Boundary regularity, uniqueness and non-uniqueness for AH Einstein metrics on 4-manifolds

This paper studies several aspects of asymptotically hyperbolic (AH) Einstein metrics, mostly on 4-manifolds. We prove boundary regularity (at infinity) for such metrics and establish uniqueness under natural conditions on the boundary data. By examination of explicit black hole metrics, it is shown that neither uniqueness nor finiteness holds in general for AH Einstein metrics with a prescribed conformal infinity. We then describe natural conditions which are sufficient to ensure finiteness.     

Minimal Bar Tableaux

Motivated by recent results of Stanley, we generalize the rank of a partition λ to the rank of a shifted partition S(λ). We show that the number of bars required in a minimal bar tableau of S(λ) is max(o, e + (ℓ(λ) mod 2)), where o and e are the number of odd and even rows of λ. As a consequence we show that the irreducible projective characters of S_n vanish on certain conjugacy classes. Another corollary is a lower bound on the degree of the terms in the expansion of Schur’s Q_λ symmetric functions in terms of the power sum symmetric functions. Received November 20, 2003     

1H and 13C NMR spectroscopic study of oxidation of D,L‐cystine and 3,3′‐dithiobis(propionic acid) with hydrogen peroxide in aqueous solution

The oxidation of symmetrical disulfides [D ,L ‐cystine ( 1 ) and 3,3′‐dithiobis(propionic acid) ( 2 )] with hydrogen peroxide in D₂O–NaOH solution (pH 10–11) was studied by NMR spectroscopy. Assignments of the proton and carbon NMR signals of starting materials ( 1 and 2 ) and products of oxidation are based on conventional 1D NMR methods (DEPT, selective spin decoupling). Formation of C—S bond cleavage products or, in case of 2 , partially oxidized intermediates was not detected. The accelerating effect of Cu²⁺ cations, but not Fe³⁺ cations, on the oxidation rate of 1 in basic medium was demonstrated. Copyright © 2002 John Wiley & Sons, Ltd.     

Expected Reflection Distance in G(r, 1, n) after a Fixed Number of Reflections

Extending to r > 1 a formula of the authors, we compute the expected reflection distance of a product of t random reflections in the complex reflection group G(r, 1, n). The result relies on an explicit decomposition of the reflection distance function into irreducible G(r, 1, n)-characters and on the eigenvalues of certain adjacency matrices.Received December 8, 2003     

Well-dispersed gold nanowire suspension for assembly application

A method for fabricating well-dispersed nanowire suspension has been demonstrated in the paper. Thin gold nanowires were prepared by template synthesis, and then functionalized with sulphonate group-terminated thiols before suspended in different solvents. The degree of aggregation of the obtained suspension was evaluated with transmission electron microscopy (TEM) and UV-vis spectroscopy. It was found that the degree of aggregation was predominated by the solvents, and the best degree of dispersion was obtained when isopropyl alcohol (IPA) was used as the solvent. The gold nanowires from the suspension can be selectively assembled onto chemically patterned substrates. This well-dispersed nanowire suspension is potentially useful for fabricating novel nanodevices.     

The role of As2O3 on the stability and some physical properties of PbO-Sb2O3 glasses

PbO-Sb₂O₃ glasses added with different concentrations of As₂O₃ (10-55 mol%) were prepared to understand their IR spectra, elastic properties (Young's modulus E, Shear modulus G, microhardness H), optical absorption and dielectric properties (constant ε, loss tan δ, ac conductivity σ_ac over a moderately wide range of frequency and temperature and breakdown strength in air medium at room temperature). Results have indicated that the structure of the PbO-Sb₂O₃-As₂O₃ glass is more rigid when the concentration of As₂O₃ is around 40 mol%.     

Exact controllability of infinite dimensional systems persists under small perturbations

This paper studies the concept of controllability for infinite-dimensional linear control systems in Banach spaces. First, we prove that the set of admissible control operators for the semigroup generator is unchanged if we perturb the generator by the Desch–Schappacher perturbations. Second we show that exact controllability is not changed by such perturbations.     

