An instanton-invariant for 3-manifolds

To an oriented closed 3-dimensional manifoldM withH ₁(M, )=0, we assign a ₈-graded homology groupI _*(M) whose Euler characteristic is twice Casson's invariant. The definition uses a construction on the space of instantons onM×.     

WKB properties of the time-dependent Schrödinger system

It is shown that the time-dependent WKB expansion highlights some of the hidden properties of the Schrödinger equation and forms a natural bridge between that equation and the functional integral formulation of quantum mechanics. In particular it is shown that the leading (zero- and first-order in ) terms in the WKB expansion are essentially classical, and the relationship of this result to the classical nature of the WKB partition function, and of the anomalies in quantum field theory, is discussed.     

Preparation,characterization and a kinetic study oftrans-[Ru(NH3)4L(H2O)](PF6)2 [L=PPh3, AsPh3, or SbPh3]

Summary The complexestrans-[Ru(NH₃)₄(H₂O)PPh₃](PF₆)₂ and [Ru(NH₃)₅L](PF₆)₂, (L=AsPh₃ or SbPh₃) have been isolated and characterized by microanalysis, cyclic voltammetry and ultraviolet-visible spectroscopy. The specific rate constants for the aquation of [Ru(NH₃)₅L]²⁺ totrans-[Ru(NH₃)₄L(H₂O)]²⁺ are (2.5±0.1)×10^–5s^–1 and (1.8±0.1)×10^–5s^–1 for L=AsPh₃ and SbPh₃, respectively, at 25.0±0.1°C; =0.10 mol dm^–3, NaO₂CCF₃. Under the same conditions, the second-order rate constants for the substitution of water intrans-[Ru(NH₃)₄(H₂O)L]²⁺ by isonicotinamide (isn) are 1.2±0.1, (6.3±0.3)×10^–2 and (3.8±0.2)×10^–2 m ^–1s^–1 for L=PPh₃, AsPh₃, and SbPh₃, respectively, suggesting that the order of decreasingtrans-effect is: PPh₃AsPh₃>SbPh₃. The formation constants for thetrans-[Ru(NH₃)₄L(isn)]²⁺ complexes are 75±3, (1.40±0.01)×10³ and (1.80±0.02)×10³M^–1 for L=PPh₃, AsPh₃, and SbPh₃, respectively, suggesting that the order of increasingtrans-influence is: SbPh₃3PPh₃.     

Energetic ion bombardment of Ag surfaces by C<Stack><Subscript>60</Subscript><Superscript>+</Superscript></Stack> and Ga<Superscript>+</Superscript> projectiles

The ion bombardment-induced release of particles from a metal surface is investigated using energetic fullerene cluster ions as projectiles. The total sputter yield as well as partial yields of neutral and charged monomers and clusters leaving the surface are measured and compared with corresponding data obtained with atomic projectile ions of similar impact kinetic energy. It is found that all yields are enhanced by about one order of magnitude under bombardment with the C60+ cluster projectiles compared with Ga+ ions. In contrast, the electronic excitation processes determining the secondary ion formation probability are unaffected. The kinetic energy spectra of sputtered particles exhibit characteristic differences which reflect the largely different nature of the sputtering process for both types of projectiles. In particular, it is found that under C60+ impact (1) the energy spectrum of sputtered atoms peaks at significantly lower kinetic energies than for Ga+ bombardment and (2) the velocity spectra of monomers and dimers are virtually identical, a finding which is in pronounced contrast to all published data obtained for atomic projectiles. The experimental findings are in reasonable agreement with recent molecular dynamics simulations.     

BIOLOGICAL ACTIVITIES OF PHTHALOCYANINES-X. SYNTHESES AND ANALYSES OF SULFONATED PHTHALOCYANINES

Abstract— Synthetic methods to obtain selectively sulfonated metallo phthalocyanines are compared. Both condensation and direct sulfonation procedures lead to mixtures of mono- to tetrasulfonated products which are resolved by reverse phase liquid chromatography in buffered aqueous-methanol. The proportion of sulfonated derivatives is examined as a function of the starting reagents in the case of the condensation method, and as a function of the temperature and reaction time in the case of the direct sulfonation procedure. The number of sulfonate groups per phthalocyanine molecule is determined by oxidative degradation of the phthalocyanine ring followed by quantitative chromatographic analysis of the sulfophthalamide and phthalamide fragments.     

On-line coupling of ion chromatography and atomic spectrometry for ultra trace analysis in high purity molybdenum- and tungsten-silicide

The well-established technique of on-line coupling ion chromatography and atomic spectrometry for ultra trace analysis in high purity molybdenum and tungsten is extended to include the silicides MoSi(x) and WSi(x). An additionally included matrix elimination step allows an almost interference-free trace analysis in the silicide matrices. Reproducibility and accuracy of the on-line method were checked by comparison with several other methods, such as isotope dilution, radiochemical neutron activation analysis, direct determination by atomic absorption analysis and not at least with glow discharge mass spectrometry. The results show the high potential of the on-line method for reaching detection limits in the pg g(-1) range, but they show also remaining problems with contamination and system calibration.     

How electrons guard the space: shape optimization with probability distribution criteria

Efficient formulas for computing the probabilities of finding exactly electrons in an arbitrarily chosen volume ³ for Hartree–Fock wavefunctions are presented. These formulas allow the use of shape optimization techniques, such as level set methods, for optimizing with respect to various criteria involving such probabilities. The criterion defined as the difference between the Hartree–Fock and the independent-particle model probabilities of finding electrons in stresses the quantum effects due to the Pauli principle. We have implemented a 2D level set method for optimizing this criterion in order to study spatial separation of electron pairs in linear molecules. The method is described and the illustrative example of the BH molecule is reported.Contribution to the Jacopo Tomasi Honorary Issue