in this paper we introduce the notions of uniformly quasi-primary ideals and uniformly classical quasi-primary submodules that generalize the concepts of uniformly primary ideals and uniformly classical primary submodules; respectively. several characterizations of classical quasi-primary and uniformly classical quasi-primary submodules are given. then we investigate for a ring $r$, when any fi...

We study the uniform convergence to quasi-stationarity of multidimensional processes absorbed when one coordinates vanishes. Our results cover competitive or weakly cooperative Lotka–Volterra birth and death Feller diffusions with interaction. To this aim, we develop an original non-linear Lyapunov criterion involving two functions, which applies general Markov processes.

For a bounded linear operator on Hilbert space we define a sequence of the so-called weakly extremal vectors‎. ‎We study the properties of weakly extremal vectors and show that the orthogonality equation is valid for weakly extremal vectors‎. ‎Also we show that any quasinilpotent operator $T$ has an hypernoncyclic vector‎, ‎and so $T$ has a nontrivial hyperinvariant subspace‎.

For a Banach algebra $A$, $A''$ is $(-1)$-Weakly amenable if $A'$ is a Banach $A''$-bimodule and $H^1(A'',A')={0}$. In this paper, among other things,  we study the relationships between the $(-1)$-Weakly amenability of $A''$ and the weak amenability of $A''$ or $A$. Moreover, we show that the second dual of every $C^ast$-algebra is $(-1)$-Weakly amenable.

Setting of this paper is Bishop's constructive mathematics. For a relation σ on a set with apartness is called quasi-antiorder if it is consistent and cotransitive. The quasi-antiorder σ is complete if holds . 0 1 / = σ σ − ∩ In this paper the following assertion ‘A quasi-antiorder is the intersection of a collection of quasi-antiorders.’ is given.

We employ the Schwinger boson mean-field approach to study the effects of arbitrary frustrated bonds and plaquettes (formed from four frustrated bonds) in two-dimensional ferro-and antiferromagnets on the spin-wave spectrum and the correlation length at finite temperatures. We distinguish between strongly frustrated bonds (plaquettes), when the frustrated coupling J ′ exceeds the spin canting t...

Sheaf theoretic notions and methods have entered model theory during recent years and important constructions like reduced powers and products, unions of chains, Boolean valued models and models for non-classical logics appear here in a unified setting. If one looks at a sheaf as a generalized structure, then forcing becomes the genuine extension of the validity relation between models and form...

1. Incompleteness of weak duals of reasonable spaces 2. Appendix: locally-convex limits and colimits 3. Appendix: ubiquity of quasi-completeness The point here is to prove that the weak duals of reasonable topological vector spaces, such as infinite-dimensional Hilbert, Banach, or Fréchet spaces, are not complete. That is, in these weak duals there are Cauchy nets which do not converge. Happily...

In Roesch (Proof of a null penrose conjecture using new quasi-local mass, arXiv:1609.02875 [gr-qc], 2016), the notion Double Convexity for foliation conical hypersurface was introduced to give proof, if satisfied, Null Penrose Inequality. constrains geometry Marginally Outer Trapped Surface (MOTS), called quasi-round MOTS. first part this paper, class strictly stable Weakly Isolated Horizons, ...

In the present paper we introduce and study the notion of pairwise weakly Lindelof bitopological spaces and obtain some results. Further, we also study the pairwise weakly Lindelof subspaces and subsets, and investigate some of their properties. It was proved that a pairwise weakly Lindelof property is not a hereditary property.