The Ginzburg-Landau phenomenological theory explains superconductivity and superfluidity as distinct thermodynamic phases. It focuses on phase transitions characterized by singularities in specific heat at the transition temperature. Derived from BCS theory, it quantifies condensation energy, emphas

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Singular integrals involving logarithmic and non-integrable singularities are discussed, emphasizing integrability in the principal value sense. Cauchy Principal Value integrals and examples of their evaluations for singularities like 1/x are explored, highlighting the necessity of passing through t

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The Residue Theorem is a powerful tool in complex analysis that allows us to evaluate line integrals around paths enclosing isolated singularities. By expanding the function in a Laurent series, deforming the contour, and summing residues, we can evaluate these integrals efficiently. This theorem ex

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Indian scholars have made significant contributions to the field of General Relativity post-independence, focusing on important problems like Big Bang singularity, gravitational collapse, black holes, gravitational waves, and quantum aspects. Notable achievements include AKR's Raychaudhury Equation,

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Delve into the profound implications of General Relativity on topics such as black holes, cosmology, and philosophical consequences from Special and General Relativity. Discover how curved geometry allows for different topologies, potential return of preferred frames, the concept of horizons near bl

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Singularities are points where a function is not analytic. Through Taylor and Laurent Series, we explore the behavior of functions near singularities, their convergence, and divergence properties. Taylor Series Examples demonstrate poles and divergent behaviors, while Laurent Series Examples illustr

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Action and stress-energy tensor, Einstein-Klein-Gordon equations, and method for constructing nonstationary configurations of a spherically symmetric scalar field are discussed in this study. The behavior of the characteristic function allows interpretations such as black holes, wormholes, or naked

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This research explores the use of quasi-interpolation techniques to approximate functions from scattered data points in high dimensions. It discusses the interpretation of Moving Least Squares (MLS) for direct pointwise approximation of differential operators, handling singularities, and improving a

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Explore characteristics and properties of good approximation operators, such as quasi-interpolation and Moving Least-Squares (MLS), for approximating functions with singularities and near boundaries. Learn about direct approximation of local functionals and high-order approximation methods for non-s

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