On the discrete spectrum of quantum layers

Consider a quantum particle trapped between a curved layer of constant width built over a complete, non-compact, $\mathcal C^2$ smooth surface embedded in $\mathbb{R}^3$. We assume that the surface is asymptotically flat in the sense that the second fundamental form vanishes at infinity, and that the surface is not totally geodesic. This geometric setting is known as a quantum layer. We consider the quantum particle to be governed by the Dirichlet Laplacian as Hamiltonian. Our work concerns the existence of bound states with energy beneath the essential spectrum, which implies the existence of discrete spectrum. We first prove that if the Gauss curvature is integrable, and the surface is weakly $\kappa$-parabolic, then the discrete spectrum is non-empty. This result implies that if the total Gauss curvature is non-positive, then the discrete spectrum is non-empty. We next prove that if the Gauss curvature is non-negative, then the discrete spectrum is non-empty. Finally, we prove that if the surface is parabolic, then the discrete spectrum is non-empty if the layer is sufficiently thin.Comment: Clarifications and corrections to previous version, conjecture from previous version is proven here (Theorem 1.5), additional references include

Alterations in Brain-Derived Neurotrophic Factor in the Mouse Hippocampus Following Acute but Not Repeated Benzodiazepine Treatment

Benzodiazepines (BZs) are safe drugs for treating anxiety, sleep, and seizure disorders, but their use also results in unwanted effects including memory impairment, abuse, and dependence. The present study aimed to reveal the molecular mechanisms that may contribute to the effects of BZs in the hippocampus (HIP), an area involved in drug-related plasticity, by investigating the regulation of immediate early genes following BZ administration. Previous studies have demonstrated that both brain derived neurotrophic factor (BDNF) and c-Fos contribute to memory- and abuse-related processes that occur within the HIP, and their expression is altered in response to BZ exposure. In the current study, mice received acute or repeated administration of BZs and HIP tissue was analyzed for alterations in BDNF and c-Fos expression. Although no significant changes in BDNF or c-Fos were observed in response to twice-daily intraperitoneal (i.p.) injections of diazepam (10 mg/kg + 5 mg/kg) or zolpidem (ZP; 2.5 mg/kg + 2.5 mg/kg), acute i.p. administration of both triazolam (0.03 mg/kg) and ZP (1.0 mg/kg) decreased BDNF protein levels within the HIP relative to vehicle, without any effect on c-Fos. ZP specifically reduced exon IV-containing BDNF transcripts with a concomitant increase in the association of methyl-CpG binding protein 2 (MeCP2) with BDNF promoter IV, suggesting that MeCP2 activity at this promoter may represent a ZP-specific mechanism for reducing BDNF expression. ZP also increased the association of phosphorylated cAMP response element binding protein (pCREB) with BDNF promoter I. Future work should examine the interaction between ZP and DNA as the cause for altered gene expression in the HIP, given that BZs can enter the nucleus and intercalate into DNA directly

Review of battery electric vehicle propulsion systems incorporating flywheel energy storage

The development of battery electric vehicles (BEV) must continue since this can lead us towards a zero emission transport system. There has been an advent of the production BEVs in recent years; however their low range and high cost still remain the two important drawbacks. The battery is the element which strongly affects the cost and range of the BEV. The batteries offer either high specific power or high specific energy but not both. To provide the BEVs with the characteristic to compete with conventional vehicles it is beneficial to hybridize the energy storage combining a high energy battery with a high power source. This shields the battery from peak currents and improves its capacity and life. There are various devices which could qualify as a secondary storage system for the BEV such as high power battery, supercapacitor and high speed flywheel (FW). This paper aims to review a specific type of hybridisation of energy storage which combines batteries and high speed flywheels. The flywheel has been used as a secondary energy system in BEVs from the early 1970s when the oil crises triggered an interest in BEVs. Since the last decade the interest in flywheels has strengthened and their application in the kinetic energy recovery system (KERS) in Formula 1 has further bolstered the case for flywheels. With a number of automotive manufacturers getting involved in developing flywheels for road applications, the authors believe commercial flywheel based powertrains are likely to be seen in the near future. It is hence timely to produce a review of research and development in the area of flywheel assisted BEVs

Self-Transcendent Emotions and Social Media: Exploring the Content and Consumers of Inspirational Facebook Posts

Although a great deal of research has examined the potential negative effects of Facebook, studies also show that Facebook use can lead to various positive effects. This study builds on this positive effects scholarship: together, the two studies presented herein aim to provide an understanding of the inspirational content available on Facebook and the way social media users in the United States encounter, recall, and interact with this content. Results from the quantitative content analysis in Study 1 show that inspirational Facebook posts contain similar frequencies of hope and appreciation of beauty and excellent elicitors when compared with other forms of media and social media. Results from the national survey conducted in Study 2 show that social media users are most often inspired by portrayals of kindness and overcoming obstacles and that Facebook users did not report different sharing behavior as compared with users of other social media sites

Conditioned Effects Produced by Naltrexone Doses That Reduce Ethanol-Reinforced Responding in Rhesus Monkeys

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/66264/1/j.1530-0277.1999.tb04173.x.pd

Hydrochloride Salt of the GABAkine KRM-II-81

Imidazodiazepine (5-(8-ethynyl-6-(pyridin-2-yl)-4H-benzo[f]imidazole[1,5-α][1,4]diazepin-3-yl) oxazole or KRM-II-81) is a potentiator of GABAA receptors (a GABAkine) undergoing preparation for clinical development. KRM-II-81 is active against many seizure and pain models in rodents, where it exhibits improved pharmacological properties over standard-of-care agents. Since salts can be utilized to create opportunities for increased solubility, enhanced absorption, and distribution, as well as for efficient methods of bulk synthesis, a hydrochloride salt of KRM-II-81 was prepared. KRM-II-81·HCl was produced from the free base with anhydrous hydrochloric acid. The formation of the monohydrochloride salt was confirmed by X-ray crystallography, as well as 1H NMR and 13C NMR analyses. High water solubility and a lower partition coefficient (octanol/water) were exhibited by KRM-II-81·HCl as compared to the free base. Oral administration of either KRM-II-81·HCl or the free base resulted in high concentrations in the brain and plasma of rats. Oral dosing in mice significantly increased the latency to both clonic and tonic convulsions and decreased pentylenetetrazol-induced lethality. The increased water solubility of the HCl salt enables intravenous dosing and the potential for higher concentration formulations compared with the free base without impacting anticonvulsant potency. Thus, KRM-II-81·HCl adds an important new compound to facilitate the development of these imidazodiazepines for clinical evaluation