Unconditional and Conditional Large Gaps between the zeros of the Riemann Zeta-Function

In this paper, first by employing inequalities derived from the Opial inequality due to David Boyd with best constant, we will establish new unconditional lower bounds for the gaps between the zeros of the Riemann zeta function. Second, on the hypothesis that the moments of the Hardy Z-function and its derivatives are correctly predicted, we establish some explicit formulae for the lower bounds of the gaps between the zeros and use them to establish some new conditional bounds. In particular it is proved that the consecutive nontrivial zeros often differ by at least 6.1392 (conditionally) times the average spacing. This value improves the value 4.71474396 that has been derived in the literature

Art museums and the incorporation of virtual reality: Examining the impact of VR on spatial and social norms

Art museums implicate established spatial and social norms. The norms that shape these behaviours are not fixed, but rather subject to change as the sociality and physicality of these spaces continues to develop. In recent years, the re-emergence of virtual reality (VR) has led to this technology being incorporated into art museums in the form of VR-based exhibits. While a growing body of research now explores the various applications, uses and effects of VR, there is a notable dearth of studies examining the impact VR might be having on the spatial and social experience of art museums. This article, therefore, reports on an original research project designed to address these concerns. The project was conducted at Anise Gallery in London, United Kingdom, between June and July 2018 and focused on the multisensory, and VR-based, exhibition, Scents of Shad Thames. The research involved 19 semi-structured interviews with participants who had just experienced this exhibition. Drawing on scholarly literature that surrounds the spatial and social norms pertaining to art museums, this study advances along three lines. First, the research explores whether the inclusion of VR might alter the practice of people watching, which is endemic of this setting. Second, the research explores whether established ways of navigating the physical setting of art museums might influence how users approach the digital space of VR. Third, the research examines whether the incorporation of VR might produce a qualitatively different experience of the art museum as a shared social space

An investigation of academic achievement of fifth-grade students missing traditional academic classes due to instrumental music participation.

The purpose of this study was to investigate and compare the academic achievement of fifth-grade students missing traditional academic classes due to instrumental music participation to students in the same class not involved in instrumental music instruction in school. Individual subjects were selected from elementary schools representing Class B school districts in Nebraska. Subjects (N = 166) were selected from a pool of all students who were fifth-graders in the 1995-1996 school year from each participating school. An equal number of subjects were students who: 1) missed traditional academic classes for instrumental music participation; and 2) non-instrumental music students from those same classrooms. Comprehensive Tests of Basic Skills or California Achievement Test reading, language, mathematics, and total battery scale scores were collected for each student from the end of the 1994-1995 and 1995-1996 school years. The two sets of scores were then analyzed for significant differences in reading, language, mathematics, and total battery achievement. The results indicated no significant differences between the subject groups in all areas except fourth-grade reading in which there was a significant difference between the instrumentalists and non­ instrumentalists. Therefore, it was concluded that elementary instrumental music students who miss part of traditional academic classroom instruction can perform equally well on standardized achievement tests as students not involved in public school instrumental music instruction

Metabolic and serotonergic modulation of hypothalamic arcuate nucleus neurones in vitro

1. The effects of glucose on the electrophysiological properties of rat hypothalamic arcuate nucleus (ARC) neurones were investigated. Neurones were recorded in 10 mM (hyperglycaemic) and 2 mM (euglycaemic) glucose-containing aCSF. The major findings were that input resistance increased in 10 mM glucose, there was an increase in the activity of neurones in 2 mM glucose and there were a greater percentage of neurones expressing lh in 10 mM glucose. Subthreshold active conductances were differentially expressed in ARC neurones including: anomalous inward rectification Q. ), time- and voltage-dependent inward rectification 00, A-like transient outward rectification (IA) and T-type calcium-like conductance. Characterisation of the differential expression of these conductances may represent one way of functionally classifying ARC neurones. 2. Whole-cell patch clamp recording techniques were used in isolated hypothalamic brain slice preparations to investigate the effects of 5-HT on ARC neurones. Bath application of 5-HT induced a membrane depolarisation in a sub-population of ARC neurones (30%), a response that persisted in the presence of TTX indicating a direct effect. 5-HT excited ARC neurones through three potential mechanisms: closure of one or more resting potassium conductances; activation of a non-selective cation channel, or a combination of the two; or activation of a pump in the membrane. This response was mediated through the 5-HT2A. 5-HT2B and/or 5-HT2C receptors revealed using a range of 5-HT receptor agonists and antagonists. 5-HT was shown to excite CART-expressing neurones suggesting an anorexigenic role for 5-HT, via 5-HT2 receptors at the level of the ARC. 3.5-HT induced a membrane hyperpolarisation in a sub-population of ARC neurones (37%). The 5-HT-induced hyperpolarisation persisted in the presence of TTX indicating a direct effect on ARC neurones. 5-HT inhibited ARC neurones most likely through the activation of one or more potassium conductances,including an inwardly rectifying potassium conductance. Potential roles for 5-HTIA, 5-HTIB and 5-HT7 receptors were suggested from studies utilising 5-HT receptor agonists and antagonists. 5-HT inhibited orexigenic NPY/AgRP neurones, identified by their response to ghrelin and by their electrophysiological properties, suggesting an anorexigenic role for 5-HT, acting via 5-HTI and 5-HT7 receptors on NPY/AgRP neurones at the level of the ARC. 4. The effects of feeding-related signals on hypothalamic neuropeptide expression were investigated using real-time-PCR. A new protocol measuring gene expression from hypothalamic explants was developed. Effects of GABA and AMPA on c-fos expression were investigated and subsequent studies showed leptin and glucose modulated the expression of NPY, POMC and AgRP, in fed and fasted animals. Further work is required to validate this novel approach to studying the central control of energy balance

On the road to sustainable growth - boosting electric vehicles in the UK

On the road to sustainable growth - boosting electric vehicles in the U

Some Opial Dynamic Inequalities Involving Higher Order Derivatives on Time Scales

We will prove some new Opial dynamic inequalities involving higher order derivatives on time scales. The results will be proved by making use of Hölder's inequality, a simple consequence of Keller's chain rule and Taylor monomials on time scales. Some continuous and discrete inequalities will be derived from our results as special cases