Quantum Foundations & Superoscillations

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• Proposing and exploring a non-standard coupling between quantum systems originated from their kinetic energy

• Providing the conditions in which single particles exhibit classical-like features in both flat and curved spacetime

• Proposing a novel setting for the analogy between the curvature of quantum particles and curved space based on quantum hydrodynamics

• Showing how the distortion of quantum trajectories shapes the fundamental statistical properties of the particles

• Deriving new methods to construct and discover superoscillations and supershifts in one variable and several variables.

• Deriving a new type of classical physics that is originated from the classical limit of quantum mechanics with two-boundary conditions.

• Proposing the super Dirac Delta distribution, based on a unique convex-sum of delta functions with applications in quantum mechanics.

• Countering the Casimir-Polder force with quantum wavepacket engineering.

Probability Distribution Theory, Risk Management, and Decision Making

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• Deriving the optimal solution for ESG optimal portfolio selection strategies. 

• Extending the class of elliptical distributions into different marginal components based on spherical symmetries, with applications in multivariate analysis.

• Proposing and studying a new class of systemic risk measures that captures the dependence structure of the risks while focusing on extreme loss events.

• Deriving the location of a minimum variance squared distance functional for a system of dependent random variables.

• Proving the existence of singularity skew-elliptical distributions, which generalizes the symmetric case.

• Developing a new analytical lens to examine the risk-return profiles of bitcoin, litecoin, ripple, and ethereum.

• Deriving explicit formulas for the tail moments of the elliptical and log-elliptical probability distributions.

• Proving a conjecture about the form of the characteristic functions of generalized skew-elliptical distributions.

• Showing that  the optimal solution of every multivariate optimization problem of elliptical weighted-sum can be projected into a non-linear univariate equation with a unique solution. 

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