In recent work, various algebras of stable degree zero operations in p-local K-theory were described explicitly [5]. The elements are certain infinite sums of Adams operations. Here we show how to make sense of the same expressions for MU(p) and BP , thus identifying the “Adams subalgebra” of the algebras of operations. We prove that the Adams subalgebra is the centre of the ring of degree zero...

This paper deals with multi- objective nonlinear programming problem having rough intervals in the constraints. The problem is approached by taking maximum value range and minimum value range inequalities as constraints conditions, reduces it into two classical multi-objective nonlinear programming problems, called lower and upper approximation problems.  All of the lower and upper approximatio...

‎Let $mathcal{A}$ be a commutative Banach algebra and $mathscr{X}$ be a left Banach $mathcal{A}$-module‎. ‎We study the set‎ ‎${rm Dec}_{mathcal{A}}(mathscr{X})$ of all elements in $mathcal{A}$ which induce a decomposable multiplication operator on $mathscr{X}$‎. ‎In the case $mathscr{X}=mathcal{A}$‎, ‎${rm Dec}_{mathcal{A}}(mathcal{A})$ is the well-known Apostol algebra of $mathcal{A}$‎. ‎We s...

Classical structure of rough set theory was first formulated by Z. Pawlak in [6]. The foundation of its object classification is an equivalence binary relation and equivalence classes. The upper and lower approximation operations are two core notions in rough set theory. They can also be seenas a closure operator and an interior operator of the topology induced by an equivalence relation on a u...

We represent a classical Maxwell-Bloch equation and related to it positive part of the AKNS hierarchy in geometrical terms. The Maxwell-Bloch evolution is given by an infinitesimal action of a nilpotent subalgebra n+ of affine Lie algebra ŝl2 on a Maxwell-Bloch phase space treated as a homogeneous space of n+. A space of local integrals of motion is described using cohomology methods. We show t...

This paper is a review of results on generalized Harish-Chandra modules in the framework of cohomological induction. The main results, obtained during the last 10 years, concern the structure of the fundamental series of (g, k)−modules, where g is a semisimple Lie algebra and k is an arbitrary algebraic reductive in g subalgebra. These results lead to a classification of simple (g, k)−modules o...

The Peterson-Thom conjecture asserts that any diffuse, amenable subalgebra of a free group factor is contained in unique maximal subalgebra. This motivated by related results Popa's deformation/rigidity theory and Peterson-Thom's on L^{2}-Betti numbers. We present an approach to this terms so-called strong convergence random matrices formulating which natural generalization the Haagerup-Thorbjo...

We introduce what we call the principal subalgebra of a lattice vertex (super) algebra associated to an arbitrary Z-basis of the lattice. In the first part (to appear), the second author considered the case of positive bases and found a description of the principal subalgebra in terms of generators and relations. Here, in the most general case, we obtain a combinatorial basis of the principal s...

In this paper we study subalgebras A of the algebra D(X) of differential operators on a smooth variety X which are big in the following sense: using the order of a differential operator, the ring D(X) is equipped with a filtration. Its associated graded algebra D(X) is commutative and can be regarded as the set of regular functions on the cotangent bundle ofX . The subalgebra A inherits a filtr...

Every lown Boolean algebra, for 1 ≤ n ≤ 4, is isomorphic to a computable Boolean algebra. It is not yet known whether the same is true for n > 4. However, it is known that there exists a low5 subalgebra of the computable atomless Boolean algebra which, when viewed as a relation on the computable atomless Boolean algebra, does not have a computable copy. We adapt the proof of this recent result ...