Crystal structure of 12-methoxy-8,8,21,21-tetramethyl-5-(3-methylbut-2,4-dienyl)-19-(3-methylpent-4-enyl)-3,7,20-trioxahexacyclo[15.4.1.0<2,15>.0<2,19>.0<4,13>.0<6,11>]docosa-4(13),5,9,11,15-pentaene-14,18-dione.

The title compound was extracted from the natural product of plant origin. It crystallizes in tetragonal space group P4(1) or P4(3), with cell parameters a = 15.795(2)A, c = 11.970(5)A and Z = 4. The structure exhibits intermolecular hydrogen bonds of the type C-H...O.     

A single server queue with cyclically indexed arrival and service rates

In this paper we consider a queueing model that results from at least two apparently unrelated areas. One motivation to study a system of this type results from a test case of a computer simulation factor screening technique calledfrequency domain methodology. A second motivation comes from manufacturing, where due to cyclic scheduling of upstream machines, the arrival process to downstream machines is periodic. The model is a single server queue with FIFO service discipline and exponential interarrival and service times where the arrival and/or service rates are deterministic cyclic functions of the customer sequence number. We provide steady state results for the mean number in the system for the model with cyclic arrival and fixed service rates and for the model with fixed arrival and cyclic service rates. For the model with both cyclic arrival and service rates, upper and lower bounds are developed for the steady state mean waiting time in the system. Throughout the paper various implications and/or insights derived from the results of this study are discussed for frequency domain methodology.The authors acknowledge the financial support of the CBA/GSB Faculty Research Committee of the College of Business Administration, The University of Texas at Austin.     

On the application of the optical method of caustics to the investigation of transient elastodynamic crack problems: Limitations of the classical interpretation

Several possible sources of inaccuracy that occur in the classical interpretation of caustics patterns generated during transient crack growth in elastic materials are examined using a ‘Bifocal Caustics’ set-up and a new full field optical technique called ‘Coherent Gradient Sensing’. During unsteady dynamic crack growth, strict K^d_I-dominance is generally absent, especially at times close to crack initiation and arrest, even in regions outside the crack-tip 3-D zone where plane stress conditions persist. In such cases a truly transient higher order expansion is found to be essential for correctly describing stress fields outside the 3-D zone.     

Superfluous matrices in linear complementarity

Superfluous matrices were introduced by Howe (1983) in linear complementarity. In general, producing examples of this class is tedious (a few examples can be found in Chapter 6 of Cottle, Pang and Stone (1992)). To overcome this problem, we define a new class of matrices and establish that in superfluous matrices of any ordern 4 can easily be constructed. For every integerk, an example of a superfluous matrix of degreek is exhibited in the end.     

Some significant advances in sol-gel processing of dense structural ceramics

This review deals with the solution-sol-gel processing of some structural ceramics such as alumina, zirconia, mullite and cordierite and brings out the most significant advances in the preparation of dense ceramics. In the Al₂O₃ system, seeding of gels with -Al₂O₃ and other isostructural seeds led not only to lower crystallization temperature but also enhanced densification with refined microstructure through solid-state epitaxy. This breakthrough of seeding has led to improved abrasive grains with large commercial market. Although highly dense, partially stabilized zirconia ceramics were prepared using monodisperse and spherical or nanophase zirconia sol-gel powders, no commercial applications seem to have been realized thus far. In the Al₂O₃–SiO₂ system, compositionally different sol-gel nanocomposites (diphasic gels) led to enhanced densification of mullite at lower temperatures because of the occurrence of densification and crystallization processes almost simultaneously. Mullite powders derived from the diphasic gel route are a breakthrough and are now commercially marketed by Chichibu Cement Company. Highly dense cordierite was prepared by using three sols, i.e., the compositionally different sol-gel nanocomposites in an analogous manner to that of mullite. Although this process appears to be highly cost-effective, especially for the fabrication of substrates, it has not yet been utilized for commercial applications. The use of sol-gel nanocomposites in the processing of various ceramics is expected to be fully exploited in the future.     

Ultrafine Na-4-mica: uptake of alkali and alkaline earth metal cations by ion exchange

The cation exchange properties of alkali and alkaline earth metal cations at room temperature were investigated on an ultrafine, highly charged Na-4-mica (with the ideal mica composition Na4Mg6Al4Si4O20F4.xH2O). Ultrafine mica crystallites of 200 nm in size led to faster Sr2+ uptake kinetics in comparison to larger mica crystallites. The alkali metal ion (K+, Cs+, and Li+) exchange uptake was rapid, and complete exchange occurred within 30 min. For the alkaline earth metal ions Ba2+, Ca2+, and Mg2+, however, the exchange uptake required lengthy periods from 3 days to 4 weeks to be completed, similar to its Sr uptake, as previously reported. Kinetic models of the modified Freundlich and parabolic diffusion were examined for the experimental data on the Ba2+, Ca2+, and Mg2+ uptakes. The modified Freundlich model described well the Ba2+ ion uptake kinetics as well as that for the Sr2+ ion, while for the Ca2+ and Mg2+ ions the parabolic diffusion model showed better fitting. The alkali and alkaline earth ion exchange isotherms were also determined in comparison to the Sr2+ exchange isotherm. The thermodynamic equilibria for these cations were compared by using Kielland plots evaluated from the isotherms.     

Copper fluorapatite catalyzed N-arylation of heterocycles with bromo and iodoarenes

Copper exchanged fluorapatite (CuFAP) is an effective heterogeneous catalyst for N-arylation of heterocycles with bromo- or iodoarenes using K₂CO₃ as base. N-Arylated products were isolated in good to excellent yields, demonstrating the versatility of the reaction.