Seminars 2010-2011

 Date  Lecturer  Topic
01/03/2011 Eraim Shmerling Simple Approximation to Geometric Distribution of Order k
26/01/2011 Eidelman Yuli (Tel-Aviv University) Global Dynamics of Nicholson-Type Delay Systems with Applications


Models of marine protected areas and B-cell chronic lymphocytic leukemia
dynamics that belong to the Nicholson-type delay differential
systems are proposed. To study the global stability of the Nicholson-type models, we construct an
exponentially stable linear system such that its solution is a
solution of the nonlinear model. Explicit conditions of the existence of positive global
solutions,  lower and upper estimations of solutions, and the
existence and uniqueness of a positive equilibrium were obtained.
New results, obtained for the global stability and instability of
equilibria solutions, extend known results for the scalar Nicholson  models.
The conditions for the stability test a! re quite practical, and the methods developed are
applicable to the modeling of a broad spectrum of
biological processes.
To illustrate our finding, we study the dynamics of the fish populations in Marine
Protected Areas.

12/01/2011 Eidelman Yuli (Tel-Aviv University) Regularity of extremal positive solutions for some quasilinear
elliptic equationsThe abstract: We consider the problem of regularity of the extremal
positive solution of the Dirichlet problem for equations involving
p-Laplacian  with a strong non-linearity and a positive parameter.
We derive regularity results for various classes of non-linearities
29/12/2010 Emilia Fridman (Tel Aviv University, School of Electrical Engineering) Stability of Systems with Time-Varying Delays: A Direct Lyapunov Approach

Exponential stability analysis via Lyapunov-Krasovskii method  is
extended to linear  time-delay systems in a Hilbert space. The
operator acting on the delayed state is supposed to be bounded.  The
system delay is admitted to be unknown and time-varying. Sufficient
delay-dependent conditions for exponential stability are derived in
the form of Linear Operator Inequalities, where the decision variables
are operators in the Hilbert space. Being applied  to a scalar heat
equation and to a scalar wave equation,  these conditions are reduced
to standard finite-dimensional
Linear Matrix Inequalities. The results are new even for systems
without delay. The proposed method is expected to provide effective
tools for stability and control of distributed parameter systems (PDEs).

15/12/2010 Dan Gamliel, Dept. of Medical Physics

Ariel University, Israel

Generalized Exchange in Magnetic Resonance

Chemical exchange of spins affects the lineshape in nuclear magnetic resonance (NMR) in a characteristic manner. The process is described by ordinary differential equations, and their solution leads to a calculation of the spectrum. In this work the exchange process is generalized by assuming non-negligible time for the exchange jump. Two approximate models of the system are proposed. In one model the slow jump is assumed to occur by fast changes to and from a transition state, which is treated in the standard equations on an equal footing with the ordinary states for the exchange process. In the other model the jump is assumed to take place directly between the ordinary states, but with a time delay. In that model the equations become differential equations with a delay, which are solved using the complex Lambert function. Some of the solution modes are calculated for several branches of the function. The results of the two models are compared.

10/11/2010 1. L.D.Menikhes (Southern Ural State University, Chelyabinsk, Russia)

2. Vladimir I. Shiryaev (Southern Ural State University, Chelyabinsk, Russia)

1. On regularizability of the inverse mapping of integral operators

2. On control of dynamic systems with the incompleteness of information.

The probability theory of the special functions.

13/10/2010 1. Peter Popivanov

2. Angela Slavova

1. Non-travelling wave type solutions with peak singularities to the generalized Camassa -Holm equation

2. Stabilizing Control of a Hysteresis Model of Pattern Formation