Harmonic Calculus on Fractals - A Measure Geometric Approach I

Differentiation of functions w.r.t. finite atomless measures with compact support on the real line is introduced. The related harmonic calculus is similar to that of the classical Lebesgue case. As an application we obtain the Weyl exponent for the spectral asymptotics of the Laplacians w.r.t. linear Cantor-type measures with arbitrary weights.     

Computational studies of Cu(II)/Met and Cu(I)/Met binding motifs relevant for the chemistry of Alzheimer's disease

A systematic study of the binding motifs of Cu(II) and Cu(I) to a methionine model peptide, namely, N-formylmethioninamide 1, has been carried out by quantum chemical computations. Geometries of the coordination modes obtained at the B3LYP/6-31G(d) level of theory are discussed in the context of copper coordination by the peptide backbone and the S atom of a methionine residue in peptides with special emphasis on Met35 of the amyloid-beta peptide (Abeta) of Alzheimer's disease. The relative binding free energies in the gas phase, DeltaG(g), are calculated at the B3LYP/6-311+G(2df,2p)//B3LYP/6-31G(d) level of theory, and the solvation affects are included by means of the COSMO model to obtain the relative binding energies in solution, DeltaG(aq). A free energy of binding, DeltaG(aq) = -19.4 kJ mol(-1), relative to aqueous Cu(II) and the free peptide is found for the most stable Cu(II)/Met complex, 12. The most stable Cu(I)/Met complex, 23, is bound by -15.6 kJ mol(-1) relative to the separated species. The reduction potential relative to the standard hydrogen electrode is estimated to be E degrees (12/23) = 0.41 V. On the basis of these results, the participation of Met35 as a low affinity binding site of Cu(II) in Abeta, and its role in the redox chemistry underlying Alzheimer's disease is discussed.     

A simple and versatile method for the synthesis of acetals from aldehydes and ketones using bismuth triflate

Acetals are obtained in good yields by treatment of aldehydes and ketones with trialkyl orthoformate and the corresponding alcohol in the presence of 0.1 mol % Bi(OTf)3.4H2O. A simple procedure for the formation of acetals of diaryl ketones has also been developed. The conversion of carbonyl compounds to the corresponding 1,3-dioxolane using ethylene glycol is also catalyzed by Bi(OTf)3.4H2O (1 mol %). Two methods, both of which avoid the use of benzene, have been developed.     

On noise and fluctuations in a synchronously mode-locked cw laser system

A single-shot and synchronously-scanned streak camera, autocorrelation and noise spectrum analysing techniques are utilized to study the output characteristics of synchronously mode-locked cw lasers. Four main conclusions are drawn: (i) the pulse train from a synchronously-pumped dye laser reveals, besides phase jitter, considerable pulse shape fluctuations; (ii) autocorrelation measurements may be highly misleading when actual pulse shapes are considered; (iii) both the phase jitter and pulse shape fluctuations of the dye laser output are caused by the phase fluctuations of the pumping ion laser pulse train; (iv) the phase jitter of the ion laser proceeds from the fluctuations in the cavity roundtrip time with a characteristic time of about 5 s. Under optimum conditions the rms noise of the dye laser output was 2% and the phase jitter with respect to the rf sine drive of the acousto-optical mode-locker, 30 ps. A qualitative explanation fo the noise properties is given.     

