Stability inL 1 of some integral operators

A class of Markov operators appearing in biomathematics is investigated. It is proved that these operators are asymptotic stable inL ¹, i.e. lim _n P ⁿ f=0 forfL ¹ and f(x) dx=0.     

Extremal problems for linear orders on [n] p

Let be a product order on [n] ^p i.e. for A, B [n] ^p , 1a ₁<a ₂<...<a _p º-n and 1<-b ₁<b ₂<...<b _p <-n we have AB iff a _i<-b _i for all i=1, 2,..., p. For a linear extension < of (ordering [n] ^p as ) let F _< ^[n],p (m) count the number of A _i 's, i<-m such that 1A _i. Clearly, for every m and <, where <l denotes the lexicographic order on [n] ^p . In this note we prove that the colexicographical order, <c, provides a corresponding lower bound i.e. that holds for any linear extension < of .This project together with [2] was initiated by the first author and continued in colaboration with the second author. After the death of the first author the work was continued and finalized by the second and the third author.Research supported by NSF grant DMS 9011850.     

Thermal behavior of multiwall carbon nanotube/zeolite nanocomposites

Summary In this study we report the synthesis and thermal characterization of multiwall carbon nanotubes containing zeolite based nanocomposites. Three different zeolites (LTA, FAU and MFI) were used in this study and it was observed that the morphologies of the synthesized nanocomposites were significantly different. For FAU zeolite nanocrystals with a few nm in diameter were nucleated on the nanotubes covering their surface, however, for LTA and MFI zeolites bulky crystals with nanotubes crossing them were observed by transmission electron microscopy. One of the most important results of our study was the generation of secondary mesoporosity in the zeolites after removing the carbon nanotubes.     

Surface recombination in breakdown time delay experiments: Effect of different cathode materials

The late afterglow in nitrogen with iron electrode is studied by the breakdown time delay method, i.e., by measuring the breakdown time delay t_d as a function of the afterglow time . It is proposed that the cause of the secondary electrons initiating the breakdown is the energy of the surface recombination of nitrogen atoms on the iron electrode. The gas-phase and macrokinetic diffusive models are used to describe the experimental breakdown time delay data. By fitting the theoretical curve to the experimental data: (1) it has been confirmed that the recombination on the molybdenum glass is of the second order and the value of the surface recombination coefficient is determined at 4 mbar; (2) it has been shown that the surface recombination on the iron electrode is of the second order, and the effective recombination coefficients are determined; (3) the analytical form of the recombination coefficient as a function of the adsorption characteristics of surfaces and the pressure of the parent gas has been derived. In addition, the orders of surface recombination on the molybdenum-, aluminum-, and gold-plated electrode were determined by the same method.     

层状LiMnO2的固相合成及电化学性能

以Mn₂O₃和氢氧化锂为原料，通过焙烧合成出o-LiMnO₂。用X射线衍射和扫描电镜对不同温度下合成的粉末样品进行了表征，并研究了材料的电化学性能。通过对不同温度条件下烧结样品的晶胞参数、布拉格(110)晶面峰半高宽及电化学性能研究发现：600 ℃下合成样品的半高宽最大，堆垛层错率高，同时电化学性能也最好，首次放电容量达到156 mAh·g^-1，20次循环后仍保持在140 mAh·g^-1以上。中高温固相合成的o-LiMnO₂材料，在晶粒范围大小相近时，材料电化学性能与材料堆垛层错率相关。     

Facile hydrothermal construction of Nb_2CT_x/Nb_2O_5 as a hybrid anode material for high-performance Li-ion batteries

Herein,a simple yet efficient hydrothermal strategy is developed to in-situ convert multi-layered niobium-based MXene(Nb_2 CT_x) to hierarchical Nb2 CTx/Nb_2O_5 composite.In the hybrid,the Nb_2O_5 nanorods are well dispersed in and/or on the Nb_2 CTx.Thanks to the synergetic contributions from the high capacity of Nb_2O_5 and superb electrical conductivity of the two-dimensional Nb_2 CT_x itself,the resultant Nb_2 CTx/Nb_2O_5 hybrid exhibits excellent rate behaviors and stable long-term cycling behaviors,when evaluated as anodes for Li-ion batteries.     

The Birch reduction-dialkylation reaction. Scope and limitations

The Birch reduction-dialkylation reaction has been studied with different aromatic carboxylic acids and primary and secondary bromides. From these results it can be concluded that it is a reasonably general reaction. However, we found important exceptions with the primary bromides: allyl bromide, β-phenethyl bromide, and 5-bromo-2-methyl-2-pentene. The unusual behavior of allyl bromide is briefly discussed.     

The effects of the nature of catalyst and of the solvent on the stereoselectivity in amine-catalyzed asymmetric synthesis of substituted cyclohexa-1,3-dienes from prenal and monoesters of ylidenemalonic acids

In the amine-catalyzed reactions of prenal with (Z)-5-methyl-2-(methoxycarbonyl)hexa-2,4-dienoic or (Z)-3-phenyl-2-(ethoxycarbonyl)prop-2-enoic acid chiral β-amino alcohols provide for higher enantiomeric purity of the resulting alkyl 4-methyl-6-(2-methylprop-1-enyl)-and 4-methyl-6-phenylcyclohexa-1,3-dienoates than that provided by related chiral amines without hydroxy group. The values ofee attained in nonpolar solvents are higher than those observed in the polar ones. Substituting stoichiometric amounts of a chiral 1-amino-3-methylbuta-1,3-diene for a combination of prenal with 0.1 equiv. of the corresponding chiral amine results in the products of much lower enantiomeric purity. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 1, pp. 84–92, January, 1998.     

Total synthesis of (+)-xyloketal D, a secondary metabolite from the mangrove fungus Xylaria sp.

(+)-Xyloketal D was prepared in a one-pot multistep domino reaction by heating optically active 5-hydroxy-4-methyl-3-methylenepentan-2-one (R) in toluene with 2,4-dihydroxyacetophenone. The absolute configuration of the natural product was confirmed by preparation of the starting enone from a lactone of established absolute configuration.     

Prediction of H-Bonding Motifs for Pyrazoles and Oximes Using the Cambridge Structural Database

H-bonding motifs for pyrazoles and oximes have been examined in the Cambridge Structural Database. The accessible surface of the N atoms has been found to be useful as a discriminator to divide structures into dimer and catemer motifs for both pyrazoles and oximes. Low accessibility favors dimers and tetramers and high values favor catemers and trimers. Total molecular volume shows some correlation for oximes, while high values favor dimers. Empirical rules were successfully applied to predict the motifs of eight new structures in the subsequent release of the CSD.