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   Brief introduction to tropical geometry
Posted on 2015-02-28 (Send to a Friend Send to a Friend )
The paper consists of lecture notes for a mini-course given by the authors at the G\"okova Geometry \& Topology conference in May 2014. We start the exposition with tropical curves in the plane and their applications to problems in classical enumerative geometry, and continue with a look at more general tropical varieties and their homology theories. . . . .
 
 
   Dark Energy: Observational Evidence and Theoretical Models
Posted on 2015-02-23 (Send to a Friend Send to a Friend )
The book elucidates the current state of the dark energy problem and presents the results of the authors, who work in this area. It describes the observational evidence for the existence of dark energy, the methods and results of constraining of its parameters, modeling of dark energy by scalar fields, the space-times with extra spatial dimensions, especially Kaluza---Klein models, the braneworld models with a single extra dimension as well as the problems of positive definition of gravitational energy in General Relativity, energy conditions a . . . .
 
 
   Superradiance
Posted on 2015-02-22 (Send to a Friend Send to a Friend )
Superradiance is a radiation enhancement process that involves dissipative systems. With a 60 year-old history, superradiance has played a prominent role in optics, quantum mechanics and especially in relativity and astrophysics. In General Relativity, black-hole superradiance is permitted by dissipation at the event horizon, that allows for energy and angular momentum extraction from the vacuum, even at the classical level. Black-hole superradiance is intimately connected to the black-hole area theorem, Penrose process, tidal forces and even H . . . .
 
 
   Making use of self-energy functionals: The variational cluster approximation
Posted on 2015-02-21 (Send to a Friend Send to a Friend )
A pedagogical introduction to the cluster-perturbation theory, the variational cluster approximation and to self-energy-functional theory is given. Some standard applications and the relation to dynamical mean-field theory are discussed. . . . .
 
 
  Advanced Topics of Theoretical Physics I: The electronic structure of matter
Posted on 2015-02-17 (Send to a Friend Send to a Friend )
Advanced Topics of Theoretical Physics I: The electronic structure of matter This book is work in progress. This book is not completed and not proofread. You can use this book currently as a basis for following through the material presented in the course. However, you should never blindly copy formulas an apply them. The chances that there are still errors is too large. This book provides an introduction into the quantum mechanics of the interacting electron gas. It aims at students at the graduate level, that already have a good understanding on one-particle quantum mechanics. My aim is to include all proofs in a . . . .
 
 
  Lecture Notes in Machine Learning
Posted on 2015-02-17 (Send to a Friend Send to a Friend )
Contents: Introduction; Concept learning; Languages for learning; Version space learning; Induction of Decision trees; Covering strategies; Searching the generalization/specialization graph; Inductive Logic Progrogramming; Unsupervised Learning; Explanation-based Learning. . . . .
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