Automatic structures,rational growth,and geometrically finite hyperbolic groups

Summary We show that the set of equivalence classes of synchronously automatic structures on a geometrically finite hyperbolic groupG is dense in the product of the sets over all maximal parabolic subgroupsP. The set of equivalence classes of biautomatic structures onG is isomorphic to the product of the sets over the cusps (conjugacy classes of maximal parabolic subgroups) ofG. Each maximal parabolicP is a virtually abelian group, so and were computed in [NS1].We show that any geometrically finite hyperbolic group has a generating set for which the full language of geodesics forG is regular. Moreover, the growth function ofG with respect to this generating set is rational. We also determine which automatic structures on such a group are equivalent to geodesic ones. Not all are, though all biautomatic structures are.Oblatum 14-VI-1993 & 4-I-1994Both authors acknowledge support from the NSF for this research.     

On the growth of meromorphic functions of infinite order

Letf be a meromorphic function of infinite order,T(r, f) its Nevanlinna (or Ahlfors-Shimizu) characteristic, andM(r, f) its maximum modulus. It is proved that $$\mathop {\lim \inf }\limits_{r \to \infty } \frac{{\log M(r,f)}}{{rT'(r,f)}} \leqslant \pi and\mathop {\lim \inf }\limits_{r \to \infty } \frac{{\log M(r,f)}}{{T(r,f)\psi (log T(r,f))}} = 0$$ . if ? (x)/x is non-decreasing, ?′(x)<-√?(x) and ∝^∞ dx/?(x) < ∞.     

Near melting point flow injection: a drastic enhancement in FAAS detection limits

The described technique is based on segregation phenomena taking place in solids near their melting point. High impurity concentration occurs in a liquid phase at the grain boundaries. A continuous flow of an adequate solvent is used in far from equilibrium conditions to reach high extraction efficiency of the analyte. As an example, the determination of trace amounts of caesium in metallic sodium is described. The 5 mg/kg detection limit of conventional FAAS is thus lowered to a few g/kg.     

Structure and reactivity of xanthocorrinoids. Part V. Formation of trans-diol derivatives of 5,6-dihydrocobyrinic acid from xanthocorrinoids under acidic conditions

On treatment with H₂SO₄/MeOH, epimerization of hexamethyl cis-5,6-dihydroxycobyrinate c,8-lactam ( 3 ) takes place quantitatively at C(6), yielding the corresponding trans-diol 4 . The corresponding lactone 7 , whose structure has been established by X-ray analysis, is obtained from xanthocorrinoids 5 and 6 under similar conditions.     

Formation of the First Trimeric Monoterpenoid Indole Alkaloids

Under O², the Aspidosperma alkaloid tabersonine ( 1 ) was converted by a crude enzyme preparation from leaves of mature plants of Catharanthus roseus G DON into the trimeric 3-hydroxy-14′-(3α″-tabersonyl)voafrine B ( 4 ) which was easily reduced by NaBH₄ to 14′-(3α″-tabersonyl)voafrine B ( = tertabersonine; 5 ). Compounds such as 4 and 5 are the first trimeric alkaloids in the series of monoterpenoid indole alkaloids.     

Eisen(III)-rhodanidpapier als analytisches Reagens bei Luftuntersuchungen

Zusammenfassung Mit Hilfe von Reagenspapierstreifen, die mit Eisen(III)-rhodanid imprÄgniert sind, lassen sich alle in der Luft gelegentlich vorkommenden, alkalisch reagierenden Gase oder DÄmpfe (Ammoniak, Amine, Äthylenoxyd) nachweisen. Das dunkelrotbraune Reagenspapier wird hierbei entfÄrbt. Das Ausma\ der EntfÄrbung folgt stöchiometrischen Gesetzen. Der Grad der EntfÄrbung lÄ\t sich daher quantitativ auswerten. Eine untere und obere Nachweisgrenze gibt es bei diesem Verfahren theoretisch überhaupt nicht. Bei der vorgeschlagenen Ausführungsmethode, die eine Absaugung von Luftmengen bis zu 1 Liter vorsieht, liegt die untere Nachweisgrenze — in AnhÄngigkeit von dem Molekulargewicht des gefundenen Stoffes — z. B. bei 0,07 g NH₃ je Liter Luft (=0,07 mg/m₃) oder bei 0,25 g Trimethylamin/1 Liter (=0,25 mg/m³). Die praktische Begrenzung nach oben liegt dort, wo sich andere bekannte Bestimmungsmethoden mit höherem Genauigkeitsgrad anbieten.Die Herstellung eines in reiner Luft auch bei Licht und Zimmertemperatur lÄngere Zeit haltbaren Reagenspapiers wird beschrieben. Die praktische Anwendbarkeit des ER-Papiers liegt vor allem bei Luftuntersuchungen im Zusammenhang mit den Exhalationen und Emanationen von Fischmehlfabriken.     

Instability of nonlinear bound states

We establish a sharp instability theorem for the bound states of lowest energy of the nonlinear Klein-Gordon equation,u _tt–u+f(u)=0, and the nonlinear Schrödinger equation, –iu _t–u+f(u)=0.Supported in part by NSF Grants MCS 81-21487 and MCS 82-01599