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The axis tilt of light beam in optical system would introduce the dispersion of orbital angular momentum (OAM) spectrum. To deal with it, a two-step method is proposed and demonstrated. First, the tilt angle of optical axis is identified…
A new analytical method for the conformal mapping of a rectangular heptagon with a straight angle at infinity to a half plane and back is proposed. The method is based on the observation that SC integral in this case is an abelian integral…
Practical methods for quantitative analysis of radial and angular coordinates of leafy organs of vascular plants are presented and applied to published phyllotactic patterns of various real systems from young leaves on a shoot tip to…
High-efficient direct numerical methods are currently in demand for optimization procedures in the fields of both conventional diffractive and metasurface optics. With a view of extending the scope of application of the previously proposed…
Observations of non-random distribution of galaxies with opposite spin directions have recently attracted considerable attention. Here, a method for identifying cosine-dependence in a dataset of galaxies annotated by their spin directions…
Contour integration is a crucial technique in many numeric methods of interest in physics ranging from differentiation to evaluating functions of matrices. It is often important to determine whether a given contour contains any poles or…
We present a semi-analytic calculation of the integrated double-emission eikonal function of two massive emitters whose momenta are at an arbitrary angle to each other. This result is needed for extending the nested soft-collinear…
Oriented circular cylinders in an opaque medium are used to represent certain microstructural objects in steel. The opaque medium is sliced parallel to the cylinder axes of symmetry and the cut-plane contains the observable rectangular…
Starting with just the assumption of uniformly distributed orbital orientations, we derive expressions for the distributions of the Keplerian orbital elements as functions of arbitrary distributions of eccentricity and semi-major axis. We…
We provide a complete description of the angular distribution of gluons in a medium-induced QCD cascade. We identify two components in the distribution, a soft component dominated by soft multiple scatterings, and a hard component dominated…
Partially coherent electromagnetic sources with cylindrical symmetry and infinite extent radiating outwards are introduced. Their $3\times3$ cross-spectral density matrix is given through expansions of the field components in terms of basis…
In this tutorial paper, we formulate a two-dimensional integral-equation based method of moments approach for numerically computing the electromagnetic fields scattered from an azimuthally-rough dielectric cylinder or an axially-rough…
We study polarized cylinders in certain rational surfaces arising from blow-ups of weighted projective planes. In particular, we consider the surfaces obtained by blowing up $m+4$ points in general position on the weighted projective plane…
We use polyhedral product models to analyse the structure of the commutator subgroup of a right-angled Artin group. In particular, we provide a minimal set of generators for the commutator subgroup, consisting of special iterated…
We fully characterize orthogonal projections of infinite right circular (round) cones in real Hilbert spaces. Another interpretation is that, given two vectors in a real Hilbert space, we establish the optimal estimate on the angle between…
We consider the scattering problem governed by the Helmholtz equation with inhomogeneity in both `conductivity' in the divergence form and `potential' in the lower order term. The support of the inhomogeneity is assumed to contain a convex…
Researchers routinely characterize optical samples by computing the scattering cross-section. However, the experimental determination of this magnitude requires the measurement and integration of the components of the scattered field in all…
The knowledge of the isotropic correlation function of a plane figure is useful to determine the correlation function of the cylinders having the plane figure as right-section and a given height as well as to analyze the out of plane…
The study of "random segments" is a classic issue in geometrical probability, whose complexity depends on how it is defined. But in apparently simple models, the random behavior is not immediate. In the present manuscript the following…
We present an algorithm of finding numerical solutions of pulsar equation. The problem of finding the solutions was reduced to finding expansion coefficients of the source term of the equation in a base of orthogo- nal functions defined on…