Description of Subtheme:
Topics cover various areas in Pure Mathematics, Applied Mathematics, Computer Science, Physics and Statistics. Mathematical and Computational Science include numerical tools based on computations to acquire a variety of research schemes in many fields of science.
Molecular Spectroscopy
Theoretical calculation of the electronic structure of a diatomic molecule via the MSSCF/MRCI (single and double excitations with Davidson correction) method using a correlation-consistent basis set. This calculation investigates the potential energy curves, spectroscopic constants, the static and transition dipole moment, the Einstein coefficients, the spontaneous radiative lifetime, and the emission oscillator strength. The ro-vibrational parameters and the abscissas of the turning points can be obtained for different electronic states with the canonical functions approach. These data are beneficial for investigating the feasibility of laser cooling and its applications, the investigation of the spectra of astrophysical molecules, and the scientific community.
- Group Representations
Braids are correlated with the study of qudits and the exchange of the anyons inside them. Representations of the braid groups have been proposed as a fractional statistics of Anyons, and used in the topological models for quantum computing. Braid groups also provide a framework for obtaining new public key cryptosystems that can be efficiently correlated with the aspect of security.
2. Partial Differential Equations
Partial Differential Equations serve as a fundamental tool in scientific and engineering disciplines, allowing us to model, analyze, and manipulate systems with partial derivatives, leading to advancements in various areas of knowledge and application.
3. Fractional Differential Equations
A generalization of the ordinary differential equations to non- integral order, fractional differential equations has many applications in engineering as in fractional cross product,, electronic circuits, control engineering, etc.
4. Probability Theory, Operations research and Statistics
This field covers a wide range of subjects within the domains of mathematics, statistics, and optimization. With applications ranging from finance to healthcare, researchers dive into cutting-edge topics like stochastic processes, Bayesian inference, and Monte Carlo simulations. Contrarily, operations research focuses on creating novel and improved techniques for simulating and enhancing complex systems in a variety of industries, including supply chain management, logistics, transportation, finance among others. The interaction between these two disciplines makes this area of research rapidly growing, with many possibilities for innovations in both theoretical underpinnings and practical implementation.
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