Turbulence is an open and challenging problem for mathematical approaches, physical modeling and numerical simulations. Numerical solutions contribute significantly to the understand of the nature and effects of turbulence. ...

In this thesis, we study the exact eigenvalue distribution of product of independent rectangular complex Gaussian matrices and also that of product of independent truncated Haar unitary matrices and inverses of truncated ...

Mechanisation of Mathematics refers to use of computers to generate or check proofs in Mathematics. It involves translation of relevant mathematical theories from one system of logic to another, to render these theories ...

Given a hyperbolic surface, the set of all closed geodesics whose length is minimal form a graph on the surface, in fact a so called fat graph, which we call the systolic graph. The central question that we study in this ...

We use transcendental shift-like automorphisms of Ck, k > 2 to construct two examples of non-degenerate entire mappings with prescribed ranges. The first example exhibits an entire mapping of Ck, k>2 whose range avoids a ...

We start with the recollection of basic results about differential manifolds and Lie groups. We also recall some preliminary terminologies in Lie algebra. Then we define the Lie algebra corresponding to a Lie group. In the ...

This work is concerned with two different problems in harmonic analysis, one on the Heisenberg group and other on Rn, as described in the following two paragraphs respectively. Let Hn be the (2n + 1)-dimensional Heisenberg ...

Let D be a smoothly bounded domain in Cn , n> 1. For each point p _ D, we have the Green function G(z, p) associated to the standard sum-of-squares Laplacian Δ with pole at p and the Robin constant __ Λ(p) = lim G(z, p) ...