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

From hybrid space to dislocated space: Mobile virtual reality and a third stage of mobile media theory

Research in the field of mobile communication studies (MCS) has generally moved away from focusing on how mobile phones distract users from their physical environment to considering how the experience of space and place can be enhanced by locative smartphone applications. This article argues that trajectory may be complicated by the emergence of a new type of mobile technology: mobile virtual reality (MVR). While an increasing number of handsets are specifically developed with MVR in mind, there is little to no research that situates this phenomenon within the continuum of MCS. The intention of this paper is accordingly twofold. First, the article conceptualizes MVR as a connective tissue between the two sequential tropes of MCS: physical distraction and spatial enhancement. Second, the article introduces the concept of ‘dislocated space’ as a way of understanding the embodied space MVR might configure

The Playeur and Pokémon Go: Examining the effects of locative play on spatiality and sociability

Pokémon Go is a hugely popular hybrid reality game (HRG) that enables players to occupy a space that is simultaneously physical and digital. The general aim of Pokémon Go is to discover and then capture Pokémon. This article reports on an original research project designed to explore the impact of Pokémon Go on spatiality and sociability. The project was conducted between May 2017 and July 2017, using an online survey which received 375 responses from users of Pokémon Go geographically spread across the globe. Drawing on the concept of the ‘playeur’ as an established approach to understanding the effects of locative play on spatiality and sociability, this research follows three lines of enquiry. First, the research examines whether the intermingling of play and ordinary life might encourage players to spend more time outside in public spaces, and how this mode of play is experienced. Second, the research explores whether the game mechanics of Pokémon Go might lead players to traverse their environment using modified routes, as well as frequent new places. Third, the research examines whether the praxis of Pokémon Go might enable new forms of sociability to emerge that extend beyond earlier HRGs

Weak solutions for the dynamic equations xΔ(m)(t)=f(t;x(t))x^{\Delta(m)}(t) = f (t; x(t)) on time scales

In this paper we prove the existence of weak solutions of the dynamic Cauchy problem \begin{equation*} \begin{split} x^{(\Delta m)}(t)&=f(t,x(t)),\quad t\in T, \\ x(0)&=0, \\ x^\Delta (0)&=\eta _1 ,\dots,x^{(\Delta (m-1))}(0)=\eta _{m-1},\quad \eta _1 ,\dots,\eta _{m-1} \in E, \end{split} \end{equation*} where $x^{(\Delta m)}$ denotes a weak $m$-th order $\Delta$-derivative, $T$ denotes an unbounded time scale (nonempty closed subset of R such that there exists a sequence $(a_n )$ in $T$ and $a_n \to \infty )$, $E$ is a Banach space and $f$ is weakly -- weakly sequentially continuous and satisfies some conditions expressed in terms of measures of weak noncompactness. The Sadovskii fixed point theorem and Ambrosetti's lemma are used to prove the main result. As dynamic equations are a unification of differential and difference equations our result is also valid for differential and difference equations. The results presented in this paper are new not only for Banach valued functions but also for real valued functions

On the oscillatory behavior for a certain class of third order nonlinear delay difference equations

By employing the generalized Riccati transformation technique, we will establish some new oscillation criteria for a certain class of third order nonlinear delay difference equations. Our results extend and improve some previously obtained ones. An example is worked out to demonstrate the validity of the proposed results

New gaps between zeros of fourth-order differential equations via Opial inequalities

In this paper, for a fourth-order differential equation, we will establish some lower bounds for the distance between zeros of a nontrivial solution and also lower bounds for the distance between zeros of a solution and/or its derivatives. We also give some new results related to some boundary value problems in the theory of bending of beams. The main results will be proved by making use of some generalizations of Opial and Wirtinger-type inequalities. Some examples are considered to illustrate the main results

Conductive-tether design for de-orbiting from given altitude and inclination

A bare tether with thin-tape cross section is both i) the most effective electrodinamic tether for given length and mass, and ii) capable of effective design for an arbitrary mission through its three disparate dimensions. It handily beats the fully insulated tether that exchanges current at both ends, a result resting in advantages of 2D current collection as against 3D collection; it has much greater perimeter than the round bare tether and much lower fatal debris-impact rate, leading to greatly faster de-orbiting and greatly higher probability of survival; and it only allows multi-line tethers reaching a few hundred lines to stand competitive. In selecting the disparate values of length L, width w, and thickness h for a de-orbit mission, performance involves three criteria: a) tether-tospacecraft mass ratio must be small; b) probability of survival against the debris environment must be high; and c) de-orbiting must be fast to reduce manoeuvres for avoiding catastrophic collisions with big active/passive satellites around. Beyond determining tether mass through the product Lwh, main dimension parameters affecting performance are L/h2li characterizing ohmic effects, and w determining electron collection. An algorithm for optimal selection of tape dimensions is elaborated