Summation formulas play a vital role in analytic number theory. Several kinds of summation formulas exist, like the Poisson summation formula, Abel summation formula, Euler-Maclaurin formula, etc. In 1904, G. F. Voronoi ...

Ergodic theory often involves dealing with transformations of measure spaces that preserve specific measures, such as volume or probability measures. These transformations establish a framework for studying the behavior ...

Universal logic, as described by Béziau, is a structural approach to logic which aims to unify the large kaleidoscopic variety of logics, while preserving their diversity. In order to do this, Béziau’s original proposal ...

Self-orthogonal codes, self-dual codes, and linear codes with complementary duals (LCD codes) constitute the three most important and well-studied classes of linear codes. These codes have nice algebraic structures and are ...

This thesis is about an analytical study of viscoelastic fingering that solves the problem of predicting the finger width when a Newtonian fluid (with negligible viscosity) drives a non-Newtonian (power-law) fluid. The ...

This thesis investigates the spectral instabilities of various nonlinear water wave models through rigorous analytical techniques. Focusing on three fundamental types of instabilities, modulational instability, transverse ...

This thesis consists of some interesting combinatorial problems on matrix poly- nomials over finite fields. Using results from control theory, we give a proof of a result of Lieb, Jordan and Helmke (2016) which solves the ...