Sliding Presentation of the Jeux de Taquin for Classical Lie Groups

The simple \(GL(n,\mathbb {C})\)-modules are described by using semistandard Young tableaux. Any semistandard skew tableau can be transformed into a well defined semistandard tableau by a combinatorial operation, the Schützenberger jeu de taquin. Associated to the classical Lie groups \(SP(2n,\mathbb {C})\), \(SO(2n+1,\mathbb {C})\), there are other notions of semistandard Young tableaux and jeux de taquin. In this paper, we study these various jeux de taquin, proving that each of them has a simple and explicit formulation as a step-by-step sliding. Any of these jeux de taquin is the restriction of the orthogonal one, associated to \(SO(2n+1,\mathbb {C})\).     

Enhancement of Exochitinase Production by <Emphasis Type="Italic">Bacillus licheniformis</Emphasis> AT6 Strain and Improvement of N-Acetylglucosamine Production

A strain producing chitinase, isolated from potato stem tissue, was identified as Bacillus licheniformis by biochemical properties and 16S RNA sequence analysis. Statistical experimental designs were used to optimize nine independent variables for chitinase production by B. licheniformis AT6 strain in submerged fermentation. Using Plackett–Burman design, (NH₄)₂SO₄, MgSO₄.7H₂O, colloidal chitin, MnCl₂ 2H₂O, and temperature were found to influence chitinase production significantly. According to Box–Behnken response surface methodology, the optimal fermentation conditions allowing maximum chitinase production were (in gram per liter): (NH₄)₂SO₄, 7; K₂HPO₄, 1; NaCl, 1; MgSO₄.7H₂O, 0.1; yeast extract, 0.5; colloidal chitin, 7.5; MnCl₂.2H₂O, 0.2; temperature 35 °C; pH medium 7. The optimization strategy led to a 10-fold increase in chitinase activity (505.26 ± 22.223 mU/mL versus 50.35 ± 19.62 mU/mL for control basal medium). A major protein band with a molecular weight of 61.9 kDa corresponding to chitinase activity was clearly detected under optimized conditions. Chitinase activity produced in optimized medium mainly releases N-acetyl glucosamine (GlcNAc) monomer from colloidal chitin. This enzyme also acts as an exochitinase with β-N-acetylglucosaminidase. These results suggest that B. licheniformis AT6 secreting exochitinase is highly efficient in GlcNAc production which could in turn be envisaged as a therapeutic agent or as a conservator against the alteration of several ailments.     

Oxazoline‐terminated macromonomers by the alkylation of 2‐methyl‐2‐oxazoline

Well‐defined macromonomers of poly(ethylene oxide) and poly(tert‐butyl methacrylate) were obtained by anionic polymerization induced directly by the carbanion issued from 2‐methyl‐2‐oxazoline. When ethylene oxide was added to this carbanion with lithium as the counterion, a new compound able to initiate the polymerization of ε‐caprolactone in an anionically coordinated way was synthesized, and this led to well‐defined poly(ε‐caprolactone) macromonomers. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 2440–2447, 2005     

General and Efficient Transesterification of β-Keto Esters with Various Alcohols Using Et3N as a Brønsted Base Additive

Transesterification of β-keto esters with a wide variety of allyl, benzyl, propargyl, and alkyl alcohols using, for the first time, commercially available and inexpensive Et₃N as a Brønsted base additive, is efficiently performed in toluene at reflux. The corresponding esters are exclusively obtained in 57–98% yields with no trace amounts of γ,δ-ketones, usually expected from the decarboxylative Carroll rearrangement.     

Adsorption equilibrium studies for O‐xylene vapour and modified clays system

Tunisian bentonites were used to prepare three modified clays: two organoclays by intercalating respectively didodecyldimethylammoniumbromide (DDMAC) and hexadecyltrimethylammoniumbromide (HDTMAC), and synthesis of NaX zeolite. The X‐ray diffraction, infrared and thermogravimetric analyses enabled us to differentiate between the structures obtained. Clay materials systems were used as adsorbent for the investigation of the adsorption isotherms and saturation capacity of O‐xylene, a toxic volatile organic compound, by gravimetric method at three different temperatures 20, 30, and 40 °C. The absolute values of the volatile organic compound adsorbed amounts in the intercalated clays (604 mg g^?1) were higher than for the zeolite (296 mg g^?1). The adsorption isotherms were analysed by the Freundlich and Langmuir equations. The latter was found to describe better the equilibrium adsorption data. Mass transfer coefficient of O‐xylene is evaluated using uptake curve method, and all values are in the order of 10^?2 s^?1. Copyright © 2014 John Wiley & Sons, Ltd.