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Nothing found here is original except for a few mistakes and misprints here and there. These notes are simply a record of what I cover in class, to spare the students the necessity of taking the lectu...
KPP invasions in periodic media:lecture notes for the Toulouse KPP school
KPP invasions periodic media Toulouse KPP
2015/7/14
KPP invasions in periodic media:lecture notes for the Toulouse KPP school.
Waves in weakly random media:lecture notes for the Vienna Inverse Problems school
weakly random media Vienna Inverse Problems
2015/7/14
Wave propagation in complex media is an ubiquitous phenomenon–applications include light propagation through the atmosphere, underwater acoustic, tomography, and innumerable other ones. These problems...
A new look at the John-Nirenberg and John-Stromberg theorems for BMO. Lecture Notes
John-Nirenberg John-Stromberg theorems BMO
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...
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...
Notes on the Parity Conjecture
Notes Parity Conjecture
2010/12/14
The main purpose of these notes is to prove, in a reasonably self-contained way, that finiteness of the Tate-Shafarevich group implies the parity conjecture for elliptic curves over number fields. Alo...
Further Notes on a Family of Continuous, Non-differentiable Functions
continuous nowhere di erentiable fractal Hausdor dimension
2011/2/23
We examine a parametrized family of functions Fa, all of which are continuous and some of which are nowhere or almost nowhere di erentiable.
In this paper, some integral inequalities are presented by analytic approach. An open question will be proposed later on.
Notes on an Open Problem of F. Qi and Y. Chen and J. Kimball
J. Kimball Y. Chen F. Qi Open Problem Notes
2008/6/30
In this paper, an integral inequality is studied. An answer to an open problem proposed by Feng Qi and Yin Chen and John Kimball is given.
Notes on Qi Type Integral Inequalities
Qi type integral inequality Reversed Hö lder inequality Reversed convolution inequality
2008/6/30
By utilizing a reversed Hölder inequality and a reversed convolution inequality, some new integral inequalities which originate from an open problem posed in [F. Qi, Several integral inequalities...
Some Notes on Reaction Diffusion Systems with Nonlinear Boundary Conditions
reaction-diffusion fast diffusion global existence blow-up
2007/12/10
This paper deals with the existence and nonexistence of global positive solution to a semilinear reaction-diffusion system with nonlinear boundary conditions. For the heat diffusion case, the necessar...