Asymptotic behavior of general M-estimates for regression and scale with random carriers

Summary Let (xini, y _i be a sequence of independent identically distributed random variables, where x _i R ^p and y _i R, and let R ^p be an unknown vector such that y _i =x _i +u _i (^*), where u _i is independent of x _i and has distribution function F(u/), where >0 is an unknown parameter. This paper deals with a general class of M-estimates of regression and scale, ( ^*,^*), defined as solutions of the system: , where r= (y _i –x _i ^1*/)^*, with R ^p ×RR and RR. This class contains estimators of (, ) proposed by Huber, Mallows and Krasker and Welsch. The consistency and asymptotic normality of the general M-estimators are proved assuming general regularity conditions on and and assuming the joint distribution of (x _i , y _i ) to fulfill the model (^*) only approximately.     

Influence of thermal fluctuations on interfacial electron transfer in functionalized TiO2 semiconductors

The influence of thermal fluctuations on the dynamics of interfacial electron transfer in sensitized TiO2-anatase semiconductors is investigated by combining ab initio DFT molecular dynamics simulations and quantum dynamics propagation of transient electronic excitations. It is shown that thermal nuclear fluctuations speed up the underlying interfacial electron transfer dynamics by introducing nonadiabatic transitions between electron acceptor states, localized in the vicinity of the photoexcited adsorbate, and delocalized states extended throughout the semiconductor material, creating additional relaxation pathways for carrier diffusion. Furthermore, it is shown that room-temperature thermal fluctuations reduce the anisotropic character of charge diffusion along different directions in the anatase crystal and make similar the rates for electron injection from adsorbate states of different character. The reported results are particularly relevant to the understanding of temperature effects on surface charge separation mechanisms in molecular-based photo-optic devices.     

Supramolecular chirogenesis in zinc porphyrins: interaction with bidentate ligands,formation of tweezer structures,and the origin of enhanced optical activity

The complexation behavior, binding properties, and spectral parameters of supramolecular chirality induction in the achiral host molecule, syn (face-to-face conformation) ethane-bridged bis(zinc porphyrin), upon interaction with chiral bidentate guests (diamines and amino alcohols) have been studied by means of UV-vis, CD, fluorescence, (1)H NMR, and ESI MS techniques. It was found that the guest structure plays a decisive role in the chirogenesis pathway. The majority of bidentate ligands (except those geometrically unsuitable) exhibit two major equilibria steps: the first guest ligation leading to formation of the 1:1 host-guest tweezer structure (K(1)) and the second guest molecule ligation (K(2)) forming the anti bis-ligated species (1:2). The second ligation is much weaker (K(1) > K(2)) due to the optimal geometry and stability of the 1:1 tweezer complex. The enhanced conformational stability of the tweezer complex ensures an efficient chirality transfer from the chiral guest to the achiral host, consequently inducing a remarkably high optical activity in the bis-porphyrin.     

Selective and quantitative separation of zinc and lead from other elements by cation-exchange chromatography in hydrohalic acid-acetone solutions

Zinc and lead can be separated from Cd, Bi(III), In and V(V) by eluting these elements with 0.2M hydrochloric acid in 60% acetone from a column of AG50W-X8 cation-exchange resin, zinc and lead being retained. Mercury(II), Tl(III), As(III), Au(III), Sn(IV), Mo(VI), W(VI) and the platinum metals have not been investigated quantitatively, but from their distribution coefficients, should also be eluted. Vanadium(V), Mo(VI) and W(VI) require the presence of hydrogen peroxide. Zinc and lead can be eluted with 0.5M hydrochloric acid in 60% acetone or 0.5M hydrobromic acid in 65% acetone and determined by AAS; the alkali and alkaline-earth metal ions, Mn(II), Co, Ni, Cu(II), Fe(III), Al, Ga, Cr(III), Ti(IV), Zr, Hf, Th, Sc, Y, La and the lanthanides are retained on the column, except for a small fraction of copper eluted with zinc and lead. Separations are sharp and quantitative. The method has successfully been applied to determination of zinc and lead in three silicate rocks and a sediment.     

Stability of inner planetary systems

The model of the planar restricted problem of three bodies is used to evaluate the stability of the inner planets of planetary systems with arbitrary mass ratios. A quantitative measure of stability is introduced by finding the difference between the critical value of the Jacobian constant (at which bifurcation may occur) and the value of the Jacobian constant that corresponds to planetary type orbits. Hill's definition of stability is used according to which inner planetary orbits are stable if they are bounded in a region enclosing only the larger primary. For small values of the massparameter (<10^–3) the maximum value of the dimensionless radius of the orbit for Hill-stability is given by 1–2.4 µ^1/3.

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Zusammenfassung Die Stabilität von inneren Planetensystemen mit beliebigen Massenverhältnissen wird am Modell des ebenen restringierten Dreikörperproblems untersucht. Aufgrund der Differenz zwischen dem kritischen Wert der Jacobi-Konstanten (wo Bifurkation eintreten kann) und dem einer Planetenbahn entsprechenden Wert wird ein quantitatives Stabilitätsmass eingeführt. Dabei wird die Hillsche Stabilitätsdefinition verwendet, d.h. eine innere Planetenbahn heisst stabil, wenn sie ein nur den grösseren Zentralkörper enthaltendes Gebiet nicht verlassen kann. Für klein Werte des Massenparameters (<10^–3) beträgt der maximale (dimensionslose) Radius einer Hill-stabilen Planetenbahn 1–2.4 µ^1/3.

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Dedicated to Professor Eduard Stiefel     

Synthesis of 2-amino-5,5-dialkyl-4-arylmethylidene-2-oxazolines from 2-alkyl-4-arylbut-3-yn-2-ols and guanidine

Reaction between 2-alkyl-4-arylbut-3-yn-2-ols and guanidine in refluxing pyridine affords 2-amino-5,5-dialkyl-4-arylmethylidene-2-oxazolines.     

Synthesis of New Heteroatomic Podands from Ethyl 2-[(2-Aminophenylamino)Methylidene]-3-Oxoalkanoates and Thiophene-2,5-Dicarboxaldehyde

Condensation of two moles of ethyl 2-[(2-aminophenylamino)methylidene]-3-oxo-3-(polyfluoroalkyl)propionates with 2,5-thiophene-dicarboxaldehyde results in new heteroatomic podands. X-ray data showed that in the solid state these molecules arrange in two independent chelating fragments of b-amino enone type, thiophene fragment being a spacer.