The phenomenology of primordial black hole (PBH) physics and the associated PBH abundance constraints can be used to probe early universe. In this work, we investigate formation during standard radiation-dominated era by studying effect an $F(R)$ modified gravity phase with a bouncing behavior which is introduced avoid initial spacetime singularity problem. particular, calculate energy density ...

Assume that $(N,L)$, is a pair of finite dimensional nilpotent Lie algebras, in which $L$ is non-abelian and $N$ is an ideal in $L$ and also $mathcal{M}(N,L)$ is the Schur multiplier of the pair $(N,L)$. Motivated by characterization of the pairs $(N,L)$ of finite dimensional nilpotent Lie algebras by their Schur multipliers (Arabyani, et al. 2014) we prove some properties of a pair of nilpoten...

Abstract We construct a Fock model of the minimal representation exceptional Lie supergroup $${\mathbb {D}}(2,1; \alpha )$$ D ( 2 , 1 ; α ) . Explicit expressions for a...

‎in this paper‎, ‎we introduce the structure of a groupoid associated to a vector field‎ ‎on a smooth manifold‎. ‎we show that in the case of the $1$-dimensional manifolds‎, ‎our‎ ‎groupoid has a‎ ‎smooth structure such that makes it into a lie groupoid‎. ‎using this approach‎, ‎we associated to‎ ‎every vector field an equivalence‎ ‎relation on the lie algebra of all vector fields on the smooth...

We have identified the first gene lying on the centromeric side of the alpha-globin gene cluster on human 16p13.3. The gene, called 16pHQG;16 (HGMW-approved symbol LUC7L), is widely transcribed and lies in the opposite orientation with respect to the alpha-globin genes. This gene may represent a mammalian heterochromatic gene, encoding a putative RNA-binding protein similar to the yeast Luc7p s...

In the present paper, we perform a sub-Planckian quantum mode analysis of linear cosmological perturbation in inflaton field over classical quasi de-Siter metric background by dynamical horizon exit (DHE) method. this way, probe inflationary regime quintessential $\alpha$-attractor model analysing COBE/Planck normalized power spectra, spectral indices, tensor to scalar ratio, number e-folds, ru...

In this article, using the definitions of central series and nilpotency in the Lie algebras, we give some results similar to the works of Hulse and Lennox in 1976 and Hekster in 1986. Finally we will prove that every non trivial ideal of a nilpotent Lie algebra nontrivially intersects with the centre of Lie algebra, which is similar to Philip Hall's result in the group theory.

Let X be a normal variety endowed with an algebraic torus action. An additive group action $\alpha$ on is called vertical if general orbit of contained in the closure and image normalizes Aut(X). Our first result this paper classification actions under assumption that proper over affine variety. Then we establish criterion as to when infinitesimal generators finite collection generate finite-di...

Let G be a finite group, and ? nontrivial character of G. The McKay graph $${\cal M}\left({G,\alpha } \right)$$ has the irreducible characters as vertices, with an edge from ?1 to ?2 if is constituent ??1. We study diameters graphs for simple groups Lie type. show that any ?, diameter bounded by quadratic function rank, obtain much stronger bounds = PSLn(q) or PSUn(q).