We provide an expansive treatment of the fundamentals of hyperbolic geometry. The explicit computation of hyperbolic isometries enables us to find geodesics, calculate the metric, define the boundary, and compute the ...

The Quasi-Geostrophic theory has been a valuable framework for understanding synopticand planetary-scale systems in the midlatitudes. By making arguments about the scale of the systems under study, we are able to filter ...

Studying the temporal behaviour of excitons in 0D-2D semiconductor structure can allow us to study the transitions between quantized energy levels. This can demonstrate quantum coherent features in time domain and establish ...

My thesis deals with the recently developed concept of response diversity, applying it to the Western Ghats of India. Simply put, this is a measure of the variation in organismal responses to the environment, and is thought ...

Arbuscules are the primary site of nutrient exchange in the arbuscular mycorrhizal symbiosis formed between land plants and Glomeromycotina fungi. Plants upregulate a suite of hydrolases and proteases to degenerate arbuscules ...

Latitudinal and elevational gradients provide a powerful natural framework to study how species interactions with changing environmental conditions shape ecological patterns across space. Elevational transects have much ...

Let $h' \in S_{k'}(N',\chi')$ and $h \in S_{k}(N,\chi)$ be normalized newforms in the respective spaces with $k',k \geq 2$ and $k' - k \geq 2.$ Let $L(s, h\times h')$ denote the completed Rankin-Selberg $L$-function ...

This thesis studies polynomial maps with constants evaluated on algebras, with particular emphasis on surjectivity and classification of images. Given an algebra $\mathcal A$ and a noncommutative polynomial $\omega$ whose ...

Bacterial cell morphology is governed by an interplay of cytoskeletal dynamics, mechanical forces, and stochastic processes. This study investigates size and shape homeostasis in rod-shaped Escherichia coli by integrating ...