Bass and Topological Stable Ranks of Complex and Real Algebras of Measures,Functions and Sequences

We compute the Bass stable rank and the topological stable rank of several convolution Banach algebras of complex measures on (-∞,∞) or on [0,∞) consisting of a discrete measure and/or of an absolutely continuous measure. We also compute the stable ranks of the convolution algebras \({\ell^1(\mathbb {N}^n)}\) , \({\ell^1(\mathbb {Z}^n)}\) , ?¹(S) and \({\ell^1(S\cap\mathbb {R}_+)}\) , where S is an arbitrary subgroup of \({\mathbb {R}}\) , of the almost periodic algebra AP and of \({{{\rm AP} \cap H^{\infty}}}\) , etc. We answer affirmatively the question posed by Mortini (Studia Mathematica 103(3):275–281, 1992). For the above algebras, the polydisc algebra \({A(\mathbb {D}^n)}\) , the algebra \({C(\mathbb T^n)}\) of continuous functions, and others, we also study their subsets (real Banach algebras) of real-valued measures, real-valued sequences or real-symmetric functions, and of corresponding exponentially stable algebras (for example, the Callier–Desoer algebra of causal exponentially decaying measures and L¹ functions), and we compute their stable ranks. Finally, we show that in some of these real algebras a variant of the parity interlacing property is equivalent to reducibility of a unimodular (or coprime) pair. Also corona theorems are presented and the existence of coprime fractions is studied; in particular, we list which of these algebras are Bézout domains.     

Syntheses and crystal structures of three novel Cu(II) coordination polymers of different dimensionality constructed from Cu(II) carboxylates (carboxylate = malonate (mal), 2 acetate (ac), fumarate (fum)) and conformationally flexible 1,4-bis(imidazole-1-yl-methylene)benzene (IX)

We herein report three new coordination polymers generated from Cu(II) carboxylates (mal, 2ac, fum) and conformationally flexible bifunctional IX as building blocks. All the three complexes adopt unique structures in the solid state. The complex [Cu₂(mal)₂(IX)₂(H₂O)₆]_n crystallizes as orthorhombic co-linear rods with space group P2(1) P2(1) P2(1). Each rod is further formed of two tightly intertwined strings. The second polymer [Cu₂(ac)₄(IX)₂]_n crystallizes with space group P1 which consists of two sets of intersecting 2D sheets composed of parallel rods which interpenetrate to form a fully interlocked 3D structure. In both these complexes IX coordinates in the anti mode. The third polymer [Cu₂(fum)₂(IX)₂(H₂O)₂]_n possesses a monoclinic crystal system with space group C₂/c and crystallizes as 1D straps. Cu–fum–Cu forms the base of the string which is alternatively garlanded by a macrocycle derived from Cu₂(IX)₂ unit, where IX coordinates in the syn fashion. The present study suggests that the use of a rigid building block with a flexible organic ligand leads to a better prediction of the final structure of the polymeric array.     

Electrogenerated chemiluminescence induced by sequential hot electron and hole injection into aqueous electrolyte solution

Hole injection into aqueous electrolyte solution is proposed to occur when oxide-coated aluminum electrode is anodically pulse-polarized by a voltage pulse train containing sufficiently high-voltage anodic pulses. The effects of anodic pulses are studied by using an aromatic Tb(III) chelate as a probe known to produce intensive hot electron-induced electrochemiluminescence (HECL) with plain cathodic pulses and preoxidized electrodes. The presently studied system allows injection of hot electrons and holes successively into aqueous electrolyte solutions and can be utilized in detecting electrochemiluminescent labels in fully aqueous solutions, and actually, the system is suggested to be quite close to a pulse radiolysis system providing hydrated electrons and hydroxyl radicals as the primary radicals in aqueous solution without the problems and hazards of ionizing radiation. The analytical power of the present excitation waveforms are that they allow detection of electrochemiluminescent labels at very low detection limits in bioaffinity assays such as in immunoassays or DNA probe assays. The two important properties of the present waveforms are: (i) they provide in situ oxidation of the electrode surface resulting in the desired oxide film thickness and (ii) they can provide one-electron oxidants for the system by hole injection either via F- and F⁺-center band of the oxide or by direct hole injection to valence band of water at highly anodic pulse amplitudes.     

Advanced glossmeters for industrial applications

In this paper, we present three new types of diffractive-optical-element (DOE)-based glossmeters (DOGs) that have been developed for both laboratory and online local specular gloss measurements of objects in industrial processes. The three are denoted as the handheld wireless glossmeter, μDOG two-dimensional (2D) and μDOG one-dimensional (1D), respectively. These glossmeters are designed to operate under conditions where gloss measurement with conventional glossmeters is impossible or difficult, or when fine structures of the gloss over a surface are an issue. Here, we show the applicability of the handheld glossmeter and μDOG 2D in the inspection of gloss from rough stainless steel plates finished by different machining methods. We also briefly introduce the concept of online gauge μDOG 1D for gloss assessment in industrial measurement environments.     

Monte Carlo simulation of Ising models by multispin coding on a vector computer

Rebbi's efficient multispin coding algorithm for Ising models is combined with the use of the vector computer CDC Cyber 205. A speed of 21.2 million updates per second is reached. This is comparable to that obtained by special- purpose computers.     

Miscibility of poly(ε-caprolactone), a semicrystalline polymer,with amorphous poly(styrene-4-hydroxystyrene) copolymers

The miscibility of poly(ε caprolactone) (PCL) with poly(styrene-co-4-hydroxystyrene) (PHS) copolymers was investigated as a function of comonomer composition experimentally and with calculations by two models; the binary interaction model and the association model. PCL was found to be completely miscible with PHS copolymers containing 5 or more mole percent of 4-hydroxystyrene (HS) comonomer units for the entire range of blend compositions. Segmental interaction densities, B_ijs, were determined by the analysis of the equilibrium melting point depression and by the application of the binary interaction model. By correlating the segmental interaction energy densities with the binary interaction model, thermodynamic miscibility is for comonomer composition over five mole percent of 4-hydroxystyrene, which is in agreement with the experimental phase behavior. Application of the association model for specific interactions to blends also predicts the experimental miscibility boundary and phase behavior for all the PHS copolymers/PCL blends. © 1995 John Wiley & Sons, Inc.