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The simulation proposes that the cylindrical cavity around a circular light source can decreases the divergence angle without changing the emission energy and source size. This result can provide a way to reduce the etendue of the light…

In this article, we prove a theorem comparing the dihedral angles of simplices in the hyperbolic, spherical and Euclidean geometries.

The shape of a liquid surface bounded by an acute or obtuse planar angular sector is considered by using classical analysis methods. For acute angular sectors the two principal curvatures are of the order of the (fixed) mean curvature. But…

We extend to higher order a recently published method for calculating the deflection angle of light in a general static and spherically symmetric metric. Since the method is convergent we obtain very accurate analytical expressions that we…

In this work we consider the method of non-linear boundary integral equation for solving numerically the inverse scattering problem of obliquely incident electromagnetic waves by a penetrable homogeneous cylinder in three dimensions. We…

The combined source integral equation (CSIE) for the electric field on the surface of a perfect electrically conducting scatterer can be discretized very accurately with lowest-order Rao-Wilton-Glisson basis and testing functions if the…

Symmetric elliptic integrals, which have been used as replacements for Legendre's integrals in recent integral tables and computer codes, are homogeneous functions of three or four variables. When some of the variables are much larger than…

Let $G$ be a planar graph and let $C$ be a cycle in $G$. Inside of each finite face of $G$, we write down the number of edges of that face which belong to $C$. This is the signature of $C$ in $G$. The notion of a signature arises naturally…

In this paper we define the notion of infinite or bounded fibre-like geodesic cylinder in $\widetilde{\mathbf{S}\mathbf{L}_2\mathbf{R}}$ space, develop a method to determine its volume and total surface area. We prove that the common part…

In this article, we determine the existing condition of cylinders in smooth minimal geometrically rational surfaces over a perfect field. Furthermore, we show that for any birational map between smooth projective surfaces, one contains a…

We study the contact angle hysteresis and morphology changes of a liquid drop sitting on a solid substrate inclined with respect to the horizontal at an angle $\alpha$. This one is always smaller than the critical one, $\alpha_{crit}$,…

There has been recent work using Shape Theory to answer the longstanding and conceptually interesting problem of what is the probability that a triangle is obtuse. This is resolved by three kissing cap-circles of rightness being realized on…

Integral representations are derived for the parabolic cylinder functions $U(a,x)$, $V(a,x)$ and $W(a,x)$ and their derivatives. The new integrals will be used in numerical algorithms based on quadrature. They follow from contour integrals…

In this paper we show explicit and direct relations between the expected quantities and the observed quantities for the components of Galactic superluminal sources. Basic formulas for calculating the real speed and the angle to the line of…

A problem of scattering by a Dirichlet right angle on a discrete square lattice is studied. The waves are governed by a discrete Helmholtz equation. The solution is looked for in the form of the Sommerfeld integral. The Sommerfeld…

We give a new perspective on the Lorentzian OPE inversion formula of arXiv:1703.00278, building on arXiv:2302.06469. We introduce an ``auxiliary'' fourpoint function that can be related to the traditionally defined ones via a Radon…

We investigate the problem of determining the shape of a rotating celestial object - e.g., a comet or an asteroid - under its own gravitational field. More specifically, we consider an object symmetric with respect to one axis - such as a…

We write down estimates for the surface area, and more generally, integral mean curvatures of an ellipsoid E in n-dimensional Euclidean space in terms of the lengths of the major semi-axes. We give applications to estimating the area of…

In a central force system the angle between two successive passages of a body through pericenters is called the apsidal angle. In this paper we prove that for central forces of the form $f(r)\sim \lambda r^{-(\alpha+1)}$ with $\alpha<2$ the…

We provide a sharp and optimal generic bound for the angle of the sectorial form associated to a non-symmetric second-order elliptic differential operator with various boundary conditions. Consequently this gives an, in general, sharper…