The notion of a quasi-free Hilbert module over a function algebra A consisting of holomorphic functions on a bounded domain Ω in complex m space is introduced. It is shown that quasi-free Hilbert modules correspond to the completion of the direct sum of a certain number of copies of the algebra A. A Hilbert module is said to be weakly regular (respectively, regular) if there exists a module map...

A Banach space E has the Grothendieck property if every (linear bounded) operator from E into c0 is weakly compact. It is proved that, for an integer k > 1, every k-homogeneous polynomial from E into c0 is weakly compact if and only if the space P(kE) of scalar valued polynomials on E is reflexive. This is equivalent to the symmetric k-fold projective tensor product of E (i.e., the predual of P...

In the present work, we introduce and study completely generalized quasi-variational inequality problem for fuzzy mappings. By using the definitions of strongly accretive and retraction mappings, we propose an iterative algorithm for computing the approximate solutions of this class of variational inequalities. We prove that approximate solutions obtained by the proposed algorithm converge to t...

IDPs (intrinsically disordered proteins) are common in eukaryotic genomes and have regulatory roles. In the cell, they are disordered, although not completely random. They bind weakly, but specifically, often remaining partially disordered even when bound. Whereas folded globular proteins have 'executive' roles in the cell, IDPs have an essential administrative function, making sure that the ex...

We prove that every quasi-Hopfian finitely presented structure A has a d- $$\Sigma _2$$ Scott sentence, and if in addition is computable Aut(A) satisfies natural condition, then sentence. This unifies several known results on sentences of structures it used to other not previously considered algebraic interest have sentences. In particular, we show right-angled Coxeter group finite rank as well...

We introduce the notions of interval-valued fuzzy prime ideals, interval-valued fuzzy completely prime ideals and intervalvalued fuzzy weakly completely prime ideals. And we give a characterization of interval-valued fuzzy ideals and establish relationships between interval-valued fuzzy completely prime ideals and interval-valued fuzzy weakly completely prime ideals.