The driving torque of a rotating levitated cylindrical permanent magnet above a superconductor

Due to the Meissner effect, a permanent magnet is levitated, when released above a high temperature superconductor. When there is an inhomogeneous temperature field around the magnet, the magnet might start to oscillate with increasing amplitude until it remains in a continuous rotation. A mathematical model for the described effect is presented which couples heat transfer and electromagnetic forces with the equation of motion, yielding to a multiphysics task. In a detailed analysis it is found, that the torque which drives the rotation of the magnet, is explicitly given in terms of Bessel functions and the Fourier coefficients of order zero and one of the temperature field of the surrounding air.     

Multiparameter Polynomial Adaptive Stabilizers

In 1983 Morse proved, for unknown scalar one-dimensional linearsystems, the nonexistence of rational or polynomial universalstabilizers (UAS). In 1983, Nussbaum gave an example of an analyticUAS. In our paper, it is shown that there exist time-invariantpolynomial UAS's with multidimensional gain adaptation. Thedesign procedure is developed for linear, minimum-phase systemsof relative degree one. Convergence of the closed-loop systemis proved. Some numerical simulations are provided.     

Electronic structures and MCD spectra of trigonal Cr(III)S6 systems

MCD, electronic absorption, external heavy atom, and crystal field data are presented for the low energy region (² E _g, ² T _1g, ⁴ T _2g) and high energy region (² T _2g, ⁴ T _1g) of Cr(dtp)₃, Cr(dtc)₃, and Cr(exan)₃. At low energy, MCD intensities of ² E(² E _g) and ² E(² T _g) are as large or larger than ⁴ T _2g, and the MCD technique is advantageous over electronic absorption in this respect. The MCD positions of ² E _g and ² T _1g are nearly the same for these molecules ( 13 kK and 13.6 kK) · ⁴ T _2g of this region appears trigonally split ( 500 cm^–1) in the MCD of dtp but to a smaller extent than in the electronic crystal spectrum of Lebedda and Palmer ( 600 cm^–1). MCD did not resolve such components for exan and dtc. The higher energy region includes ² T _2g and ⁴ T _1g, and the combined MCD and electronic absorption data of the three compounds taken together lead us to conclude the ordering ² A ₁(² T _2g)<² E(² T _2g)<⁴ E(⁴ T _1g). The potentially useful external heavy atom affect on the solution-observed electronic ² E and ⁴ E bands of Cr(dtp)₃ did not shed additional light on this order of E states. Finally, it is concluded that the order of ⁴ T _1g and ² T _2g cannot be decided from O _h crystal field calculations because of experimental uncertainties about choosing centers of gravity. In addition, ⁴ T _1g and ² T _2g are close together so that ordering ² E<⁴ E does not guarantee ² T _2g<⁴ T _1g. However, it can be concluded that the ratio C/B4 is not correct, whereas the larger 7<(C/B)<8 is consistent with the data of all three molecules because of small B parameters ( 0.4). Locating OO transitions may somewhat decrease C/B and Dq.

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Zusammenfassung In der vorliegenden Arbeit werden folgende Meßergebnisse mitgeteilt; MCD, elektronische Absorption, Einfluß eines äußeren schweren Atoms sowie Kristallfelddaten für den Bereich niedriger Energie (² E _g, ² T _1g, ⁴ T _2g) und den Bereich hoher Energie (² T _2g, ⁴ T _1g) von Cr(dtp)₃, Cr(dtc)₃ und Cr(exan). Bei niedriger Energie sind die MCD-Intensitäten von ² E(² E _g) und ² E(² T _1g) genau so groß, oder größer als ⁴ T _2g, und die MCD-Technik bietet Vorteile gegenüber der elektronischen Absorptionsmethode. Die MCD-Werte von ² E _g und ² T _1g sind für die genannten Moleküle etwa gleich ( 13 kK und 13,6 kK). ⁴ T _2g dieses Gebietes erscheint trigonal aufgespalten ( 500 cm^–1) bei MCD von dtp, aber in einem geringeren Maß als im elektronischen Kristallspektrum von Lebedda und Palmer ( 600 cm^–1) MCD löste solche Komponenten bei exan und dtc nicht auf. Der Bereich höherer Energie enthält ² T _2g und ⁴ T _1g, und aus der Kombination von Daten der MCD-Methode sowie der elektronischen Absorption schlossen wir auf die Anordnung ² A _1g(² T _2g)<² E(² T _2g)<⁴ E(⁴ T _1g). Der möglicherweise nützliche Effekt eines äußeren schweren Atoms auf die in Lösung beobachteten elektronischen ² E- und ⁴E-Banden von Cr(dtp)₃ brachte bezüglich dieser Anordnung der E-Zustände nichts Neues. Weiterhin wird gefolgert, daß die Ordnung von ⁴ T _1g und ² T _2g nicht aus O _h-Kristallfeldberechnungen entschieden werden kann, da experimentelle Unsicherheiten bezüglich der Wahl von Schwerpunkten bestehen. Außerdem liegen ⁴ T _1g und ² T _2g nahe zusammen, sodaß aus der Anordnung ² E<⁴ E nicht notwendig ² T _2g<⁴ T _1g folgt. Es kann jedoch gefolgert werden, daß das Verhältnis C/B4 nicht korrekt ist, während 7<(C/B)<8 konsistent mit den Daten aller drei Moleküle ist, da die B-parameter klein sind (0,4). Die Vokalisierung der OO-Übergänge könnten C/B und Dq etwas erniedrigen.

