A functional inequality for real-analytic functions

Summary Forf ( C ⁿ() and 0 t x letJ _n (f, t, x) = (–1)ⁿ f(–x)f ⁽ⁿ⁾(t) +f(x)f ⁽ⁿ⁾ (–t). We prove that the only real-analytic functions satisfyingJ _n (f, t, x) 0 for alln = 0, 1, 2, are the exponential functionsf(x) = c e ^x,c, . Further we present a nontrivial class of real-analytic functions satisfying the inequalitiesJ ₀ (f, x, x) 0 and ₀ ^x (x – t)^{n – 1}J_n(f, t, x)dt 0 (n 1).     

Infinitesimal obstructions to weakly mixing

Let ^t be the flow (parametrized with respect to arc length) of a smooth unit vector field v on a closed Riemannian manifold M ⁿ , whose orbits are geodesics. Then the (n-1)-plane field normal to v, v, is invariant under d ^t and, for each x M, we define a smooth real function _x (t) : (1 + _i (t)), where the _i(t) are the eigenvalues of AA ^T, A being the matrix (with respect to orthonormal bases) of the non-singular linear map d^2t , restricted to v at the point _x ^-t M ⁿ.Among other things, we prove the Theorem (Theorem II, below). Assume v is also volume preserving and that _x ^' (t) 0 for all x M and real t; then, if _x ^t : M M is weakly missng for some t, it is necessary that vx 0 at all x M.     

Another remark on twisted convolution

SiaF un gruppo di Lie connesso. Una distribuzioneT a supporto compatto inF e un 2-cociclo diF a valori complessi di modulo 1, definiscono, mediante la convoluzione «twisted», un operatore lineareT _c nello spazio (F). Per il «cociclo triviale»e≡1 l'operatoreT _e è la convoluzione ordinaria. Si dimostra cheT _c permette un'estensione continua suL ^p (F), 1T _e permette una tale estensione. PerF=C _n si ottiene, come caso speciale, un teorema di M. Cowling.     

Microscopic study of a lattice defect trapped at in impurities in plastically deformed Al

¹¹¹In doped Al specimes (c _In1 ppm) were cold worked by extension at 77 K to several amounts of strain. The PAC method was applied to study the trapping of lattice defects at the indium impurities between 77 K and 293 K. From electron irradiation experiments it is known that the In probes are suitable traps for self-interstitials in Al. Since in the present experiment no such effect is observed, it is concluded that by extension at 77 K in Al essentially no freely migrating interstitials are created. Between 110 K and 210 K an increasing fraction of the indium impurities traps a well defined defect. The symmetry axis of the resulting indium-defect-complex is found to point along 111 crystallographic directions. It is proposed that the In impurity traps a divacancy at nearest neighbour sites and relaxes into the open space, thus forming an equilateral triangle of three vacancies in a {111} plane with the In atom in its centre. Reasons for the formation of this complex at rather low annealing temperatures are discussed.     

Cyclic Heptapeptides Axinastatin 2, 3, and 4: Conformational analysis and evaluation of the biological potential

The conformational analysis of naturally occurring cytostatic cyclic heptapeptides axinastatin 2, 3, and 4 was carried out by two-dimensional NMR spectroscopy in combination with distance-geometry (DG) and molecular-dynamics (MD) calculations in explicit solvents. The synthesized secondary metabolites were examined in (D₆)DMSO. Axinastatin 2 was also investigated in CD₃OH. In all structures, Pro² is in the i + 1 position of a βI turn and Pro⁶ occupies the i + 2 position of a βVIa turn about the cis amide bond between residue 5 and Pro^6. In all peptides, a bifurcated H-bond occurs between residue 4 CO and the amide protons of residue 1 and 7. For axinastatin 2 and 3, an Asn I_g turn was found about Asn¹ and Pro^2. We compared these structures with conformations of cyclic heptapeptides obtained by X-ray and NMR studies. A β-bulge motif with two β turns and one bifurcated H-bond is found as the dominating backbone conformation of cyclic all-L-heptapeptides. Axinastatin 2, 3, and 4 can be characterized by six trans and one cis amide bond resulting in a β/βVI(a)-turn motif, a conformation found for many cyclic heptapeptides. Detailed biological tests of the synthetic compounds in different human cancer cell lines indicates these axinastatins to be inactive or of low activity.     

Zur deprotonierung von chloromethyleniminiumchloriden

Deprotonation of chloromethyleniminium chlorides ($\text{1}$, $\text{13}$) leads to cis-trans-isomeres 1,2-diamino-1,2-dichloro-ethenes ($\text{3a}$, $\text{3b}$ resp. $\text{14a}$, $\text{14b}$); their reactivity is described.     

Preparation,structure and catalytic properties of a binuclear Pd(0) complex with bridging silylene ligands

In contrast to the N-heterocyclic carbene (NHC) 1, the homologous N-heterocyclic silylene (NHS) 4 acts as a bridging ligand to Pd(0), giving rise to the dinuclear complex 5 which is catalytically active in Suzuki reactions.     

Untersuchungen über die Adsorption von Gasgemischen

Zusammenfassung Es werden Mischadsorptionsmessungen am SystemAceton-Chloroform mit einem Dampfdrukminimum an homogenen Oberflächen an Mikroglaskügelchen (2 bis 12 ) in einem rel. Druckbereich zwischen 0,1 und 0,9 ausgeführt. Dabei ist der Sättigungsdruck jeweils der Dampfdruck der mit der Gasphase im Adsorptionsgleichgewicht korrespondierenden flüssigen Phase imp _o , -Diagramm. Zugleich wurde die Zusammensetzung der adsorbierten Mischphase bestimmt und daraus die partielle Adsorption der Komponenten als Funktion des rel. Druckes bei verschiedener Zusammensetzungen der Gasphase.Für partielle Adsorption wurde auf der Grundlage eines vonHill entwickelten Ansatzes in Verbindung mit einer Gl. vonTheimer eine Formel aufgestellt, die die experimentellen Ergebnisse gut wiedergibt.Es werden Adsorptionswärmen für die verschiedenen Belegungsdichten in Abhängigkeit von der Zusammensetzung der Gasphase bestimmt.Mit 18 AbbildungenHerrn Prof.L. Ebert zum 60. Geburtstag gewidmet.