Introduction: Finite element methods (FEM) have become a widely used tool in structural analysis due to their ability to model complex structures and analyze their behavior under various loading conditions. This thesis aims to explore…
Read MoreIntroduction Markov chains are stochastic processes that evolve over time in a probabilistic manner, where the future state of the system only depends on the current state and not on the previous states. They have…
Read MoreIntroduction Markov chains are stochastic processes that transition from one state to another based on a set of probabilities. They have been extensively studied in various fields such as mathematics, statistics, physics, and computer science…
Read MoreIntroduction Probability theory plays a crucial role in the field of artificial intelligence (AI) as it provides a mathematical framework for reasoning under uncertainty. Advanced probability theory in AI extends beyond basic concepts of probability…
Read MoreIntroduction Combinatorial optimization is a field of study that involves finding the best solution from a finite set of possible solutions to a problem that typically involves a large number of variables and constraints. Heuristic…
Read MoreIntroduction: Lattice theory is a branch of mathematics that studies the structure of partially ordered sets that satisfy certain properties. Lattices have applications in various fields such as computer science, physics, chemistry, and economics. This…
Read MoreIntroduction Information theory is a branch of applied mathematics and computer science that deals with the quantification of information. It was first introduced by Claude Shannon in 1948 as a means to study the fundamental…
Read MoreIntroduction: Partial differential equations (PDEs) play a crucial role in various engineering applications, providing a mathematical framework to model and analyze complex physical phenomena. These equations are used to describe how quantities such as temperature,…
Read MoreIntroduction Partial differential equations (PDEs) play a fundamental role in various engineering applications, providing a mathematical framework to describe physical phenomena such as heat transfer, fluid dynamics, and structural mechanics. As a PhD student in…
Read MoreIntroduction Homotopy theory is a branch of algebraic topology that studies continuous mappings between topological spaces up to homotopy equivalence. It provides a powerful framework for understanding the shape and structure of spaces and has…
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