The Al-Salam & Carlitz polynomials are q-generalizations of the classical Hermite polynomials. Multivariable generalizations of these polynomials are introduced via a generating function involving a multivariable hypergeometric function which is the q-analogue of the type-A Dunkl integral kernel. An eigenoperator is established for these polynomials and this is used to prove orthogonality with ...

In supersymmetric theories with extra dimensions, the Higgs and matter fields can be part of the gauge multiplet, so that the Yukawa interactions can arise from the gauge interactions. This leads to the possibility of gauge–Yukawa coupling unification, gi = yf , in the effective four dimensional theory after the initial gauge symmetry and the supersymmetry are broken upon orbifold compactificat...

This research was initiated with the objective of investigating the potential of constructed wetlands covered by duckweeds and connected to the branches of Bahr Hadous drain on its salinity, and subsequently, its discharge into El-Salam canal. Primarily, literature was reviewed. Data was assembled and analysed. The water quality model QUAL2K was used in this investigation. Moreover, electrical ...

An anomaly free model of strong and electro-weak interactions involving leptons and quarks in the SU(4) x Slam x U(1) gauge theory is C constructed. After spontaneous symmetry breaking, it reduces itself into the quantum chromodynamics for strong interactions and a broken SU(3) x U(1) model for electro-weak interactions. As a limiting case it gives the same results as those of the Weinberg-Sala...

The Al-Salam & Carlitz polynomials are q-generalizations of the classical Hermite polynomials. Multivariable generalizations of these polynomials are introduced via a generating function involving a multivariable hypergeometric function which is the q-analogue of the type-A Dunkl integral kernel. An eigenoperator is established for these polynomials and this is used to prove orthogonality with ...

The renormalization group equations (RGEs) of the mass matrices of quarks and leptons in a SO(10) model with two Higgs scalars in the Yukawa coupling are studied. This model is the minimal model of SUSY and non-SUSY SO(10) GUT which can reproduce all the experimental data. Non-SUSY SO(10) GUT model has the intermediate energy phase, Pati-Salam phase, and passes through the symmetry breaking pat...

We explore the possibility of embedding the Pati–Salam model in the context of Type I brane models. We study a generic model with U(4) C × U(2) L × U(2) R gauge symmetry and matter fields compatible with a Type I brane configuration. Examining the anomaly cancellation conditions of the surplus abelian symmetries we find an alternative hypercharge embedding that is compatible with a low string/b...