Sulfonierte ?le

Ohne Zusammenfassung     

Lattice path combinatorics and asymptotics of multiplicities of weights in tensor powers

We give asymptotic formulas for the multiplicities of weights and irreducible summands in high-tensor powers V_λ^⊗N of an irreducible representation V_λ of a compact connected Lie group G. The weights are allowed to depend on N, and we obtain several regimes of pointwise asymptotics, ranging from a central limit region to a large deviations region. We use a complex steepest descent method that applies to general asymptotic counting problems for lattice paths with steps in a convex polytope.     

Photocrosslinked poly(vinylbenzophenone)‐core micelles via mild Friedel–Crafts benzoylation of polystyrene amphiphiles

Photocrosslinkable poly(vinylbenzophenone)‐containing polymers were synthesized via a one‐step, Friedel–Crafts benzoylation of polystyrene‐containing starting materials [including polystyrene, polystyrene‐block‐poly(tert‐butyl acrylate), polystyrene‐block‐poly(ethylene oxide), polystyrene‐block‐poly(methyl methacrylate), and polystyrene‐block‐poly(n‐butyl acrylate)] with benzoyl trifluoromethanesulfonate as a benzoylation reagent. The use of this mild reagent (which required no added Lewis acid) permitted polymers with well‐defined compositions and narrow molecular weight distributions to be synthesized. Micelles formed from one of these benzoylated polymers, [polystyrene_0.25‐co‐poly(vinylbenzophenone)_0.75]₁₁₅‐block‐poly(acrylic acid)₁₄, were then fixed by the irradiation of the micelle cores with UV light. As the irradiation time was increased, the pendent benzophenone groups crosslinked with other chains in the glassy micelle cores. Dynamic light scattering, spectrofluorimetry, and Fourier transform infrared spectroscopy were all used to verify the progress of the crosslinking reaction. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 2604–2614, 2006     

On assignment of fundamental vibrational modes of hypophosphite anion and its deuterated analogue

Results of ab initio and density functional theory calculations on the structure and vibrational frequencies of hypophosphite anion indicate earlier experimental assignments of the fundamental vibrational modes are correct while the recent reassignments of several modes proposed by Bickley et al. are inconsistent with the calculated results.     

Teaching Operational Research Technique

Good technique, i.e. competence in carrying out operational research, is as vital for the practitioner to acquire as competence in the traditional ‘techniques’. It is suggested that universities should teach students how to conduct simple projects prior to alerting them to more sophisticated methodological issues.As an aid to this task, the traditional five or six parts of an operational research project are broken down and extended into 39 steps, and regrouped into three phases. Also, five skills are identified as being conceptually essential to "good" operational research, which students can develop through tackling suitable case studies.     

Preparation of 5-substituted benzylbarburituric acids and investigation of the effect of the benzyl and substituted benzyl groups on the acidity of barbituric acid

The acidity of 5-benzylbarbituric acid and a series of 5-substituted benzylbarbituric acids has been determined in 50% ethanol/water and they were found to be more acidic than barbituric acid. The pK_as of these derivatives obey Hammett's equation indicating that their acidity is affected by substituents in the same manner as the benzoic acid ionization constants. A synthesis of these acids is described.     

Synthesis and complexing properties of bis-crown ethers incorporating benzo-15-crown-5 and metallocene

Bis-crown ethers in which the benzo-15-crown-5 units were linked to 1,1′-positions of metallocene (M = Fe or Ru) with amide, ester, or ? C? C? bonds were synthesized. Complexing ability of the compounds with alkali, alkali earth, and transition metal cations were measured by the solvent extraction method. The results showed that these crown ethers had high affinity toward alkali metal cations (Li⁺, Na⁺, K⁺, and Rb⁺) and heavy-metal cations (Ag⁺ and Tl⁺). The difference of complexing ability for metal cations between ferrocene and ruthenocene derivatives could not be detected significantly. The extractability of metallocene-bis-crown ethers for metal cations was more larger than that of the corresponding mono-crown ethers, and irregular increments of extractability were explained by assuming the existence of a mixture of 1:1 and 2:1 complexes.     

Plasma desorption mass spectrometry of transition metal complexes of thio- and selenosemicarbazones of 2-acetylpyridines

Summary Californium-252 plasma desorption mass spectra were recorded for complexes of the anions of various thio-and seleno-semicarbazones of 3-acetylpyridines(1–4) with the transition metal ions iron(III) and cobalt(II). Positive ion spectra gave clear evidence of the cation present and fragmentation with loss of ligands or parts of ligands was straightforward. Negative ion spectra likewise provided evidence of the intact anion except with tetracoordinate metal halide systems [MX₄]^– which lost one or more halide atoms. Evidence of fragmentation of the ligand and recombination of the fragments with the metal ion was also observed in the negative ion mode. Spectra were used to revise the structure of a complex previously reported as [FeLCl₂]⁽¹⁾ to [FeL₂]⁺[FeCl₄]^–.     

A simple route to derivatives of benzo[j]fluoranthene

3,6,8,11-Tetramethoxybenzo[j]fluoranthene can be made from 1,6-dimethoxynaphthalene in a one-pot ferric chloride oxidation/methanol reduction procedure. The reaction is tolerant of the presence of substituents in the 7-position of the naphthalene nucleus and provides a quick and easy route to these particular benzo[j]fluoranthenes. The reactions presumably proceed through initial formation of a bond between the 4-positions of two naphthalene molecules followed by closure of the five-membered ring. Indeed in one case some 4,4′-binaphthyl was isolated from the reaction mixture and it was generally found that better yields of the benzo[j]fluoranthrenes were obtained starting from the 4,4′-binaphthyl rather than by using the naphthalene as the starting material. In an analogous manner to the ring-closure of the 4,4′-binaphthyls, starting from a hexakisalkoxyphenylnaphthalene, a hexakisalkoxyfluoranthene could be obtained.     

Weyl Pseudo-Differential Operator and Wigner Transform on the Poincaré Disk

The purpose of this paper is to investigate some relations between the kernel of a Weyl pseudo-differential operator and the Wigner transform on Poincaré disk defined in our previous paper [11]. The composition formula for the class of the operators defined in [11] has not been proved yet. However, some properties and relations, which are analogous to the Euclidean case, between the Weyl pseudo-differential operator and the Wigner transform have been investigated in [11]. In the present paper, an asymptotic formula for the Wigner transform of the kernel of a Weyl pseudo-differential operator as 0 is given. We also introduce a space of functions on the cotangent bundle T ^* D whose definition is based on the notion of the Schwartz space on the Poincaré disk. For an S ¹-invariant symbol in that space, we obtain a formula to reproduce the symbol from the kernel of the Weyl pseudo-differential operator.