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

Boundedness and Stability of Impulsively Perturbed Systems in a Banach Space

Consider a linear impulsive equation in a Banach space $$\dot{x}(t)+A(t)x(t) = f(t), ~t \geq 0,$$ $$x(\tau_i +0)= B_i x(\tau_i -0) + \alpha_i,$$ with $\lim_{i \rightarrow \infty} \tau_i = \infty$. Suppose each solution of the corresponding semi-homogeneous equation $$\dot{x}(t)+A(t)x(t) = 0,$$ (2) is bounded for any bounded sequence $\{ \alpha_i \}$. The conditions are determined ensuring (a) the solution of the corresponding homogeneous equation has an exponential estimate; (b) each solution of (1),(2) is bounded on the half-line for any bounded $f$ and bounded sequence $\{ \alpha_i \}$ ; (c) $\lim_{t \rightarrow \infty}x(t)=0$ for any $f, \alpha_i$ tending to zero; (d) exponential estimate of $f$ implies a similar estimate for $x$.Comment: 19 pages, LaTex-fil

A real-time test of food hazard awareness

Purpose - Food poisoning attributable to the home generates a large disease burden, yet is an unregulated and largely unobserved domain. Investigating food safety awareness and routine practices is fraught with difficulties. The purpose of this paper is to develop and apply a new survey tool to elicit awareness of food hazards. Data generated by the approach are analysed to investigate the impact of oberservable heterogeneity on food safety awareness. Design/methodology/approach - The authors develop a novel Watch-and-Click survey tool to assess the level of awareness of a set of hazardous food safety behaviours in the domestic kitchen. Participants respond to video footage stimulus, in which food hazards occur, via mouse clicks/screen taps. This real-time response data is analysed via estimation of count and logit models to investigate how hazard identification patterns vary over observable characteristics. Findings - User feedback regarding the Watch-and-Click tool approach is extremely positive. Substantive results include significantly higher hazard awareness among the under 60s. People who thought they knew more than the average person did indeed score higher but people with food safety training/experience did not. Vegetarians were less likely to identify four of the five cross-contamination hazards they observed. Originality/value - A new and engaging survey tool to elicit hazard awareness with real-time scores and feedback is developed, with high levels of user engagement and stakeholder interest. The approach may be applied to elicit hazard awareness in a wide range of contexts including education, training and research

Mapping provision of enterprise education and support for entrepreneurship in England's higher education institutions

The aim of this paper is to provide a comprehensive overview of the state of support for enterprise and entrepreneurship education within England's Higher Education Institutions (HEIs). The paper is based upon the National Council for Graduate Entrepreneurship (NCGE) Mapping Study of this activity. Research commissioned by NCGE (NCGE 2004; Hannon, 2005) has shown that there is a growing knowledge base about enterprise education but less so concerning the provision for student enterprise and graduate entrepreneurship. There has been no recent study that has comprehensively mapped enterprise education activity in all higher education institutions across England. Institutional contacts in 94% of all the HEIs for this study entered data into an online institutional mapping template containing questions on modules/courses, non-accredited support and other institutional characteristics. The researchers maintained regular telephone contact and made personal visits to maximise data entry and to provide support where needed. This approach has led to the collection of a unique and robust data set that has been thoroughly and empirically analysed using SPSS. The paper presents a national overview and highlights selected regional variations in enterprise education and non–accredited entrepreneurship support. This includes: current and planned course provision over time; student profiles and targets; primary learning outcomes; non-accredited provision and student engagement; primary funding sources; and the development of a range of institutional characteristics conducive to supporting student enterprise and graduate entrepreneurship. The findings from the mapping study illuminate the current HE landscape of support for enterprise and entrepreneurship thereby providing HEIs and educators with a valuable national resource as well as informing other key stakeholders – RDAs and central government – of the scope and scale of the contribution that HEIs offer to regional economic and social agendas. From such a unique evidence base more informed decisions can be taken in considering effective mechanisms for the future growth and development of HEI contributions. This paper offers the findings from a current comprehensive dataset on the HE provision of enterprise and entrepreneurship education in England. With 94% of the HEIs in the study providing data online the study has also created a nationaldatabase that can be a platform for sharing knowledge and experience across the community. Furthermore conducting a repeat online study on an annual basis will provide valuable time series data. The study findings will help shape the future environment for student enterprise and graduate entrepreneurship across England