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Presented in part at the 161st American Chemical Society National Meeting, Los Angeles, California, March–April, 1971.

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NDEA Pre-Doctoral Fellow.     

1,4-Addition of benzene to a dihydrocyclopent[a]indene diradical: synthesis and DFT study

Photochemical cyclization of compound 1, a homoenediyne (-CCC=CCH2CC-) bearing two ethynylanthracene chromophores, yields two isomeric dihydrocyclopent[a]indene ring systems, spiro-fused to the 9-position of a 9,10-dihydroanthracene moiety. Evidence of a photochemically initiated diradical cyclization pathway is proposed on the basis of (i) hydrogen abstraction from reaction with 1,4-cyclohexadiene (1,4-CHD) and (ii) the observation of 1,4-addition of benzene (solvent). The reaction was further analyzed by a complete density functional theory (DFT) study, using an unrestricted approach (UBLYP) with a 6-31G* basis set for the open-shell triplet states of the reactants, products, and diradical intermediates to model the photochemical nature of observed transformation. A mechanism detailing the observed cyclization/addition reaction is proposed.     

Thermal and magnetization studies on Heusler alloys

Saturation magnetization measurements as a function of temperature were performed on Cu₂Mn(Al_1–xSn_x) Heusler alloys to study the existence of stable structures. The derivatograph was applied to study the thermal effects.

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Zusammenfassung Sättigungsmagnetisierungsmessungen als Funktion der Temperatur sowie Derivatographie wurden an Heusler-Legierungen der Formel Cu₂Mn(Al_1–xSn_x) zu Untersuchungen der Existenz einer stabilen Struktur vorgenommen.

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Résumé Etude de l'existence d'une structure stable dans les alliages de Heusler Cu₂Mn(Al_1–xSn_x), à l'aide d'un Derivatograph et par des mesures de magnétisation à saturation en fonction de la température.

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XecnepaCu₂Mn(Al_1–xSn_x), , , . .

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Work supported in part by Conselho Nacional de Desenvolvimento Cientifico e Tecnologico and Banco Nacional de Desenvolvimento Economico, Brasil.     

Which electron count rules are needed for four-center three-dimensional aromaticity?

A series of charged and neutral four-center n-electron (4c-ne, n = 1-4) molecules based on the adamantane framework, but which include combinations of boron, nitrogen, and phosphorus atoms at bridgehead positions, were studied computationally at the B3LYP/6-31G* level of density functional theory (DFT). The three-dimensional aromaticity, observed earlier for the 1,3,5,7-bisdehydroadamantane dication (1), is found to be general for 4c-2e electron systems. The degree of electron delocalization, evaluated by energetic, geometric, and various magnetic criteria, is quite independent of the molecular symmetry (point groups vary from Td to Cs), the degeneracy of the orbitals, the molecular charges, and the nature of the atoms participating in the delocalized bonding. Although the multiple positive (e.g., in 1 and some of the heteroatom systems) and multiple negative charges are strongly repulsive, the rigid adamantane frameworks help hold the bridgehead atoms within bonding distances with the fewer available electrons. The corresponding 4c-1e doublets are approximately half as aromatic as the 4c-2e singlets based on the same criteria. However, the three-electron systems may either adopt distorted but still four-center delocalized structures, or alternative 3c-2e two-dimensional arrangements in which the fourth bridgehead atom is more distant. There is no need to derive special rules for each point group for 4c-ne systems. Although the three-dimensional stabilization is computed to be quite appreciable, ranging between 10 and 50 kcalmol(-1), this delocalization energy is generally not sufficient to overcome distortion due to strain in higher homologues of 1 and in analogous noncage systems. Among the various 4c-2e homoadamantanedehydro dications studied, only the 1,8-dehydrohomoadamandiyl-3,6-dication forms a three-dimensional aromatic system.     

A convenient protocol for selective cleavage of 2-hydroxy acid amides. Application to semisynthesis of the cyclic heptapeptide aza HUN-7293

A two-step protocol for the first chemoselective cleavage of 2-hydroxy acid amides has been developed. Mesylation of the model substrate 2-(hydroxypropionylamino)-4-methylpentanoic acid methyl ester (11) followed by treatment with N-ethylthiourea (13) allows cleavage of 2-hydroxy acid amides under smooth conditions. Successful application of this methodology to the open-chain transesterification product 15 (methylester) of the cyclic heptadepsipeptide HUN-7293, a potent inhibitor of inducible cell adhesion molecule expression, delivered the corresponding hexapeptide 18 with unprotected N-terminus in 70-75% yield. This result demonstrates that the protocol developed even works in the presence of an ester and several methylated and unmethylated amide bonds. Finally, a sequence of ligation of methyl D-dehydroglutaminate (20) to the C-terminus of the saponification product 21, followed by the degradation protocol and ring closure, allowed chemical "point mutation" at the DGCN site affording the aza analogue of HUN-7293 (24) in 15% overall yield. To the best of our knowledge this is the first report on chemoselective cleavage of 2-hydroxy acid amides.