On the supercritical KDV equation with time-oscillating nonlinearity

For the initial value problem (IVP) associated to the generalized Korteweg-de Vries (gKdV) equation with supercritical nonlinearity, \begin{equation*} u_{t}+\partial_x^3u+\partial_x(u^{k+1}) =0,\qquad k\geq 5, \end{equation*} numerical evidence [Bona J.L., Dougalis V.A., Karakashian O.A., McKinney W.R.: Conservative, high-order numerical schemes for the generalized Korteweg–de Vries equation. Philos. Trans. Roy. Soc. London Ser. A 351, 107–164 (1995) ] shows that, there are initial data $\phi\in H^1(\mathbb{R})$ such that the corresponding solution may blow-up in finite time. Also, with the evidence from numerical simulation [Abdullaev F.K., Caputo J.G., Kraenkel R.A., Malomed B.A.: Controlling collapse in Bose–Einstein condensates by temporal modulation of the scattering length. Phys. Rev. A 67, 012605 (2003) and Konotop V.V., Pacciani P.: Collapse of solutions of the nonlinear Schrödinger equation with a time dependent nonlinearity: application to the Bose–Einstein condensates. Phys. Rev. Lett. 94, 240405 (2005) ], it has been claimed that a periodic time dependent coefficient in the nonlinearity would disturb the blow-up solution, either accelerating or delaying it. In this work, we investigate the IVP associated to the gKdV equation \begin{equation*} u_{t}+\partial_x^3u+g(\omega t)\partial_x(u^{k+1}) =0, \end{equation*} where $g$ is a periodic function and $k\geq 5$ is an integer. We prove that, for given initial data $\phi \in H^1(\mathbb{R})$, as $|\omega|\to \infty$, the solution $u_{\omega}$ converges to the solution $U$ of the initial value problem associated to \begin{equation*} U_{t}+\partial_x^3U+m(g)\partial_x(U^{k+1}) =0, \end{equation*} with the same initial data, where $m(g)$ is the average of the periodic function $g$. Moreover, if the solution $U$ is global and satisfies $\|U\|_{L_x^5L_t^{10}}<\infty$, then we prove that the solution $u_{\omega}$ is also global provided $|\omega|$ is sufficiently large.M. P. was partially supported by the Research Center of Mathematics of the University of Minho, Portugal through the FCT Pluriannual Funding Program, and through the project PTDC/MAT/109844/2009, and M. S. was partially supported by FAPESP Brazil

Manufacturing process for high aspect ratio metallic micro parts made by electroplating on partially conductive templates

Extended Abstract In supporting structural integrity of a miniature component, or for providing electric conduction of a through-silicon via (TSV) in three-dimensional integrated circuits (3D-IC), micro-or nano-hole filling with metallic material becomes increasing important in various micro-electrical mechanical systems (MEMSs) In this study, an anodic aluminum oxide (AAO) template containing numerous high aspect ratio nano-sized holes (an average diameter of 130 nm and an aspect-ratio about 20) was used as the cathode. The hydrophobicity/hydrophilicity of the AAO template was adjusted before Cu electrodeposition. Electrodeposition of Cu was carried out in an emulsified sc-CO2 bath containing cupric sulfate aqueous solution as the precursor. Cu deposition into the nano-holes was performed at an apparent constant current density of 2 A/dm 2 for 5 minutes. After electrodeposition, the cross section morphology and chemical composition of the AAO cathode was examined by transmission electron microscopy (TEM) and energy dispersive spectroscopy (EDS) with the aid of a focused-ion-beam (FIB). The experimental results showed that electrodeposition employing sc-CO2 bath to fill Cu into nano-sized holes was successful and superior to that of conventional process carried out at ambient pressure, in terms of uniformity and deposition rate. The high solubility of hydrogen gas in sc-CO2 fluid is the key factor. Moreover, the advantage of sc-CO2 electrodeposition is more pronounced for the AAO cathode exhibiting hydrophobic nature with respect to aqueous bath. References [1] Z

Bright light treatment of depression for older adults [ISRCTN55452501]

BACKGROUND: The incidence of insomnia and depression in the elder population is significant. It is hoped that use of light treatment for this group could provide safe, economic, and effective rapid recovery. METHODS: In this home-based trial we treated depressed elderly subjects with bright white (8,500 Lux) and dim red (<10 Lux) light for one hour a day at three different times (morning, mid-wake and evening). A placebo response washout was used for the first week. Wake treatment was conducted prior to the initiation of treatment, to explore antidepressant response and the interaction with light treatment. Urine and saliva samples were collected during a 24-hour period both before and after treatment and assayed for aMT6s and melatonin respectively to observe any change in circadian timing. Subjects wore a wrist monitor to record light exposure and wrist activity. Daily log sheets and weekly mood (GDS) and physical symptom (SAFTEE) scales were administered. Each subject was given a SCID interview and each completed a mood questionnaire (SIGH-SAD-SR) before and after treatment. Also, Hamilton Depression Rating (SIGH-SAD version) interviews were conducted by a researcher who was blind to the treatment condition. A control group of healthy, age-matched, volunteers was studied for one day to obtain baseline data for comparison of actigraphy and hormone levels. RESULTS: Eighty-one volunteers, between 60 and 79 years old, completed the study. Both treatment and placebo groups experienced mood improvement. Average GDS scores improved 5 points, the Hamilton Depression Rating Scale (HDRS) 17 scores (extracted from the self-rated SIGH-SAD-SR) improved 6 points. There were no significant treatment effects or time-by-treatment interactions. No significant adverse reactions were observed in either treatment group. The assays of urine and saliva showed no significant differences between the treatment and placebo groups. The healthy control group was active earlier and slept earlier but received less light than the depressed group at baseline. CONCLUSION: Antidepressant response to bright light treatment in this age group was not statistically superior to placebo. Both treatment and placebo groups experienced a clinically significant overall improvement of 16%

Composition of the Top Management Team and Firm International Diversification

This study investigates the impact of various top management team characteristics on firm international diversification. Relying on data from 126 firms in the electronics industry, we find that certain top management team characteristics are related to international expansion. Specifically, results indicate that lower average age, higher average tenure, higher average elite education, higher average international experience, and higher tenure heterogeneity are associated with firm international diversification. The study reinforces the importance of top management team composition in internationalization decisions and suggests further research in this context.Yeshttps://us.sagepub.com/en-us/nam/manuscript-submission-guideline