Hypergraph polytopes

We investigate a family of polytopes introduced by E.M. Feichtner, A. Postnikov and B. Sturmfels, which were named nestohedra. The vertices of these polytopes may intuitively be understood as constructions of hypergraphs. Limit cases in this family of polytopes are, on the one end, simplices, and, on the other end, permutohedra. In between, as notable members one finds associahedra and cyclohedra. The polytopes in this family are investigated here both as abstract polytopes and as realized in Euclidean spaces of all finite dimensions. The later realizations are inspired by J.D. Stasheff ?s and S. Shnider?s realizations of associahedra. In these realizations, passing from simplices to permutohedra, via associahedra, cyclohedra and other interesting polytopes, involves truncating vertices, edges and other faces. The results presented here reformulate, systematize and extend previously obtained results, and in particular those concerning polytopes based on constructions of graphs, which were introduced by M. Carr and S.L. Devadoss.     

Simultaneous determination of ursodeoxycholic acid and its glycine-conjugate in serum as phenacyl esters using multidimensional liquid chromatography

Summary A narrowbore high-performance liquid chromatographic (HPLC) method using column switching is described for the simultaneous determination of ursodeoxycholic acid (UDCA) and glyco-UDCA (GUDCA) from serum samples as their phenacyl esters. Serum samples were subjected to a preliminary clean-up using octadecylsilane reversed-phase extraction and derivatized with phenacylbromide. The purification, fractionation and concentration of UDCA and GUDCA from the esterified serum sample were performed on-line by appropriate switching of columns. Limit of detection (LOD) of UDCA and GUDCA were 5 ng and the absolute mean recoveries averaged 84.4±8.2% and 85.2±8.4%, respectively. This method was successfully applied to the pharmacokinetic study of UDCA in rats and human.     

Multigrid algorithms for a vertex–centered covolume method for elliptic problems

Summary. We analyze V–cycle multigrid algorithms for a class of perturbed problems whose perturbation in the bilinear form preserves the convergence properties of the multigrid algorithm of the original problem. As an application, we study the convergence of multigrid algorithms for a covolume method or a vertex–centered finite volume element method for variable coefficient elliptic problems on polygonal domains. As in standard finite element methods, the V–cycle algorithm with one pre-smoothing converges with a rate independent of the number of levels. Various types of smoothers including point or line Jacobi, and Gauss-Seidel relaxation are considered. Received August 19, 1999 / Revised version received July 10, 2000 / Published online June 7, 2001     

环境监测仪器精密度及总不确定度初探

本文以日立１８０－８０原子吸收分光光度计为例进行了仪器精密度及总不确定度实验的初步探讨，同时作出了该仪器适用性的判断。     

Optical and acoustic study of nucleation and growth of bubbles at a liquid-solid interface induced by nanosecond-pulsed-laser heating

The dynamics of liquid-vapor phase-change in the nanosecond time-scale induced by pulsed-laser heating of a liquid on a solid sample is studied by means of optical reflectance and scattering measurements, and the piezoelectric detection technique. The liquids studied include water, ethanol, methanol, IsoproPropyl Alcohol (IPA), and mixtures of water and IPA. The threshold fluence for nucleation is determined with high accuracy using the optical and acoustic signals. Heat diffusion calculations performed for the threshold fluences indicate that the liquids are sufficiently superheated before nucleation sets on. The transient optical reflectance signal is analyzed by an effective-medium theory to provide bubble-growth kinetics, so that the bubble-growth velocity for the test liquids could be estimated. In addition, it is observed that, following the thermally induced nucleation, repetitive acoustic cavitation at the surface of the solid sample occurs, with a time interval related to the speed of sound in the liquid.     

Structural cascade decomposition of stationary linear systems that is connected with the Kalman decomposition

The structure of a cascade decomposition of stationary linear systems is considered. It is shown that each system with Hilbert spaces of states of input and output data can be represented in the form of a cascade composition of a controlled and a completely uncontrolled (or of a completely unobservable and an observable) system. Also, the connection between the various decompositions, corresponding to the same invariant subspace, is considered.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 2, pp. 250–252, February, 1990.     

Comparison of V‐cycle multigrid method for cell‐centered finite difference on triangular meshes

We consider a multigrid algorithm (MG) for the cell centered finite difference scheme (CCFD) on general triangular meshes using a new prolongation operator. This prolongation is designed to solve the diffusion equation with strongly discontinuous coefficient as well as with smooth one. We compare our new prolongation with the natural injection and the weighted operator in Kwak, Kwon, and Lee ( 8 ) and the behaviors of these three prolongation are discussed. Numerical experiments show that (i) for smooth problems, the multigrid with our new prolongation is fastest, the next is the weighted prolongation, and the third is the natural injection; and (ii) for nonsmooth problems, our new prolongation is again fastest, the next is the natural injection, and the third is the weighted prolongation. In conclusion, our new prolongation works better than the natural injection and the weighted operator for both smooth and nonsmooth problems. © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2006     

On Hyers-Ulam-Rassias stability of functional equations

In this paper, we investigate the stability of functional equation given by the pseudoadditive mappings of the mixed quadratic and Pexider type in the spirit of Hyers, Ulam, Rassias and Gavruta.