We presented a family of finite elements that use a polynomial space augmented by certain matrix bubbles in [Math. Comp., 79 (2010), 1331–1349]. In this sequel, we exhibit a second family of elements that use the same matrix bubble. This second element uses a stress space smaller than the first, while maintaining the same space for rotations (which are the Lagrange multipliers corresponding to ...

Osteopathic physicians may use regional diagnostic rotation tests of the spine during physical examinations for patient evaluations. Clinical judgments of these responses relate to symmetry as a criterion for mobility. This first part of a two-part study reports the authors' investigation of regional ipsilateral myoelectric activity during responses to active and passive shoulder and trunk rota...

We investigate the role of symmetry as a possible origin of chaos in the nuclear shell model. For this purpose we disentangle purely geometrical effects due to spin and isospin coupling of the many–body states, from effects of the reduced two– body interaction. We compare a model without symmetry (the embedded two– body ensemble of random matrices) with the two–body random ensemble (TBRE) of th...

An unambiguous determination of the pairing electrons origination in copper oxide superconductors in necessary to understanding the origin of high-temperature superconductivity. Several years ago, several experiments have produced strong evidence for d-wave pairing symmetry. This result also rules out different from the symmetry in conventional superconductors. Using quantum chemical bond theor...

The related physical equations of linear elasticity are the equilibrium equation and the constitutive equation, which expresses a relation between the stress and strain tensors. This is a first-order partial differential system such that a least squares method based on a stress-displacement formulation can be used whose corresponding finite element approximation does not preserve the symmetry o...

In this paper, the region in which the structural system is situated is divided into four subregions, namely upper, lower, left and right subregions. The stiffness matrix of the entire system is then formed and using the existing direct symmetry and reverse symmetry, the relationships between the entries of the matrix are established. Examples are included to illustrate the steps of the method.