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We present further properties of a previously proposed recursive scheme for parameterisation of n-by-n unitary matrices. We show that the factors in the recursive formula may be introduced in any desired order. The method is used to study…
Discrete mechanics is used to present fluid mechanics, fluid-structure interactions, electromagnetism and optical physics in a coherent theoretical and numerical approach. Acceleration considered as an absolute quantity is written as a sum…
We consider estimation procedures which are recursive in the sense that each successive estimator is obtained from the previous one by a simple adjustment. We study rate of convergence of recursive estimation procedures for the general…
A quantum trajectory describes the evolution of a quantum system undergoing indirect measurement. In the discrete-time setting, the state of the system is updated by applying Kraus operators according to the measurement results. From an…
Using Euler's equations of motion and the Hamiltonian formulation, we obtain the equations of motion of systems with internal angular momentum that are moving with respect to a given reference frame, when subjected to a torque which is…
In this paper we establish a formalism for the computation of observables due to acceleration-induced particle physics processes. General expressions for the transition rate, multiplicity, power, spectra, and displacement law of particles…
The uniform acceleration of a point charge moving along a stationary worldline, which emits constant radiated power was investigated. A classification of motion of a particle along stationary worldlines into six types is made. The angular…
A new formula for the probability that a standard Brownian motion stays between two linear boundaries is proved. A simple algorithm is deduced. Uniform precision estimates are computed. Different implementations have been made available…
In this paper, we construct rotating frames for curves, including plane curves, space curves and curves on surfaces. Hence, the behaviour of an arbitrary moving point on a curve can be seen as the composite of linear motion and rotation.…
General covariant expressions for measurable angles, distances, velocities, and accelerations are provided in terms of fundamental parameters that can be applied in any setup. The relativistic aberration of light relationship is presented…
An exact expression for the phase of an atomic interferometer located in a non-inertial reference frame (platform) moving along an arbitrary trajectory and with an orientation that changes arbitrarily over time is obtained. This expression…
Asymptotic expansions are derived for solutions of the parabolic cylinder and Weber differential equations. In addition the inhomogeneous versions of the equations are considered, for the case of polynomial forcing terms. The expansions…
Understanding transverse coupling dynamics is crucial for beam physics, accelerator design, and operations. Currently, most accelerators are designed for uncoupled beams, and coupling is treated as an error or perturbation. Many transverse…
In many cases, the values of some model parameters are determined by maximising the likelihood of a set of data points given the parameter values. The presence of outliers in the data and correlations between data points complicate this…
The angular and the radial parts of the dynamics of the perturbed Kepler motion are separable in many important cases. In this paper we study the radial motion and its parametrizations. We develop in detail a generalized eccentric anomaly…
Regularized estimation of quantitative ultrasound (QUS) parameters, such as attenuation and backscatter coefficients, has gained research interest. Recently, the alternating direction method of multipliers (ADMM) has been applied…
Covariant form of equation of motion for arbitrarily shaped particle in the electromagnetic radiation field is presented. Equation of motion in the proper frame of the particle uses the radiation pressure cross section 3 $\times$ 3 matrix.…
Solving for the minimum time bounded acceleration trajectory with prescribed position and velocity at endpoints is a highly nonlinear problem. The methods and bounds developed in this paper distinguish when there is a continuous…
We use path integrals to calculate perturbative corrections to the correlation function of a particle under the action of nonlinear optical tweezers, both in the overdamped and underdamped regimes. In both cases, it is found that to leading…
We derive a closed-form expression for the finite predictor coefficients of multivariate ARMA (autoregressive moving-average) processes. The expression is given in terms of several explicit matrices that are of fixed sizes independent of…