Structural characterization of single-walled carbon nanotube bundles by experiment and molecular simulation

A procedure, combining molecular simulation, Raman spectroscopy, and standard nitrogen adsorption, is developed for structural characterization of single-walled carbon nanotube (SWNT) samples. Grand canonical Monte Carlo simulations of nitrogen adsorption are performed on the external and internal adsorption sites of homogeneous arrays of SWNTs of diameters previously determined by Raman spectroscopy of the sample. The results show the importance of the peripheral grooves of a nanotube bundle at low relative pressure and the insensitivity of nanotube diameter toward adsorption on the external surface of the bundle at higher pressures. Simulations also reveal that samples containing thin nanotubes have less internal adsorption capacity that saturates at lower pressure than those comprising large diameter nanotubes. The fraction of open-ended nanotubes in a sample can be estimated by scaling the simulated internal adsorption inside nanotubes to obtain a near perfect fit between simulated and experimental isotherms. This procedure allows extrapolation of adsorption properties to conditions in which all nanotubes in the sample are open-ended.     

On the notion of Cohen–Macaulayness for non-Noetherian rings

There exist many characterizations of Noetherian Cohen–Macaulay rings in the literature. These characterizations do not remain equivalent if we drop the Noetherian assumption. The aim of this paper is to provide some comparisons between some of these characterizations in non-Noetherian case. Toward solving a conjecture posed by Glaz, we give a generalization of the Hochster–Eagon result on Cohen–Macaulayness of invariant rings, in the context of non-Noetherian rings.     

On the maximum of per(I-A)

The purpose of this paper is to give some necessary conditions on a substochastic matrix which maximizes the values of Per(I-A) for A taken in the semigroup of n × n substochastic matrices, and to determine the exact value of the maximum which is found to be 2^[n/2].     

Sequentially Cohen-Macaulay Modules Under Base Change

ABSTRACT

Assume that ?:(R, ± 𝔪) → (S, ± 𝔫) is a local flat homomorphism between commutative Noetherian local rings R and S. Let M be a finitely generated R-module. We investigate the ascent and descent of sequentially Cohen-Macaulay properties between the R-module M and the S-module M ? _R  S.     

Weak Module Amenability for Semigroup Algebras

We study the weak module amenability of Banach algebras which are Banach module over another Banach algebra with compatible actions. As an example we show that the semigroup algebra of a commutative inverse semigroup is always weakly amenable as a module over the semigroup algebra of its subsemigroup of idempotents.     

Fourier Algebras on Topological Foundation *-Semigroups.

We introduce the notion of the Fourier and Fourier-Stieltjes algebras of a topological *-semigroup and show that these are commutative Banach algebras. For a class of foundation semigroups, we show that these are preduals of von Neumann algebras.     

Module derivations on semigroup algebras

We show that for an inverse semigroup S with the set idempotents E acting on S trivially from left and by multiplication from right, any bounded module derivation from \(\ell ^1(S)\) to \(({\ell ^1(S)}/{J})^*=J^{\perp }\) is inner, where J is the closed ideal generated by elements of the form \(\delta _{set}-\delta _{st}\) with \(s,t\in S\) and \(e\in E\).     

Module character amenability of Banach algebras

In this paper we introduce the notion of module character amenable Banach algebras and show that they possess module character virtual (approximate) diagonals. As a basic example, we show that for an inverse semigroup S with the set of idempotents E, the semigroup algebra ? ¹(S) is module character amenable as an ? ¹(E)-module if only if S is amenable.