The electronic structure and optical activity of conjugated dienes: 1,3-Butadiene and α- and β-phellandrene

The optical activity of conjugated dienes is investigated by means of ab initio SCF–CI calculations. The computed electronic spectrum of trans-1,3-butadiene is shown to be in good agreement with the results of more rigorous calculations of the valence transitions and in satisfactory agreement with experiment. The optical rotatory strengths of the lower electronic transitions of twisted 1,3-butadiene as a function of dihedral angle are presented and simulated CD spectra are produced. The N → V₁ (π₂ → π₃*) transition is predicted to have a positive rotational strength for all dihedral angles that correspond to a right-handed twist of the chromophore, in accord with the empirically deduced “diene rule” although for a twist angle of 60°, the rotatory strength is calculated to be almost zero. The role of the orientation of allylic bonds is investigated in the model system 1-butene in which the rotational strength of the π → π* transition as a function of rotation about the 2,3 bond is determined. The effect of allylic bond disposition in dienes on the optical activity of the long-wavelength π₂ → π₃* transition is simulated by use of the exciton coupling model of Harada and Nakanishi in which two 1-butene molecules with suitable geometries are coupled via interactions of the electric dipole transition moments of their π → π* transitions. The model systems 1,3-butadiene and 1-butene are used to rationalize the apparently anomalous optical activity of (?)-α-phellandrene and (?)-β-phellandrene, both of which should have a diene chromophore with a right-handed twist in their most stable conformers and so should be dextrorotatory. The experimental CD spectrum of α-phellandrene is determined at several temperatures down to ?180°C. The observed variation of the apparent rotational strength of the N → V₁ transition is in good agreement with that predicted by use of the exciton coupling model.     

Reduction of the pertechnetate anion with bidentate phosphine ligands

The reduction of ammonium pertechnetate with bis(diphenylphosphino)methane (dppm), and with diphenyl-2-pyridyl phosphine (Ph(2)Ppy), has been investigated. The neutral Tc(II) complex, trans-TcCl(2)(dppm)(2) (1), has been isolated from the reaction of (NH(4))[TcO(4)] with excess dppm in refluxing EtOH/HCl. Chemical oxidation with ferricinium hexafluorophosphate results in formation of the cationic Tc(III) analogue, trans-[TcCl(2)(dppm)(2)](PF(6)) (2). The dppm ligands adopt the chelating bonding mode in both complexes, resulting in strained four member metallocycles. With excess PhPpy, the reduction of (NH(4))[TcO(4)] in refluxing EtOH/HCl yields a complex with one chelating Ph(2)Ppy ligand and one unidentate Ph(2)Ppy ligand, mer-TcCl(3)(Ph(2)Ppy-P,N)(Ph(2)Ppy-P) (3). The cationic Tc(III) complexes, trans-[TcCl(2)(Ph(2)P(O)py-N,O)(2)](PF(6)) (4) and trans-[TcCl(2)(dppmO-P,O)(2)](PF(6)) (5) (Ph(2)P(O)py = diphenyl-2-pyridyl phosphine monoxide and dppmO = bis(diphenylphosphino)methane monoxide), have been isolated as byproducts from the reactions of (NH(4))[TcO(4)] with the corresponding phosphine. The products have been characterized in the solid state and in solution via a combination of single-crystal X-ray crystallography and spectroscopic techniques. The solution state spectroscopic results are consistent with the retention of the bonding modes revealed in the crystal structures.     

Underwater and water-assisted laser processing: Part 1—general features, steam cleaning and shock processing

Water is always present in laser processing in air: as vapor, condensate or adsorbate. Water is the working environment in underwater processing—but it can also be added on purpose to gain better results: to avoid redeposition of debris, to cool the material, to increase plasma pressure or to conduct light. Water can also act as a chemical reagent. The first part of the article will review the advantages and disadvantages of laser processing in the presence of water, light transmission by water, and the two most mature methods of water-assisted laser processing: steam cleaning and shock processing.     

Analysis on Fractal Objects

Irregular objects are often modeled by fractals sets. In order to formulate partial differential equations on these nowhere differentiable sets the development of a “new analysis” is necessary. With the help of the model case of the Sierpinski gasket the definition of energy forms and Laplacians on self-similar finitely ramified fractals is explained. Moreover, some results for certain classes of non-self-similar fractals are presented. 2000 Math. Subj. Class.: Primary 28A80, 35J15; Secondary 31C25, 35P05