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     

Linear Independence of q-Analogues of Certain Classical Constants

Let K be ? or an imaginary quadratic number field, and q ∈ K an integer with ¦q¦ > 1. We give a quantitative version of Σ_n≥1 a_n/(qⁿ ? 1) ? K for non-zero periodic sequences (a_n) in K of period length ≤ 2. As a corollary, we get a quantitative version of the linear independence over K of 1, the q-harmonic series, and a q-analogue of log 2. A similar result on 1, the q-harmonic series, and a q-analogue of ζ(2) is also proved. Mathematics Subject Classification (2000): 11J72, 11J82     

On a compromise social choice correspondence

This paper analyzes the compromise social choice correspondence derived from the τ-value of digraph games. Monotonicity of this correspondence is shown. A connection between several properties of social choice correspondences based on game theoretical solutions and game theoretical properties of the underlying solutions is given. Applications to several game theoretic solutions are provided.     

Pd-catalyzed one-pot coupling of allylamines, activated alkenes, and unsaturated halides (or triflate): an atom efficient synthesis of highly functionalized pyrrolidines

A Pd-catalyzed three-component assembling of highly functionalized 4-benzyl-(and allyl-)pyrrolidines was achieved based on a combination of allyl amines, gem-diactivated alkenes, and unsaturated halides (or triflate).     

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.     

Phase modulation in dipolar-coupled A2 spin systems: effect of maximum state mixing in H NMR in vivo

Coupling constants of nuclear spin systems can be determined from phase modulation of multiplet resonances. Strongly coupled systems such as citrate in prostatic tissue exhibit a more complex modulation than AX connectivities, because of substantial mixing of quantum states. An extreme limit is the coupling of n isochronous spins (A_n system). It is observable only for directly connected spins like the methylene protons of creatine and phosphocreatine which experience residual dipolar coupling in intact muscle tissue in vivo. We will demonstrate that phase modulation of this “pseudo-strong” system is quite simple compared to those of AB systems. Theory predicts that the spin-echo experiment yields conditions as in the case of weak interactions, in particular, the phase modulation depends linearly on the line splitting and the echo time.     

New 7‐membered diazepanone alkoxyamines for nitroxide‐mediated radical polymerization

The synthesis of new 7‐membered diazepanone alkoxyamines [2,2,7,7‐tetramethyl‐1‐(1‐phenyl‐ethoxy)‐[1,4]diazepan‐5‐one ( 3 ) and 2,7‐diethyl‐2,3,7‐trimethyl‐1‐(1‐phenyl‐ethoxy)‐[1,4]diazepan‐5‐one ( 8 )] through the Beckmann rearrangement of piperidin‐4‐one alkoxyamines was developed. Both 3 and 8 were evaluated as initiators and regulators for the nitroxide‐mediated radical polymerization of styrene and n‐butyl acrylate. 8 , a sterically highly hindered alkoxyamine readily available as a crystalline solid, allowed the fast and controlled polymerization and preparation of polymers with low polydispersity indices (1.2–1.4) up to a degree of polymerization of about 100. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 3332–3341, 2004     

Differential scanning calorimetry and thermogravimetric analysis investigation of the thermal properties and degradation of some radiation‐grafted films and membranes

The influence of irradiation and grafting on the crystallinity of three base polymers has been investigated with differential scanning calorimetry. Grafting has the largest effect on the base polymer crystallinity and results in a reduction of the crystallinity. The thermal degradation of the base polymers and grafted films has been investigated with thermogravimetric analysis. The extent of the fluorination of the base polymer, the irradiation method, and the graft level all influence the thermal degradation and its activation energy. It is proposed that the variation of the chain lengths of the grafted polystyrene chains is actually a primary underlying factor responsible for the influence of these various parameters on the degradation process. The first results of a comparative thermal analysis of some fuel‐cell membranes are also presented, and the promise and shortcomings of this method are discussed. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 2612–2624, 2004     

Enlightened sonochemistry

Sonochemistry and photochemistry are initiated by high-energy transient species, which may be prone to mutual interaction. Electronic excitation of solutes by energy transfer from high energy species generated in collapsing bubbles is already supported by experimental evidence. The rates of photochemical reactions can be affected by ultrasound-induced mixing of liquids caused by microstreaming near pulsating cavitation bubbles and shockwaves due to bubble collapse. This may not only improve light absorption but also modify the pathway of reaction by increasing the contact between reagents. Finally, one may speculate about a potentially new chemistry of photoexcited solutes under the extreme conditions inside cavitation microreactors. This work reviews research on the excitation of solutes by sonoluminescence, the combined effects of ultrasound and light on liquid systems and the effect of ultrasound on photocatalytic reactions.