Tail-homogeneity of stationary measures for some multidimensional stochastic recursions

We consider a stochastic recursion X _n+1 = M _n+1 X _n  + Q _n+1, ( ${n\in \mathbb {N}}$ ), where (Q _n , M _n ) are i.i.d. random variables such that Q _n are translations, M _n are similarities of the Euclidean space ${\mathbb {R}^d}$ and ${X_n\in \mathbb {R}^d}$ . In the present paper we show that if the recursion has a unique stationary measure ν with unbounded support then the weak limit of properly dilated ν exists and defines a homogeneous tail measure Λ. The structure of Λ is studied and the supports of ν and Λ are compared. In particular, we obtain a product formula for Λ.     

Comparison of the thermal stability of the α, β and γ phases in poly(vinylidene fluoride) based on in situ thermal Fourier transform infrared spectroscopy

The electroactive β phase of poly(vinylidene fluoride) (PVDF) is induced due to the aging time of PVDF solutions. The feasibility of the combination of the three crystalline polymorphs (α, β and γ) is demonstrated where their relative proportion within the PVDF film can be tailored by the simple monitoring of the preparation conditions. To identify all these phases, Fourier transform infrared (FT-IR) spectroscopy is carried out and it is spotlighted that the vibrational bands at 510 and 841 cm^?1 are not sufficient to state the formation of the β phase. The main aim of this work is devoted to develop a better understanding on the thermal stability of these several phases of PVDF, which has a longstanding ambiguity persisting in this area. It has been found that the in situ thermal FT-IR spectroscopy is one of the best alternatives to understand this important issue. It is ascertained that the β phase is the least thermally stable phase among α, β and γ phases, whereas the γ phase is the most thermally stable phase.     

Pycnangloside: a new cerebroside from bark of Pycnanthus angolensis

Pycnanthus anglonensis is known for its medicinal value. This paper deals with a phytochemical investigation of this species, from which pycnangloside (1), a new cerebroside has been isolated. Its structure was determined by comprehensive analyses of its 1D and 2D NMR spectroscopic, and ESI mass spectrometric data. Four known compounds were also isolated and identified as biochanin A, formonentin, beta-sitosterol, and beta-sitosterol glucopyranoside.     

Hyloglyceride and hylodiglyceride: two new glyceride derivatives from Hylodendron gabunensis

Phytochemical investigation of Hylodendron gabunensis resulted in the isolation of two new glyceride derivatives, hyloglyceride (1) and hylodiglyceride (2). The structures of the two new compounds were determined by comprehensive analysis of their 1D and 2D NMR spectroscopic, and HREIMS data. One known compound was also isolated and identified as beta-sitosterol.     

Amorphous drug nanosuspensions. 2. Experimental determination of bulk monomer concentrations

A simple turbidimetric method was developed to measure the bulk concentration of drug in nanosuspensions. The bulk concentrations measured were in the range from 1 microM to 1 mM. The accuracy of the method was checked by determination of the bulk concentration of crystalline nanosuspensions, i.e., the crystalline solubility, which compared favorably to solubilities measured by a conventional method. Results obtained for amorphous nanosuspensions agreed with predictions using a theory describing the relative solubility between a supercooled liquid and a crystal. Further, it was found that the bulk concentration in Ostwald ripening inhibited amorphous nanosuspensions and could be lowered by incorporation of higher amounts of the inhibitor, in agreement with predictions using the Bragg-Williams theory of nonideal solutions.     

Halogen - metal exchange of 3-substituted 1,2-dibromoarenes: the use of long-range JCH coupling constants to determine regiochemistry

Regioselective halogen/metal exchange reactions were carried out on a series of 3-substituted- 1,2-dibromoarenes. Product mixtures were quenched with CO2 to form the corresponding benzoic acid analogs to facilitate HPLC and NMR analysis. Substitution at the 3-position could readily be assigned on the basis of 2D HMBC long-range correlations, while assignment at the 2-position was not as straightforward. The use of three-bond J(CH) coupling constant measurements, extracted from 1-D 1H coupled 13C experiments, were necessary to render unequivocal regio assignments.     

Macropodumines A-C: novel pentacyclic alkaloids with an unusual skeleton or zwitterion moiety from Daphniphyllum macropodum Miq

Three novel alkaloids, macropodumines A-C (1-3), were isolated from the stem of Daphniphyllum macropodum Miq. Interestingly, the structure of macropodumine A (1) was characterized as having a fused pentacyclic system including an unusual eleven-membered macrolactone ring, whereas macropodumine B (2) contains a rare cyclopentadienyl carbanion, which is stabilized as a zwitterion by an internal iminium cation. The structures of these new metabolites were established on the basis of their detailed spectroscopic analysis. In particular, the unique structure of zwitterion 2 was further confirmed by using single-crystal X-ray diffraction analysis.     

Interaction-induced resonance in conductance and thermopower of quantum wires

We study the effect of electron-electron interaction on the transport properties of short clean quantum wires adiabatically connected to reservoirs. Interactions lead to resonances in a multichannel wire at particular values of the Fermi energy. We investigate in detail the resonance in a two-channel wire. The (negative) conductance correction peaks at the resonance, and decays exponentially as the Fermi energy is tuned away, the resonance width being given by the temperature. Likewise, the thermopower shows a characteristic structure, which is surprisingly well approximated by the so-called Mott formula. Finally, fourfold splitting of the resonance in a magnetic field provides a unique signature of the effect.     

Biomechanical modelling of cellular articular cartilage replacement tissues

The aim of the present study is to investigate the strength and damping properties of cellular articular cartilage replacement material. For this purpose, a viscoelastic-diffusion model for the acellular water-saturated condensed collagen gel type I is proposed and validated experimentally. Moreover, a remodelling law for the cell seeded collagen gel is introduced. For an experimental study of the interaction between fibre growth and mechanical stimulation, bioreactors are developed and histological investigations are carried out. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Cyaarside (CAs−) and 1,3‐Diarsaallendiide (AsCAs2−) Ligands Coordinated to Uranium and Generated via Activation of the Arsaethynolate Ligand (OCAs−)

Reaction of the trivalent uranium complex [((^Ad,MeArO)₃N)U(DME)] with one molar equiv [Na(OCAs)(dioxane)₃], in the presence of 2.2.2‐crypt, yields [Na(2.2.2‐crypt)][{((^Ad,MeArO)₃N)U^IV(THF)}(μ‐O){((^Ad,MeArO)₃N)U^IV(CAs)}] ( 1 ), the first example of a coordinated η¹‐cyaarside ligand (CAs^?). Formation of the terminal CAs^? is promoted by the highly reducing, oxophilic U^III precursor [((^Ad,MeArO)₃N)U(DME)] and proceeds through reductive C?O bond cleavage of the bound arsaethynolate anion, OCAs^?. If two equiv of OCAs^? react with the U^III precursor, the binuclear, μ‐oxo‐bridged U₂^IV/IV complex [Na(2.2.2‐crypt)]₂[{((^Ad,MeArO)₃N)U^IV}₂(μ‐O)(μ‐AsCAs)] ( 2 ), comprising the hitherto unknown μ:η¹,η¹‐coordinated (AsCAs)^2? ligand, is isolated. The mechanistic pathway to 2 involves the decarbonylation of a dimeric intermediate formed in the reaction of 1 with OCAs^?. An alternative pathway to complex 2 is by conversion of 1 via addition of one further equiv of OCAs^?.