A method for predicting the anharmonicity constants ωeχe of halides of sodium

A method is proposed for estimation of the vibrational anharmonicity constants ω_eχ_e of diatomic molecules. The procedure involves fitting of the potential energy curve obtained by the RKRV method with that obtained by using the 5-parameter Hulburt-Hirschfelder potential function. We have predicted values of ω_eχ_e for alkali halides for which accurate data are not available.     

A generalization of a theorem of Ky Fan on simplicial maps

A combinatorial result is proved which generalizes a theorem of Ky Fan on simplicial maps from a pseudomanifold. A version of the Kronecker Theorem in Topology is also derived as a special case.     

Identities for minors of the Laplacian, resistance and distance matrices

It is shown that if L and D are the Laplacian and the distance matrix of a tree respectively, then any minor of the Laplacian equals the sum of the cofactors of the complementary submatrix of D, up to sign and a power of 2. An analogous, more general result is proved for the Laplacian and the resistance matrix of any graph. A similar identity is proved for graphs in which each block is a complete graph on r vertices, and for q-analogues of such matrices of a tree. Our main tool is an identity for the minors of a matrix and its inverse.     

On the first passage time of a simple random walk on a tree

We consider a simple random walk on a tree. Exact expressions are obtained for the expectation and the variance of the first passage time, thereby recovering the known result that these are integers. A relationship of the mean first passage matrix with the distance matrix is established and used to derive a formula for the inverse of the mean first passage matrix.     

Dynamic-covalent macromolecular stars with boronic ester linkages

Macromolecular stars containing reversible boronic ester linkages were prepared by an arm-first approach by reacting well-defined boronic acid-containing block copolymers with multifunctional 1,2/1,3-diols. Homopolymers of 3-acrylamidophenylboronic acid (APBA) formed macroscopic dynamic-covalent networks when cross-linked with multifunctional diols. On the other hand, adding the diol cross-linkers to block copolymers of poly(N,N-dimethylacrylamide (PDMA))-b-poly(APBA) led to nanosized multiarm stars with boronic ester cores and PDMA coronas. The assembly of the stars under a variety of conditions was considered. The dynamic-covalent nature of the boronic ester cross-links allowed the stars to reconfigure their covalent structure in the presence of monofunctional diols that competed for bonding with the boronic acid component. Therefore, the stars could be induced to dissociate via competitive exchange reactions. The star formation-dissociation process was shown to be repeatable over multiple cycles.     

Electrical and electrochemical properties of pretreated thermally and γ-irradiated TiO2

Electrical conductivity and Seebeck voltage developed in thermally pretreated and -irradiated TiO₂ was measured as a function of temperature. The conversion of n-type TiO₂ into p-type and vice versa observed after irradiation was explained in terms of ionization of Ti³⁺ donors and lattice O⁼ species, subsequent trapping of carriers in adsorbed oxygen and further formation of p-type inversion layer on the oxide surface during irradiation. The sign of the EMF of the electrochemical Ag/Ag⁺ concentration cell by the addition of heated and -irradiated TiO₂ in one of the compartment of the cell was found to be opposite to that due to the addition of the corresponding heated but non-irradiated oxide sample.     

Lifetime measurements for some levels in Be-like Cl XIV and S XIII

Lifetime measurements have been carried out for some low lying (n = 2) levels in the four-electron ions Cl XIV and S XIII using the beam-foil technique. Accurate oscillator strengths for the 2 s2 ¹ S - 2 s 2 p ¹ P o transition have been determined by the inclusion of prominent cascades in the analysis. Lifetimes of the levels of the 2 p2 ³ P j multiplet have also been measured for both ions. The results are compared with theoretical predictions and earlier measurements. Received: 29 October 1997 / Revised: 10 February 1998 / Accepted: 5 March 1998     

Stable periodic vibroimpacts of an oscillator

The asymptotically stable vibrations of a loaded oscillator colliding periodically with a rigid mass are described. Comparison of the numerical results with the few existing examples is encouraging but inconclusive. Better overall agreement is demonstrated with fairly comprehensive measurements from a specially built experimental rig. Impact motions are shown to be very sensitive to small fluctuations in the clearance between masses and the stiffness and loading of the oscillator near its linear, or collisionless, resonant frequency. The rigid mass is quite an effective damper at or just above this frequency condition.