I present several applications of the Dirac inequality to determination isolated unitary representations and associated “spectral gaps” in case unramified principal series. The method works particularly well order attach irreducible large nilpotent orbits (e.g., regular, subregular) Langlands dual complex Lie algebra. results could be viewed as a p-adic analogue Salamanca-Riba’s classification ...

Following Birkhoff and von Neumann, quantum logic has traditionally been based on the lattice of closed linear subspaces of some Hilbert space, or, more generally, on the lattice of projections in a von Neumann algebra A. Unfortunately, the logical interpretation of these lattices is impaired by their nondistributivity and by various other problems. We show that a possible resolution of these d...

Let $R$ be a commutative ring and let $I$ be an ideal of $R$. In this paper, we will introduce the notions of 2-absorbing $I$-prime and 2-absorbing $I$-second submodules of an $R$-module $M$ as a generalization of 2-absorbing and strongly 2-absorbing second submodules of $M$ and explore some basic properties of these classes of modules.

Let Γ denote a distance-regular graph with diameter D ≥ 3. Assume Γ has classical parameters (D, b, α, β) with b < −1. Let X denote the vertex set of Γ and let A ∈ MatX(C) denote the adjacency matrix of Γ. Fix x ∈ X and let A ∈ MatX(C) denote the corresponding dual adjacency matrix. Let T denote the subalgebra of MatX(C) generated by A,A . We call T the Terwilliger algebra of Γ with respect to ...

We introduce and study the concept of $alpha $-semi short modules.Using this concept we extend some of the basic results of $alpha $-short modules to $alpha $-semi short modules.We observe that if $M$ is an $alpha $-semi short module then the dual perfect dimension of $M$ is $alpha $ or $alpha +1$.%In particular, if a semiprime ring $R$ is $alpha $-semi short as an $R$-module, then its Noetheri...

In this paper, a system for efficient removal of carbon dioxide by hollow fiber membranes is proposed. The system is compact, and it is very useful for application in the offshore energy industries. In particular, it is used to removing CO2 from the exhaust of power generation facilities on offshore platforms.The proposed dual membrane contactor contains two types of membranes (polypropylene me...

Let $R$ be a commutative ring with identity and let $M$ be an $R$-module. In this paper, we will introduce the secondary radical of a submodule $N$ of $M$ as the sum of all secondary submodules of $M$ contained in $N$, denoted by $sec^*(N)$, and explore the related properties. We will show that this class of modules contains the family of second radicals properly and can be regarded as a dual o...