It is shown that a simple breaking of the subnuclear democracy leads to a successful description of the mixing between the second and third family. In the lepton channel the ν µ − ν τ oscillations are expected to be described by a mixing angle of 2.65 • which might be observed soon in neutrino experiments.

‎In this work‎, ‎a regular polygon with $n$ sides is described by a periodic (circular) sequence with period $n$‎. ‎Each element of the sequence represents a vertex of the polygon‎. ‎Each symmetry of the polygon is the rotation of the polygon around the center-point and/or flipping around a symmetry axis‎. ‎Here each symmetry is considered as a system that takes an input circular sequence and g...

The advantages to study charge–symmetry breaking and especially the phenomenon of f0 −a0 mixing in nucleon–nucleon and deuteron–deuteron induced reactions are discussed.

The main physical result of this paper are exact analytical solutions of the heavenly equation, of importance in the general theory of relativity. These solutions are not invariant under any subgroup of the symmetry group of the equation. The main mathematical result is a new method of obtaining noninvariant solutions of partial differential equations with infinite dimensional symmetry groups. ...

Motivated by the recent work of Kachru-Vafa in string theory, we study in Part A of this paper, certain identities involving modular forms, hypergeometric series, and more generally series solutions to Fuchsian equations. The identity which arises in string theory is the simpliest of its kind. There are nontrivial generalizations of the identity which appear new. We give many such examples – al...

Fullerene chemistry is nowadays a well-established field of both theoretical and experimental investigations‎. This study considers the symmetry of small fullerenes cage C24 and C28‎. ‎Using PM3 program for C24 and C28 fullerenes, Oh and Td symmetry were confirmed, respectively‎. ‎ The mentioned algorithm to compute the automorphism group of these fullerenes with connectivity and geometry of th...

In this paper, we give the sharp estimates for the degree of symmetry and the semi-simple degree of symmetry of certain four dimensional fiber bundles by virtue of the rigidity theorem of harmonic maps due to Schoen and Yau. As a corollary of this estimate, we compute the degree of symmetry and the semi-simple degree of symmetry of CP 2 × V , where V is closed smooth manifold admitting a real a...

Using the theory of the symmetry groups for PDEs of order two ([7], [17], [20]), one finds the symmetry group G associated to Ţiţeica surfaces PDE. One proves that Monge-Ampère-Ţiţeica PDE which is invariant with respect to G, where G is the maximal solvable subgroup of the symmetry group G, is just the PDE of Ţiţeica surfaces. One studies the inverse problem and one shows that the Ţiţeica surf...

Hyers-Ulam-Rassias stability have been studied in the contexts of several areas of mathematics. The concept of fuzziness and its extensions have been introduced to almost all branches of mathematics in recent times.Here we define the cubic functional equation in 2-variables and establish that Hyers-Ulam-Rassias stability holds for such equations in intuitionistic fuzzy Banach spaces.