On the algebraic structure of rational discrete dynamical systems

We show how singularities shape the evolution of rational discrete dynamical systems. The stabilisation of the form of the iterates suggests a description providing among other things generalised Hirota form, exact evaluation of the algebraic entropy as well as remarkable polynomial factorisation properties. We illustrate the phenomenon explicitly with examples covering a wide range of models

Algebraic entropy for differential-delay equations

We extend the definition of algebraic entropy to a class of differential-delay equations. The vanishing of the entropy, as a structural property of an equation, signals its integrability. We suggest a simple way to produce differential-delay equations with vanishing entropy from known integrable differential-difference equations

Lagrange mesh, relativistic flux tube, and rotating string

The Lagrange mesh method is a very accurate and simple procedure to compute eigenvalues and eigenfunctions of nonrelativistic and semirelativistic Hamiltonians. We show here that it can be used successfully to solve the equations of both the relativistic flux tube model and the rotating string model, in the symmetric case. Verifications of the convergence of the method are given.Comment: 2 figure

Tau-aggregation inhibitor therapy for Alzheimer's disease

Article Accepted Date: 9 December 2013 Copyright © 2014 The Authors. Published by Elsevier Inc. All rights reserved.Peer reviewedPublisher PD

The Contribution of Douglass North to New Institutional Economics

Douglass North, along with Ronald Coase and Oliver Williamson, transformed the early intuitions of new institutional economics into powerful conceptual and analytical tools that spawned a robust base of empirical research. NIE arose in response to questions not well explained by standard neoclassical models, such as make or buy and why rich or poor? Today NIE is a success story by many measures: four Nobel laureates in under 20 years, increasing penetration of mainstream journals, and significant impact on major policy debates from anti-trust law to development aid. This paper provides a succinct overview of North's evolving ideas about institutions and explains how North's work shaped the emerging field of new institutional economics and had a potent impact on economics and the social sciences more broadly. North provides a powerful example of how persistent and well placed confidence and hard work can productively transform the status quo. North's influence continues strong and his enthusiasm for exploring new frontiers and cooperating across artificial academic boundaries has never waned.New Institutional Economics, institutions, transaction costs, development and growth

Sintering and densification of nanocrystalline ceramic oxide powders: a review

Observation of the unconventional properties and material behaviour expected in the nanometre grain size range necessitates the fabrication of fully dense bulk nanostructured ceramics. This is achieved by the application of ceramic nanoparticles and suitable densification conditions, both for the green and sintered compacts. Various sintering and densification strategies were adopted, including pressureless sintering, hot pressing, hot isostatic pressing, microwave sintering, sinter forging, and spark plasma sintering. The theoretical aspects and characteristics of these processing techniques, in conjunction with densification mechanisms in the nanocrystalline oxides, were discussed. Spherical nanoparticles with narrow size distribution are crucial to obtain homogeneous density and low pore-to-particle-size ratio in the green compacts, and to preserve the nanograin size at full densification. High applied pressure is beneficial via the densification mechanisms of nanoparticle rearrangement and sliding, plastic deformation, and pore shrinkage. Low temperature mass transport by surface diffusion during the spark plasma sintering of nanoparticles can lead to rapid densification kinetics with negligible grain growth

Permutations preserving divisibility

We give a proof of a theorem on the common divisibility of polynomials and permuted polynomials (over GF(2)) by a polynomial g(x)

Duality relations in the auxiliary field method

The eigenenergies $\epsilon^{(N)}(m;\{n_i,l_i\})$ of a system of $N$ identical particles with a mass $m$ are functions of the various radial quantum numbers $n_i$ and orbital quantum numbers $l_i$. Approximations $E^{(N)}(m;Q)$ of these eigenenergies, depending on a principal quantum number $Q(\{n_i,l_i\})$, can be obtained in the framework of the auxiliary field method. We demonstrate the existence of numerous exact duality relations linking quantities $E^{(N)}(m;Q)$ and $E^{(p)}(m';Q')$ for various forms of the potentials (independent of $m$ and $N$) and for both nonrelativistic and semirelativistic kinematics. As the approximations computed with the auxiliary field method can be very close to the exact results, we show with several examples that these duality relations still hold, with sometimes a good accuracy, for the exact eigenenergies $\epsilon^{(N)}(m;\{n_i,l_i\})$

Local metrics admitting a principal Killing-Yano tensor with torsion

In this paper we initiate a classification of local metrics admitting the principal Killing--Yano tensor with a skew-symmetric torsion. It is demonstrated that in such spacetimes rank-2 Killing tensors occur naturally and mutually commute. We reduce the classification problem to that of solving a set of partial differential equations, and we present some solutions to these PDEs. In even dimensions, three types of local metrics are obtained: one of them naturally generalizes the torsionless case while the others occur only when the torsion is present. In odd dimensions, we obtain more varieties of local metrics. The explicit metrics constructed in this paper are not the most general possible admitting the required symmetry, nevertheless, it is demonstrated that they cover a wide variety of solutions of various supergravities, such as the Kerr-Sen black holes of (un-)gauged abelian heterotic supergravity, the Chong-Cvetic-L\"u-Pope black hole solution of five-dimensional minimal supergravity, or the K\"ahler with torsion manifolds. The relation between generalized Killing--Yano tensors and various torsion Killing spinors is also discussed.Comment: 36pages, no figure