Characterizing projective bundles by means of ample divisors

Let X be a complex projective manifold and AX a non-singular hypersurface which is an ample divisor having characteristic cycles A_i non-singular in every dimension i0. The pairs (X,A) such that g(A₁)=h^1,0 (X) are characterized.     

Small carbon clusters doped with early transition metals: a theoretical study of ScCn, ScCn+, and ScCn- (n = 1-8) open-chain clusters

A theoretical study of the ScCn, ScCn+, and ScCn- (n = 1-8) open-chain clusters has been carried out. Predictions for their electronic energies, rotational constants, dipole moments and vibrational frequencies have been made using the B3LYP method with different basis set including effective core potentials, ECPs. For the ScCn open-chain clusters the lowest-lying states correspond to quartet states for n-odd members, whereas for n-even species the ground state is found to be a doublet. In the cationic and anionic species, the electronic ground state is found to be a singlet for even n and a triplet for odd n. An even-odd parity effect (n-even clusters being more stable than n-odd ones) is observed in neutral and charged clusters. Ionization energies and electron affinities also exhibit a clear parity alternation trend, with n-even clusters having higher values than n-odd ones.     

Photochemical Rearrangement of a Steroidal α,β-Epoxylactone. Photochemical reactions,XI [1]

The UV. irradiation of 17β-acetoxy-4α, 5α-epoxy-2-oxaandrostan-3-one ( 7 ) yields 17β-acetoxy-2-oxa-10(5 → 4)abeo-4ζ (H)-androsta-3,5-dione ( 11 ). A non-photochemical synthesis of 11 , proceeding in lower yield, is also described.     

Mikrobestimmung von Quecksilber in organischen Verbindungen

Zusammenfassung Eine Methode zur Mikrobestimmung von Quecksilber in organischen Verbindungen wurde beschrieben. 3–5 mg Substanz werden in einem Sauerstoffkolben verbrannt und die Produkte in 4 ml konz. Salpetersäure absorbiert. Die Absorptionslösung wird dann für 6 min gekocht, wobei die vollständige Oxydation zu Quecksilber(II) abläuft. Dieses wird mit 0,005 M Kaliumjodidlösung potentiometrisch titriert. Zur Indikation des Endpunktes wird eine Meßkette aus einer ionenselektiven Elektrode für Jodid und einer Referenzelektrode mit KNO₃-Zwischenelektrolyt verwendet. Die Resultate liegen innerhalb der üblichen Fehlergrenze von ± 0,30%.

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Microassay of mercury in organic substances

Summary A method for microassay of mercury in organic compounds was described. 3–5 mg substance are combusted in an oxygen flask and the products absorbed in 4 ml conc. nitric acid. The absorption solution is then boiled for 6 minutes, during which complete oxidation to mercury(II) occurs. This is titrated potentiometrically with 0.005M potassium iodide solution. A measuring chain consisting of an ion-selective electrode for iodide and a reference electrode with KNO₃ intermediate electrode was used to indicate the endpoint. The results are within the usual ±0.30% limit of error.

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Herrn Prof. Dr. Hans Lieb zum 90. Geburtstag gewidmet.

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Frl. Mirella Piccinini hat an dem experimentellen Teil dieser Arbeit mitgeholfen, wofür ich bestens danke.     

Paired electrosynthesis of cyanoacetic acid

Cyanoacetic acid is formed by cathodic reduction of CO(2) and anodic oxidation of the tetraalkylammonium salt anion; the process is conduced in acetonitrile using a divided cell with a medium porosity glass-frit diaphragm. A mechanism for this paired electrochemical reaction is proposed.     

An alternative multipolar expansion for intermolecular potential functions

We have derived a new multipolar expansion for intermolecular potential-energy functions with applications in molecular physics, theoretical chemistry, and mathematical physics. The new formulation employs a separation of radial and angular terms with a simple index structure that leads to computational efficiency and ease of physical interpretation. For the case of the Coulomb interaction, we compare the present formulation with two conventional multipole expansions: the Cartesian tensor and the irreducible spherical tensor expansions. The new formalism leads to efficient numerical algorithms that are useful for general applications beyond intermolecular potentials. In addition to the electrostatic Coulomb interaction, we illustrate the formalism with applications to special function theory and a bipolar expansion involved in potential theory.     

