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Presents a short proof of a conjecture by Erdös, exploring related questions and detailed proof of the proposition.

Explores ergodic theory, spectral operators, and almost periodic factors in dynamical systems and spectral theory.

Explores scaling and renormalization in statistical mechanics, emphasizing critical points and invariant properties.

Covers determinantal point processes, sine-process, and their extrapolation in different spaces.

Explores molecular dynamics simulations under holonomic constraints, focusing on numerical integration and algorithm formulation.

Explores isometries in Euclidean spaces, including translations, rotations, and linear symmetries, with a focus on matrices.

Covers the Stochastic Block Model and its application in community detection, exploring its mathematical formulation and challenges.

Discusses isometries and orthonormal bases in mathematics.

Covers the limitations of Lagrange formalism and the transition to Hamiltonian formalism for dynamic variables.

Explores one-dimensional maps, periodic solutions, and bifurcations in dynamical systems.

Introduces constraints, Lagrange multipliers, and generalized coordinates in physics.

Explores the modern definition of symmetry and its practical applications.

Introduces the Random-Subcube Model (RSM) for constraint satisfaction problems, exploring its structure, phase transitions, and variable freezing.

Covers the KKT conditions for optimization with constraints, essential for solving constrained optimization problems efficiently.

Covers dynamic systems, trajectories, growth models, stability of fixed points, and linearization of models.

Explores the Kuramoto model for synchronization in phase oscillators and discusses stability criteria and critical coupling values.

Covers the equilibrium conditions in 3D, system isolation, free-body diagrams, and constraints.