Boundary and Lens Rigidity of Lorentzian Surfaces

Let be a Lorentzian metric on the plane that agrees with the standard metric outside a compact set and so that there are no conjugate points along any time-like geodesic of . Then and are isometric. Further, if and are two dimensional compact time oriented Lorentzian manifolds with space--like boundaries and so that all time-like geodesics of maximize the distances between their points and and are ``boundary isometric', then there is a conformal diffeomorphism between and and they have the same areas. Similar results hold in higher dimensions under an extra assumption on the volumes of the manifolds.

     

Electronic structure of the permanganate ion

The electronic structure of the permanganate ion has been investigated, using a semiquantitative LCAO MO method without empirical parameters. The atomic orbital basis set for the central ion has been varied systematically, and the effect of symmetric changes of bond distances has also been examined. In addition, calculations have been performed in which the regions around the ligands have been made more attractive for electrons, to simulate the presence of cations in solution and in the crystalline state. The electronic absorption spectrum of MnO ₄ ^– has been tentatively assigned, on the basis of predicted band shapes and transition energies.

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Zusammenfassung Die Elektronenstruktur des Permanganations wurde mit einer halbquantitativen LCAO-MO Methode ohne empirische Parameter behandelt. Die Zustandsfunktionen des Zentralatoms wurden variiert und der Einflu\ symmetrische Änderungen der BindungsabstÄnde untersucht. Um die Gegenwart von Kationen in Lösung und im Kristall zu simulieren, wurden daneben auch Rechnungen durchgeführt, bei denen einer stÄrkeren Elektronenanziehung durch die Liganden Rechnung getragen wird. Ferner wurde versucht, das Absorptionsspektrum von MnO ₄ ^– auf Grund der vorausgesagten Bandenform und übergangsenergien zu deuten.

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Résumé La structure électronique de l'ion permanganate est étudiée à l'aide d'une méthode LCAO MO semi-quantitative sans paramètres empiriques. La base d'orbitales atomiques pour l'ion central a été systématiquement variée et l'effet de changements symétriques des longueurs de liaison a été aussi examiné. Pour simuler la présence des cations dans la solution et dans le cristal on a fait des calculs dans lesquels la région autour des ligands était rendue plus attractive pour les électrons. Le spectre d'absorption de MnO ₄ ^–1 est interprété à l'aide des prédictions sur les formes des bandes et les énergies de transition.

     

An alternative preparation of the 2-dimethylaminomethylene-1,3-bis(dimethylimmonio)propane salt from phosphonoacetic acids and some applications in heterocyclic synthesis

An alternative preparation of a 2-iminovinamidinium salt from phosphonoacetic acids is described along with its application to the synthesis of 5-formylpyrimidines and masked 4-formylpyrazoles.     

Self consistent field molecular orbital calculation for pyrrole

The electronic structure and spectrum of pyrrole have been studied using the semiempirical LCAO SCF MO method. With configuration interaction included, low excited singlet states are calculated to occur at 5.98 ev, 6,74 ev, 7,33 ev, and 8,20 ev, in good agreement with the experimental values of about 5.88 ev, 6.77 ev, and 7,21 ev. The dipole moment of the molecule is calculated to 1.84 D, to be compared with the experimental value 1.80 D. Tables of coreattraction integrals for combinations of carbon and nitrogen atoms are presented.

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Zusammenfassung Elektronenstruktur und -spektrum des Pyrrols wurden nach, der halbempirischen LCAO SCF MO-Methode untersucht. Unter Einschluß der Konfigurationenwechselwirkung wurden niedrigliegende angeregte Singulettniveaus bei 5,98, 6,74, 7,33 und 8,20 eV (über dem Grundzustand) errechnet, in guter Übereinstimmung mit den experimentellen Werten von etwa 5,88, 6,77 und 7,21 eV. Das Dipolmoment des Moleküls ergibt sich zu 1,84 D, bei einem experimentellen Wert von 1,80 D.Tabellen von (sphärischen) Rumpf-Elektron-Integralen für alle vier Kombinationen von C und N werden angegeben.