A Revised Stern Equation for Ion Exchange at Charged Membranes

We revised the classical Stern equation for ion exchange at charged membranes using the statistical mechanics concept of chemical potential and ion activity in nonhomogeneous systems. Our proposed equation does not require an iterative procedure to obtain the self-regulated surface charge at the membranes. We predict significant differences with the classical results. When compared with experimental results, our approach not only gives a better fit but also predicts dissociation constants that are physically more reasonable than those from the classical approach. Copyright 2001 Academic Press.     

Stericaliy Congested Molecules: 2,2′-[(Biaryldiyl)bis(oxy)]bis[1,3,2-oxazaphospholidines]

The original suggestion that a through-space mechanism was operative in the seven-bond J(P, P) coupling constant of 30.3 Hz observed for 3.3′-bis(1,1-dimethylethyl)-2,2′-[3,3′,5,5′-tetrakis(1,1-dimethylethyl)-1,1′-biphenyl-2,2′-diyl]bis(oxy)}bis[1,3,2-oxazaphospholidine] ( 1a )) was investigated. In the solid-state CP-MAS ³¹PNMR spectrum of 1a , two nonequivalent P -atoms were observed; sufficient resolution could not be obtained to determine whether P, P coupling was present. The preparation and spectral data of the N-methyl analogue 1b and of the acyclic N-isopropyl analogue 6 (Scheme 1) provided evidence that a) the essentially exclusive formation (R*, R*,S*)- 1a in the reaction of the disodium biphenyldiolate 3a with the phosphorochloridite 4a is the result of significant differences in the free energy of activation (ΔG*) for the formation of the various diastereoisomers due to the steric congestion within the molecule and that b) the magnitude of the observed P,P coupling is dependent upon the degree of conformational freedom within the molecule. In the ³¹P-NMR spectrum of the P-sulfide 7 , which was prepared by the reaction of la with sulfur, 2s resonances were observed that strongly suggested that the lone electrons pair on P are involved in the mechanism for the transmission of coupling data. The (4S,5R) -12 and (4R, 5S) -12 of la were prepared in a three-step reaction sequence starting from the corresponding enantiomerically pure norephredine 8 (Scheme 2). Both (4S, 5R)- and (4R, 5S) -12 were obtained as a diastereoisomer mixture that differ by the configuration of the axis of chirality, i.e., (R*R*,R*)- and (R*,S*,R*) -12 were obtained. The major diastereoisomer was obtained upon recrystallization, and the atropisomers were observed to equilibrate in solution by monitoring the H? C(5) resonance in the ¹H-NMR with time (ΔG° = 0.4 kcal/mol; Fig. 2). The process observed corresponds to the restricted rotation about the central single bond of the biphenyl system. The isolation of an atropisomer with only a single ortho substituent on each aryl ring is quite rare. In the ¹³C-NMR spectrum of both (R*,R*,R*)- and (R*,S*,R*) -12 , C(5) is two-bond-coupled to the oxazaphospholidine P-atom (²J(C(5),P((2)) = 8.5 Hz) that is further virtually coupled to the P-atom of the other oxazaphospholidine ring (7J(P(2),P(2′)) = 30 Hz; ⁹J(C(5),P(2′)) = 0 Hz; δ(P(2)) = δ(P(2′)) = 136 ppm. In the ³¹P-NMR spectrum of (R*,R*,S*) -12 , which was prepared from the racemic chloridite (mixture of three diastereoisomers was obtained), a ⁷J(P(2),P(2′) of 36 Hz was observed. These observations provide strong evidence that seven-bond P,P coupling occurs in all three diastereoisomers of 12 . The observed P,P coupling is both independent of the configuration of the chiral axis and the configuration of the asymmetric P-centers. This independence of P,P coupling upon the configuration on P implies also the independence of the observed coupling upon the orientation of the lone-pair of electrons on P provided that the conformations of the diastereoisomers are similar in solution. The X-ray crystal structure of the complex formed from 1a and dichloro(cycloocta-1,5-diene)platinum(II) was obtained and the solid-state structure discussed. The major diastereoisomer of (4S,5R) -12 was used as a chiral ligand in asymmetric hydrosilylation and hydrogenation reactions (Scheme 3).     

Stepwise retro 1,3-dipolar cycloaddition induced by electron. Impact on 3,5-diphenyl-1,2,4-oxadiazole

The retro 1,3-dipolar cycloaddition induced by electron impact on 3,5-diphenyl-1,2,4-oxadiazole is interpreted as a two-step process on the basis of the energetics and kinetics of the fragments [C₇H₅NO]⁺., [C₆H₅CN]⁺. and [C₆H₅CO]⁺.