjectures in potential theory relating to our investigation

The influence of fractional diffusion in Fisher-KPP equations

We study the Fisher-KPP equation where the Laplacian is replaced by the generator of a Feller semigroup with power decaying kernel, an important example being the fractional Laplacian. In contrast with the case of the stan- dard Laplacian where the stable state invades the unstable one at constant speed, we prove that with fractional diffusion, generated for instance by a stable L\'evy process, the front position is exponential in time. Our results provide a mathe- matically rigorous justification of numerous heuristics about this model

Resolvent estimates for normally hyperbolic trapped sets

We give pole free strips and estimates for resolvents of semiclassical operators which, on the level of the classical flow, have normally hyperbolic smooth trapped sets of codimension two in phase space. Such trapped sets are structurally stable and our motivation comes partly from considering the wave equation for Kerr black holes and their perturbations, whose trapped sets have precisely this structure. We give applications including local smoothing effects with epsilon derivative loss for the Schr\"odinger propagator as well as local energy decay results for the wave equation.Comment: Further changes to erratum correcting small problems with Section 3.5 and Lemma 4.1; this now also corrects hypotheses, explicitly requiring trapped set to be symplectic. Erratum follows references in this versio