On Some Integral Equations in Hilbert Space with an Application to the Theory of Elasticity

A Volterra type integral equation in a Hilbert space with an additional linear operator L and a spectral parameter depending on time is considered. If the parameter does not belong to the spectrum of L unconditional solvability of the considered problem is proved. In the case where the initial value of the parameter coincides with some isolated point of the spectrum of the operator L sufficient conditions for solvability are established. The obtained results are applied to the partial integral equations associated with a contact problem of the theory of elasticity.     

Commutant Lifting Theorem for the Bergman Space

The central question of this paper is the one of finding the right analogue of the Commutant Lifting Theorem for the Bergman space L_a². We also analyze the analogous problem for weighted Bergman spaces L_a,α², − 1 < α < ∞.     

Syntactic characterization of closure under connected limits

Summary We give a syntactic characterization of (finitary) theories whose categories of models are closed under the formation of connected limits (respectively the formation of pullbacks and substructures) in the category of all structures. They are also those theories whose consistent extensions by new atomic facts admit in each component an initial structure (respectively an initial term structure), and also thoseT for whichM(T) is locally finitely multi-presentable in a canonical way. We also show that these two properties of theories are nonuniform.     

Rehabilitation of the Gauss-Jordan algorithm

Summary In this paper a Gauss-Jordan algorithm with column interchanges is presented and analysed. We show that, in contrast with Gaussian elimination, the Gauss-Jordan algorithm has essentially differing properties when using column interchanges instead of row interchanges for improving the numerical stability. For solutions obtained by Gauss-Jordan with column interchanges, a more satisfactory bound for the residual norm can be given. The analysis gives theoretical evidence that the algorithm yields numerical solutions as good as those obtained by Gaussian elimination and that, in most practical situations, the residuals are equally small. This is confirmed by numerical experiments. Moreover, timing experiments on a Cyber 205 vector computer show that the algorithm presented has good vectorisation properties.     

Fibrations of bigroupoids

Using Brown's construction (J. Algebra 15 (1970) 103) of an exact 6-term sequence for a fibration of groupoids we show how an exact 9-term sequence can be associated to a fibration of bigroupoids. Applications to topology and algebra are given.     

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.     

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.