Lifting modules and their various generalizations as some main concepts in module theory have been studied and investigated extensively in recent decades. Some authors tried to present some homological aspects of lifting modules and -supplemented modules. In this work, we shall present a homological approach to -supplemented modules via fully invariant submodules. Lifting modules and H-suppleme...

Here H0 is the Hamiltonian for the nearest-neighbor coupled harmonic chain which consists of a one-dimensional lattice lZ with lattice constant l > 0 and a set of N+1 point particles of mass m > 0 distributed along the Euclidean line IR at positions jl + qj , j = 1, 2, . . . , N + 1. The momentum of the j-th particle is denoted by pj and the spring constant of this chain is mω 0. We assume now ...

The motion of an object (such as a wheel rotating) is seen as consistent independent of its position and size on the retina. Neurons in higher cortical visual areas respond to these global motion stimuli invariantly, but neurons in early cortical areas with small receptive fields cannot represent this motion, not only because of the aperture problem but also because they do not have invariant r...

We study complexified Harmonic Oscillator models in two and three dimensions. Our work is a generalization of the work of Smilga [4] who initiated the study of these Crypto-gauge invariant models that can be related to PT -symmetric models. We show that rotational symmetry in higher spatial dimensions naturally introduces more constraints, (in contrast to [4] where one deals with a single const...

We study critical invariant circles of several noble rotation numbers at the edge of break-up for an area-preserving map of the cylinder, which violates the twist condition. These circles admit essentially unique parametrizations by rotational coordinates. We present a high accuracy computation of about 107 Fourier coefficients. This allows us to compute the regularity of the conjugating maps a...

The equations of motion are coupled with a dynamical variable, referred to as twirler, which randomizes the angular momentum. The equations are time-reversal invariant, just as those for the standard Gaussian, Nosé-Hoover and configurational thermostats. The derivation of the basic equations is outlined. Test calculations are performed for the two-dimensional isotropic harmonic oscillator and f...

Disclinations, concave and convex, are the canonical point defects of twodimensional planar patterns in systems with translational and rotational symmetries. From these, all other point defects (vortices, dislocations, targets, saddles and handles) can be built. Moreover, handles, coupled concave–convex disclination pairs arise as instabilities, symmetry breaking events. The purpose of this art...

It is often assumed that primordial perturbations are statistically isotropic, which implies, among other properties, that their power spectrum is invariant under rotations. In this article, we test this assumption by placing bounds on deviations from rotational invariance of the primordial spectrum. Using five-year Wilkinson Microwave Anisotropy Probe cosmic microwave anisotropy maps, we set l...

An isothermal model on the standard two-dimension nine-velocity lattice (D2Q9) is proposed and analyzed. It originates from the thermal model with energy conservation introduced by N. I. Prasianakis and I. V. Karlin [Phys. Rev. E 76, 016702 (2007)]. The isothermal and the thermal equivalent models are tested through the simulation of the decay of a shear wave and of a temperature wave. Both are...

• New geometric vector modelling of SCARA robot. Definition independent parameters based on robot joints invariants. A direct identification method “Circle Point Analysis”. Improvement the accuracy a (mean transformation error less than 0.03 mm). final compared to first and second-order Denavit–Hartenberg geometrical model. This article introduces new modeling serial kinematic consistent with p...