Semiovals contained in the union of three concurrent lines

Semiovals which are contained in the union of three concurrent lines are studied. The notion of a strong semioval is introduced, and a complete classification of these objects in PG(2,p) and PG(2,p²), p an odd prime, is given. © 2007 Wiley Periodicals, Inc. J Combin Designs 15: 491–501, 2007     

On weighted multiway cuts in trees

A min—max theorem is developed for the multiway cut problem of edge-weighted trees. We present a polynomial time algorithm to construct an optimal dual solution, if edge weights come in unary representation. Applications to biology also require some more complex edge weights. We describe a dynamic programming type algorithm for this more general problem from biology and show that our min—max theorem does not apply to it.Corresponding author.Research of the author was supported by the A. v. Humboldt-Stiftung and the U.S. Office of Naval Research under the contract N-0014-91-J-1385.     

The employment of relativistic adapted Gaussian basis sets in Douglas–Kroll–Hess scalar calculations with diatomic molecules

The prolapse-free relativistic adapted Gaussian basis sets (RAGBSs), developed by our research group on the basis of the four-component approach, are used for the first time in Douglas–Kroll–Hess 2nd order scalar relativistic calculations (DKH2) of simple diatomic molecules containing Hydrogen and the halogens from Fluorine up to Iodine: HX and X₂, where X = F, Cl, Br, and I. To this end, the RAGBSs were contracted with the general contraction scheme to triple-, quadruple-, and quintuple-zeta sets. Polarization functions were also added to the basis sets by optimization with the configuration interaction method including single and double excitations into the DKH2 environment, DKH2-CISD. The molecular properties were then calculated with the coupled cluster electronic correlation treatment and the DKH2 scalar relativistic method, DKH2-CCSD(T), and indicated that our RAGBSs should be contracted as quadruple-zeta basis sets. The results achieved with the DKH2-CCSD(T) calculations and the selected quadruple-zeta RAGBSs are able to reproduce the experimental data of equilibrium distances, dissociation energies, and harmonic vibrational frequencies with root-mean-square (rms) errors of 0.015 Å, 3.6 kcal mol⁻¹, and 21.7 cm⁻¹, respectively.     

Undecidable hopf bifurcation with undecidable fixed point

We exhibit a polynomial dynamical system where one cannot decide whether a Hopf bifurcation occurs. Therefore one cannot decide whether there will be parameter values such that a stable fixed point becomes an unstable one. Related incompleteness results for previously described axiomatized versions of dynamical systems theory are also discussed.Dedicated to the memory of Leopoldo Nachbin (1922–1993), mathematician, mentor, and friend.     

Chemical separation of thallium from mercury by extraction chromatography

Thallium-201 was obtained by irradiating natural mercury with protons from IPEN's CV-28 Cyclotron. The chemical separation process chosen to separate thallium from mercury was an extraction chromatography technique. It consists on the passage of aqueous solutions (mobile phase), containing the elements that will be separated, through a glass column packed with an inert powder (support) saturated with the extractant (stationary phase).     

Explicit inverse of a tridiagonal k−Toeplitz matrix

Summary We obtain explicit formulas for the entries of the inverse of a nonsingular and irreducible tridiagonal k–Toeplitz matrix A. The proof is based on results from the theory of orthogonal polynomials and it is shown that the entries of the inverse of such a matrix are given in terms of Chebyshev polynomials of the second kind. We also compute the characteristic polynomial of A which enables us to state some conditions for the existence of A^–1. Our results also extend known results for the case when the residue mod k of the order of A is equal to 0 or k–1 (Numer. Math., 10 (1967), pp. 153–161.).The work was supported by CMUC (Centro de Matemática da Universidade de Coimbra) and by Acção Integrada Luso-Espanhola E-6/03     

A “transversal” fundamental theorem for semi-dispersing billiards

Communicated by A. Jaffe     

Switching layer stability in a polymer bilayer by thickness variation

We use optical and scanning force microscopy to explore the possibility of switching the stability of a bilayer of poly(methyl methacrylate) (PMMA) on polystyrene by simply changing the film thickness. We show that for thin PMMA layers on thicker polystyrene films the PMMA layer is unstable to thickness fluctuations. However, polystyrene layers are unstable when they are substantially thinner than the now stable PMMA film. Dewetting morphologies are cataloged as a function of the thickness of individual polymer layers by identifying which layer is unstable by which mechanism, be it spinodal dewetting or heterogeneous thermal nucleation. Our results are in good agreement with a linear stability analysis of the influence of long-range dispersion forces, but also indicate the influence of film preparation and small variations of material properties.