3. Prerequisites for the workshop. They are mentioned or reviewed in sect. 1 of [17]: class field theory, especially local class field theory; elliptic curves over finite, local and global fields, some basic things about the set of Diophantine geometry conjectures the theory of Mochizuki deals with, basics of (classical) anabelian geometry. For the latter Ch.4 of [21] is a very easy to read sou...

In this investigation, a mathematical model for studying oscillatory flow of blood in a stenosed artery under the influence of transverse magnetic field through porous medium has been developed. The equations of motion of blood flow are solved analytically. The analytical expressions for axial velocity, volumetric flow rate, pressure gradient, resistance to blood flow and shear stress have been...

Direct numerical simulations have been performed to study the behaviour of multiple square jets issuing normally into a cross-flow. The jets are arranged side-by-side in spanwise direction in twin jet configuration and with addition third jet downstream along the centre line in tandem jets configuration. The simulations are carried out for the jet-to-jet adjacent edge distances of 1D and 2D in ...

Recent progress in theoretical modeling of a sunspot is reviewed. The observed properties of umbral dots are well reproduced by realistic simulations of magnetoconvection in a vertical, monolithic magnetic field. To understand the penumbra, it is useful to distinguish between the inner penumbra, dominated by bright filaments containing slender dark cores, and the outer penumbra, made up of dark...

In this study, a multivariable control structure is developed to simultaneously control the concentrations of cells and of one of the nutrients in an animal cell cultivation system operated in perfusion. A cascade control structure is considered consisting of (i) an inner loop with a partially linearizing feedback controller, tuned so as to ensure robustness with respect to parameter uncertaint...

We investigate the effect of the heat source distribution on the behavior of the magnetohydrodynamic (MHD) dynamo action. We consider three models in which the ratio of the heat flow at the inner core boundary to that extracted away from the core to the mantle varies from 0%, 50% to 100%. The most frequently studied geodynamo model with a temperature difference between the upper and lower bound...