Related papers: An Approximate Expression for the Large Angle Peri…
We provide direct elementary proofs of several explicit expressions for Bernoulli numbers and Bernoulli polynomials. As a byproduct of our method of proof, we provide natural definitions for generalized Bernoulli numbers and polynomials of…
In this paper we will show that purely classical concepts based on a few heuristic considerations about extended field configurations are enough to compute the leptonic magnetic moment with corrections in $\alpha$-power perturbative…
We derive an explicit formula for the action of a geometric Hecke correspondence on special cycles on a Shimura variety in terms of such cycles at a fixed neat level and compare it with another closely related expression sometimes used in…
The shapelet transform is a form of feature extraction for time series, in which a time series is described by its similarity to each of a collection of `shapelets'. However it has previously suffered from a number of limitations, such as…
We introduce the definition of conformable derivative on time scales and develop its calculus. Fundamental properties of the conformable derivative and integral on time scales are proved. Linear conformable differential equations with…
Inspired by Edgar Allan Poe's The Pit and the Pendulum, we investigate a radially driven, lengthening pendulum. We first show that increasing the length of an undriven pendulum at a uniform rate does not amplify the oscillations in a manner…
The problem of calculating the period of second order nonlinear autonomous oscillators is formulated as an eigenvalue problem. We show that the period can be obtained from two integral variational principles dual to each other. Upper and…
The paper presents linear integral predictors for continuous time high-frequency signals with a a finite spectrum gap. The predictors are based on approximation of a complex valued periodic exponential (complex sinusoid) by rational…
An effective hamiltonian is derived exactly for the one-dimensional periodic Anderson model via a canonical transformation. The canonical transformation has been calculated up to infinite order, thus an exact transformation was performed in…
Some years ago I demonstrated a simulated annealing heuristic for the Hamiltonian cycle problem (Science 273, 413 (1996)). Here I propose an improved version of this heuristic.
Integration of Hamiltonian systems by reduction to action-angle variables has proven to be a successful approach. However, when the solution depends on elliptic functions the transformation to action-angle variables may need to remain in…
The stationary and highly non-stationary resonant dynamics of the harmonically forced pendulum are described in the framework of a semi-inverse procedure combined with the Limiting Phase Trajectory concept. This procedure, implying only…
The small discrepancy between the observed orbit of Mercury and the orbit predicted by Newtonian gravity was a key test of Einstein's theory, and a dramatic verification of the correctness of General Relativity. This `anomalous precession'…
The electromagnetic fields of the hybrid modes of an optical fiber are reformulated using bi-complex mathematics, which leads to simpler expressions relative to those found with the widely used, conventional complex formulation. Generalized…
A formula for the apparent rotation of a relativistically moving object has been known for some time, but it seems not to have been realized that this formula has a very pretty interpretation in terms of formal group laws. Version 2…
The pendulum, in the presence of linear dissipation and a constant torque, is a non-integrable, nonlinear differential equation. In this paper, using the idea of rotated vector fields, derives the relation between the applied force $\beta$…
The paper proposes an approximate expression for calculating very complex one-dimensional integrals depending on the parameter $a$. These integrals often occur in computational problems theory of magnetic solitons. The resulting analytical…
We investigate the nonlinear effect of a pendulum with the upper end fixed to an elastic rod which is only allowed to vibrate horizontally. The pendulum will start rotating and trace a delicate stationary pattern when released without…
A simple and transparent derivation of the formally exact probability distribution for classical non-equilibrium systems is given. The corresponding stochastic, dissipative equations of motion are also derived.
We set up a trace formula for the relativistic density of states in terms of a topological sum of classical periodic orbits. The result is applicable to any relativistic integrable system.