Matched asymptotic expansions for the determination of the electromagnetic field near the edge of a patch antenna

We consider a simple but representative model incorporating the main behavior of the electromagnetic field near the edge of a patch antenna. Recall that this kind of antenna is obtained by a metal patch laying on a dielectric substrate covering a ground metallic plane. The functioning principle of such an electric device is based on the matching of an N-dimensional behavior of the field outside the antenna with an (N-1)-dimensional one inside the zone limited by the patch and the ground plane, N = 3 or 2 according to the considered model. In this study, we make use of the technique of matched asymptotic expansions and computation of singularities to describe this behavior for the two-dimensional case. Proved error estimates enable us to give a rigorous background to the underlying asymptotic analysis. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Magnetic properties of fcc (Co95Fe5)1-xAlx ribbons

Rapidly quenched (Co₉₅Fe₅)_1-xAl_x ribbons are investigated by X‐ray diffraction, magnetization, and Mössbauer effect measurements. A single fcc phase is obtained for all ribbons x ? 10 at.%. The lattice constant increases linearly with x and is discussed in connection with magnetic moment. The influence of Al substitution on both magnetization and Fe‐atom hyperfine field (H) is studied. At 296 K, the magnetization decreases linearly while H drops nonlinearly as x increases. Al substitution leads to substantial differences in iron hyperfine fields in bcc and fcc systems. Fe moment is perturbed differently by Al substitution in fcc (Co₉₅Fe₅)_1-xAl_x and bcc Fe–Al systems.     

A study of random Weyl trees

We study binary search trees constructed from Weyl sequences {nθ}, n≥1, where θ is an irrational and {·} denotes “mod 1.” We explore various properties of the structure of these trees, and relate them to the continued fraction expansion of θ. If H_n is the height of the tree with n nodes when θ is chosen at random and uniformly on [0, 1], then we show that in probability, H_n∼(12/π²)log n log log n. © 1998 John Wiley & Sons, Inc. Random Struct. Alg., 12, 271–295, 1998     

A nearly optimal preconditioning based on recursive red–black orderings

Considering matrices obtained by the application of a five-point stencil on a 2D rectangular grid, we analyse a preconditioning method introduced by Axelsson and Eijkhout, and by Brand and Heinemann. In this method, one performs a (modified) incomplete factorization with respect to a so-called ‘repeated’ or ‘recursive’ red–black ordering of the unknowns while fill-in is accepted provided that the red unknowns in a same level remain uncoupled. Considering discrete second order elliptic PDEs with isotropic coefficients, we show that the condition number is bounded by 𝒪(n ${}^{\text{½ log}{}_{\text{2}}\text{(√(5) −1)}}$ ) where n is the total number of unknowns (½ log₂(√(5) − 1) = 0.153), and thus, that the total arithmetic work for the solution is bounded by 𝒪(n^1.077). Our condition number estimate, which turns out to be better than standard 𝒪(log² n) estimates for any realistic problem size, is purely algebraic and holds in the presence of Neumann boundary conditions and/or discontinuities in the PDE coefficients. Numerical tests are reported, displaying the efficiency of the method and the relevance of our analysis. © 1997 John Wiley & Sons, Ltd.     

Synthesis of a novel highly efficient flame-retardant coating for cotton fabrics with low combustion toxicity and antibacterial properties

Cellulose - The synthesis of multi-function flame retardants is widely increasing to fulfill industrial and economic goals. In this work, a novel flame retardant, melamine salt of tannic phosphate...     

Newly Generated Atractylon Derivatives in Processed Rhizomes of Atractylodes macrocephala Koidz

Thermally processed rhizomes of Atractylodes macrocephala (RAM) have a long history of use in traditional Chinese medicine (TCM) for treating various disorders, and have been an integral part of various traditional drugs and healthcare products. In TCM, herbal medicines are, in most cases, uniquely processed. Although it is thought that processing can alter the properties of herbal medicines so as to achieve desired functions, increase potency, and/or reduce side effects, the underlying chemical changes remain unclear for most thermally processed Chinese herbal medicines. In an attempt to shed some light on the scientific rationale behind the processes involved in traditional medicine, the RAM processed by stir-frying with wheat bran was investigated for the change of chemical composition. As a result, for the first time, five new chemical entities, along with ten known compounds, were isolated. Their chemical structures were determined by spectroscopic and spectrometric analyses. The possible synthetic pathway for the generation of such thermally-induced chemical entities was also proposed. Furthermore, biological activity evaluation showed that none of the compounds possessed cytotoxic effects against the tested mammalian cancer and noncancer cell lines. In addition, all compounds were ineffective at inhibiting the growth of the pathogenic microorganisms.     

Energetics and structure in I 2 − (CO2) n clusters

We have implemented a model of I ₂ ^? (CO₂) _n (2 ≤n ≤ 17) clusters and present an analysis of the minimum energy structures obtained from a quenching procedure. A discussion of the importance of various potential contributions to the energetics of the clusters is also presented. Given the current state of understanding of structural control of caging and the time scales of recombination and evaporation, this model has important implications for understanding the picosecond dynamics observed by the Lineberger group and for rigorous studies of evaporation rates.     

Pancyclism in Chvátal-Erdös's graphs

LetG = (X, E) be a simple graph of ordern, of stability numberα and of connectivityk withα ≤ k. The Chvátal-Erdös's theorem [3] proves thatG is hamiltonian. We have investigated under these conditions what can be said about the existence of cycles of lengthl. We have obtained several results:

1. IfG ≠ K _k,k andG ≠ C ₅,G has aC _n?1 .
2. IfG ≠ C ₅, the girth ofG is at most four.
3. Ifα = 2 and ifG ≠ C ₄ orC ₅,G is pancyclic.
4. Ifα = 3 and ifG ≠ K _3,3,G has cycles of any length between four andn.
5. IfG has noC ₃,G has aC _n?2 .

     

One-step,stereoselective synthesis of octahydrochromanes via the Prins reaction and their cannabinoid activities

Novel, functionalized octahydrochromane derivatives were synthesized in a single step via the Prins reaction. Enantiomerically pure (+)-isopulegol was reacted with benzaldehyde to stereoselectively yield the corresponding octahydro-2H-chromen-4-ol derivative containing five stereocenters. A total of 10 compounds were synthesized by altering the enantiomer of isopulegol and the substituted benzaldehyde, and the resulting enantiopure octahydrochromanes were screened in vitro against the cannabinoid receptor isoforms CB1 and CB2. Compounds containing an olefin at the C4 position [(+)-3c, (?)-3c, (?)-7c, (?)-9c and (?)-11c] of the octahydrochromane scaffold were found to exhibit reasonable displacement of [³H] CP55,940 from the CB receptors, whereas the corresponding hydroxy analogs [(+)-3a, (+)-3b, (?)-3a, (?)-3b and (+)-5a] had very little or no effect.