Author Archives: anuj
Examples of Taylor SEries versus Fourier Series
Intro Which works better for a given function - a Taylor expansion or a Fourier Expansion? This post explores the pros and cons of each, using specific examples. Examples of…
Taylor Series versus Fourier Series for a function
. Domain of Representation Taylor Series: Works best for local approximations around a single point (Maclaurin series if centered at zero). Fourier Series: Represents a function over an entire interval…
Neutron Stars and Pulsars – Mathematical Differences
Mathematical Difference: Neutron Star vs Pulsar Neutron Star A neutron star is a highly dense remnant of a massive star after a supernova explosion. It is characterized by: Mass: \(…
Bells’ Theorem and Thermodynamics
Bell’s Theorem and Its Relation to Thermodynamics 1. Fundamental Differences Bell's Theorem: Demonstrates that no local hidden variable theory can fully explain quantum correlations observed in entangled systems. It is…
Non Stationary Spacetime Metric and redshift
Redshift from a Non-Stationary Metric 1. Understanding Redshift from a Non-Stationary Metric The redshift arises because the wavelength of light is stretched as it propagates through a dynamically changing…
Convolution Integrals for Entangled Quantum States
Convolution Integrals in Schrödinger’s Equation for Entangled Systems 1. Green's Functions and Propagators The solution to the time-dependent Schrödinger equation often involves propagators, which describe the evolution of a wavefunction…
Functions ONLY definable by their integrals – with applications
Functions ONLY Defined by Their Integrals 1. The Gamma Function \( \Gamma(x) \) \( \Gamma(x) = \int_0^\infty t^{x-1} e^{-t} \, dt \), for \( x > 0 \). Applications: Generalization…
Functions Defined by Their Integrals – with applications
Functions Defined by Their Integrals Functions that are defined by their integrals often arise in fields like physics, probability theory, and engineering, where the direct formulation of a function may…
Tangent Vectors, Affine Parametrization of Curves
Tangent Vectors, Affine Parameterization, and Tangent Spaces Tangent Vectors Definition: A tangent vector at a point on a manifold (a space that locally resembles Euclidean space) represents the "direction" and…
Godel’s Consistency of Axiom of Choice Paper
Gödel's Landmark Paper The Consistency of the Axiom of Choice and the Generalized Continuum-Hypothesis with the Axioms of Set Theory Background Set Theory and ZFC: The Zermelo-Fraenkel axioms with the…