D-Domains of attraction of stable measures on stratified Lie groupsof attraction of stable measures on stratified Lie groups

LetG be a stratified Lie group and (_t)_{t 0} be a continuous convolution semigroup of probability measures onG. A probability measurev is said to belong to the -domain of attraction of ₁, if there exists a sequence (a _n ) of positive real numbers such that weakly, where ₁ denotes the natural dilation onG. We prove convergence criteria for discrete convolution semigroups. These are used to obtain a simple necessary and sufficient condition for the existence of sucha _n if (_t)_{t 0} has no Gaussian component. For the proof we introduce the notion of regularly varying measures onG and develop the necessary theory of regular variation.     

1,3,5-Triamino-1,3,5-trideoxy-cis-inositol,a New Ligand with a Remarkable Versatility for Metal Ions. Part 2. Safe and efficient ligand preparation and structure of the free ligand and the CoIII complex

A new, convenient, and safe route to 1,3,5-triamino-1,3,5-trideoxy-cis-inositol (taci) was investigated by hydrogenation of azo-coupled derivatives of phloroglucinol. In the presence of acetic anhydride, the reduction of trisphenylazophloroglucinol (H₂/Pd(5%) on C) resulted in the formation of tri-, hexa-, and nona-acetylated derivatives of triaminophloroglucinol. All three compounds are air-stable, colorless solids. However, the succeeding hydrogenation to the cyclohexane derivative failed. Trisodiumtris(p-sulfonatophenylazo)phloroglucinol could be hydrogenated in a one-pot reaction to the desired taci· 1.5H₂SO₄ using a Pt/Rh oxide as catalyst. taci provides two distinct chair conformations with either three amino or three hydroxy groups for metal binding. The unique metal-binding properties are discussed in terms of minimal conformational changes required for coordination. Conformational analysis, based on X-ray structural data of [BiCl₆][H₃(taci)] ·2 H₂O (Pnma, a = 24.314 (5) Å, b = 10.215 (2) Å, c = 7.422 (8) Å, R = 5.8%) and [Co(taci)₂(NO₃)₃]·2H₂O (C2/c, a = 22.912 (8) Å, b = 8.942 (2) Å, c = 14.731 (3) Å, β = 128.66 (2)°, R = 4.9%) and the previously investigated [Cr(taci)₂]³⁺ revealed an almost ideal chair conformation in all three molecules.     

Structures and Mutagenic Properties of Products Obtained by C-Nitrosation of Opipramol

Reaction of the tricyclic psychotropic drug opipramol ( 1 ) with an excess of HNO₂ affords a product mixture mutagenic for Salmonella typhimurium. The main product is a tetracyclic furoxan 2 (yield ca. 80%), resulting from nitrosation at C(10) and C(11) of 1 . Compound 2 is not mutagenic. The essential mutagen is a nitroarene 3 formed via contraction of the central ring of 1 , and nitrosation at C(2). Its yield is extremely low (<0.1%). Nitroarenes have previously not been encountered as mutagenic products of the interaction of drugs with nitrite.     

Desoxy-nitrozucker. 2. Mitteilung Herstellung geschützter 1-Desoxy-1-nitroaldosen

Synthesis of Protected 1-Deoxy-1-nitroaldoses The direct oxidation of the oxime 1 with t-butyl hydroperoxide and vanadyl acetylacetonate yielding the nitro derivative 2 (54%, Scheme 1) could not be applied to other oximes. Diastereoselective bromination of the aldonolactone oxims 7 and 10–12 according to known procedures gave the corresponding bromonitroso compounds which were oxidized to the bromonitro compounds 9, 14, 18 and 22 , respectively. Oxidation of the bromonitroso compound in the D-mannopyranose series proved difficult, but the corresponding chloronitro derivative 23 was easily obtained according to Corey & Estreicher (Scheme 2 and 3). The structure of the bromonitro compound 9 was determined by an X-ray analysis, and the configurations of the bromonitro compounds 14, 18 and 22 were deduced from their molecular rotations. Reduction of the bromonitro compounds gave the protected 1-deoxy-l-nitroaldoses 2 , 15/16 , 19/20 , and 24/25 , respectively, in good overall yields. The ribose derivatives 15 and 16 were detritylated to give the nitro compound 4 , and the mannose derivative 2 was partially deprotected to give the monoisopropylidene compound 26 . The nitro group shows a normal anomeric effect which is reflected in the IR . spectra of the pyranose derivatives 19 and 20 , and 24 and 25 .     

