The cosmological constant problem is principally concerned with trying to understand how the zeropoint energy of quantum fields contributes to gravity. Here we take the approach that by addressing a fundamental unresolved issue in quantum theory we can gain a better understanding of the problem. Our starting point is the observation that the notion of classical time is external to quantum mecha...

Despite enormous strides recently, it remains difficult for researchers to find relevant resources that are not 'flat' html files and may be hidden within web services. This paper will draw upon recent experiences at the UK's largest academic data centre providing web services to the education community. Since May 2001 a project has been underway attempting to make the resources more visible by...

We explore the following problem: given a collection of creases on a piece of paper, each assigned a folding direction of mountain or valley, is there a flat folding by a sequence of simple folds? There are several models of simple folds; the simplest one-layer simple fold rotates a portion of paper about a crease in the paper by ±180◦. We first consider the analogous questions in one dimension...

The ability to form tiny droplets of liquids and control their movements is important in printing or patterning, chemical reactions and biological assays. So far, such nanofluidic capabilities have principally used components such as channels, nozzles or tubes, where a solid encloses the transported liquid. Here, we show that liquids can flow along the outer surface of solid nanowires at a scal...

Variational methods have proved popular and effective for inference and learning in intractable graphical models. An attractive feature of the approaches based on the KullbackLeibler divergence is a rigorous lower bound on the normalization constants in undirected models. In the suggested work we explore the idea of using auxiliary variables to improve on the lower bound of standard mean field ...

Compact localized modes of ring type exist in many two-dimensional lattices with a flat linear band, such as the Lieb lattice. The uniform Lieb lattice is gapless, but gaps surrounding the flat band can be induced by various types of bond alternations (dimerizations) without destroying the compact linear eigenmodes. Here, we investigate the conditions under which such diffractionless modes can ...

we study topological von neumann regularity and principal von neumann regularity of banach algebras. our main objective is comparing these two types of banach algebras and some other known banach algebras with one another. in particular, we show that the class of topologically von neumann regular banach algebras contains all $c^*$-algebras, group algebras of compact abelian groups and cer...

Let $ (A,| cdot |) $ be a real Banach algebra, a complex algebra $ A_mathbb{C} $ be a complexification of $ A $ and $ | | cdot | | $ be an algebra norm on  $ A_mathbb{C}  $  satisfying a simple condition together with the norm $ | cdot | $ on $ A$.  In this paper we first show that $ A^* $ is a real Banach $ A^{**}$-module if and only if $ (A_mathbb{C})^* $ is a complex Banach $ (A_mathbb{C})^{...

We study a special class of Finsler metrics which we refer to as Almost Rational (shortly, AR-Finsler metrics). give necessary and sufficient conditions for an manifold (M, F) be Riemannian. The rationality some geometric objects such Cartan torsion, geodesic spray, Landsberg curvature S-curvature is investigated. For particular subfamily have proved that if F has isotropic S-curvature, then th...