Consider a random three-coordinate lattice of spherical topology having 2v vertices and being densely covered by a single closed, self-avoiding walk, i.e. being equipped with a Hamiltonian cycle. We determine the number of such objects as a function of v. Furthermore we express the partition function of the corresponding statistical model as an elliptic integral. PACS codes: 05.20.y, 04.60.Nc, ...

• The LWE error distribution Φαq is a continuous one-dimensional Gaussian, which is a projection of the spherical n-dimensional distribution Dαq onto its first coordinate. • The distribution Dαq is smooth in the following sense: If L is some lattice (or coset of a lattice) with λn(L) αq, then if we choose ~x← DL,r and ~y ← Ds such that r2 + s2 = (αq)2 then the induced distribution on ~x+ ~y is ...

This paper describes error compensation methods for parallel kinematics machines (PKMs). First, joint errors and link deformations caused by external forces and heat are discussed. Because a linear scale unit is connected to each spherical joint located at both ends of an extensible limb through two rods, the scale unit can measure not only displacement of the prismatic joint but also the limb’...

The paper compares the features of three extensions of the notion of the Gabor’s analytic signal for 2-D signals: the analytic signals with single-quadrant spectra (AS), the quaternionic signals with quaternionic single-quadrant spectra (QS) and the monogenic signals (MS). A good platform of comparison are the polar representations of the AS and the QS and the spherical coordinate representatio...

A problem of propagation of very long planetary waves in the upper atmosphere of the Earth is investigated. A new exact solution of the magnetohydrodynamics equations of the ionosphere in the spherical coordinate system is found taking into account the Earth’s rotation and geomagnetic field. The general dispersion equation for the planetary waves in the E and F regions of the ionosphere is deri...

Abstract. In this work we study the influence of expanding spherical impulsive gravitational waves on geodesics in spacetimes of constant curvature. In the case of a non-zero cosmological constant, for general C1 geodesic in continuous coordinate system, we derive the refraction formulae which identify the positions and the velocity vector inclinations of free test particles on both sides of th...

The exact path integration for a family of maximally super-integrable systems generalizing the hydrogen atom in the n-dimensional Euclidean space is presented. The Green’s function is calculated in parabolic rotational and spherical coordinate systems. The energy spectrum and the correctly normalized wave functions of the bound states are obtained from the poles of the Green’s function and thei...

Three types of spherical splines are presented as developed in the recent literature on constructive approximation, with a particular view towards global (and local) geopotential modeling. These are the tensor-product splines formed from polynomial and trigonometric B-splines, the spherical splines constructed from radial basis functions, and the spherical splines based on homogeneous Bernstein...

We consider, in a superspace, new operator dependent noncommutative (NC) geometries of the nonlinear quantum Hall limit related to classes of f -deformed Landau operators in the spherical harmonic well. Different NC coordinate algebras are determined using unitary representation spaces of Fock-Heisenberg tensored algebras and of the Schwinger-Fock realisation of the su(1, 1) Lie algebra. A redu...