Structure of norbornene-fused 3,1-oxazine double cycloadducts

Pentacyclic isoxazolines were obtained by the cycloaddition of benzonitrile oxide to norbornene-azetidinone-fused 3,1-oxazines. The constitutions of two of the isomers obtained, and the configurations and conformations of all products, were determined by means of ¹H and ¹³C NMR spectroscopy and DNOE experiments.     

Optimal Control in Heterogeneous Domain Decomposition Methods for Advection-Diffusion Equations

New domain decomposition methods (DDM) based on optimal control approach are introduced for the coupling of first and second order equations on overlapping subdomains. Several cost functionals and control functions are proposed. Uniqueness and existence results are proved for the coupled problem, and the convergence of iterative processes is analyzed. The work was supported by the Russian Foundation for Basic Research (04-01-00615) and it was partly carried out while the first author was visiting the IACS at EPFL.     

牛顿弦截法预估校正迭代格式的收敛阶

研究如下形式的牛顿弦截法的预估校正(P.C.)格式:P(预估):~xk+1=xk-(xk-xk-1)f(xk)f(xk)-f(xk-1)C(校正):xk+1=xk-(~xk+1-xk)f(xk)f~(xk+1)-f(xk)证明了它的收敛阶为2.618.     

Long-time dynamics of von Karman semi-flows with non-linear boundary/interior damping

We study von Karman evolution equations with non-linear dissipation and with partially clamped and partially free boundary conditions. Two distinctive mechanisms of dissipation are considered: (i) internal dissipation generated by non-linear operator, and (ii) boundary dissipation generated by shear forces friction acting on a free part of the boundary. The main emphasis is given to the effects of boundary dissipation. Under suitable hypotheses we prove existence of a compact global attractor and finiteness of its fractal dimension. We also show that any solution is stabilized to an equilibrium and estimate the rate of the convergence which, in turn, depends on the behaviour at the origin of the functions describing the dissipation.     

Stability radii of positive linear Volterra-Stieltjes equations

We study stability radii of linear Volterra-Stieltjes equations under multi-perturbations and affine perturbations. A lower and upper bound for the complex stability radius with respect to multi-perturbations are given. Furthermore, in some special cases concerning the structure matrices, the complex stability radius can precisely be computed via the associated transfer functions. Then, the class of positive linear Volterra-Stieltjes equations is studied in detail. It is shown that for this class, complex, real and positive stability radius under multi-perturbations or multi-affine perturbations coincide and can be computed by simple formulae expressed in terms of the system matrices. As direct consequences of the obtained results, we get some results on robust stability of positive linear integro-differential equations and of positive linear functional differential equations. To the best of our knowledge, most of the results of this paper are new.     

Measures on minimally generated Boolean algebras

We investigate properties of minimally generated Boolean algebras. It is shown that all measures defined on such algebras are separable but not necessarily weakly uniformly regular. On the other hand, there exist Boolean algebras small in terms of measures which are not minimally generated. We prove that under CH a measure on a retractive Boolean algebra can be nonseparable. Some relevant examples are indicated. Also, we give two examples of spaces satisfying some kind of Efimov property.     

Predicting automobile claims bodily injury severity with sequential ordered logit models

Despite the large cost of bodily injury (BI) claims in motor insurance, relatively little research has been done in this area. Many companies estimate (and therefore reserve) bodily injury compensation directly from initial medical reports. This practice may underestimate the final cost, because the severity is often assessed during the recovery period. Since the evaluation of this severity is often only qualitative, in this paper we apply an ordered multiple choice model at different moments in the life of a claim reported to an insurance company. We assume that the information available to the insurer does not flow continuously, because it is obtained at different stages. Using a real data set, we show that the application of sequential ordered logit models leads to a significant improvement in the prediction of the BI severity level, compared to the subjective classification that is used in practice. We also show that these results could improve the insurer’s reserves notably.     

Packing Non-Zero A-Paths In Group-Labelled Graphs

Let G=(V,E) be an oriented graph whose edges are labelled by the elements of a group Γ and let A⊂V. An A-path is a path whose ends are both in A. The weight of a path P in G is the sum of the group values on forward oriented arcs minus the sum of the backward oriented arcs in P. (If Γ is not abelian, we sum the labels in their order along the path.) We are interested in the maximum number of vertex-disjoint A-paths each of non-zero weight. When A = V this problem is equivalent to the maximum matching problem. The general case also includes Mader's S-paths problem. We prove that for any positive integer k, either there are k vertex-disjoint A-paths each of non-zero weight, or there is a set of at most 2k −2 vertices that meets each of the non-zero A-paths. This result is obtained as a consequence of an exact min-max theorem. These results were obtained at a workshop on Structural Graph Theory at the PIMS Institute in Vancouver, Canada. This research was partially conducted during the period the first author served as a Clay Mathematics Institute Long-Term Prize Fellow.     

新疆野生黑加仑与马林果实的营养成分分析

通过对新疆野生黑加仑和野生马林的脂肪油，8种微量元素，17种氨基酸以及维生素C的含量进行测定得出：黑加仑脂肪油含量为17．9％，马林的脂肪油含量为22．3％，其中，黑加仑脂肪油中，r－亚麻酸的含量为19．02％，而马林中，其含量为9．40％，黑加仑中K，Na,Ca,Cu,Zn,Fe的含量比马林中的含量高，而Mn,Mg元素的含量却比马林含量低；马林的维生素C含量为16．22mg/g，黑加仑的含量为108mg/g，黑加仑的氨基酸的总量为1．63％，马林为1．14％。