Continuous convolution semigroups integrating a submultiplicative function

Let be a submultiplicative function on a locally compact group G and let S be a convolution semigroup on G with Lévy measure . It is shown that the measures of S integrate if and only if integrates outside some neighbourhood of the identity of G (Theorem 1). Moreover if (X(t);t0) is the G-valued process with independent increments associated with the semigroup S it is shown that the measures of S integrate if and only if the random variable sup { (X(t)):0t1} is integrable (Theorem 2).     

Tetradentate bis(o-iminobenzosemiquinonate(1-)) pi radical ligands and their o-aminophenolate(1-) derivatives in complexes of nickel(II), palladium(II), and copper(II)

The coordination chemistries of the potential tetradentate ligands N,N'-bis(3,5-di-tert-butyl-2-hydroxyphenyl)ethylenediamine, H4[L1], the unsaturated analogue glyoxal-bis(2-hydroxy-3,5-di-tert-butylanil), H2[L2], and N,N'-bis(2-hydroxy-3,5-di-tert-butylphenyl)-2,2-dimethylpropylenediamine, H4[L3], have been investigated with nickel(II), palladium(II), and copper(II). The complexes prepared and characterized are [Ni(II)(H3L1)2] (1), [Ni(II)(HL2)2].5/8CH2Cl2 (2), [Ni(II)(L3**)] (3), [Pd(II)(L3**)][Pd(II)(H2L3) (4), and [Cu(II)(H2O)(L4)] (5), where (L4)2- is the oxidized diimine form of (L3)4- and (L3**)2- is the bis(o-iminosemiquinonate) diradical form of (L3)4-. The structures of compounds 1-5 have been determined by single crystal X-ray crystallography. In complexes 1 and 2, the ligands (H3L1)- and (HL2)- are tridentate and the nickel ions are in an octahedral ligand environment. The oxidation level of the ligands is that of an aromatic o-aminophenol. 1 and 2 are paramagnetic (mu(eff) approximately 3.2 mu(B) at 300 K), indicating an S = 1 ground state. The diamagnetic, square planar, four-coordinate complexes 3 and [Pd(II)(L3**)] in 4 each contain two antiferromagnetically coupled o-iminobenzosemiquinonate(1-) pi radicals. Diamagnetic [Pd(II)(H2L3)] in 4 forms an eclipsed dimer via four N-H.O hydrogen bonding contacts which yields a nonbonding Pd.Pd contact of 3.0846(4) A. Complex 5 contains a five-coordinate Cu(II) ion and two o-aminophenolate(1-) halves in (L4)2-. The electrochemistries of complexes 3 and 4a ([Pd(II)(L3**)] of 4) have been investigated, and the EPR spectra of the monocations and -anions are reported.     

Zur Kennzeichnung der Lorentz-Transformationen

Let (V, f) be a real Minkowski space of any, not necessarily finite, dimension, and letd be the corresponding distance function (taking negative values for timelike distances). Then the following statement (among others) is proved: If ? :V →V is a surjective mapping such that $$d(P,Q) = a \Leftrightarrow d(P^\varphi ,Q^\varphi ) = a\forall P,Q \in V$$ is true for some fixeda εR,a<0, then ? is a Lorentz transformation (including a possible translation).     

An ALE finite element method for a coupled Stefan problem and Navier–Stokes equations with free capillary surface

In this article, an ALE finite element method to simulate the partial melting of a workpiece of metal is presented. The model includes the heat transport in both the solid and liquid part, fluid flow in the liquid phase by the Navier–Stokes equations, tracking of the melt interface solid/liquid by the Stefan condition, treatment of the capillary boundary accounting for surface tension effects and a radiative boundary condition. We show that an accurate treatment of the moving boundaries is crucial to resolve their respective influences on the flow field and thus on the overall energy transport correctly. This is achieved by a mesh‐moving method, which explicitly tracks the phase boundary and makes it possible to use a sharp interface model without singularities in the boundary conditions at the triple junction. A numerical example describing the welding of a thin‐steel wire end by a laser, where all aforementioned effects have to be taken into account, proves the effectiveness of the approach.Copyright © 2012 John Wiley & Sons, Ltd.     