Molecular dynamics and information on possible sites of interaction of intramyocellular metabolites in vivo from resolved dipolar couplings in localized H NMR spectra

Proton NMR resonances of the endogenous metabolites creatine and phosphocreatine ((P)Cr), taurine (Tau), and carnosine (Cs, β-alanyl-l-histidine) were studied with regard to residual dipolar couplings and molecular mobility. We present an analysis of the direct ¹H–¹H interaction that provides information on motional reorientation of subgroups in these molecules in vivo. For this purpose, localized ¹H NMR experiments were performed on m. gastrocnemius of healthy volunteers using a 1.5-T clinical whole-body MR scanner. We evaluated the observable dipolar coupling strength SD₀ (S = order parameter) of the (P)Cr-methyl triplet and the Tau-methylene doublet by means of the apparent line splitting. These were compared to the dipolar coupling strength of the (P)Cr-methylene doublet. In contrast to the aliphatic protons of (P)Cr and Tau, the aromatic H2 (δ = 8 ppm) and H4 (δ = 7 ppm) protons of the imidazole ring of Cs exhibit second-order spectra at 1.5 T. This effect is the consequence of incomplete transition from Zeeman to Paschen-Back regime and allows a determination of SD₀ from H2 and H4 of Cs as an alternative to evaluating the multiplet splitting which can be measured directly in high-resolution ¹H NMR spectra. Experimental data showed striking differences in the mobility of the metabolites when the dipolar coupling constant D₀ (calculated with the internuclear distance known from molecular geometry in the case of complete absence of molecular dynamics and motion) is used for comparison. The aliphatic signals involve very small order parameters S ≈ (1.4 − 3) × 10⁻⁴ indicating rapid reorientation of the corresponding subgroups in these metabolites. In contrast, analysis of the Cs resonances yielded S ≈ (113 − 137) × 10⁻⁴. Thus, the immobilization of the Cs imidazole ring owing to an anisotropic cellular substructure in human m. gastrocnemius is much more effective than for (P)Cr and Tau subgroups. Furthermore, ¹H NMR experiments on aqueous model solutions of histidine and N-acetyl-l-aspartate (NAA) enabled the assignment of an additional signal component at δ = 8 ppm of Cs in vivo to the amide group at the peptide bond. The visibility of this proton could result from hydrogen bonding which would agree with the anticipated stronger motional restriction of Cs. Referring to the observation that all dipolar-coupled multiplets resolved in localized in vivo ¹H NMR spectra of human m. gastrocnemius collapse simultaneously when the fibre structure is tilted towards the magic angle (θ ≈ 55°), a common model for molecular confinement in muscle tissue is proposed on the basis of an interaction of the studied metabolites with myocellular membrane phospholipids.     

Two‐stage copolycondensation of preformed oligomers with bisphenols by tosyl chloride/dimethylformamide/pyridine from distributions of resulting oligomers determined by a combination of gel permeation chromatography and NMR

A two‐stage co‐oligomerization of the oligomers initially formed from an equimolar mixture of isophthalic acid (IPA) and terephthalic acid (TPA) and 2,2‐bis(4‐hydroxyphenyl)propane (BPA, 50 mol %) with bisphenols (BPs, 20 mol %) was carried out using a tosyl chloride/dimethylformamide/pyridine condensing agent. The distributions of the resulting oligomers (n_x‐mers), which were quenched with methanol, were determined by a combination of gel permeation chromatography (GPC) and NMR. These distributions (presented by molar percentage) were conveniently calculated with the equation n_x (mol %) = n_x (% mol by GPC) × n₀ (mol % by NMR)/n₀ (% mol by GPC), where n_x (% mol) = n_x (wt % by GPC)/its molecular weight. The results showed the distributions of the preformed IPA/TPA‐BPA oligomers to be in fairly good accord with those obtained directly from GPC and to be supported by the NMR results. The calculation was applied to the co‐oligomers prepared up to a reaction of 0.7, at which there was an increase in the number of higher oligomers indivisible by GPC and the distributions could no longer be determined by molar percentage. The calculated distributions are discussed in relation to the results of copolycondensation. The sequence distributions in the resulting co‐oligomers, which were also examined by NMR, are compared with those in the copolymers. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 44–51, 2004