Archives for October, 2024
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…