This article is to contribute to the classification of finite-dimensional complex pointed Hopf algebras with Weyl groups of E6, E7, F4, G2. Many papers are about the classification of finite dimensional pointed Hopf algebras, for example, [AS98, AS02, AS00, AS05, He06, AHS08, AG03, AFZ, AZ07, Gr00, Fa07, AF06, AF07, ZZC, ZC]. In these research ones need the centralizers and character tables of ...

In the present paper, we characterize all possible Hilbert functions of graded ideals in a polynomial ring whose regularity is smaller than or equal to d, where d is a positive integer. In addition, we prove the following result which is a generalization of Bigatti, Hulett and Pardue’s result: Let p ≥ 0 and d > 0 be integers. If the base field is a field of characteristic 0 and there is a grade...

This work presents emissive Cr(0), Mo(0) and W(0) complexes that contain a bidentate pyridyl-mesoionic carbene ligand CO coligands. These systems exhibit dual visible NIRII emission at room temperature represent milestone in the design of noble-metal-free NIR luminophores. The excited states were characterized by luminescence lifetime investigations step-scan FTIR spectroscopy, supported densit...

We prove that, for any > 0, there exist a constant C > 0 such that the interval [x, x + C √ x] contains numbers whose all prime factors are smaller than x √ e)+ .

Abstract An investigation about localized CP asymmetries for the processes of $${\bar{B}}_{s}^{0} \rightarrow \pi ^{+}\pi ^{-}\pi ^{0} (K^{0})$$ B ¯ s 0 → π</...