Introduction. Let Q be an open, convex subset of R^. At almost every point x of dQ, with respect to surface measure da, there is a unique outer unit normal 6. The map g: dQ -* S given by g(x) = 9 and defined almost everywhere is called the Gauss map. (S, n = N 1, is the unit sphere in R^.) Suppose that the origin 0 belongs to Q. Harmonic measure for fit at 0 is the probability measure co such t...

Recently, Piri and Kumam [Fixed Point Theory and Applications 2014, 2014:210] improved concept of F -contraction and proved some Wardowski and Suzuki type …xed point results in metric spaces. The aim of this article is to de…ne generalized GF -contraction and establish Wardowski and Suzuki type …xed point results in metric and ordered metric spaces and derive main results of Piri et al. as coro...

We shall consider slightly more general problems. Namely, we shall investigate the existence of continuous: piecewise monotone, piecewise strictly monotone, and piecewise linear n-th roots of interval maps which have a continuous n-th root. Here by an n-th root of f we mean a map g such that f = g (g is the n-th iterate of g). A continuous map f : I → J , where I, J are closed intervals, is pie...

Saccharomyces cerevisiae mating pheromones trigger dissociation of a heterotrimeric G protein (G ) into G guanosine triphosphate (GTP) and G . The G dimer regulates both mitogen-activated protein (MAP) kinase cascade signaling and cell polarization. Here, by independently activating the MAP kinase pathway, we studied the polarity role of G in isolation from its signaling role. MAP kinase signal...

We prove that for every proper Hamiltonian action of a Lie group G in finite dimensions the momentum map is locally G-open relative to its image (i.e. images of G-invariant open sets are open). As an application we deduce that in a Hamiltonian system with continuous Hamiltonian symmetries, extremal relative equilibria persist for every perturbation of the value of the momentum map, provided the...

Abstract: The problem is to create a hybrid periodic motion, reminiscent of walking, for a model of an underactuated biped robot. We show how to construct a transverse linearization analytically and how to use it for stability analysis and for design of an exponentially orbitally stabilizing controller. In doing so, we extend a technique recently developed for continuous-time controlled mechani...

The variational inclusion of spin-orbit coupling in self-consistent field (SCF) calculations requires a generalised two-component framework, which permits the single-determinant wave function to completely break spin symmetry. individual components molecular g-tensor are commonly obtained from separate SCF solutions that align magnetic moment along one three principal tensor axes. However, this...

Let G be a non-elementary word-hyperbolic group acting as a convergence group on a compact metrizable space Z so that there exists a continuous G-equivariant map i : ∂G → Z, which we call a Cannon-Thurston map. We obtain two characterizations (a dynamical one and a geometric one) of conical limit points in Z in terms of their pre-images under the CannonThurston map i. As an application we prove...