A semi-invertible Oseledets Theorem with applications to transfer operator cocycles

Oseledets' celebrated Multiplicative Ergodic Theorem (MET) is concerned with the exponential growth rates of vectors under the action of a linear cocycle on R^d. When the linear actions are invertible, the MET guarantees an almost-everywhere pointwise splitting of R^d into subspaces of distinct exponential growth rates (called Lyapunov exponents). When the linear actions are non-invertible, Oseledets' MET only yields the existence of a filtration of subspaces, the elements of which contain all vectors that grow no faster than exponential rates given by the Lyapunov exponents. The authors recently demonstrated that a splitting over R^d is guaranteed even without the invertibility assumption on the linear actions. Motivated by applications of the MET to cocycles of (non-invertible) transfer operators arising from random dynamical systems, we demonstrate the existence of an Oseledets splitting for cocycles of quasi-compact non-invertible linear operators on Banach spaces.Comment: 26 page

Coherent sets for nonautonomous dynamical systems

We describe a mathematical formalism and numerical algorithms for identifying and tracking slowly mixing objects in nonautonomous dynamical systems. In the autonomous setting, such objects are variously known as almost-invariant sets, metastable sets, persistent patterns, or strange eigenmodes, and have proved to be important in a variety of applications. In this current work, we explain how to extend existing autonomous approaches to the nonautonomous setting. We call the new time-dependent slowly mixing objects coherent sets as they represent regions of phase space that disperse very slowly and remain coherent. The new methods are illustrated via detailed examples in both discrete and continuous time

L’aide par les pairs et les groupes d’entraide comme solutions de rechange et comme compléments à l’aide professionnelle

Compte tenu que le nombre de personnes ayant une formation professionnelle ne sera jamais suffisant pour affronter la crise du VIH, on doit trouver des solutions de rechange. Deux types de ressources sont ici proposées : l'aide par les pairs et les groupes d'entraide. La mise en place de ces formes d'aide exige une formation appropriée. Elles peuvent être des compléments essentiels aux stratégies de prévention, de contrôle et d'aide, et en ce sens, elles devront être intégrées à l'ensemble du système de soins

Utilization of moisture by Kent and Clark 63 soybeans

Call number: LD2668 .T4 1967 C65Master of Scienc

Reimagining Middle Leadership in Further Education

During the Re-imagine 2018 conference held at Birmingham City University, one of the several discussion streams was tasked with identifying issues faced by current middle leaders in further education. The purpose of the ongoing discussions was to then re-imagine a future where middle leaders could meet these challenges, develop plans the further education sector they imagined and provide a space to make suggestions for action. This paper distils these extensive conversations and casts a spotlight over several areas of significance. The paper offers an idealised approach towards a utopian goal for middle leaders in Further education while drawing attention to real and current problems. Beyond its utopian goals, the paper further draws attention to pertinent current issues that given appropriate support and autonomy, middle leaders may wish to explore and seek to engage in ongoing discussions for the benefit of learners in the sector

A computerized model for retail fertilizer dealers' inventory management

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