Following Ellis, [9], we investigate the notion of totally free crossed square and related squared complexes. It is shown how to interpret the information in a free simplicial group given with a choice of CW-basis, interms of the data for a totally free crossed square. Results of Ellis then apply to give a description in terms of tensor products of crossed modules. The paper ends with a purely ...

We explore the relations among quadratic modules, 2crossed modules, crossed squares and simplicial groups with Moore complex of length 2. Introduction Crossed modules defined by Whitehead, [23], are algebraic models of connected (weak homotopy) 2-types. Crossed squares as introduced by Loday and GuinWalery, [22], model connected 3-types. Crossed n-cubes model connected (n + 1)types, (cf. [21])....

A holomorphic quadratic differential on a hyperbolic Riemann surface has an associated measured foliation, which can be straightened to yield a measured geodesic lamination. On the other hand, a quadratic differential can be considered as the Schwarzian derivative of a CP1 structure, to which one can naturally associate another measured geodesic lamination (using grafting). We compare these two...

3. Elementary processes in QED Scattering amplitudes and the differential cross-section Kinematics of binary processes, decay rate of an unstable particle The scattering e− e → μ− μ, the square of the scattering amplitude Unpolarized scattering and its differential cross-section The scattering e− μ− → e− μ−, the square of the scattering amplitude Crossing symmetry, Mandelstam variables, crossed...

The problem of inserting a complex propagator in the crossed channel of the square diagram is considered. The propagator is spectrally represented and the square diagram with full propagator insertion is expressed as a spectral integral of square diagrams over an internal mass variable. The analytic properties of such diagrams in two complex variables, one internal mass and one external energy,...

A novel, compact, probe-fed microstrip patch antenna for operation in dual-polarization mode is proposed. The novel design is achieved by etching out a symmetric pattern of crossed slots from the surface of a square probe-fed patch. Reduction in patch size of up to 51% with respect to a traditional dual-polarized square patch operating at the same frequency is obtained. Results show linear pola...

Purpose: The present study aimed to investigate the effect of six weeks of Pilates exercises on upper and lower extremities function in middle-aged females with lower crossed syndrome. Methods: This study was a quasi-experimental research with pretest- post-test design. The participants were 30 females with lower crossed syndrome from Tiam Sport Club. They were selected using purposeful sampl...

In this paper, we present a generalization of the concept bimultiplication algebra by defining crossed modules in associative algebras. Using structure, construct actor module algebras, and obtain annihilators as kernel morphism from to its actor. Moreover, link between square, two-dimensional module.