Global well-posedness and scattering for the energy-critical, defocusing Hartree equation for radial data

We consider the defocusing, $\dot{H}^1$-critical Hartree equation for the radial data in all dimensions $(n\geq 5)$. We show the global well-posedness and scattering results in the energy space. The new ingredient in this paper is that we first take advantage of the term $\displaystyle - \int_{I}\int_{|x|\leq A|I|^{1/2}}|u|^{2}\Delta \Big(\frac{1}{|x|}\Big)dxdt$ in the localized Morawetz identity to rule out the possibility of energy concentration, instead of the classical Morawetz estimate dependent of the nonlinearity.Comment: 23 pages, 1 figur

The dynamics of the NLS with the combined terms in five and higher dimensions

In this paper, we continue the study in \cite{MiaoWZ:NLS:3d Combined} to show the scattering and blow-up result of the solution for the nonlinear Schr\"{o}dinger equation with the energy below the threshold $m$ in the energy space $H^1(\R^d)$, iu_t + \Delta u = -|u|^{4/(d-2)}u + |u|^{4/(d-1)}u, \; d\geq 5. \tag{CNLS} The threshold is given by the ground state $W$ for the energy-critical NLS: $iu_t + \Delta u = -|u|^{4/(d-2)}u$. Compared with the argument in \cite{MiaoWZ:NLS:3d Combined}, the new ingredient is that we use the double duhamel formula in \cite{Kiv:Clay Lecture, TaoVZ:NLS:mass compact} to lower the regularity of the critical element in $L^{\infty}_tH^1_x$ to $L^{\infty}\dot H^{-\epsilon}_x$ for some $\epsilon>0$ in five and higher dimensions and obtain the compactness of the critical element in $L^2_x$, which is used to control the spatial center function $x(t)$ of the critical element and furthermore used to defeat the critical element in the reductive argument.Comment: To publish in: Some Topics in Harmonic Analysis and Applications, Pages265-298, Advanced Lectures in Mathematics, ALM34, Higher Education Press, Beijing, and International Press, USA, 201

Global well-posedness and scattering for the mass-critical Hartree equation with radial data

We establish global well-posedness and scattering for solutions to the mass-critical nonlinear Hartree equation $iu_t+\Delta u=\pm(|x|^{-2}*|u|^2)u$ for large spherically symmetric $L^2_x(\Bbb{R}^d)$ initial data; in the focusing case we require, of course, that the mass is strictly less than that of the ground state.Comment: 38 pages, 1 figur

Global well-posedness, scattering and blow-up for the energy-critical, focusing Hartree equation in the radial case

We establish global existence, scattering for radial solutions to the energy-critical focusing Hartree equation with energy and $\dot{H}^1$ norm less than those of the ground state in $\mathbb{R}\times \mathbb{R}^d$, $d\geq 5$.Comment: 35 pages, 2 figure

An Analysis of Language as a Barrier to Receiving Influenza Vaccinations among an Elderly Hispanic Population in the United States

Background. The Hispanic population in the United States is growing, and disparities in the receipt of healthcare services as a result of limited English proficiency have been demonstrated. We set out to determine if Spanish language preference was a barrier to receiving influenza vaccinations among Hispanic persons 65 years and older in the USA. Methods. Differences in the receipt of vaccinations by language preference were tested with both Chi-square analyses and adjusted logistic regression analyses. Results. Findings suggest that elderly Hispanic persons, 65 years of age and older, who prefer to communicate in Spanish instead of English, are significantly less likely to have received influenza vaccinations when compared to their Hispanic counterparts who prefer to communicate in English. Conclusions. Influenza infections can more often be fatal in older persons and may disparately affect minority populations such as Hispanic persons. Therefore, understanding barriers to the receipt of effective preventive health measures is necessary

Weight control behaviors in overweight/obese U.S. adults with diagnosed hypertension and diabetes