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Résumé La structure et le spectre électroniques du pyrrole ont été étudiés à l'aide de la méthode sémiempirique LCAO SCF MO. L'interaction de configurations inclue, le calcul donne des états excités à 5,98, 6,74, 7,33 et 8,20 eV (au-dessus de l'état fondamental), en bon accord avec les valeurs expérimentales de 5,88, 6,77 et 7,21 eV. Le moment dipolaire calculé de la molécule est 1,84 D, l'expérience donnant 1,80 D. Des tables d'intégrales d'attraction entre un coeur sphérique et un électron d'un autre atome sont données pour les quatre combinaisons d'atomes C et N.

     

Molecular gradients: an efficient approach for optimizing the surface properties of biomaterials and biochips

A variety of molecular gradients of alkanethiols with the structure HS-(CH(2))(m)-X (m = 15; X = COOH, CH(2)NH(2), or CH(3)) and oligo(ethylene glycol)-terminated alkanethiols with the structures HS-(CH(2))(15)-CO-NH-Eg(n) (n = 2, 4, or 6), HS-(CH(2))(15)-CO-NH-Eg(2)-(CH(2))(2)-NH-CO-(CH(2))(4)-biotin, and HS-(CH(2))(15)-CO-NH-Eg(6)-CH(2)-COOH were prepared on polycrystalline gold films. These gradients were designed to serve as model surfaces for fundamental studies of protein adsorption and immobilization phenomena. Ellipsometry, infrared spectroscopy, and X-ray photoelectron spectroscopy, operating in scanning mode, were used to monitor the layer composition, gradient profiles, tail group conformation, and overall structural quality of the gradient assemblies. The gradient profiles were found to be 4-10 mm wide, and they increased in width with increasing difference in molecular complexity between the thiols used to form the gradient. The oligo(ethylene glycol) thiols are particularly interesting because they can be used to prepare so-called conformational gradients, that is, gradients that display a variation in oligo(ethylene glycol) chain conformation from all trans on the extreme Eg(2,4) sides, via an amorphous-like phase in the mixing regimes, to helical at the extreme Eg(6) sides. We demonstrate herein a series of experiments where the above gradients are used to evaluate nonspecific binding of the plasma protein fibrinogen, and in agreement with previous studies, the highest amounts of nonspecifically bound fibrinogen were observed on all-trans monolayers, that is, on the extreme Eg(2,4) sides. Moreover, gradients between Eg(2) and a biotinylated analogue have been prepared to optimize the conditions for the immobilization of streptavidin. Ellipsometry and infrared spectroscopy reveal high levels of immobilization over a fairly broad range of compositions in the gradient regime, with a maximum between 50 and 60% of the biotinylated analogue in the monolayer. A pI gradient composed of (NH(3)(+)/COO(-))-terminated thiols was also prepared and evaluated with respect to its ability to separate differently charged proteins, pepsin, and lysozyme, on a solid surface.     

A CNDO-MO calculation of VCl4

The electronic structure of the tetrahedral molecule VCL₄ is investigated within the CNDO-MO approximations. The metal and ligand valence orbitals, 3d, 4s, 4p; and 3s, 3p; respectively, have been systematically varied in an attempt to minimize the total energy; “optimum” V 4s(χ₄ = 1.10) and 4p(d ³ p ²) orbitals have been established, but V 3d(d ⁿ ) and Cl(-δ) valence orbitals are only seen to favor lower energy for expanded orbitals. Since determining the one-electron molecular orbital level which is occupied by the vanadium lone electron is a major aspect of this investigation, all calculations have been performed in triplicate: calculations assuming the unpaired electron occupies the 3a ₁, 2 _e and 4t ₂ molecular orbital (ground state electronic configurations² A ₁,² E, and² T ₂, respectively). The Hartree-Fock equations have been solved by Roothaan's SCF method for open shells, but off-diagonal multipliers between filled and partly filled molecular orbitals of the same symmetry have been neglected. As a qualitative estimate of the error introduced by this simplification, the pertinent overlap integrals between the eigenfunctions from calculations for the three possible configurations,² A ₁,² E, and² T ₂, are investigated as functions of the component 3d(d ⁿ ) and Cl(-δ) valence orbitals. The overlap integrals from the relevant² A ₁ and² T ₂ calculations are reasonably small, but the neglect of off-diagonal multipliers in calculations on the² E state is found to be a poor approximation. An ordering of the non-filled molecular orbitals in VCl₄ of 4t ₂ < 3a ₁ < 2e < 5t ₂ seems most consistent with the numerous calculations. This suggested ground state electronic configuration of² T ₂ introduces new aspects to the consideration of a (dynamic) Jahn-Teller effect in VCl₄. Experimental data pertinent to the electronic structure of VCl₄ has been briefly summarized, but unfortunately it is inadequate to confirm or deny the present calculations.     