A high-order full-discretization method using Hermite interpolation for periodic time-delayed differential equations

A high-order full-discretization method(FDM)using Hermite interpolation(HFDM) is proposed and implemented for periodic systems with time delay. Both Lagrange interpolation and Hermite interpolation are used to approximate state values and delayed state values in each discretization step. The transition matrix over a single period is determined and used for stability analysis. The proposed method increases the approximation order of the semidiscretization method and the FDM without increasing the computational time. The convergence, precision, and efficiency of the proposed method are investigated using several Mathieu equations and a complex turning model as examples. Comparison shows that the proposed HFDM converges faster and uses less computational time than existing methods.     

A NEW SYNTHETIC ROUTE TO SULFINIC ACID ESTERS

Abstract

Dialkylsulfoxylates undergo reactions with alkylhalides and other alkylating agents to give sulfinic acid esters, which were characterized by IR-, ¹H-NMR- and mass-spectra.     

Intramolecular [2+2] Photocycloaddition of 3‐ and 4‐(But‐3‐enyl)oxyquinolones: Influence of the Alkene Substitution Pattern,Photophysical Studies,and Enantioselective Catalysis by a Chiral Sensitizer

The intramolecular [2+2] photocycloaddition of four 4‐(but‐3‐enyl)oxyquinolones (substitution pattern at the terminal alkene carbon atom: CH₂, Z‐CHEt, E‐CHEt, CMe₂) and two 3‐(but‐3‐enyl)oxyquinolones (substitution pattern: CH₂, CMe₂) was studied. Upon direct irradiation at λ=300 nm, the respective cyclobutane products were formed in high yields (83–95 %) and for symmetrically substituted substrates with complete diastereoselectivity. Substrates with a Z‐ or E‐substituted terminal double bond showed a stereoconvergent reaction course leading to mixtures of regio‐ and diastereomers with almost identical composition. The mechanistic course of the photocycloaddition was elucidated by transient absorption spectroscopy. A triplet intermediate was detected for the title compounds, which–in contrast to simple alkoxyquinolones such as 3‐butyloxyquinolone and 4‐methoxyquinolone–decayed rapidly (τ≈1 ns) through cyclization to a triplet 1,4‐diradical. The diradical can evolve through two reaction channels, one leading to the photoproduct and the other leading back to the starting material. When the photocycloaddition was performed in the presence of a chiral sensitizer (10 mol %) upon irradiation at λ=366 nm in trifluorotoluene as the solvent, moderate to high enantioselectivities were achieved. The two 3‐(but‐3‐enyl)oxyquinolones gave enantiomeric excesses (ees) of 60 and 64 % at ?25 °C, presumably because a significant racemic background reaction occurred. The 4‐substituted quinolones showed higher enantioselectivities (92–96 % ee at ?25 °C) and, for the terminally Z‐ and E‐substituted substrates, an improved regio‐ and diastereoselectivity.     

A quantitative HPLC–MS/MS method for studying internal concentrations and toxicokinetics of 34 polar analytes in zebrafish (Danio rerio) embryos

An analytical method using high-performance liquid chromatography–tandem mass spectrometry was developed to determine internal concentrations of 34 test compounds such as pharmaceuticals and pesticides in zebrafish embryos (ZFE), among them, cimetidine, 2,4-dichlorophenoxyacetic acid, metoprolol, atropine and phenytoin. For qualification and quantification, multiple reaction monitoring mode was used. The linear range extends from 0.075 ng/mL for thiacloprid and metazachlor and 7.5 ng/mL for coniine and clofibrate to 250 ng/mL for many of the test compounds. Matrix effects were strongest for nicotine, but never exceeded ±20 % for any of the developmental stages of the ZFE. Method recoveries ranged from 90 to 110 % from an analysis of nine pooled ZFE. These findings together with the simple sample preparation mean this approach is suitable for the determination of internal concentrations from only nine individual ZFE in all life stages up to 96 h post-fertilization. Exemplarily, the time course of the internal concentrations of clofibric acid, metribuzin and benzocaine in ZFE was studied over 96 h, and three different patterns were distinguished, on the basis of the speed and extent of uptake and whether or not a steady state was reached. Decreasing internal concentrations may be due to metabolism in the ZFE.