Seminars, 2006
Lectures:
• 13.12.2006
Dr. D. Katz, Ben Gurion University, Israel
Radiation effect on thermal explosion in a gas containing evaporating fuel
droplets

Abstract
The dynamics of thermal explosion in a fuel droplets/ hot air mixture is investigated using the geometrical version of the Method of Integral Manifolds. The results are applied to the modelling of the ignition process in diesel engines. Effects of the thermal radiation, semi-transparency of droplets and oxidizer are taken into account. In contrast to the previous studies, the difference between gas temperature (responsible for convective heating of droplets) and external
temperature (responsible for radiative heating of droplets) is taken into account. The dynamics of the explosion is presented in terms of the dynamics of a multi-scale, singularly perturbed system. The relevant parametric regions of this system are analyzed. Explicit analytical formulae for the ignition delay in the presence of thermal radiation are derived. It is shown that the effect of thermal radiation can lead to considerable reduction (up to about 30%) of the total ignition delay time.

• 27.11.2006
Prof. L. Aizenberg, Bar-Ilan University, Israel
Generalization of results about the Bohr radius for power series and the Bohr abscissa for ordinary Dirichlet series

Abstract
Let $G\subset\mathbb C$ be any domain. A point $p\in\partial G$ is called a point of convexity if $p\in\partial\tilde G.$ Here $\tilde G$ is the convex hull of $G.$ A point of convexity $p$ is called regular if there exists a disk $U\subset G$ so that $p\in\partial U.$ The following result is proved.
{\bfTheorem.}Ifthefunction$$f(z)=\sum\limits_{k=0}^{\infty}c_k z^k$$ is such that $f(U_1)\subset G,$ with $\tilde G\neq\mathbb C$ and $U_1$ the unit disk, then for $|z|<1/3$ the inequality $$\sum\limits_{k=0}^{\infty }\vert c_k z^k\vert <\mbox{\rm dist}(c_0,\partial\tilde G)$$ is valid. The constant ${1/3}$ cannot be improved if $\partial G$
contains at least one regular point of convexity.
A multidimensional analog of this theorem is given as well as first results concerning the Bohr phenomenon for ordinary Dirichlet series.

• 13.11.2006
Professor Victor Khatskevich, ORT Braude College, Israel

• 3.07.2006
Prof. A. Ukhlov, Ben-Gurion University of the Negev, Israel
Weighted Quasiconformal Mappings and Sobolev Spaces

Abstract
We study a relation between weighted Sobolev spaces and mappings connected to them by means of composition operator. For weights satisfying Muckenhoupt condition, we give complete description of the mappings inducing a bounded composition operator of weighted Sobolev spaces. This approach gives a new scale of mappings.

• 3.07.2006
Prof. V. Rabinovich, Instituto Polit&eacute;cnico Nacional, Mexico
Pseudodifferential Operators and Signal Processing

Abstract
We consider the problem of invertibility of pseudodifferential operators in the L.Hצrmander class OPS_{0,0}. Effective conditions of invertibility for pseudodifferential operators with globally slowly varying symbols and for casual pseudodifferential operators have been obtained. We study also the stability of the finite sections method with respect to the time and the frequency. The problems under consideration are inspired by the problems of reconstruction of input signals from output signals in the time-varying filters.

• 30.05.2006
Prof. Y. Verbin, Open University, Israel

Abstract
The properties of several types of Q-stars are studied: solitonic ones whose flat space limit are Q-balls, non-solitonic ones which do not have a flat space limit and a new type, Sigma stars. These are self-gravitating solutions of a non-linear Sigma model with a global U(1) symmetry. The analysis is based on calculating the mass, global U(1) charge and the binding energy (their difference) for families of solutions parameterized by the central value of the scalar field. The two most frequently used Q-star potentials are studied and although the general properties are similar in both models, there are important differences. The non-solitonic Q-stars are also analyzed with a special attention to the region of a weak scalar field where an overlap with the solitonic type is expected. Sigma stars are discussed along similar lines stressing the relation with the other two types of Q-stars. In a sense they reside somewhere in between.

• 16.01. 2006
Prof. O. Kounchev, Institute of Mathematics and Informatics Bulgarian Academy of Sciences, Bulgaria
On new PDE methods in Wavelet analysis

Abstract
The theory of polysplines, see "Multivariate polysplines. Applications to Numerical
and Wavelet Analysis", Academic Press, 2001, has provided a new multivariate analog to the spline analysis. Based on it a new Wavelet analysis has appeared which is a generalization of the spline wavelet construction of Chui in one dimension. We outline new results and applications to, say, astronomical data. These provide an alternative to some other recent methods for sparse representations in Image processing as the curvelets/ridgelets approach of Donoho-Candes, and the bandlets of Mallat.