Mathematical articles

Contour plots for Newtonian and relativistic elastic collision equations

by Dr Christian P. H. Salas

Python simulation of a threshold phenomenon in a general epidemic

by Dr Christian P. H. Salas

On the equilibration of M/M/1 queues

by Dr Christian P. H. Salas

Why we can omit the modulus symbol in ln(|x|) in the integrating factor method

by Dr Christian P. H. Salas

Using Prüfer sequences to count and classify irreducible labelled 10-node trees

by Dr Christian P. H. Salas

A max-flow/min-cut network problem solved both manually and with Python

by Dr Christian P. H. Salas

Using the Python library NetworkX to find all Hamiltonian cycles in a graph

by Dr Christian P. H. Salas

Boltzmann distribution, Gibbs-Shannon entropy and Helmholtz free energy

by Dr Christian P. H. Salas

Zero-field singularity of magnetic susceptibility in a 4-D Ising model

by Dr Christian P. H. Salas

Fourier transform of a function that is scaled and translated in either order

by Dr Christian P. H. Salas

Ornstein-Uhlenbeck process: derivation and simulation of its pdf and moments

by Dr Christian P. H. Salas

From simple random walk to Wiener process and diffusion equation

by Dr Christian P. H. Salas

Canonical derivation of the mean and variance of the binomial distribution

by Dr Christian P. H. Salas

Using wxdrawdf in MAXIMA to plot a phase portrait with a stable limit cycle

by Dr Christian P. H. Salas

A note on an unusual system of two masses connected by a spring

by Dr Christian P. H. Salas

Quadratic B-Spline interpolation of points on a modulus function

by Dr Christian P. H. Salas

Fast Fourier Transform by hand

by Dr Christian P. H. Salas

Boolean array indexing and finding multiple zeros of a function at once

by Dr Christian P. H. Salas

A note on Singular Value Decomposition and Principal Components

by Dr Christian P. H. Salas

Overview of mathematical modelling ideas in single particle quantum mechanics

by Dr Christian P. H. Salas

Legendre-transforming a Lagrangian mechanics problem into a Hamiltonian one

by Dr Christian P. H. Salas

A note on a Fourier sine series solution to a heat flow problem

by Dr Christian P. H. Salas

Equivalent integral formulae for Bessel functions of the first kind, order zero

by Dr Christian P. H. Salas

Useful formula for integrating integer powers of a sine function over a period

by Dr Christian P. H. Salas

Surface charge density of a conducting disk from that of a conducting ellipsoid

by Dr Christian P. H. Salas

Integrating integer powers of a sine function via a hypergeometric function

by Dr Christian P. H. Salas

Quick memo on five basic types of first-order differential equation

by Dr Christian P. H. Salas

Royal Holloway lectures (Quantitative Methods in Economics II)

by Dr Christian P. H. Salas

Derivation and manipulation of a generalised Erlang distribution

by Dr Christian P. H. Salas

A spline approximation scheme for large deviation theory problems

by Dr Christian P. H. Salas

Study of a Lagrangian function approach to analysing raindrop growth

by Dr Christian P. H. Salas

Monomer injections leading to oscillatory behaviour in a mathematical model of rain formation

by Dr Christian P. H. Salas

A note on mathematics in Latin

by Dr Christian P. H. Salas

Accurate analytical approximation formulae for large-deviation analysis of rain formation

by Dr Christian P. H. Salas

A Phys. Rev. Letter by M Wilkinson on large deviation analysis of rapid-onset rainfall

by Dr Christian P. H. Salas

Using Lagrange’s interpolation formula to prove complicated sum/product identities

by Dr Christian P. H. Salas

Using an asymptotic approximation to obtain a closed form solution

by Dr Christian P. H. Salas

Applying the Bromwich integral to a cumulant generating function

by Dr Christian P. H. Salas

Inverse Fourier transform of a characteristic function

by Dr Christian P. H. Salas

Two versions of the exponential cumulant generating function

by Dr Christian P. H. Salas

The role of the Legendre transform in large deviation theory

by Dr Christian P. H. Salas

Markov’s inequality and the Cramér-Chernoff bounding method

by Dr Christian P. H. Salas

Differentiating a double integral with respect to its upper limits

by Dr Christian P. H. Salas

Bra-ket formalism of quantum mechanical measurement

by Dr Christian P. H. Salas

Free particle in a ring with a periodic boundary condition

by Dr Christian P. H. Salas

Some mathematics relating to phonons

by Dr Christian P. H. Salas

Quick way to explain the concept of a solid angle

by Dr Christian P. H. Salas

Useful methods in Laplace transform theory

by Dr Christian P. H. Salas

A couple of results involving the beta function

by Dr Christian P. H. Salas

Strange notations in mathematical probability

by Dr Christian P. H. Salas

From random walk to Brownian motion with drift

by Dr Christian P. H. Salas

Approximating logarithms of large numbers

by Dr Christian P. H. Salas

A simple Yule-Simon process and Zipf’s law

by Dr Christian P. H. Salas

A scale-free probability distribution must be a power law

by Dr Christian P. H. Salas

Classical and quantum harmonic oscillators

by Dr Christian P. H. Salas

Decomposition of Lorentz transformations using orthogonal matrices

by Dr Christian P. H. Salas

Proving the relativistic rotation paradox

by Dr Christian P. H. Salas

Solving Schrödinger’s equation by B-spline collocation

by Dr Christian P. H. Salas

Overview of the Lie theory of rotations

by Dr Christian P. H. Salas

Dirichlet character tables up to mod 11

by Dr Christian P. H. Salas

Invariance under rotations in space and conservation of angular momentum

by Dr Christian P. H. Salas

Proving Noether’s theorem

by Dr Christian P. H. Salas

Alternative approaches to formulating geodesic equations on manifolds

by Dr Christian P. H. Salas

Simple variational setups yielding Newton’s second law and Schrödinger’s equation

by Dr Christian P. H. Salas

Changing variables in the square of the angular momentum operator

by Dr Christian P. H. Salas

Matrix calculus approach to changing variables in Laplace’s equation

by Dr Christian P. H. Salas

On classifying singularities, with a quick look at a Schwarzschild black hole

by Dr Christian P. H. Salas

Different branch cuts for the principal argument, log and square root functions

by Dr Christian P. H. Salas

A note on the quaternion rotation operator

by Dr Christian P. H. Salas

A division algorithm for converting prime reciprocals into ternary numbers

by Dr Christian P. H. Salas

A variant of Einstein’s partial differential equation for Brownian motion

by Dr Christian P. H. Salas

Applying Chebyshev’s inequality and the Borel-Cantelli lemma to Brownian motion

by Dr Christian P. H. Salas

Brownian motion and fractional Brownian motion as self-similar stochastic processes

by Dr Christian P. H. Salas

Gauss’s flux theorem for gravity, Poisson’s equation and Newton’s law

by Dr Christian P. H. Salas

Pythagorean triples in a homeomorphism between the 1-sphere and the extended real line

by Dr Christian P. H. Salas

Topological equivalence of the 2-sphere and the extended complex plane (the `Riemann sphere’)

by Dr Christian P. H. Salas

The p-adic number field as a completion of the rationals

by Dr Christian P. H. Salas

Maple code for quantum scattering from an Eckart potential

by Dr Christian P. H. Salas

Overview of Sturm-Liouville theory: the maths behind quantum mechanics

by Dr Christian P. H. Salas