The state of education provision for enterprise and entrepreneurship: A mapping study of England’s HEIs

The aim of this paper is to provide a comprehensive overview of the state of provision for enterprise and entrepreneurship education within England’s Higher Education Institutions (HEIs). The paper is based on the National Council for Graduate Entrepreneurship (NCGE) Mapping Study of enterprise education in England. Research commissioned by NCGE (ISBA 2004) has shown that there is a growing knowledge base about the nature of enterprise education but less so evidence concerning the provision for enhancing student enterprise and graduate entrepreneurship. Although studies have taken place in the US and Levie undertook a study of the UK published in 1999, there has been no recent study that has comprehensively mapped enterprise education activity in all higher education institutions across England. Institutional contacts in 94% of all the HEIs for this study entered data into an online institutional mapping template containing questions on modules/courses, non-accredited support and other institutional characteristics. The researchers maintained regular telephone contact and made personal visits to maximise data entry and to provide support where needed. This approach has led to the collection of a unique and robust data set that has been analysed using SPSS. The paper presents a national overview and highlights selected regional variations in enterprise education and non–accredited entrepreneurship support. This includes: current and planned course provision over time; student profiles and targets; primary learning outcomes; non-accredited provision and student engagement; primary funding sources; and the development of a range of institutional characteristics conducive to supporting student enterprise and graduate entrepreneurship. The findings from the mapping study illuminate the current HE landscape of support for enterprise and entrepreneurship thereby providing HEIs and educators with a valuable national resource. Additionally, this informs other key stakeholders – RDAs and central government – of the scope and scale of the contribution that HEIs offer to regional economic and social agendas. From such a unique evidence base more informed decisions can be taken when considering effective mechanisms for the future growth and development of HEI contributions. This paper offers the findings from a unique and current comprehensive dataset on the HE provision of enterprise and entrepreneurship education in England. With 94% of the HEIs in the study providing data online the study has created a national database that can be a platform for sharing knowledge and experience across the community. Furthermore conducting a repeat online study on an annual basis will provide valuable time series data. The study findings will help shape the future environment for student enterprise and graduate entrepreneurship across England

Effect of Piglet Age on Distress Associated with Gas Euthanasia, Neonate vs. Weaned

The objective of this study was to compare the effectiveness of euthanasia gases administered to 2 age groups of piglets: neonates (less than 3 days, n=160, BW 2.61 ± 0.81 kg) and weaned (16 to 24 days, n=160, BW 4.62 ± 0.76 kg). Two different gases were explored in this study: 100% CO2 and a 50:50 CO2:Argon (CA) gas mixture. Each gas was administered at 3 flow rates: 35%, 50% and Prefill + 20%, chamber volume exchange rate per minute. Latencies, durations and occurrence of behavior and physiologic changes were observed using direct observationand video. Neonate piglets were euthanized as quickly as or faster than weaned piglets for all gases and flow rates. For the neonate relative to the weaned piglet, average loss of posture over all gas treatments was 99 vs. 142 (seconds) and last movement was 360 vs. 392 (seconds). Neonates also displayed fewer incidences and shorter durations of behavioral indicators of distress and sensation relative to the weaned piglets. Thus concerns for gas euthanasia, when applied appropriately, are not greater for the neonate relative to the weaned piglet. Additionally, procedures developed to euthanize weaned piglets will likely be successful when applied for the neonate, but not viceversa