On the Dirac–Kepler problem: The Johnson–Lippmann operator,supersymmetry, and normal-mode representations

The relativistic Kepler problem is discussed, with emphasis on the exact supersymmetry of the problem. It is shown that the supersymmetry is generated by the Johnson–Lippmann operator. Two related operators are found to generate new supersymmetries in an extended function space. Each of these supersymmetries may be disguised as radial supersymmetries. The radial supersymmetries are discussed and it is shown that each of them defines a normal-mode representation of the hydrogen-atom radial functions. Thus, one obtains two different, but equivalent, analytical expressions for these functions. The expressions are well known, but are rederived here in the light of the new understanding. Finally, the nonrelativistic image of the relativistic supersymmetry is constructed and its generators shown to be identical with those recently presented in the literature. © 1995 John Wiley & Sons, Inc.     

Improved synthesis of oligonucleotides with an allylic backbone. Oligonucleotides containing acyclic, achiral nucleoside analogues: N-1 or N-9-[3-hydroxy-2-(hydroxymethyl)prop-1-enyl]nucleobases

An improved phosphoramidite method is described to prepare oligonucleotides modified with the acyclic, achiral monomers 1. Examination of dimers, prepared on solid support or in solution, showed that phosphortriester dimers containing the allylic unit 1 were unstable towards bases, whereas phosphordiester dimers were stable. Phosphordiester dimers were obtained by replacing cyanoethyl phosphoramidites 2 with phosphoramidites 3, which gave phosphordiesters directly upon oxidation. The phosphordiester dimers were found to be stable towards capping and oxidation, but were somewhat labile towards acids. By reducing the contact time to acids during detritylation it was possible to prepare oligonucleotides containing 4 or 8 modified A, G or T units. The modified oligonucleotides hybridized to complementary DNA and RNA, although with reduced affinity (DeltaT(m) per modification -1 to -5 degrees C).     

Tunneling of an energy eigenstate through a parabolic barrier viewed from Wigner phase space

We analyze the tunneling of a particle through a repulsive potential resulting from an inverted harmonic oscillator in the quantum mechanical phase space described by the Wigner function. In particular, we solve the partial differential equations in phase space determining the Wigner function of an energy eigenstate of the inverted oscillator. The reflection or transmission coefficients R or T are then given by the total weight of all classical phase-space trajectories corresponding to energies below, or above the top of the barrier given by the Wigner function.     

Surgery and the Spinorial τ-Invariant

We associate to a compact spin manifold M a real-valued invariant τ(M) by taking the supremum over all conformal classes of the infimum inside each conformal class of the first positive Dirac eigenvalue, when the metrics are normalized to unit volume. This invariant is a spinorial analogue of Schoen's σ-constant, also known as the smooth Yamabe invariant. We prove that if N is obtained from M by surgery of codimension at least 2 then τ(N) ≥ min{τ(M), Λ _n }, where Λ _n is a positive constant depending only on n = dim M. Various topological conclusions can be drawn, in particular that τ is a spin-bordism invariant below Λ _n . Also, below Λ _n the values of τ cannot accumulate from above when varied over all manifolds of dimension n.     

Pricing of Claims in Discrete Time with Partial Information

We consider the pricing problem of a seller with delayed price information. By using Lagrange duality, a dual problem is derived, and it is proved that there is no duality gap. This gives a characterization of the seller’s price of a contingent claim. Finally, we analyze the dual problem, and compare the prices offered by two sellers with delayed and full information respectively.     

Brans–Dicke geometry

We reveal the non-metric geometry underlying ω→0$\omega \to 0$ Brans–Dicke theory by unifying the metric and scalar field into a single geometric structure. Taking this structure seriously as the geometry to which matter universally couples, we show that the theory is fully consistent with solar system tests. This is in striking contrast with the standard metric coupling, which grossly violates post-Newtonian experimental constraints.     

The interaction between model biomaterial coatings and nylon microparticles as measured with a quartz crystal microbalance with dissipation monitoring

The interaction between cells and biomaterials has been mimicked using nylon microparticles as pseudo-cells and PLMA and PIBMA as biomaterial model acrylate polymers. The shift of fundamental resonance frequencies was negative for both polymers, indicating mass-coupling to the sensor surface. The shifts of the 3rd, 5th and 7th overtone frequencies were initially positive for both polymers, indicating a particle slip or wobbling on the surface. The QCM technique could discriminate between the two different polymers, showing increased interaction between microparticle and PLMA. The dissipation shift was positive for all overtones on both polymers, but again with faster and more prominent response for PLMA.     

Antiaromatic spacer-bridged bisfluorenyl dications generated by superacid induced ionization

Derivatives of the dication of tetrabenzo[5.5]fulvalene were prepared with phenyl and ethynyl spacers through ionization of the appropriate bis-methylethers. The antiaromaticity shown by the parent dication was demonstrated for these dications with spacers, although it was attenuated by the presence of the spacer. It was substantially greater than that of fluorenyl monocations with similar substituents. Antiaromaticity was evaluated through comparison of (1)H NMR shifts with those of acyclic analogues, through nucleus independent chemical shifts, and through magnetic susceptibility exaltation. Although the fluorenyl systems are separated by spacers, the antiaromaticity of one system is affected by the other remote fluorenyl system. An explanation for this interaction may lie in the ability of a remote cationic substituent to attenuate delocalization in the spacer. The use of spacers is designed to prevent side reactions in less stable antiaromatic dications, allowing exploration of a number of species that have previously been inaccessible.