相关论文: Simple Linearizations of the Simple Pendulum for A…
This study is on small oscillations of a heavy symmetric top. A different method than previous works is applied, and differently from previous works, the explicit formulas for the amplitudes for oscillations are given. This method can be…
We construct affine algebras with an arbitrary amount of simple modules of each dimension.
We describe how weak phase modulations applied to classical coherent light in specially modified linear interferometers can be used to perform primitive computational tasks. Instead of encoding operations within a fixed unitary state, the…
In this paper, we study how to quickly compute the <-minimal monomial interpolating basis for a multivariate polynomial interpolation problem. We address the notion of "reverse" reduced basis of linearly independent polynomials and design…
The period of oscillation of a simple pendulum ($T = 2\pi\sqrt{l/g}$) is a familiar formula to the average first-year physics student. However, deriving this expression from first principles involves solving a non-linear differential…
We propose and experimentally demonstrate a novel type of polarization rotator which is capable of rotating the polarization plane of a linearly polarized light at any desired angle in either broad or narrow spectral bandwidth. The rotator…
This study is concerned with the design of a Mueller imaging polarimeter for the visualization of spatially-varying Mueller matrix fields. A simplified calibration procedure is advocated, where all the optical elements are calibrated…
We characterize the extendibility of the normal curvature on frontals and we give a representation formula of this type of frontals. Also we give representation formulas for wavefronts on all types of singularities and others sub classes of…
A simple permutation is one which maps no proper non-singleton interval onto an interval. We consider the enumeration of simple permutations from several aspects. Our results include a straightforward relationship between the ordinary…
We compute two infinite series of tree-level amplitudes with a massive scalar pair and an arbitrary number of gluons. We provide results for amplitudes where all gluons have identical helicity, and amplitudes with one gluon of opposite…
In this short note we discuss ordinary differential equations which linearize upon one (or more) differentiations. Although the subject is fairly elementary, equations of this type arise naturally in the context of integrable systems.
I give simple elementary proofs for some well-known Hankel determinants and their q-analogues.
The methods of approximation, regularization and smoothing of trigonometric interpolation splines are considered in the paper. It is shown that trigonometric splines can be considered from two points of view - as a trigonometric Fourier…
A worldline with a time-independent spectrum is called stationary. Such worldlines are arguably the most simple motions in physics. Barring the trivially static motion, the non-trivial worldlines are uniformly accelerated. As such, a point…
It is well known that one can find a rational normal curve in $\mathbb P^n$ through $n+3$ general points. We prove a generalization of this to higher dimensional varieties, showing that smooth varieties of minimal degree can be interpolated…
General equations for the calculation of amplitudes are presented. As an illustration of application of proposed formulae we calculate electron-electron scattering amplitudes.
We consider quasi-interpolation with a main application in radial basis function approximations and compression in this article. Constructing and using these quasi-interpolants, we consider wavelet and compression-type approximations from…
We treat interpolation for various logics.
In this paper we consider the approximation of a function by its interpolating multilinear spline and the approximation of its derivatives by the derivatives of the corresponding spline. We derive formulas for the uniform approximation…
A modeling methodology and matrix formalism is presented that permits analysis of arbitrarily complex interferometric waveguide systems, including polarization and backreflection effects. Considerable improvement results from separation of…