<p>Abstract</p> <p>Background</p> <p>Obesity is a major risk factor for development and progression of hypertension and diabetes, which often coexist in obese patients. Losing weight by means of energy restriction and physical activity has been effective in preventing and managing these diseases. However, weight control behaviors among overweight/obese adults with these conditions are poorly understood.</p> <p>Methods</p> <p>Using self-reported data from 143,386 overweight/obese participants (aged ≥ 18 years) in the 2003 Behavioral Risk Factor Surveillance System, we examined the proportion of overweight/obese adults who tried to lose weight and their weight control strategies by hypertension and/or diabetes status.</p> <p>Results</p> <p>Among all participants, 58% of those with hypertension, 60% of those with diabetes, and 72% of those with both diseases tried to lose weight, significantly higher than the 50% of those with neither condition (Bonferroni corrected P < 0.017 for all comparisons). The multivariate-adjusted odds ratio (AOR) for trying to lose weight was 1.11 (95% confidence interval [CI]: 1.05–1.17) in participants with hypertension, 1.02 (95% CI: 0.90–1.15) in participants with diabetes, and 1.18 (95% CI: 1.07–1.29) in participants with both diseases (participants with neither condition as the referent). Among 78,446 participants who tried to lose weight, 23% of those with hypertension only and 28% of those with both hypertension and diabetes reported adopting a low fat/low calorie (LF/LC) diet in controlling their weight, significantly higher than 19% of those with neither disease (Bonferroni corrected P < 0.017 for all comparisons). Participants with both diseases had a significantly lower percentage of adopting physical activity in controlling their weight than those with neither condition (6% versus 12%, P < 0.01). After multivariate adjustment, the AOR for adopting a LF/LC diet plus physical activity to lose weight was 1.46 (95% CI: 1.15–1.84) in participants with both diseases. The AOR for adopting a LF/LC diet only to lose weight was 1.72 (95% CI: 1.35–2.20) in participants with both diseases and was 1.21 (95% CI: 1.03–1.40) in participants with hypertension only.</p> <p>Conclusion</p> <p>The proportion of overweight/obese patients with diagnosed hypertension and/or diabetes who attempted to lose weight remains suboptimal and the weight control strategies varied significantly among these patients.</p

Daucosterol pretreatment ameliorates myocardial ischemia reperfusion injury via ROS-mediated NLRP3 inflammasome activation

Purpose: To determine the involvement of NLRP3 signaling pathway in the preventive role of daucosterol in acute myocardial infarction (AMI).Methods: H9C2 cells were pretreated with daucosterol before hypoxia/reoxygenation (HR) injury. Myocardial ischemia reperfusion (IR) was established in male SD rats, followed by reperfusion. Myocardial infarct size was measured. The serum levels of creatine kinase (CK), lactate&nbsp; dehydrogenase (LDH), total superoxide dismutase (T-SOD), and malondialdehyde (MDA) were determined using commercial kits. NLRP3 inflammasome activation was assessed by western blotting.Results: Myocardial infarct size was smaller after IR injury in rats pretreated with daucosterol (10 and 50 mg/kg) than that pretreated with daucosterol (0 and 1 mg/kg). The increase in LDH, CK, and MDA levels after IR injury was reduced following daucosterol pretreatment. Reactive oxygen species (ROS) production increased, whereas T-SOD activity decreased after IR injury. These changes were prevented by pretreatment of daucosterol (10 and 50 mg/kg). Protein expression of NLRP3 inflammasome increased after IR injury in H9C2 cells while pretreatment with daucosterol inhibited the upregulation of NLRP3 inflammasome.Conclusion: The cardioprotective effect of daucosterol pretreatment appears to be mediated via the inactivation of ROS-related NLRP3 inflammasome, suggesting that daucosteol might be a potential therapeutic drug for AMI. Keywords: Daucosterol, Myocardial ischemia, Reperfusion injury, Reactive oxygen species, NLRP3 inflammasom

Factors Associated with Vitamin D Deficiency and Inadequacy among Women of Childbearing Age in the United States

Objective. To examine the prevalence and correlates of vitamin D deficiency and inadequacy among US women of childbearing age. Methods. Data from 1,814 female participants (20–44 y) in the 2003–2006 NHANES were analyzed to estimate the age-adjusted prevalence and prevalence ratios with 95% confidence intervals (CIs) for vitamin D deficiency (defined as serum 25-hydroxyvitamin D [25(OH)D] <12.0 ng/mL) and inadequacy (defined as 25(OH)D: 12.0–<20.0 ng/mL). Results. The age-adjusted prevalence was 11.1% (95% CI: 8.8–14.0%) for vitamin D deficiency and 25.7% (95% CI: 22.3–29.5%) for vitamin D inadequacy. Race/ethnicity other than non-Hispanic white and obesity were associated with increased risks, whereas dietary supplement use, milk consumption of ≥1 time/day, and potential sunlight exposure during May-October were associated with decreased risks for both vitamin D deficiency and inadequacy (P < 0.05). Current smoking and having histories of diabetes and cardiovascular disease were also associated with an increased risk for vitamin D deficiency (P < 0.05). Conclusions. Among women of childbearing age, periconceptional intervention programs may focus on multiple risk factors for vitamin D deficiency and inadequacy to ultimately improve their vitamin D nutrition