Cyclic chronocoulemetry: Disproportionation and dimerization reactions coupled to electron transfer

An extension of double-potential-step chronocoulemetry to multiple or cyclic techniques has been developed, and its potential applications in the study of coupled chemical reactions in electrochemistry are discussed. Disproportionation and dimerization mechnisms are considered. Wroking curves have been calculated with the use of the finite difference digital simulation method. It is shown that better resolution for disproportionation and dimerization reactions can be obtained with cyclic chronocoulometry than with double-potential-step chronocoulemetry. The method has been experimentally verified measuring the disproportionation reaction U(V) in 1 mol dm^?3 sodium hydrogen carbonate solutions. A rate coefficient of 15.6 dm³ mol^?1 was calculated for this reaction.     

On the z-counting polynomial for edge-weighted graphs

The construction of the Z-counting polynomial for edge-weighted graphs is discussed.Dedicated to Professor Haruo Hosoya (Tokyo) on the occasion of his 55th birthday for enriching chemical graph theory with the elegant concept of the Z-counting polynomial.     

Interactions of proteins with uniform colloidal hematite and chromium hydroxide particles. I. Adsorption

The adsorption of ovalbumin, -globulin, and lysozyme on uniform spherical hematite and chromium hydroxide particles in aqueous media has been studied as a function of the pH at a constant ionic strength. The uptake of ovalbumin and -globulin was greatest at their isoelectric points and differed little at 10^–2 and 10^–3 mol dm^–3 NaNO₃. The adsorption of lysozyme was strongly influenced by the ionic strength.The deposition of ovalbumin on hematite in the presence of Mg (NO₃)₂ was significantly greater than that with NaNO₃ under otherwise comparable conditions. Dialysis experiments with ovalbumin against magnesium nitrate solutions showed Mg²⁺ to be specifically bound to the protein.The shapes of isotherms indicated monolayer coverage for ovalbumin and multilayer coating for lysozyme for both adsorbents. The shapes of isotherms of -globulin on hematite point to a rearrangement of the protein on the particle surface, while a monolayer was found on chromium hydroxide particles.Supported by the NSF Grant CHE-9108420Part of a Ph.D. thesis     

Lifshitz tails for Schrödinger operators with random breather potential

We prove a Lifshitz tail bound on the integrated density of states of random breather Schrödinger operators. The potential is composed of translated single-site potentials. The single-site potential is an indicator function of the set tA where t is from the unit interval and A is a measurable set contained in the unit cell. The challenges of this model are that, since A is not assumed to be star-shaped, the dependence of the potential on the parameter t is not monotone. It is also non-linear and not differentiable.     

On quasi-contraction mappings of Ćirić and Fisher type via ω-distance

Kada, Suzuki, and Takahashi introduced and studies the concept of ω- distance in fixed point theory. In this paper, we generalize and unify ?iri?’ and Fisher fixed points results for quasi-contractions on metric space to ω-distance on complete metric spaces. We also extend some results of Kada, Suzuki and Takahashi, and Suzuki. Our methods of proofs are new and even simpler than the corresponding methods in metric spaces.     

Weighted core–EP inverse of an operator between Hilbert spaces

We introduce and study the weighted core–EP inverse of an operator between two Hilbert spaces as a generalization of the weighted core–EP inverse for a rectangular matrix. Several new properties of weighted core–EP inverses are given and some known results are extended. Using a weighted operator, the core–EP pre-order and the minus partial order of corresponding operators, we define new pre-orders on the set of all Wg–Drazin invertible operators between two Hilbert spaces. As consequences of our results, we present a new characterization and new representations of the core–EP inverse, new characterizations of the core–EP pre-order and extend the core–EP pre-order to a partial order.     

The isomorphism relation between tree-automatic Structures

An ω-tree-automatic structure is a relational structure whose domain and relations are accepted by Muller or Rabin tree automata. We investigate in this paper the isomorphism problem for ω-tree-automatic structures. We prove first that the isomorphism relation for ω-tree-automatic boolean algebras (respectively, partial orders, rings, commutative rings, non commutative rings, non commutative groups, nilpotent groups of class n ≥ 2) is not determined by the axiomatic system ZFC. Then we prove that the isomorphism problem for ω-tree-automatic boolean algebras (respectively, partial orders, rings, commutative rings, non commutative rings, non commutative groups, nilpotent groups of class n ≥ 2) is neither a Σ₂¹-set nor a Π₂¹-set.