Two-photon state selection and angular momentum polarization probed by velocity map imaging: application to H atom photofragment angular distributions from the photodissociation of two-photon state selected HCl and HBr

A formalism for calculating the angular momentum polarization of an atom or a molecule following two-photon excitation of a J-selected state is presented. This formalism is used to interpret the H atom photofragment angular distributions from single-photon dissociation of two-photon rovibronically state selected HCl and HBr prepared via a Q-branch transition. By comparison of the angular distributions measured using the velocity map imaging technique with the theoretical model it is shown that single-photon dissociation of two-photon prepared states can be used for pathway identification, allowing for the identification of the virtual state symmetry in the two-photon absorption and/or the symmetry of the dissociative state. It is also shown that under conditions of excitation with circularly polarized light, or for excitation via non-Q-branch transitions with linearly polarized light the angular momentum polarization is independent of the dynamics of the two-photon transition and analytically computable.     

Absolute Configuration of 2-Substituted 2-Azabicyclo[2.2.1]hept-5-enes

The diastereoisomeric 2-substituted 2-azabicyclo[2.2.1]hept-5-enes 2 – 4 were prepared by aza-Diels-Alder reaction of cyclopentadiene with the corresponding methaniminium ions. Their relative configurations were deduced using ¹H, ¹H-ROESY experiments, and their absolute configurations were assigned from the crystal structure of the aziridinium derivative (?)- 5 . The absolute configuration of (+)- 1 , i.e. (1R), was assigned by CD spectroscopy.     

Reactive groups on polymer-covered electrodes

Polythiophene films containing ester groups on the surface of electrodes are interesting potential carrier materials for reagents. Methyl thiophene-3-acetate (3) can be copolymerized with 3-methylthiophene (1) and 3-butylthiophene (2) by means of cyclic voltammetry (CV) at potentials of 0–2.2 V. Higher potentials (0–2.4 V) lead to overoxidation of the copolymers. The ester groups were confirmed by FTIR spectra. Electrochemical investigations of 2,2′-bithiophene (6) and 3 at equimolar ratios showed no successful copolymerization at potentials of 0–1.3 V. If the copolymerization experiments of 6 with 1 or 3 were carried out at molar ratios of 1:50 at 1.3 V, 6 with its low oxidation potential was polymerized without copolymerization of the other monomers. However, if the oxidation potential was increased stepwise from 1.3 V, the oxidation of 1 or 3 occurred, forming copolymers containing both monomer components. HPLC investigations of solutions containing mixtures of 6 and 3 and also 6 and 1 in acetonitrile/TEABF₄ showed, after exhaustive oxidation at a potential of 1.3 V, the complete absence of 6; 1 and the ester 3 were not oxidized and copolymerized at these potentials. From the results of the copolymerization experiments, as well as the HPLC investigations, it can be concluded that the dominant mechanism of the electrochemical polymerization is radical cation dimerization. Received: 21 August 1998 / Accepted: 11 January 2000     

Flavonoids in Treatment of Chronic Kidney Disease

Chronic kidney disease (CKD) is a progressive systemic disease, which changes the function and structure of the kidneys irreversibly over months or years. The final common pathological manifestation of chronic kidney disease is renal fibrosis and is characterized by glomerulosclerosis, tubular atrophy, and interstitial fibrosis. In recent years, numerous studies have reported the therapeutic benefits of natural products against modern diseases. Substantial attention has been focused on the biological role of polyphenols, in particular flavonoids, presenting broadly in plants and diets, referring to thousands of plant compounds with a common basic structure. Evidence-based pharmacological data have shown that flavonoids play an important role in preventing and managing CKD and renal fibrosis. These compounds can prevent renal dysfunction and improve renal function by blocking or suppressing deleterious pathways such as oxidative stress and inflammation. In this review, we summarize the function and beneficial properties of common flavonoids for the treatment of CKD and the relative risk factors of CKD.     

Triangular array limits for continuous time random walks

A continuous time random walk (CTRW) is a random walk subordinated to a renewal process, used in physics to model anomalous diffusion. Transition densities of CTRW scaling limits solve fractional diffusion equations. This paper develops more general limit theorems, based on triangular arrays, for sequences of CTRW processes. The array elements consist of random vectors that incorporate both the random walk jump variable and the waiting time preceding that jump. The CTRW limit process consists of a vector-valued Lévy process whose time parameter is replaced by the hitting time process of a real-valued nondecreasing Lévy process (subordinator). We provide a formula for the distribution of the CTRW limit process and show that their densities solve abstract space–time diffusion equations. Applications to finance are discussed, and a density formula for the hitting time of any strictly increasing subordinator is developed.     

Thermal expansion in the Burns-phase of barium titanate stannate

The thermal expansion S_T has been measured in the system BaTi_1−xSn_xO₃, both for the pure compositions x=0 (BT) and x=1 (BS), and for solid solutions 0.025≤x≤0.2 (BTS). For all ceramics examined, a non-linear temperature dependence S_T(T) has been observed at elevated temperatures This is related to thermally generated impurities and, below the Burns-temperature T_d of BT and BTS, to the non-linear strain contribution of polar nanoregions. With increasing Sn-content x, a steep increase of the Burns-temperature is found in BTS for compositions x≥0.025.