The goal of this paper is to demonstrate how the internal symmetry of the N-body celestial-mechanics problem can be exploited in orbit calculation. We start with summarising research reported in (Efroimsky 2002, 2003; Newman & Efroimsky 2003; Efroimsky & Goldreich 2003) and develop its application to planetary equations in non-inertial frames. This class of problems is treated by the variationo...

An analysis is given for a class of nonconforming Lagrange-type finite elements which have been successfully utilized to approximate the solution of a variational problem modeling the deformation of martensitic crystals with microstructure. These elements were first proposed and analyzed in 1992 by Rannacher and Turek for the Stokes equation. Our analysis highlights the features of these elemen...

We study the small-scale topology of dynamical phenomena in the quiet-sun internetwork atmosphere, using short-duration Fourier analysis of high-resolution filtergram sequences to obtain statistical estimates for the co-location probability of different fine-structure elements and wave modes. In this initial paper we concentrate on the topology of shortduration Fourier amplitude maps for the ph...

We describe in this work the numerical treatment of the Filament-Based LamellipodiumModel (FBLM). This model is a two-phase two-dimensional continuum model, describing the dynamics of two interacting families of locally parallel F-actin filaments. It includes, among others, the bending stiffness of the filaments, adhesion to the substrate, and the cross-links connecting the two families. The nu...

We investigate Fourier multipliers on the compact dual of arbitrary discrete groups. Our main result is a Hörmander-Mihlin multiplier theorem for finite-dimensional cocycles with optimal smoothness condition. We also find Littlewood-Paley type inequalities in group von Neumann algebras, prove Lp estimates for noncommutative Riesz transforms and characterize L∞ → BMO boundedness for radial Fouri...

Models of texture segregation frequently feature two processing mechanisms: simple, linear channels (1st-order, Fourier mechanisms) and complex channels (2nd-order, non-Fourier mechanisms). Using texture patterns designed to segregate primarily as a result of activity in one set of channels or the other, we employed the method of cued response to obtain speed-accuracy tradeoff (SAT) functions m...

Numerical theory provides the basis for quantification on the accuracy and reliability of a FEM solution by error estimates on the FEM error vs. the mesh spacing of the FEM mesh. This paper presents techniques needed in COMSOL 5.1 to perform computational studies for an elliptic test problem in two and three space dimensions that demonstrate this theory by computing the convergence order of the...