Random inscribing polytopes

For convex bodies K with boundary in , we explore random polytopes with vertices chosen along the boundary of K. In particular, we determine asymptotic properties of the volume of these random polytopes. We provide results concerning the variance and higher moments of this functional, as well as an analogous central limit theorem.     

Synthesis and Properties of TRANSDIP,a Rigid Chelator Built upon a Cyclodextrin Cavity: Is TRANSDIP an Authentic trans‐Spanning Ligand?

The C2-symmetrical diphosphane TRANSDIP was obtained in high yield by treating 6A,6B,6D,6E-tetramesylated, permethylated alpha-cyclodextrin with PPhLi2 in excess. The double cascade cyclisation thus produced is regioselective as phosphinidene capping involves only adjacent glucose units. It is also stereospecific, as both lone pairs on the phosphorus atoms are orientated towards the cyclodextrin axis. The restricted flexibility of the phosphorus atoms, which are part of nine-membered heterocyclic rings, is responsible for JP,C spin-spin couplings with the eight-bond distant CH2OMe carbon atoms of glucose units C and F. The treatment of TRANSDIP with Group 10 metal dihalides quantitatively gave square-planar chelate complexes, in which a M--X bond points towards the centre of the cavitand. The favourable P...P separation and the directional control of the lone pairs on the phosphorus atoms rule out the possibility of forming binuclear complexes or higher oligomers. Further, in all the complexes, the phosphorus atoms are in a trans arrangement. TRANSDIP may therefore be regarded as an authentic trans-spanning diphosphane. In the complex [NiBr2TRANSDIP], the cavity provides effective protection of the encapsulated M--X bond towards nucleophilic attack by MeLi. The same complex, upon activation with methylaluminoxane, efficiently dimerises ethene and propene.     

Investigation for Differentiation of Bounding Strength Of Metals in Sediments

Only part of the metal present in sediments are involved in short-term geochemical processes and/or are bioavailable. Hydrous Fe- and Mn-oxides as well as organic matter partly as coatings on films on detail grains, are important substances for the interaction with dissolved metal species in aquatic systems.     

On the embedding of graphs into graphs with few eigenvalues

A graph is called of type k if it is connected, regular, and has k distinct eigenvalues. For example graphs of type 2 are the complete graphs, while those of type 3 are the strongly regular graphs. We prove that for any positive integer n, every graph can be embedded in n cospectral, non-isomorphic graphs of type k for every k ≥ 3. Furthermore, in the case k ≥ 5 such a family of extensions can be found at every sufficiently large order. Some bounds for the extension will also be given. © 1996 John Wiley & Sons, Inc.     

Comparison of Pore-Level and Volume-Averaged Computations in Highly Conductive Spherical-Void-Phase Porous Materials

A study has been carried out to compare results obtained from pore-level simulations conducted on three-dimensional idealized spherical-void-phase geometric models to similar results obtained from a solver based on volume-averaging and local thermal non-equilibrium. The purpose of the comparison is to establish closure coefficients for the viscous and form drag terms in the volume-averaged momentum equations and the interstitial convective exchange coefficient required to couple the volume-averaged energy equations for the solid and fluid constituents. A method is also described for determining the solid-phase conduction shape factor, which is shown to be important for accurate volume-average simulation of highly conductive porous materials. The shape factor has been addressed in previous literature (using various terminology) and accounts in a bulk manner for resistance due to the elongated conduction path and for changes in the effective heat flow area along the conduction path. The conduction shape factor is a function of the geometry only and is found herein from a detailed comparison between pore-level and volume-averaged simulations of conjugate heat transfer. The conduction shape factor vastly improves volume-averaged predictions of the overall heat transfer and the temperature distributions in the porous material.     

Transmission properties of electromagnetic metamaterials: From split-ring resonator to fishnet structure

We experimentally presented the electromagnetic behavior of transformative magnetic metamaterials: from the early invented split-ring resonator to its improvement, the cut-wire pair, for providing a negative magnetic permeability. By adding the continuous wire to cut-wire pair structure, the left-handed (LH) transmission made by doubly negative permittivity and permeability was demonstrated in combined structure. Interestingly, until the width of cut-wire pair increases to be physically merged with the adjacent continuous wire, in other words, to form the so-called fishnet structure, the LH behavior is still observed. This result indicates that in a broad sense, the essence of the electromagnetic response in the fishnet structure is similar to that in a combined structure. Our experimental results show a good agreement with previous theoretical study.     

New Quenching Procedure for Preservation of Initial Polymer/Catalyst Particle Morphology in Ziegler–Natta Olefin Polymerization

Preservation of initial polymer/catalyst particle morphology under air, was examined using stopped‐flow Ziegler–Natta polymerization with various quenching conditions and post‐chemical treatments. The exposure of the initial particles to air caused the fast formation of cracks on the surface, finally leading to significant reformation of the particle shape, when polymerizing particles were washed with heptane at ?65 °C under N₂ or under CO₂. On the other hand, when the particles were washed with heptane containing an appropriate amount of tetrahydrofuran under CO₂, the particle morphology under air was almost completely maintained even after 1 h exposure. The present results are useful for various ex situ characterizations of unstable initial polymer/catalyst particles.

     

Exponential stabilization for a class of hybrid systems with mixed delays in state and control

This paper proposes a switching design for the exponential stabilization problem of hybrid systems with mixed time-delays in both the state and control. By using an improved Lyapunov–Krasovskii functional, a memoryless switching controller for the exponential stabilization of the system is designed in terms of linear matrix inequalities. The approach also allows us to compute simultaneously the two bounds that characterize the exponential stability rate of the solution.