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.     

Zur Minimalität trigonometrischer Polynomoperatoren

Cheney and others [2] have shown that, with respect to the norm of uniform convergence, the Fourier operator F_n:C₂p_n is the only minimal projection. For a more detailed study of operators A:C₂P_n we investigate the evaluation functionals respectively the mean of their norms . We give a complete characterization of polynomial operators which minimize this quantity. As an application we can simplify the proof in [2]. Moreover, we show that the trigonometric interpolation operators, having the above minimal-property,are exactly those with equidistant nodes.

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Diese Arbeit enthält die wesentlichen Resultate einer Diplomarbeit, die der Verfasser an der Eberhard-Karls-Universität Tübingen unter der Anleitung von A.Schönhage angefertigt hat.     

Seedling Development and Evaluation of Genetic Stability of Cryopreserved Dendrobium Hybrid Mature Seeds

Vitrification, a simple, fast, and recommended cryopreservation method for orchid germplasm conservation, was evaluated for Dendrobium hybrid “Dong Yai” mature seeds. The genetic stability of regenerated seedlings was also evaluated using flow cytometry. Mature seeds from this hybrid were submitted to plant vitrification solution (PVS2) for 0, 0.5, 1, 2, 3, 4, 5, or 6 h at 0 °C. Subsequently, they were plunged into liquid nitrogen (LN) at ?196 °C for 1 h and recovered in half-strength Murashige and Skoog culture medium (1/2 MS), and seed germination was evaluated after 30 days. Seeds directly submitted to LN did not germinate after cryopreservation. Seeds treated with PVS2 between 1 and 3 h presented the best germination (between 51 and 58 %), although longer exposure to PVS2 returned moderated germination (39 %). Germinated seeds were further subcultured in P-723 culture medium and developed whole seedlings in vitro after 180 days, with no abnormal characteristics, diseases, or nutritional deficiencies. Seedlings were successfully acclimatized under greenhouse conditions with over 80 % survival. Flow cytometry analysis revealed no chromosomal changes on vitrified seedlings, as well as seedlings germinated from the control treatment (direct exposure to LN). These findings indicate that vitrification is a feasible and safe germplasm cryopreservation method for commercial Dendrobium orchid hybrid conservation.     

An elementary proof of a converse mean-value theorem

We present a new converse mean value theorem, with a rather elementary proof.     

Fibrous Networks with Incorporated Macrocycles: A Chiral Stimuli‐Responsive Supramolecular Supergelator and Its Application to Biocatalysis in Organic Media

A new and versatile, crown ether appended, chiral supergelator has been designed and synthesized based on the bis‐urea motif. The introduction of a stereogenic center improved its gelation ability significantly relative to its achiral analogue. This low‐molecular‐weight gelator forms supramolecular gels in a variety of organic solvents. It is sensitive to multiple chemical stimuli and the sol–gel phase transitions can be reversibly triggered by host–guest interactions. The gel can be used to trap enzymes and release them on demand by chemical stimuli. It stabilizes the microparticles in Pickering emulsions so that enzyme‐catalyzed organic reactions can take place in the polar phase inside the microparticles, the organic reactants diffusing through the biphasic interface from the surrounding organic phase. Because of the higher interface area between the organic and polar phases, enzyme activity is enhanced in comparison with simple biphasic systems.     

Lifshitz tails for Schrödinger operators with random breather potential

We prove a Lifshitz tail bound on the integrated density of states of random breather Schrödinger operators. The potential is composed of translated single-site potentials. The single-site potential is an indicator function of the set tA where t is from the unit interval and A is a measurable set contained in the unit cell. The challenges of this model are that, since A is not assumed to be star-shaped, the dependence of the potential on the parameter t is not monotone. It is also non-linear and not differentiable.     

Development and validation of a rapid RP‐HPLC method for analysis of (−)‐copalic acid in copaíba oleoresin

The Copaifera species (Leguminoseae) are popularly known as ‘copaíba’ or ‘copaíva’ and are grown in the states of Amazonas, Pará and Ceará in northern Brazil. The oleoresins obtained from these species have been extensively used owing to their pharmacological potential and their application in cosmetic and pharmaceutical preparations. In the present study, the development and validation of a novel, rapid and efficient RP‐HPLC methodology for the analysis of the diterpene (?)‐copalic acid (CA), pointed out as the only chemical marker of the Copaifera genus, are described. The regression equation (Y = 26,707x ? 29,498) was obtained with good linearity (r² = 0.9993) and the limits of quantification and detection were 9.182 and 3.032 µg/mL, respectively. The precision and the accuracy of the method were adequate (lower than 4%). Finally, the validation parameters evaluated were satisfactorily met, so the developed method represents a suitable tool for application in the quality control of such natural products. Further studies aiming to develop analytical methodologies for each Copaifera species using a more representative number of chemical markers should be performed. Copyright © 2012 John Wiley & Sons, Ltd.     

Fluorinated Musk Fragrances: The CF2 Group as a Conformational Bias Influencing the Odour of Civetone and (R)‐Muscone

The difluoromethylene (CF₂) group has a strong tendency to adopt corner over edge locations in aliphatic macrocycles. In this study, the CF₂ group has been introduced into musk relevant macrocyclic ketones. Nine civetone and five muscone analogues have been prepared by synthesis for structure and odour comparisons. X‐ray studies indeed show that the CF₂ groups influence ring structure and they give some insight into the preferred ring conformations, triggering a musk odour as determined in a professional perfumery environment. The historical conformational model of Bersuker and co‐workers for musk fragrance generally holds, and structures that become distorted from this consensus, by the particular placement of the CF₂ groups, lose their musk fragrance and become less pleasant.