Interactions between synthetic and indigenous naphthenic acids and divalent cations across oil–water interfaces: effects of addition of oil-soluble non-ionic surfactants

Interactions between naphthenic acids and divalent metal cations across model oil–alkaline water interfaces were investigated by correlating changes in dynamic interfacial tension (IFT), to plausible reaction mechanisms. The measurements were carried out by using a CAM 200 optical instrument, which is based on the pendant drop technique. The naphthenic acids used were synthesised model compounds as well as commercial acid mixtures from crude distillation and extracted acid fractions from a North Sea crude oil. The divalent cations involved Ca²⁺, Mg²⁺, Sr²⁺, and Ba²⁺, which are all common in co-produced formation water and naphthenate deposits. The results show that the dynamic IFT strongly depends on naphthenic acid structure, type of divalent cation, and the concentration of the compounds as well as the pH of the aqueous phase. Introducing divalent cations to systems involving saturated naphthenic acids caused mostly a permanent lowering of the IFT. The decline in IFT is due to electrostatic attraction forces across the interface between the cations in the aqueous phase and the carboxylic-groups at the o/w interface, which cause a higher interfacial density of naphthenic acid monomers. The permanent lowering in IFT is likely due to formation of positively charged monoacid complexes, which possess high interfacial activity. On the other hand, in the case of the aromatic model compounds, the cations affected the IFT differently. This is mainly discussed in light of degree of cation hydration and steric conditions. Various oil-soluble non-ionic surfactant mixtures were also introduced to systems involving a model naphthenic acid and Ca²⁺ in order to investigate how the interfacial competition affected the local interactions. Based on the behaviour of dynamic IFT, probable inhibition mechanisms are discussed.Electronic Supplementary Material Supplementary material is available for this article at     

PURE SINGLET OXYGEN CYTOTOXICITY FOR BACTERIA

We have modified the separated-surface-sensitizer singlet oxygen generating system previously described (Midden and Wang, 1983) for the efficient exposure to pure singlet oxygen of bacteria collected on membrane filters. Physical separation of the photosensitizer and the bacteria eliminates the possibility of direct interaction between bacteria and photoexcited sensitizers that could lead to Type I (non-singlet oxygen) photooxidation processes. This system was used to examine the bacterial cytotoxicity of singlet oxygen. The role of singlet oxygen was confirmed by measuring the decrease in cytotoxicity as the distance between the singlet oxygen source and the bacteria was increased. The gas phase half-life of the intermediate responsible for cell killing, determined from this distance dependence analysis (24 ± 6 ms), is the same as that calculated from literature data for the gas phase half-life of singlet oxygen (53 ± 37 ms). Killing of various strains of Salmonella lyphimurium and Escherichia coli was compared at the same dose of singlet oxygen. Bacteria were killed by singlet oxygen at levels several orders of magnitude lower than those effective in killing by H₂O₂. Altered DNA repair capacities (uvrB, recA, xth, nth , pKM101) did not affect survival. Incomplete cell wall lipopolysaccharide formation decreased survival following singlet oxygen exposure. Overproduction of the singlet oxygen quencher histidine increased survival, as did accumulation of the dipeptide carnosine (β-alanyl-L-histidine). No evidence for mutagenicity of exogenous singlet oxygen exposure was obtained in a variety of S. typhimurium strains killed to 35% survival.