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Notes on the Sigma-invariants - Part 1
Notes Sigma-invariants Group Theory
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2012/4/17
Memoir on the Sigma-invariants and their applications, Part 1.
Notes on a slice distance for singular Lp-bundles
Notes slice distance singular Lp-bundles Differential Geometry
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2012/4/17
A slice distance for the class of weak abelian Lp-bundles in 3 dimensions was introduced in a previous article in collaboration with Tristan Rivi\`ere, where it was used to prove the closure of such c...
Notes on area operator, geometric 2-rough paths and Young integral when p^-1+q^-1=1
Notes area operator geometric 2-rough paths Young integral
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2012/4/17
1.When equipped with 2-rough norm and restricted to continuous paths with bounded variation, the area operator is a closable unbounded operator. 2.The area defined through Riemann-Stieltjes integral i...
Notes on the Gabriel-Roiter measure
Notes the Gabriel-Roiter measure Combinatorics
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2011/9/5
Abstract: These notes give an introduction to the Gabriel-Roiter measure of a finite dimensional algebra. They are based on a series of four lectures at the "Advanced School and Conference on Represen...
IMPANGA lecture notes on log canonical thresholds
IMPANGA lecture notes log canonical thresholds Algebraic Geometry
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2011/9/6
Abstract: These are lecture notes from the IMPANGA 2010 Summer school. They give an introduction to log canonical thresholds, covering some basic properties, examples, and some recent results and open...
Notes on dark energy interacting with dark matter and unparticle in loop quantum cosmology
Notes dark energy dark matter unparticle loop quantum cosmology
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2011/8/3
Abstract: We investigate the behavior of dark energy interacting with dark matter and unparticle in the framework of loop quantum cosmology. In four toy models, we study the interaction between the co...
Notes on Ding-Iohara algebra and AGT conjecture
Ding-Iohara algebra AGT conjecture High Energy Physics Theory
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2011/7/26
Notes on Ding-Iohara algebra and AGT conjecture.
Notes on amenability
Notes amenability
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2011/1/19
We show that for a Banach algebra A with a bounded approximate identity, the amenability of Ab⊗A, the amenability of Ab⊗Aop and the amenability of A are equivalent. Also if A is a closed i...
Lecture notes on stabilization of contact open books
Open books stabilization contact structures surgery
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2011/2/24
This note explains how to relate some contact geometric opera-tions, such as surgery, to operations on an underlying contact open book. In particular, we shall give a simple proof of the fact that sta...
Notes on The Feynman Checkerboard Problem
Notes Feynman Checkerboard Problem
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2011/1/19
The Feynman checkerboard problem is an interesting path integral approach to the Dirac equation in ‘1+1’ dimensions. I compare two approaches reported in the literature and show how they may be reconc...
Notes on Ghost Dark Energy
Notes Ghost Dark Energy
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2010/12/27
We study a phenomenological dark energy model which is rooted in the Veneziano ghost of QCD. In this dark energy model, the energy density of dark energy is proportional to Hubble parameter and the pr...
Notes on the Poisson formula
the Poisson formula math
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2010/11/19
These notes are a part of my lectures on representations of adelic groups attached to two-dimensional schemes. They contain a study of the one-dimensional case as a preliminary step to the case of di...
Notes on factor-criticality, extendibility and independence number
Notes on factor-criticality independence number
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2010/11/19
In this paper, we give a sufficient and necessary condition for a $k$-extendable graph to be $2k$-factor-critical when $k=\nu/4$, and prove some results on independence numbers in $n$-factor-critical ...
A new look at the John-Nirenberg and John-Stromberg theorems for BMO. Lecture Notes
John-Nirenberg John-Stromberg theorems BMO
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2010/11/9
We develop some techniques for studying various versions of the function space BMO. Special cases of one of our results give alternative proofs of the celebrated John- Nirenberg inequality and of rel...
Notes about extended real- and set-valued functions
extended real- set-valued functions
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2010/11/19
An order theoretic and algebraic framework for the extended real numbers is established which includes extensions of the usual difference to expressions involving $-\infty$ and/or $+\infty$, so-calle...