Assembling Quasi‐enantiomeric Octahedral Complexes of Different Metals via Quasi‐racemate Crystallization

Aiming at a general methodology for binary co‐assembly of complexes of different metals through quasiracemate crystallization, the hexadentate ligand 1 comprised of the chiral bipyrrolidine core and two bipyridine peripheral arms is introduced. Ligand 1 was found to bind in a fully diastereoselective and uniform mode around Zn^II, Fe^II and Cd^II giving coordinatively inert octahedral “chiral‐at‐metal” complexes with the Δ₄Λ₂/Λ₄Δ₂ wrapping mode. Equimolar mixtures of quasienantiomeric pairs of these complexes exhibited a clear tendency to pack as quasiracemates as was revealed from the crystallographic structures of [(R,R)‐ 1 ‐Zn](PF₆)₂/[(S,S)‐ 1 ‐Fe](PF₆)₂ and [(R,R)‐ 1 ‐Zn](PF₆)₂/[(S,S)‐ 1 ‐Cd](PF₆)₂, in an isomorphous fashion to that of the racemic compound [rac‐ 1 ‐Zn](PF₆)₂ in space group C2/c.     

Electron-electron scattering in conducting materials

Recent developments are reviewed in the theory and measurement of electron-electron scattering and its contribution to the electrical and thermal resistivities for different types of conducting materials, such as extremely impure metals, one-dimensional and two-dimensional conductors, the simple metals, transition metals, semimetals, organic conductors and the A15 compounds. The discussion includes the following topics: quantum corrections to the Fermi-liquid theory of electron-electron scattering (EES) due to static disorder, the effect of the dimensionality of the system on EES, the measurement and the calculation of the EES contribution to the resistivity of metals, the observed sample dependence of EES for the simple metals, the effect of EES on electron-surface scattering for thin wires, the contribution of EES to the anomalous surface impedance and to the optical relaxation time and the effect of a magnetic field on EES. Comparison is made between theory and recent experimental data for each of these topics.     

Flame acceleration in long narrow open channels

We study the propagation of premixed flames in long but finite channels, when the mixture is ignited at one end and both ends remain open and exposed to atmospheric pressure. Thermal expansion produces a continuous flow of burned gas directed away from the flame and towards the end of the channel where ignition took place. Owing to viscous drag, the flow is retarded at the walls and accelerated in the center, producing a pressure gradient that pushes the unburned gas ahead of the flame towards the other end of the channel. As a result the flame accelerates when it travels from end to end of the channel. The total travel time depends on the length of the channel and is proportional to γ^?1ln(1 + γ), where γ is the heat release parameter.     

Distribution function of the intensity of optical waves in random systems

Statistics of coherent radiation propagating in a random medium is analyzed in the framework of diagram technique. The distribution function for radiation intensity is calculated and it is shown, that only for small values of the argument the distribution function is a simple exponential, as predicted by Rayleigh statistics. For larger values of intensity the distribution function differs drastically from the simple exponential, and the asymptotical behavior is a stretched exponential. The results obtained are confirmed by numerical simulations.     

Nash Equilibrium and Subgame Perfection in Observable Queues

A subgame perfection refinement of Nash equilibrium is suggested for games of the following type: each of an infinite number of identical players selects an action using his private information on the system's state; any symmetric strategy results in a discrete Markov chain over such states; the player's payoff is a function of the state, the selected action, and the common strategy selected by the other players. The distinction between equilibria which are subgame perfect and those which are not, is made apparent due to the possibility that some states are transient. We illustrate the concept by considering several queueing models in which the number of customers in the system constitutes the state of the system.     

KeV astrophysics with GeV beams; blazing a new trail on the summit of Nuclear Astrophysics

GeV beams of light ions and electrons are used for creating a high flux of real and virtual photons, with which some problems in Nuclear Astrophysics are studied. GeV ⁸B beams are used to study the Coulomb dissociation of ⁸B and thus the ⁷Be(p,γ)⁸B reaction. This reaction is one of the major source of uncertainties in estimating the ⁸B solar neutrino flux and a critical input for calculating the ⁸B solar neutrino flux. The Coulomb dissociation of ⁸B appears to provide a viable method for measuring the ⁷Be(p,γ)⁸B reaction rate, with a weighted average of the RIKEN1, RIKEN2, GSI1 and MSU published results of S ₁₇(0)=18.9±1.0 eV-b. This result, however, does not include a theoretical error estimated to be ±10%. GeV electron beams on the other hand, are used to create a high flux of real and virtual photons at TUNL-HIGS and MIT-Bates, respectively, and we discuss two new proposals to study the ¹²C(α,γ)¹⁶O reaction with real and virtual photons. The ¹²C(α,γ)¹⁶O reaction is essential for understanding Type II and Type Ia supernova. It is concluded that virtual and real photons produced by GeV light ions and electron beams are useful for studying some problems in Nuclear Astrophysics.     

The Cosmic Time in Terms of the Redshift

In cosmology one labels the time t since the Big Bang in terms of the redshift of light emitted at t, as we see it now. In this Note we derive a formula that relates t to z which is valid for all redshifts. One can go back in time as far as one wishes, but not to the Big Bang at which the redshift tends to infinity.     

K+ uptake by root systems grown in soil under salinity: I. A mathematical model

A novel theoretical model is proposed for K⁺ uptake by intact root systems from saline soil considering interactions with Na⁺, Ca²⁺ and Mg²⁺. The model assumes radial movement of ions towards the root governed by advection and diffusion flux mechanisms, and chemical exchange of the four cations according to Gapon isotherms, with Cl^? as the accompanying anion. Influx of K⁺ to the root surface is assumed as a function of its concentration in the soil solution at the root. This influx is governed by a saturable-cooperative term and a linear term for low and high K⁺ concentrations, respectively. Influx of Na⁺, above a critical value of its concentration, increases linearly with its concentration in the soil solution at the root surface. Uptake of Ca^{+ 2+} is controlled by the balance between influxes of anions and cations, which induces efflux of H⁺ or HCO ₃ ^? , and interacts with calcite in a calcareous soil. The model may provide information about the behavior of ions at the root-soil interface which cannot be measuredin situ.