We study modular forms, Jacobi forms, and hermitian formal Fourier-Jacobi series over imaginary quadratic fields. In the first section, we prove that the ring of classical Jacobi forms of a fixed genus g, varying index m and weight k is generated by theta functions. From this result we show that...
Recent advances in high-performance computing have resulted in massive databases of materials properties calculated with techniques such as ab initio density functional theory. In fact, some of the largest of such databases have calculations of nearly all distinct, ordered, experimentally-reported compounds. This thesis discusses the application of data in one...
Central nervous system (CNS) regeneration is one of the most challenging regenerative medicine targets in mammals due to the natural inhibitory mechanisms that occur in response to injury. In the case of spinal cord injury (SCI), the initial inflammatory response protects damaged tissue, but over time creates a hostile microenvironment...
Transition Metal Dichalcogenides (TDMCs) are one of many families of two-dimensional (2D) beyond graphene, that started to gain more attention due to the need for miniaturization and their unique electrical, mechanical, and optical properties. Some members of TMDCs, such as MoS2, has direct band gap in its monolayer form, making...
Living organisms undergo morphogenesis as they develop and change shape to fit their evolved niche in natural ecosystems. The biological processes underlying morphogenesis involve sophisticated feedback loops between spatiotemporal release of morphogenic molecules that diffuse and signal cell differentiation, as well as contextual interaction with the physical surroundings of the...
Natural gas is likely to become one of the main sources of carbon-based chemicals in the next century due to rapidly increasing natural gas production levels. This has created new incentives to find materials that are active and selective towards alkane partial oxidation reactions that are relevant for natural gas...
The unique ability of plasmonic nanoparticles to localize and enhance resonant electromagnetic fields has enabled a wealth of discoveries from enhanced spectroscopies to driving chemical reactions on the nanoscale. In this thesis, we strive to both drive and observe chemistry on plasmonic surfaces. First, we examine the possibility of driving...
Subchalcogenides are rare compounds that have both metal-metal and metal-chalcogenide (sulfur, selenium, tellurium) interactions. Unlike conventional semiconductors, the metals do not obey the so-called 8-N octet rule for oxidation states, often resulting in low or zero valent metal atoms. The presence of both metal-metal and metal-chalcogenide bonding can also lead...
Super-resolution (SR) has become one of the most critical problems in image and video processing. In Chapter 2 of this thesis, a detailed review of existing Deep Learning (DL) techniques for addressing the SR task, with an emphasis on how DL and analytical techniques can be combined, is provided. Chapter...
Conventional cross-linked polymers are widely used owing to their outstanding stability and performance. However, permanent cross-links in these polymer networks prevent them from being recycled or reprocessed at the end of life, leading to major sustainability and economic losses. The recycling issue associated with polyurethane (PU) thermoset wastes exemplifies such...