To intelligently and effectively use crystallographic databases, mathematical and computer tools are required that can elucidate diverse types of intra- and interlattice relationships. Two such tools are the normalized reduced form and normalized reduced cell. Practical experience has revealed that the first tool-the normalized reduced form-is very helpful in establishing lattice metric symmetr...

Chiral symmetry breaking in a non-local Nambu-Jona-Lasinio like 4-fermi model, derived from the intersecting brane model of Sakai and Sugimoto in the weak coupling limit, was found to occur only above a critical value of the coupling. Numerical investigations showed, contrary to what had been suggested in the literature, that this feature persists even when the radius of the circle on which the...

In this article, we consider a small SO(2)-equivariant perturbation of a reaction-diffusion system on the sphere, which is equivariant with respect to the group SO(3) of all rigid rotations. We consider a normally hyperbolic SO(3)-group orbit of a rotating wave on the sphere that persists to a normally hyperbolic SO(2)-invariant manifold M(ε). We investigate the effects of this forced symmetry ...

Analogies have had and continue to have an important role in the development of theoretical physics. They may start from similarities of physical concepts followed by similarities in the mathematical formalization or it may be a purely mathematical aspect to suggest the development of analogous physical concepts. More often a subtle nonobvious interplay between these levels is involved. In this...

In recent years, some investigations have been carried out to examine the assumptions like stationarity, symmetry and separability of spatio-temporal covariance function which would considerably simplify fitting a valid covariance model to the data by parametric and nonparametric methods. In this article, assuming a Gaussian random field, we consider the likelihood ratio separability test, a va...

In this paper we discuss the implementation of methods to derive 3D Symmetry Sets, given a parameterized shape, as well as an unorganized point cloud. It presents a geometric method to derive the Symmetry Set, that is an extension of the one given in [6]. Although the mathematics is a simple extension of the 2D case, the visualization, numerical computations and their stability are much more co...

We classify from Lie symmetry standpoint the hyperbolic heat equation with temperature-dependent medium properties. We prove that the hyperbolic heat equation may admit a two-, three-, fouror infinitedimensional symmetry Lie algebra depending on the functional form of density, thermal conductivity, and specific heat. The last possibility corresponds to exactly linearizable hyperbolic heat equat...

We develop a systematic approach to confinement in N = 1 supersymmetric theories. We identify simple necessary conditions for theories to confine without chiral symmetry breaking and to generate a superpotential non-perturbatively (sconfine). Applying these conditions we identify all N = 1 theories with a single gauge group and no tree-level superpotential which s-confine. We give a complete li...

Group theoretical arguments seem to indicate the discrete symmetry S4 as the minimal flavor symmetry compatible with tribimaximal neutrino mixing. We prove in a model-independent way that indeed S4 can realize exact tribimaximal mixing through different symmetry breaking patterns. We present two models in which lepton tribimaximal mixing is realized in different ways and for each one we discuss...

I study the conceptual framework of protein folding considering an exactly solvable model — the Rubik’s magic snake model. I discuss the mathematical representation of the model, the model Levinthal paradox, the non-unique compact folded structure, the function of the chain, the ground state energy, the commensurability between the folded structure and the potential sequence, the relationship b...