A Note on Intuitionistic Fuzzy Hypervector Spaces

The notion of Intuitionistic fuzzy hypervector space has been generalized and a few basic properties on this concept are studied. It has been shown that the intersection and union of an arbitrary family of Intuitionistic fuzzy hypervector spaces are also Intuitionistic fuzzy hypervector space. Lastly, the notion of a linear transformation on a hypervector space is introduced and established an important theorem relative to Intuitionistic fuzzy hypervector spaces.Comment: 13 page

A Note on Hypervector Spaces

The main aim of this paper is to generalize the concept of vector space by the hyperstructure. We generalize some definitions such as hypersubspaces, linear combination, Hamel basis, linearly dependence and linearly independence. A few important results like deletion theorem, extension theorem, dimension theorem have been established in this hypervector space.Comment: 17 page

Non-Hermitian Quantum Mechanics with Minimal Length Uncertainty

We study non-Hermitian quantum mechanics in the presence of a minimal length. In particular we obtain exact solutions of a non-Hermitian displaced harmonic oscillator and the Swanson model with minimal length uncertainty. The spectrum in both the cases are found to be real. It is also shown that the models are $\eta$ pseudo-Hermitian and the metric operator is found explicitly in both the cases

Cosmological magnetic fields from nonlinear effects

In the standard cosmological model, magnetic fields and vorticity are generated during the radiation era via second-order density perturbations. In order to clarify the complicated physics of this second-order magnetogenesis, we use a covariant approach and present the electromagneto-dynamical equations in the fully nonlinear regime. We use the tight-coupling approximation to analyze Thomson and Coulomb scattering. At the zero-order limit of exact tight-coupling, we show that the vorticity is zero and no magnetogenesis takes place at any nonlinear order. We show that magnetogenesis also fails at all orders if either protons or electrons have the same velocity as the radiation, and momentum transfer is neglected. At first-order in the tight-coupling approximation, magnetic fields and vorticity still cannot be generated even via nonlinear effects. However, at second-order both of them are generated, and we derive a closed set of nonlinear evolution equations that governs this generation