Structures and stability of Al<Subscript><Emphasis Type="Bold">7</Emphasis></Subscript>C and Al<Subscript><Emphasis Type="Bold">7</Emphasis></Subscript>N clusters

We report results of the atomic and electronic structures of Al₇C cluster using ab initio molecular dynamics with ultrasoft pseudopotentials and generalized gradient approximation. The lowest energy structure is found to be the one in which carbon atom occupies an interstitial position in Al₇ cluster. The electronic structure shows that the recent observation [Chem. Phys. Lett. 316, 31 (2000)] of magic behavior of Al₇C^- cluster is due to a large highest occupied and lowest unoccupied molecular orbital (HOMO-LUMO) gap which makes Al₇C^- chemically inert. These results have further led us to the finding of a new neutral magic cluster Al₇N which has the same number of valence electrons as in Al₇C^- and a large HOMO-LUMO gap of 1.99 eV. Further, calculations have been carried out on (Al₇N)₂ to study interaction between magic clusters. Received 28 July 2001     

Wechselnde Bindungen in einem Zweikörpersystem mit trockener Reibung

Übersicht Betrachtet wird ein zwangserregtes Zweikörpersystem mit wechselnden Bindungen infolge trockener Reibung. Stationäre Bewegungen werden als Grenzfall instationärer Einschwingvorgänge berechnet. Abhängig von den Systemparametern ergeben sich drei typische Bewegungsformen. Ihnen entsprechen dauernde Haftzustände, wechselnde Haft-Gleitzustände oder dauernde Gleitzustände an der Berührfläche beider Körper.

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Intermittant constraints in a two-body-system with dry friction

Summary An externally excited two-body-system with intermittant constraints due to dry friction is considered. Stationary motions are calculated as limit cases of instationary transients. Depending on the parameters of the system, three typical modes are of interest. These correspond to permanent sticking, slipstick behaviour, or to permanent slipping in the contact surface of the bodies, respectively.

     

System Identification Models of the Equivalent Permittivity for Rain Medium

The dielectric constant for rain medium is investigated by utilizing the system identification method. The rain rate model and frequency model of permittivity in millimeter waves band for rain medium are presented. The results obtained with models are in very good agreement with references in calculating the attenuation of electromagnetic waves induced by rain, which Shows that the obtained models are valid and practicable. The cross-polar discrimination gotten with rain rate model is in agreement with references.     

Selective Propargylation of Carbonyl Compounds and Imines with Barium Reagents

A Barbier‐type regioselective propargylation of aldehydes and ketones with (3‐bromobut‐1‐ynyl)trimethylsilane has been achieved using reactive barium as a low‐valent metal in THF. Especially in the case of ketones, the corresponding homopropargylic alcohols form almost exclusively. In the reaction of α,β‐unsaturated carbonyl compounds, only 1,2‐adducts have been observed. This method is also applicable to propargylation of imines, and the corresponding homopropargylic amines are obtained regiospecifically in good yields with diastereomeric ratios of up to 87:13.     

Mathematics achievement and interest in mathematics from a differential perspective

In this article, we present results of an empirical study with 500 German students of grades 7 and 8. The study focussed on students' mathematics achievement and their interest in mathematics as well as on the relation between these two constructs. In particular, the results show that the development of an individual student's achievement between grade 7 and grade 8 depends on the achievement level of the specific classroom and therefore on the specific mathematics instruction Interest in mathematics could be regarded a predictor for mathematics achievement Moreover, our findings suggest that the students show hardly any fear of mathematics independent of their achievement level.     

Electrochemical determination of serotonin and the competitive adsorption with dopamine at 5,5-ditetradecyl-2-(2-trimethylammonioethyl)-1,3-dioxane bromide lipid film modified by glassy carbon electrode.

A novel and effective approach to sensitively determine serotonin, known as 5-hydroxytryptamine (5-HT), has been proposed based on a 5,5-ditetradecyl-2-(2-trimethylammonioethyl)-1,3-dioxane bromide (DTDB) self-assembled lipid bilayer membrane modified glassy carbon electrode (DTDB/GCE). A DTDB/GCE shows the strong electrocatalysis for the oxidation of 5-HT, with the peak potential shifted to less positive value of 0.376 V vs. SCE, and effectively eliminates the interference from ascorbic acid (AA), even in the presence of 100-fold concentration of AA. Differential pulse voltammetry (DPV) gave a linear current for 5-HT from 2.0 x 10(-7) to 1.0 x 10(-5) M. At the DTDB/GCE, the oxidation of 5-HT was controlled by the adsorption process; for 5-HT coexisting with DA, the competitive adsorption was observed.     

Control Policy for a Manufacturing System with Random Yield and Rework

We develop a production policy that controls work-in-process (WIP) levels and satisfies demand in a multistage manufacturing system with significant uncertainty in yield, rework, and demand. The problem addressed in this paper is more general than those in the literature in three aspects: (i) multiple products are processed at multiple workstations, and the capacity of each workstation is limited and shared by multiple operations; (ii) the behavior of a production policy is investigated over an infinite-time horizon, and thus the system stability can be evaluated; (iii) the representation of yield and rework uncertainty is generalized. Generalizing both the system structure and the nature of uncertainty requires a new mathematical development in the theory of infinite-horizon stochastic dynamic programming. The theoretical contributions of this paper are the existence proofs of the optimal stationary control for a stochastic dynamic programming problem and the finite covariances of WIP and production levels under the general expression of uncertainty. We develop a simple and explicit sufficient condition that guarantees the existence of both the optimal stationary control and the system stability. We describe how a production policy can be constructed for the manufacturing system based on the propositions derived.     

DISTORTION THEOREM FOR BIHOLOMORPHIC MAPPINGS IN TRANSITIVE DOMAINS (III)

The distortion theorem for biholomorphic convex mappings in bounded symmetric domains are considered. Especially the distortion theorem for biholomorphic convex mappings in classical domain of type IV and two exceptional domains are given.