Related papers: Analytical calculation of the solid angle defined …
The wavefronts from a point source in a solid with cubic symmetry are examined with particular attention paid to the contribution from the conical points of the slowness surface. An asymptotic solution is developed that is uniform across…
A fast and practical method is described for calculating the microlensed flux variance of an arbitrary source by uncorrelated stars. The required inputs are the mean convergence and shear due to the smoothed potential of the lensing galaxy,…
We propose an orthogonal series density estimator for complex surveys, where samples are neither independent nor identically distributed. The proposed estimator is proved to be design-unbiased and asymptotically design-consistent. The…
A simple model for the angular dependent interaction between C_60 molecules on the face-centered cubic lattice is proposed. The bifurcations of the solutions of the nonlinear integral equations for orientational distribution functions in…
Every polyhedral cone can be described either by its facets or by its extreme rays. Computation of one description from the other is a problem that can be very complex, i.e. one encounter the combinatorial explosion. We present here several…
We provide an elementary derivation of an orthogonal coordinate system for boundary layers around evolving smooth surfaces and curves based on the signed-distance function. We go beyond previous works on the signed-distance function and…
We study scattering for the linear Helmholtz operator in two dimensions and develop a technique, which can be used to ascertain scattering of a given incident wave from very regular inhomogeneities. This technique is then applied to a…
Calculating by analytical theory the deformation of finite-sized elastic bodies in response to internally applied forces is a challenge. Here, we derive explicit analytical expressions for the amplitudes of modes of surface deformation of a…
We suggest a new approach to Artin's constant that leads to its representation as an infinite sum divided by another infinite sum. The same approach works well for Stephens' constant and higher rank Artin's constants. The main results are…
We present some formulae for the moments of inertia of homogeneous solids of revolution in terms of the functions that generate the solids. The development of these expressions exploits the cylindrical symmetry of these objects, and avoids…
We classify the dihedral edge-to-edge tilings of the sphere by regular polygons and quadrilaterals with equal opposite edges (edge configuration xyxy).
In this paper we compute the distributions of various markings on smooth cubic surfaces defined over the finite field $\mathbb{F}_q$, for example the distribution of pairs of points, `tritangents' or `double sixes'. We also compute the…
Giving a new form of the vortex mode equation by a proper change of parameter, our aim is to analyze the point and contact symmetries of the new equation. Fundamental invariants and a form of general solutions of point transformations along…
Let $I \subseteq \R$ be an open interval, $f : I \to \R$ a strictly positive function and denote by $\E^2$ the Euclidean plane. We classify all surfaces in the warped product manifold $I \times_f \E^2$ for which the unit normal makes a…
We propose and demonstrate a computational imaging technique that uses structured illumination based on a two-dimensional discrete cosine transform to perform imaging with a single-pixel detector. A scene is illuminated by a projector with…
The principle of the momentum computed tomography of charged particles is presented. It may be useful for momentum spectroscopy of various beam-matter interactions, especially when very intense beams are involved. It is able to collect the…
A method to calculate particle fluxes applicable in most of the spectroscopy techniques is described. Flux intensities of backscattered or absorbed electrons and emitted photons are calculated using a method of convergence to solve the…
The expression for the total angular momentum carried by a laser optical vortex beam, splits, in the paraxial approximation, into two terms which seem to represent orbital and spin angular momentum respectively. There are, however, two very…
Objective: To derive a closed-form analytical solution to the swing equation describing the power system dynamics, which is a nonlinear second order differential equation. Existing challenges: No analytical solution to the swing equation…
A simple model for the estimation of the light yield of a scintillation detector is developed under general assumptions and relying exclusively on the knowledge of its optical properties. The model allows to easily incorporate effects…