Beweis und Verschärfung eines Satzes von Kronecker

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Über lineare Differenzen- und Differentialgleichungen

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Über die Bedingungen,daß eine binäre Formn-ten Grades einen-te Potenz ist,und über die rationale Kurven-ter Ordnung imR n

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Über Lineare Differenzengleichungen

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H?here Manganoxyde in der Silicatgesteins-Analyse

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Comparison of Results in Flexible Multibody Dynamics Using Various Approaches

Throughout the past decades a considerable amount of work has been dedicated to the development and application of formalisms to simulate flexible bodies in a multibody system (MBS). The two most common approaches to describe the deformation of a flexible body with respect to their floating frame of reference are to apply the linear finite-element formulation and the linearmodal approach using global mode shapes.On the field of flexible body modelling, this paper discusses two topics: (a) the consideration of quadratic terms in the equations of deformation and (b) the presentation of methods for global mode preparation to reduce the computer time for dynamic simulations without loss of accuracy regarding deformations.The proposed methods are applied in two examples, for the deformation of a stabilisation linkage of a car's front suspension and for the simulation of the deployment of a flexible solar array.     

Photochemische Reaktionen. 78. Mitteilung. Anwendung der π → π*-induzierten Cyclisierung von α,β-ungesättigten γ-Dimethoxymethylketonen auf 19-Methoxy- bzw. 19-Dimethoxy-Steroid-enone und -dienone

Irradiation at 254 nm of 19-dimethoxyandrost-4-en-17 β-ol-3-one acetate ( 8 ) afforded the epimeric cyclization products 9 (yield 20%) and 10 (4%). Similar transformations were also achieved with the analogous dimethoxy-enone 24 (→ 25 , 65%), and-dienone 30 (→ 31 , 72%), and with the methoxy-enone 33 (→ 34 , 30%), and-dienone 35 (→ 36 , 17%).     

Wetting of structured hydrophobic surfaces by water droplets

Super-hydrophobic surfaces may arise due to an interplay between the intrinsic, relatively high, contact angle of the more or less hydrophobic solid surface employed and the geometric features of the solid surface. In the present work, this relationship was investigated for a range of different surface geometries, making use of surface free energy minimization. As a rule, the free energy minima (and maxima) occur when the Laplace and Young conditions are simultaneously fulfilled. Special effort has been devoted to investigating the free energy barriers present between the Cassie-Baxter (heterogeneous wetting) and Wenzel (homogeneous wetting) modes. The predictions made on the basis of the model calculations compare favorably with experimental results presented in the literature.     

Photochemische Reaktionen. 117. Mitteilung [1] Zur Photochemie von 5,6-Epoxydienen und konjugierten 5,6-Epoxytrienen

Photochemistry of 5,6-Epoxydienes and of Conjugated 5,6-Epoxytrienes On singulet excitation (δ = 254 nm) the 5,6-epoxydiene 6 and the conjugated 5,6-epoxytrienes 7 and 8 exclusively give products arising from cleavage of the C, C-bond of the oxirane (cf. 6 → 9 , 10 , 11 ; 7 → (E)- 15 , 16 , 17 ; 8 → 18 (A+B) , 19 (A+B) , 20 , 21 ). The dihydrofuran compounds 11 and (E/Z)- 15 are formed by cyclization of a ketonium-ylide a and d , respectively. Photolysis of a gives the carbene b which yields the cyclopropene 9 , whereas d forms photochemically the carbenes f and g which yield the methano compounds 16 and 17 . The isomeric cyclopropene derivatives 20 and 21 are products of the intermediates h and i , respectively, which are formed by photolysis of the ylide e . The cyclopropene 21 isomerizes by intramolecular cycloadditions to 18 (A+B) and 19 (A+B) . - On triplet excitation (λ?LD nm; 280 nm; acetone) 6 undergoes cleavage of the C(5), O-bond and isomerizes to 12 and 14 . However, 7 is converted by cleavage of the C, C-bond of the oxirane to yield 15 . On treatment with BF₃O(C₂H₅)₂ 6 gives 14 , whereas 7 yields 22 , and 8 forms 23 and 24 .