The submodules with the property of the title ( a submodule $N$ of an $R$-module $M$ is called strongly dense in $M$, denoted by $Nleq_{sd}M$, if for any index set $I$, $prod _{I}Nleq_{d}prod _{I}M$) are introduced and fully investigated. It is shown that for each submodule $N$ of $M$ there exists the smallest subset $D'subseteq M$ such that $N+D'$ is a strongly dense submodule of $M$ and $D'bi...

We study the behavior of two-flavor dense quark matter under influence an external magnetic field in framework a nonlocal chiral model with separable interactions. The nonlocality is incorporated by using Gaussian form factor. It found that for low and moderate values there decrease critical restoration chemical potential $$\mu _c$$ , i.e. inverse catalysis effect observed. For larger eB become...

In any Banach space a monotone operator with a norm-to-weak upper semicontinuous multivalued selection on an open set D is singlevalued and normto-norm upper semicontinuous at the points of a dense Gδ subset of D. Monotone operators — and especially a special case of them, subdifferentials of convex functions — play an important role in various parts of nonlinear analysis. One of the often inve...

In any Banach space a monotone operator with a norm-to-weak upper semicontinuous multivalued selection on an open set D is singlevalued and norm-to-norm upper semicontinuous at the points of a dense G subset of D. Monotone operators | and especially a special case of them, subdiierentials of convex functions | play an important role in various parts of nonlinear analysis. One of the often inves...

Given an infinite graph of profinite groups ( $${\cal G}$$ , Γ) we construct a $$\overline {\cal G} ,\overline \Gamma $$ ) such that Γ is densely embedded in the fundamental group $${\Pi _1}\left( {\overline } \right)$$ completion $${\pi {{\cal G},\Gamma and standard tree $$S\left( embeds . This answers Ribes’ question [5, Question 6.7.1]. Generalizing main results [8] [2] answer two other ques...

In this paper, we introduce a novel 6-D representation of plenoptic point clouds, enabling joint, non-separable transform coding signals defined along both spatial and angular (viewpoint) dimensions. This representation, which is built in global coordinate system, can be used multi-camera studio capture video fly-by scenarios, with various viewpoint (camera) arrangements densities. We show that...

let c be a field of subsets of a set i. also, let     1 i i be a non-decreasing positivesequence of real numbers such that 1, 1 0 1   i  and    11 i i . in this paper we prove thatbv of all the games of -bounded variation on c is a non-separable and norm dual banach space of thespace of simple games on c . we use this fact to establish the existence of a linear mapping t from...

Working over infinite dimensional separable Hilbert spaces, residual results have been achieved for the space of contractive C0-semigroups under topology uniform weak operator convergence on compact subsets R+. Eisner and Serény raised in [6] [3] open problem: Does this constitute a Baire space? Observing that subspace unitary semigroups is completely metrisable appealing to known density resul...