Characterizing Local Rings via Test Modules

This article shows some instances where properties of a local ring are closely connected with the homological properties of a single module.     

Crossed product of C*‐algebras by hypergroups

The crossed product of ‐algebras by groups, groupoids and semigroups are well studied. In this paper we introduce and study the crossed product of ‐algebras by (locally compact) hypergroups. We calculate the crossed products by finite hypergroups of orders 2 and 3.     

Bis[4‐(dimethylamino)pyridine‐κN1]silver(I) nitrate dihydrate

The title compound, [Ag(C₇H₁₀N₂)₂]NO₃·2H₂O or [Ag(dmap)₂]NO₃·2H₂O, where dmap is 4‐(dimethylamino)pyridine, has a distorted linear coordination geometry around the Ag^I ion. A novel pattern of water–nitrate hydrogen‐bonded anionic strands is formed in the c direction, with the cationic [Ag(dmap)₂]⁺ monomers trapped between them. The Ag^I ion and the nitrate group atoms, as well as the water molecules (including the H atoms), are on a crystallographic mirror plane (Wyckoff position 4a). The influence of bulky methyl substituents in position 4 of the 4‐(dimethylamino)pyridine ligand on packing is discussed. The absolute structure was determined unequivocally.     

The finiteness dimension of local cohomology modules and its dual notion

Let a be an ideal of a commutative Noetherian ring R and M a finitely generated R-module. We explore the behavior of the two notions f_a(M), the finiteness dimension of M with respect to a, and, its dual notion q_a(M), the Artinianness dimension of M with respect to a. When (R,m) is local and r?f_a(M) is less than , the m-finiteness dimension of M relative to a, we prove that is not Artinian, and so the filter depth of a on M does not exceed f_a(M). Also, we show that if M has finite dimension and is Artinian for all i>t, where t is a given positive integer, then is Artinian. This immediately implies that if q?q_a(M)>0, then is not finitely generated, and so f_a(M)≤q_a(M).     

Self-aggregated perfluoroalkylated hexa-peri-hexabenzocoronene fibers observed by cryo-SEM and fluorescence spectroscopy

The self-assembled architectures in solution of a new HBC derivative bearing perfluoroalkylated side chains were investigated by optical excitation and emission spectroscopy and correlated to cryo-SEM, a new technique in organic chemistry.     

Module amenability of the second dual and module topological center of semigroup algebras

In this paper we define the module topological center of the second dual $\mathcal{A}^{**}$ of a Banach algebra $\mathcal{A}$ which is a Banach $\mathfrak{A}$ -module with compatible actions on another Banach algebra $\mathfrak{A}$ . We calculate the module topological center of ? ¹(S)^**, as an ? ¹(E)-module, for an inverse semigroup S with an upward directed set of idempotents E. We also prove that ? ¹(S)^** is ? ¹(E)-module amenable if and only if an appropriate group homomorphic image of S is finite.     

Chromatographic separation of In(III) from Cd(II) in aqueous solutions using commercial resin (Dowex 50W-X8)

This work assesses the potential of an adsorptive material, Dowex 50w-x8, for the separation of indium ions from cadmium ions in aqueous media. The adsorption behavior of Dowex 50 w-x8 for indium and cadmium ions was investigated. The effect of pH, initial concentration of metal ions, the weight of resins, and contact time on the sorption of each of the metal ions were determined. It was found that the adsorption percentage of the indium ions was more than 99% at pH 4.0. The result shows that In (III) was most strongly extracted, while Cd(II) was slightly extracted at this pH value. The recovery of In(III) and Cd(II) ions is around 98% using hydrochloric acid as the best eluent.      

Chain conditions for C*-algebras coming from Hilbert C*-modules

In this paper we define and study chain conditions for Hilbert C*-modules through their C*-algebras of compact operators and discuss their perseverance under Morita equivalence and tensor products. We show that these chain conditions are passed from the C*-algebra to its Hilbert module under certain conditions. We also study chain conditions for Hilbert modules coming from inclusion of C*-algebra with a faithful conditional expectation.     

Influence of solvent structure on the aquation of K‐chloro(diethylenetriamine)(ethylenediamine) cobalt(III) ion in water and mixed aqueous solvents

The aquation of K‐[Co(dien)(en)Cl]²⁺ was followed spectrophotometrically within the temperature range (40–60°C) in water, water–isopropyl alcohol, and water–tert‐butyl alcohol media of varying solvent composition up to 50 and 60 vol% of the organic solvent component respectively. The nonlinear plot of log k vs. D^?1_s was attributed to the differential solvation of the initial and transition states. The variation of ΔH^≠, ΔS^≠, and ΔG^≠ with the mole fraction of the organic component was analyzed and discussed. The isokinetic temperatures were found to be 330 and 317 K for water–isopropyl alcohol and water–tert‐butly alcohol mixtures respectively, indicating that the aquation reaction is entropy controlled. The application of free energy cycle at 25°C for the aquation reaction in both co‐solvents suggests that the transition state is more stable than the initial one. © 2001 John Wiley & Sons, Inc. Int J Chem Kinet 34: 1–6, 2002     

Design optimization of switchable multi-port spiral inductors

In this paper, we develop a design optimization methodology for switchable multi-port spiral inductors in fully integrated wireless systems. The methodology simultaneously maximizes the inductor’s performance for multiple inductance values and operating frequencies. We utilize multi-level optimization techniques to efficiently design the geometry of the switchable inductor structure. The methodology can produce designs with significantly larger quality factors than those obtained by optimizing the inductor design for a single inductance value and operating frequency.