Mathematical theory of stationary miscible filtration

Mathematical Theory of Flight

We show by computational solution of the incompressible Navier-Stokes equations with friction force boundary conditions, that the classical inviscid circulation theory by Kutta-Zhukovsky for lift of a wing and laminar viscous boundary layer theory by Prandtl for drag, which have dominated 20th century flight mechanics, do not correctly describe the real turbulent airflow around a wing. We show ...

Mathematical Theory of Resonances

The resonance counting function for Schrödinger operators HV = −∆ + V on L(R), for d ≥ 1, with compactly-supported, realor complex-valued potentials V is known to be bounded above by CV (r +1). The main result is that for a dense Gδ-set of such potentials, the resonance counting functions have the maximal order of growth d. For the even dimensional case, it is shown that the resonance counting ...

Fuzzy relations, Possibility theory, Measures of uncertainty, Mathematical modeling.

A central aim of educational research in the area of mathematical modeling and applications is to recognize the attainment level of students at defined states of the modeling process. In this paper, we introduce principles of fuzzy sets theory and possibility theory to describe the process of mathematical modeling in the classroom. The main stages of the modeling process are represented as fuzz...

Mathematical Theory of Sailing

We show by computational solution of the incompressible Navier-Stokes equations with friction force boundary conditions, that the classical inviscid circulation theory by Kutta-Zhukovsky for lift and laminar viscous boundary layer theory by Prandtl for drag, which have dominated 20th century fluid dynamics, do not correctly describe the real turbulent airflow around a sail under tacking. We sho...

Mathematical Theory of Communication