Author Archives: anuj - Page 13
Richard Gott’s Three Universes at the Big Bang
Gott's Theory on the Big Bang Singularity J. Richard Gott, a Princeton physicist, proposed an intriguing theory concerning the Big Bang Singularity. His idea explores what happens if we consider…
Fault Tolerant, Error Correcting Computers for Quantum Computing
Fault Tolerant Computers for Quantum Computing Errors are part of the Quantum Computing equation. By 2035, IBM envisions fault tolerant computers, capable of breaking encryption algorithms. Quantum Safe Algorithms? There's…
Nowhere Differentiable Functions and Integration of such functions
Nowhere Differentiable Functions Nowhere differentiable functions are functions that are continuous everywhere but do not have a well-defined derivative at any point. They exhibit erratic behavior, and although they can…
Analytic Within and On the Unit Circle
Analytic Within and On the Unit Circle When discussing whether a function is analytic within or on the unit circle, we are referring to complex analysis, which deals with functions…
Curves Over Finite Fields
Curves Over Finite Fields Curves over finite fields are algebraic curves defined by equations where the coefficients come from a finite field. A finite field is a field with a…
Examples of Non-Measurable Sets in Lebesgue Measure Theory
Examples of Non-Measurable Sets in Lebesgue Measure Theory 1. Vitali Set One of the most famous examples of a non-measurable set is the Vitali set. The construction begins by…
Relationship Between Measure Theory, Lebesgue Integrals, and Hilbert Spaces
Understanding the Relationship Between Measure Theory, Lebesgue Integrals, and Hilbert Spaces To understand the relationship between measure theory, Lebesgue integrals, and Hilbert spaces, we need to break down each…
Lebesgue Integral Solved Problems
Lebesgue Integral Solved Problems Problem 1: Simple Example of a Lebesgue Integral Problem: Compute the Lebesgue integral of the function f(x) = 2 over the interval using the Lebesgue measure.…
The Separability Problem in Quantum Mechanics for Mixed States
Separability Problem in Quantum Mechanics for Mixed States The **separability problem** in quantum mechanics refers to the task of determining whether a given **mixed quantum state** is **separable** or **entangled**.…
Hawking Radiation, How black holes evaporate
Stephen Hawking's seminal paper on black hole radiation, often referred to as **Hawking Radiation**, explains how black holes, previously thought to only absorb matter and energy, can actually emit radiation…