We call a local vector lattice any vector lattice with a distinguished positive strong unit and having exactly one maximal ideal (its radical). We provide a short study of local vector lattices. In this regards, some characterizations of local vector lattices are given. For instance, we prove that a vector lattice with a distinguished strong unit is local if and only if it is clean with non no-...

in this paper, we prove some results on characterization of $varepsilon$-simultaneous approximations of downward sets in vector lattice banach spaces. also, we give some results about simultaneous approximations of normal sets.

in this paper, we prove some results on characterization of $varepsilon$-simultaneous approximations of downward sets in vector lattice banach spaces. also, we give some results about simultaneous approximations of normal sets.

In this paper we will construct a lattice-based public-key cryptosystem using non-commutative quaternion algebra, and since its lattice does not fully fit within Circular and Convolutional Modular Lattice (CCML), we prove it is arguably more secure than the existing lattice-based cryptosystems such as NTRU. As in NTRU, the proposed public-key cryptosystem relies for its inherent securi...

In this paper, we prove some results on characterization of $varepsilon$-simultaneous approximations of downward sets in vector lattice Banach spaces. Also, we give some results about simultaneous approximations of normal sets.

This thesis studies the multiple description vector quantization with lattice codebooks (MDLVQ). The design of index assignment is crucial to the performance of MDLVQ. However, to our best knowledge, none of previous index assignment algorithms for MDLVQ is optimal. In this thesis, we propose a simple linear-time index assignment algorithm for MDLVQ with any K ≥ 2 balanced descriptions. We prov...

In this paper, we introduce admissible vectors of covariant representations of a dynamical system which are extensions of the usual ones, and compare them with each other. Also, we give some sufficient conditions for a vector to be admissible vector of a covariant pair of a dynamical system.  In addition, we show the existence of Parseval frames for some special subspaces of $L^2(G)$ related to...