A closure approximation for nematic liquid crystals based on the canonical distribution subspace theory

 A closure approximation for nematic polymers is presented. It approximates the fourth rank order tensor in terms of lower rank tensors, and is derived in the framework of the canonical distribution subspace theory. This approach requires a choice of the class of distributions: Here the set of Bingham distributions is chosen, as already introduced by Chaubal and Leal (1998). The closure is written in a generic frame of reference, and in an explicit form, so that it can be easily implemented. Such formulation also permits studying the closure approximation with continuation tools, which rather completely describe the system dynamics. The predictions can then be compared with those obtained with the exact model. The shear flow is considered as a test, since this flow condition appears to be the most demanding for closure approximations for nematic polymers. Received: 30 November 1999/Accepted: 30 November 1999     

Production and Purification of Pectinase from Bacillus subtilis 15A-B92 and Its Biotechnological Applications

Enzymes that degrade pectin are called pectinases. Pectinases of microbial origin are used in juice clarification as the process is cost-effective. This study screened a pectinase-producing bacterium isolated from soil and identified as Bacillus subtilis 15A B-92 based on the 16S rRNA molecular technique. The purified pectinase from the isolate showed 99.6 U/mg specific activity and 11.6-fold purity. The molecular weight of the purified bacterial pectinase was 14.41 ± 1 kD. Optimum pectinase activity was found at pH 4.5 and 50 °C, and the enzyme was 100% stable for 3.5 h in these conditions. No enzymatic inhibition or activation effect was seen with Fe²⁺, Ca²⁺, or Mg²⁺. However, a slight inhibition was seen with Cu²⁺, Mn²⁺, and Zn²⁺. Tween 20 and 80 slightly inhibited the pectinase, whereas iodoacetic acid (IAA), ethylenediaminetetraacetate (EDTA), urea, and sodium dodecyl sulfate (SDS) showed potent inhibition. The bacterial pectinase degraded citrus pectin (100%); however, it was inactive in the presence of galactose. With citrus pectin as the substrate, the Km and Vmax were calculated as 1.72 mg/mL and 1609 U/g, respectively. The high affinity of pectinase for its substrate makes the process cost-effective when utilized in food industries. The obtained pectinase was able to clarify orange and apple juices, justifying its application in the food industry.     

A unifying 2D action for integrable $$\sigma $$σ-models from 4D Chern–Simons theory

Letters in Mathematical Physics - In the approach recently proposed by K. Costello and M. Yamazaki, which is based on a four-dimensional variant of Chern–Simons theory, we derive a simple and...     

The importance of peri-interactions in determining the half-chair conformation of the dihydropyran ring in 2-benzopyrans. Stereochemical consequences

peri-Interactions are important in determining both the conformation of the dihydropyran ring of 2-benzopyrans as well as the stereochemistry of its substituents.     

Equilibria of a class of transport equations arising in congestion control

We consider a multi-queue multi-server system with n servers (processors) and m queues. At the system there arrives a stationary and ergodic stream of m different types of requests with service requirements which are served according to the following k-limited head of the line processor sharing discipline: The first k requests at the head of the m queues are served in processor sharing by the n processors, where each request may receive at most the capacity of one processor. By means of sample path analysis and Loynes’ monotonicity method, a stationary and ergodic state process is constructed, and a necessary as well as a sufficient condition for the stability of the m separate queues are given, which are tight within the class of all stationary ergodic inputs. These conditions lead to tight necessary and sufficient conditions for the whole system, also in case of permanent customers, generalizing an earlier result by the authors for the case of n=k=1. This work was supported by a grant from the Siemens AG.     

Hybrid Organic-Inorganic Materials Based on Nanobuilding Blocks Assembled through Electrostatic Interactions

Hybrid copolymers have been prepared by free radical polymerization, in toluene, of methylacrylate (MA) and varying amounts of an organotin oxo-cluster functionalized with two acrylamido groups, {(BuSn)₁₂O₁₄(OH)₆}(AMPS)₂. The tin based nanobuilding block is fully preserved in the final materials. These copolymers formed networks where the cross-linking is based on the electrostatic interactions that take place between the macrocation {(BuSn)₁₂O₁₄(OH)₆}^{2 +} and its two functional anions (AMPS^–). Accordingly, these copolymers can yield gels or solutions depending on the solvent used to swell them.     

Ribbon tableaux, ribbon rigged configurations and Hall-Littlewood functions at roots of unity

Hall-Littlewood functions indexed by rectangular partitions, specialized at primitive roots of unity, can be expressed as plethysms. We propose a combinatorial proof of this formula using Schilling's bijection between ribbon tableaux and ribbon rigged configurations.     

A radial-partition fluoroimmunoassay for the detection of Hepatitis B surface antigen with the streptavidin/biotin complex

A sandwich technique based on the very affinity between avidin and biotin is used. Antibodies are covalently bound to glass-fibre on which the antigen is captured. The discs are then treated in sequence with monoclonal antibodies of high selectivity, species-specific anti-IgG (biotin-linked), streptavidin and β-galactosidase, (biotin-linked). The discs are then incubated with the substrate, 4-methylumbelliferyl-β-d-galactopyranoside and the fluorescence is measured in an automatic immunoassay system.     

Redox active electrolytes in carbon/carbon electrochemical capacitors

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Vacuum flash pyrolysis (VFP) of malonyl peroxides: decarboxylation versus decarbonylation of the intermediary α-lactones

Vacuum Flash Pyrolysis (VFP) at ca. 450–500°C and ca. 0.1–0.3 Torr of the spirocyclic malonyl peroxides ($\text{2a,b}$) affords high yields of allenes ($\text{5a,b}$), while the simple malonyl peroxide ($\text{2c}$) leads to ketone ($\text{4}$), derived respectively from decarboxylation and decarbonylation of the intermediary α-lactones ($\text{3}$).