On the Kullback information measure as a basis for information theory: Comments on a proposal by Hobson and Chang

Hobson and Chang recommend that the Kullback information measure replace the Shannon information measure as a basis for information theory. They cite several items in support of their proposal. The items are considered individually and it is shown that they do not in fact constitute sufficient reasons for accepting the Hobson/Chang proposal. It is concluded that the Shannon information measure should be retained as the basis of information theory.     

The electronic structure of ZrSe32

The energy bands of the semiconductor ZrSe₃ have been evaluated using the KKR method. The general features of the electronic structure are expected to pertain to other transition metal trichalcogenides which have similar trigonal prismatic coordination. The calculated density of states agrees well with X-ray photoemission spectra for the valence band. The joint density of states has been evaluated and is discussed in terms of optical measurements.     

Difference approximations for wave equations via finite elements II. Error analysis

Difference-like schemes for the wave equation arise naturally from a Galerkin finite-element formulation, if we adopt certain quadrature rules in evaluating the mass and stiffness matrices. One can extend these schemes to problems involving sharp interfaces by applying the quadrature on a refinement of the finite-element grid that includes the interfaces. We develop error estimates for this modified scheme that corroborate numerical results for acoustic and elastic wave equations, presented in a companion article. © 1995 John Wiley & Sons, Inc.     

Electronically induced lattice instabilities in b.c.c. Zr

Electronically induced lattice instabilities in metals are discussed by means of an accurate determination of the generalized susceptibility function, χ(q), from a KKR band structure and Fermi surface determined for b.c.c. Zr. We describe how the detailed behavior of χ(q) for b.c.c. Zr may be related to the omega phase upon alloying with Nb or upon application of pressure to the b.c.c. lattice.     

Computer simulation of the chemical catalysis of DNA polymerases: discriminating between alternative nucleotide insertion mechanisms for T7 DNA polymerase

Understanding the chemical step in the catalytic reaction of DNA polymerases is essential for elucidating the molecular basis of the fidelity of DNA replication. The present work evaluates the free energy surface for the nucleotide transfer reaction of T7 polymerase by free energy perturbation/empirical valence bond (FEP/EVB) calculations. A key aspect of the enzyme simulation is a comparison of enzymatic free energy profiles with the corresponding reference reactions in water using the same computational methodology, thereby enabling a quantitative estimate for the free energy of the nucleotide insertion reaction. The reaction is driven by the FEP/EVB methodology between valence bond structures representing the reactant, pentacovalent intermediate, and the product states. This pathway corresponds to three microscopic chemical steps, deprotonation of the attacking group, a nucleophilic attack on the P(alpha) atom of the dNTP substrate, and departure of the leaving group. Three different mechanisms for the first microscopic step, the generation of the RO(-) nucleophile from the 3'-OH hydroxyl of the primer, are examined: (i) proton transfer to the bulk solvent, (ii) proton transfer to one of the ionic oxygens of the P(alpha) phosphate group, and (iii) proton transfer to the ionized Asp654 residue. The most favorable reaction mechanism in T7 pol is predicted to involve the proton transfer to Asp654. This finding sheds light on the long standing issue of the actual role of conserved aspartates. The structural preorganization that helps to catalyze the reaction is also considered and analyzed. The overall calculated mechanism consists of three subsequent steps with a similar activation free energy of about 12 kcal/mol. The similarity of the activation barriers of the three microscopic chemical steps indicates that the T7 polymerase may select against the incorrect dNTP substrate by raising any of these barriers. The relative height of these barriers comparing right and wrong dNTP substrates should therefore be a primary focus of future computational studies of the fidelity of DNA polymerases.     

Thermodynamic and kinetic parameters associated with the fluxional behavior of 2-methyl- and 2,6-dimethyltroponeiron tricarbonyl complexes

The kinetic and thermodynamic parameters for regioisomerisation of 2-methyl- and 2,6-dimethyl-derivatives of tricarbonyl[η⁴-tropone]iron complexes have been studied by ¹H NMR spectrometry over a range of 40 °C. Regioisomerisation of these complexes proceeds by an intramolecular first-order process and results in the almost complete conversion of the less stable complexes (4, 8) to more stable regioisomers (1, 5). The activation energies and half lifes for the conversion (4 → 1) and (8 → 5) were found to be ΔG^#=92 kJ mol⁻¹; τ_1/2=12.8 h, and ΔG^#=107 kJ mol⁻¹; τ_1/2=26.8 h, respectively, at 23 °C. Complex 1 reacts with (1R,2S,5R)-menthol in sulphuric acid solution, followed by neutralisation with sodium carbonate to give a separable mixture of diastereomeric tricarbonyl[(2,3,4,5-η)-(1R^′,2S^′,5R^′)-6-menthyloxy-2-methyltropone]iron complexes, 9 and 10. The corresponding dimethylated complex 5 fails to react under these conditions.     

Solid-state photopolymerization of α,α′-bis(4-acetoxy-3-methoxybenzylidene)-p-benzenediacetonitrile

One crystalline form of α,α′-bis(4-acetoxy-3-methoxybenzylidene)-p-benzenediacetonitrile is photopolymerized by a four-center reaction to give a polymer containing alternating benzene and cyclobutane rings. The polymer is highly crystalline and insoluble in most solvents. Location of groups around the cyclobutane ring is deduced from the products obtained on thermal decomposition. Chain contained benzene rings are located in positions 1 and 3; aromatic groups alternate sides of the cyclobutane ring. Special characterization and quantum yield of the polymerization are reported, as well as polymer solution viscosity and alkaline depolymerization of the polymer.     

On the Multiplicity of Solutions Of a Differential Equation Arising in Chemical Reactor Theory

Consider the boundary value problem where β ? 0, τ ? 0. We are concerned with a mathematically rigorous numerical study of the number of solutions in any bounded portion of the positive quadrant (τ ? 0, β ? 0) of the τ, β plane. These correct computational results may then be matched with asymptotic (β→∞, τ ? 0) results developed earlier. These numerical results are based on the development of a posteriori error estimates for the numerical solution of an associated initial-value problem and a priori bounds on .