Die Einheiten in der K?lte-Industrie

Ohne Zusammenfassung     

Ueber die Integration der trigonometrischen Reihe

Ohne Zusammenfassung     

Ueber Darstellungsfunctione

Ohne ZusammenfassungAus einer brieflichen Mittheilung des Verfassers an Hrn. C. Neumann.     

Predominant time scales in fission processes in reactions of S, Ti and Ni with W: zeptosecond versus attosecond

The inhibition of fusion by quasifission is crucial in limiting the formation of superheavy elements in collisions of heavy nuclei. Time scales of ～10(-18) s inferred for fissionlike events from recent crystal blocking measurements were interpreted to show either that quasifission itself is slower than previously believed, or that the fraction of slow fusion-fission is higher than expected. New measurements of mass-angle distributions for (48)Ti and (64)Ni bombarding W targets show that in these reactions quasifission is the dominant process, typically occurring before the system formed after contact has made a single rotation, corresponding to time scales of ≤10(-20) s.     

On the Eigenvalues and Eigenvectors of a Lorentzian Rotation Matrix by Using Split Quaternions

In this paper, we examine eigenvalue problem of a rotation matrix in Minkowski 3 space by using split quaternions. We express the eigenvalues and the eigenvectors of a rotation matrix in term of the coefficients of the corresponding unit timelike split quaternion. We give the characterizations of eigenvalues (complex or real) of a rotation matrix in Minkowski 3 space according to only first component of the corresponding quaternion. Moreover, we find that the casual characters of rotation axis depend only on first component of the corresponding quaternion. Finally, we give the way to generate an orthogonal basis for ${\mathbb{E}^{3}_{1}}$ by using eigenvectors of a rotation matrix.     

Studies on the Regioselectivity of Horner-Wadsworth-Emmons (Hwe) Reactions on 3,4-Enuloses. Further Evidence of Phosphonate-Phosphate Rearrangements Through Five Membered Cyclic Intermediates.

ABSTRACT

The Horner-Wadsworth-Emmons (HWE) reaction was performed on methyl 3,6-di-O-benzoyl-2-deoxy-α-D-glycero-hex-2-enopyranosid-4-ulose (1) with the potassium enolates of dimethyl [(methoxycarbonyl)methyl]phosphonate (2) or diethyl [(ethoxycarbonyl) methyl]phosphonate (3) under different conditions (metallic cation and solvent) in order to study regio- and stereochemical aspects of the reaction. In the presence of lithium ions, no reaction took place. When sodium enolates were employed, 1,2-addition was the main reaction in chelating solvents, whereas the 1,4-adduct is favoured in the less polar, non chelating toluene. Only 1,2-addition was observed with potassium enolates. Evidence of phosphonate-phosphate rearrangements through five membered cyclic intermediates is described.     

Zusatz zu dem Aufsatze „Ueber den Gültigkeitsbereich der Taylor'schen Reihenentwickelung”

Ohne Zusammenfassung