Related papers: The Bohr Radius for an Elliptic Condenser
We study numerical conformal mapping of multiply connected planar domains with boundaries consisting of unions of finitely many circular arcs, so called polycircular domains. We compute the conformal capacities of condensers defined by…
We explore the Bohr inequality involving the Fourier transforms of complex valued integrable and square integrable functions defined on a second countable compact topological group. We also investigate the connection of the Bohr phenomenon…
We introduce two explicit examples of polynomials orthogonal on the unit circle. Moments and the reflection coefficients are expressed in terms of Jacobi elliptic functions. We find explicit expression for these polynomials in terms of a…
A conformal factor in the Bohr model embeds Bohr space in six dimensions, revealing the $O(6)$ symmetry and its contraction to the $E(5)$ at infinity. Phenomenological consequences are discussed after the re-formulation of the Bohr…
We study numerical computation of conformal invariants of domains in the complex plane. In particular, we provide an algorithm for computing the conformal capacity of a condenser. The algorithm applies for wide kind of geometries: domains…
Our main result is that any real cubic algebraic number has a continued fraction expansion with polynomial coefficients. Some generalizations are mentioned.
The volume charge density for a conducting ellipsoid is expressed in simple geometrical terms, and then used to obtain the known surface charge density as well as the uniform charge per length along any principal axis. Corresponding results…
We derive an explicit formula for the volume of a regular simplex in the hyperbolic space of any dimension.
The formula for the area of a rhumb polygon, a polygon whose edges are rhumb lines on an ellipsoid of revolution, is derived and a method is given for computing the area accurately. This paper also points out that standard methods for…
We present lower bounds for the coefficients of Ehrhart polynomials of convex lattice polytopes in terms of their volume. Concerning the coefficients of the Ehrhart series of a lattice polytope we show that Hibi's lower bound is not true…
The manuscript provides formulas for the volume of a body defined by the intersection of a solid cone and a solid sphere as a function of the sphere radius, of the distance between cone apex and sphere center, and of the cone aperture…
We determine the Bohr radius for the class of all functions $f$ of the form $f(z)=\sum_{k=1}^\infty a_{kp+m} z^{kp+m}$ analytic in the unit disk $|z|<1$ and satisfy the condition $|f(z)|\le 1$ for all $|z|<1$. In particular, our result also…
This paper describes a method for the explicit reconstruction and visualization of various polarization ellipses from the intensities measured after a rotating polarizer. The state of polarization of a light beam is represented by the…
Using a mixture of classical and probabilistic techniques we investigate the convexity of solutions to the elliptic pde associated with a certain generalized Ornstein-Uhlenbeck process.
We establish derivative estimates of solution of elliptic system in narrow regions.
We consider the multilinear polytope defined as the convex hull of the set of binary points satisfying a collection of multilinear equations. The complexity of the facial structure of the multilinear polytope is closely related to the…
We derive easy-to-handle approximations for the polar gap electric field due to inertial frame dragging as derived by Harding & Muslimov 1998. A simple formula valid for polar gap height comparable to the polar cap radius is presented.
We compute the Hilbert coefficients of a graded module with pure resolution and discuss lower and upper bounds for these coefficients for arbitrary graded modules.
This letter describes a method for obtaining an explicit expression for the electrostatic energy of a charged elliptical infinitely thin disc. The charge distribution is assumed to be polynomial. Such explicit values for this energy are…
We use the Bohr-Sommerfeld quantization approach in the context of constituent quark models. This method provides, for the Cornell potential, analytical formulae for the energy spectra which closely approximate numerical exact calculations…