A dual-halo dual-dielectric triple-material cylindrical-gate-all-around/surrounding gate (DH-DD-TM-CGAA/SG) MOSFET has been proposed and an analytical model for the transconductance-to-drain current ratio (TDCR) has been developed. It is verified that incorporation of dual-halo with dual-dielectric and triple-material results in enhancing the device performance in terms of improved TDCR. The ef...

Let be a ring with identity. Recall that submodule of left -module is called strongly essential if for any nonzero subset , there such i.e., . This paper introduces class submodules se-closed, where se-closed it has no proper extensions inside We show by an example the intersection two may not se-closed. say module have se-Closed Intersection Property, briefly se-CIP, every again in Several cha...

Let G be a finite group, and let Ω := {t ∈ G | t = 1}. Then Ω is a G-set under conjugation. Let k be an algebraically closed field of characteristic 2. It is shown that each projective indecomposable summand of the G-permutation module kΩ is irreducible and self-dual, whence it belongs to a real 2-block of defect zero. This, together with the fact that each irreducible kG-module that belongs to...

Now choose a Borel subgroup B in G and a maximal torus T in B so that, if B is the opposite Borel subgroup, then B ∩ H and B ∩ H are a Borel subgroups in H and T ∩H is a maximal torus in H . We follow the convention that the roots of B are positive. If λ ∈ X(T ), then indGB(−λ) is the dual Weyl module ∇G(λ ) with highest weight λ = −w0λ and lowest weight −λ. Its dual is the Weyl module ∆G(λ). I...

For each reductive algebraic group G we introduce and study unipotent bicrystals which serve as a regular version of birational geometric and unipotent crystals introduced earlier by the authors. The framework of unipotent bicrystals allows, on the one hand, to study systematically such varieties as Bruhat cells in G and their convolution products and, on the other hand, to give a new construct...