On the Computational Complexity of the Rooted Subtree Prune and Regraft Distance

The graph-theoretic operation of rooted subtree prune and regraft is increasingly being used as a tool for understanding and modelling reticulation events in evolutionary biology. In this paper, we show that computing the rooted subtree prune and regraft distance between two rooted binary phylogenetic trees on the same label set is NP-hard. This resolves a longstanding open problem. Furthermore, we show that this distance is fixed parameter tractable when parameterised by the distance between the two trees.Received March 16, 2004     

Cochran's statistical theorem for outer inverses of matrices and matrix quadratic forms

We extend the matrix version of Cochran's statistical theorem to outer inverses of a matrix. As applications, we investigate the Wishartness and independence of matrix quadratic forms for Kronecker product covariance structures.     

Admissible slopes for monotone and convex interpolation

Summary In many applications, interpolation of experimental data exhibiting some geometric property such as nonnegativity, monotonicity or convexity is unacceptable unless the interpolant reflects these characteristics. This paper identifies admissible slopes at data points of variousC ¹ interpolants which ensure a desirable shape. We discuss this question, in turn for the following function classes commonly used for shape preserving interpolations: monotone polynomials,C ¹ monotone piecewise polynomials, convex polynomials, parametric cubic curves and rational functions.     

EPR and XPS measurements of polymeric catalysts doped with hereopolyacids in oxygen adsorption studies

The goal of our studies was to determine the nature of interactions between catalytic active samples, such as polypyrrole (PPy) doped with: chloride anions, heteropolyacids such as H₅PMo₁₀V₂O₄₀, or H₄SiW₁₂O₄₀, and oxygen particles. In order to reveal the mechanism of the linkage between the catalysts and oxygen we provided the electron paramagnetic resonance (EPR) measurements of synthesized samples in O₂ and N₂ flow. Moreover, the X-ray photoelectron spectroscopy (XPS) measurements were performed to show the properties of doped heteropolyacids and the state of nitrogen in polypyrrole matrix. The results of EPR studies of PPy(Cl), PPy(H₄SiW₁₂O₄₀), PPy(H₅PMo₁₀V₂O₄₀) samples, show that the polypyrrole doped with chloride anions interacts much easier with oxygen than polypyrrole doped with heteropolyacids (in the above given order, of preference with the most active polypyrrole system first). It correlates with XPS results, which show that a molybdenium-vanadium anion is more reduced than a silicon-tungsten one. The redox reactions of heteropolyacids involve the oxidation-reduction of the conjugated polymer chain, leaving no or little place for interactions with oxygen. Polypyrrole doped with H₄SiW₁₂O₄₀ shows some oxygen sensitivity as observed in the EPR studies, as opposed to polypyrrole doped with H₅PMo₁₀V₂O₄₀, which is in line with the XPS results.     

More on Kleinewillinghöfer Types of Flat Laguerre Planes

Polster and Steinke [Result. Math., 46 (2004), 103–122] determined the possible Kleinewillingh?fer types of flat Laguerre planes. These types reflect transitivity properties of groups of certain central automorphisms. We exclude three more types from the list given there with respect to Laguerre homotheties. This yields a complete determination of all possible single types with respect to Laguerre homotheties that can occur in flat Laguerre planes. Building on results by M?urer and Hartmann to characterize ovoidal or miquelian Laguerre planes we further characterize certain flat Laguerre planes in terms of their Kleinewillingh?fer types. Received: January 16, 2007. Revised: July 26, 2007.     

Attractors for 2D-Navier-Stokes models with delays

The existence of an attractor for a 2D-Navier-Stokes system with delay is proved. The theory of pullback attractors is successfully applied to obtain the results since the abstract functional framework considered turns out to be nonautonomous. However, on some occasions, the attractors may attract not only in the pullback sense but in the forward one as well. Also, this formulation allows to treat, in a unified way, terms containing various classes of delay features (constant, variable, distributed delays, etc.). As a consequence, some results for the autonomous model are deduced as particular cases of our general formulation.     

Expected Reflection Distance in G(r, 1, n) after a Fixed Number of Reflections

Extending to r > 1 a formula of the authors, we compute the expected reflection distance of a product of t random reflections in the complex reflection group G(r, 1, n). The result relies on an explicit decomposition of the reflection distance function into irreducible G(r, 1, n)-characters and on the eigenvalues of certain adjacency matrices.Received December 8, 2003     

Synthesis under Micromave Irradition and Crystal Structure of 4''-Acetylbenzo-15 -crown-5thiosemicarbazone

The title compound is a bifunctional receptors including a thiourea group and a crown ether ring. Due to many possible potentials as a new class of reagents for membrane transports,ion-selective electrodes as well as reaction catalysts, the design and synthesis of bifunctional receptors for simultaneous binding of cations and anions is of ongoning interest in srprarnolecular chemistry1-5. In bifunctional receptors, the binding sites for anions and cations are covalently linked so as to exhibit allosteric or cooperative complexation where the binding affinity for anions(cations)is modified as a result of the cation(anion) complexation.Literature[6] reported that the ability of the thiourea group to bind anions is significantly enhanced when Na+ is bound to the crown moiety. To date, however only a few receptors of this class have been reported.6-8In this paper, we report an improved procedure under microwave irradiation that gives higher yields of title compound and needs fewer reaction times than traditional method.The structure of this compound was determined by IR ,element analysis and X-ray analysis.Scheme 1 The reaction equationThe crystal belongs to triclinic crystal system, P-1 space group, a=0.9547(0)nm, b=1.3637(3)nm,c=1.6029(3)nm, α =75.33(3) , β =83.62(3) , γ =70.99(3) ,Z=4,Dc=1.335g/cm3,F(000)=816,R1= 0.0557 ,wR2=0.1281. It is assembled into a three-dimensionalsupramolecule by intermolecular hydrogen bonds.     

On the recognition problem of quasi-homogeneous locally nilpotent derivations in dimension three

We give a criterion to decide if a given w-homogeneous derivation on A?k[X₁,X₂,X₃] is locally nilpotent. We deduce an algorithm which decides if a k-subalgebra of A, which is finitely generated by w-homogeneous elements, is the kernel of some locally nilpotent derivation.