Isolation and structure elucidation of a flavanone, a flavanone glycoside and vomifoliol from Echiochilon fruticosum growing in Tunisia

A flavanone and a flavanone glycoside, together with vomifoliol, have been isolated for the first time from the aerial parts of the plant Echiochilon fruticosum and identified. Their structures were established on the basis of spectroscopic measurements, mainly 2D NMR using COSY, HMQC and HMBC experiments.     

Some properties of the <Emphasis Type="Italic">ɛ</Emphasis><Subscript>∞</Subscript>-product of quotient bornological spaces

Some properties of the ? _∞-product defined in [4] are obtained by a study of a kind of isomorphism between the computation of this ? _∞-product and the ordinary ?-product of L. Schwartz [9]. The paper contains several corollaries.     

Use of Ph3P=N‐Li: Synthesis of α,β‐unsaturated nitriles from α,β‐unsaturated esters via the formation of N‐(α,β‐unsaturated acyl) phosphinimines

The reaction of Ph₃P=NLi with various α,β‐unsaturated esters gives access to new N‐(α,β‐unsaturated acyl) phosphinimines, which can undergo intramolecular aza‐Wittig reactions (at 65–110°C) to afford the corresponding nitriles. The structures of all new compounds were established by elementary analyses, IR, ¹H‐, ¹³C‐, and ³¹P‐NMR spectroscopy. © 1999 John Wiley & Sons, Inc. Heteroatom Chem 10: 49–54, 1999     

Robust stability of uncertain piecewise-linear systems: LMI?approach

In this paper we propose sufficient conditions for the robust stability of time-invariant uncertain piecewise-linear systems using homogeneous polynomial Lyapunov functions. The proposed conditions are expressed in terms of linear matrix inequalities, which can be numerically determined. We solve the stabilization of piecewise uncertain linear control systems by using state piecewise-linear feedback. We propose an illustrative example to show the efficiency of the proposed approach.     

Sign‐changing bubble for Neumann problem with critical nonlinearity on the boundary

The main purpose of this paper is to construct sign‐changing solution for the following Neumann problem: where n≥3 and K is a bounded and continuous function on , which concentrate around two critical points satisfying some conditions. Copyright © 2016 John Wiley & Sons, Ltd.     

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.     

Practical Uniform Stability of Nonlinear Differential Delay Equations

In this paper, we investigate the problem of global uniform practical exponential stability of a general nonlinear non autonomous differential delay equations. Using the global uniform practical exponential stability of the corresponding differential equation without delay, we show that the differential delay equation will remain globally uniformly practically exponentially stable provided that the time-lag is small enough. Finally, some illustrative examples are given to demonstrate the validity of the results.     

Multiplicity Results of a Nonlocal Problem Involving Concave-Convex Nonlinearities

Mathematical Notes - In this work, we investigate the following fractional $$p$$ -Laplacian equation involving a concave-convex nonlinearities as follows, $${\rm (P_\lambda)} \begin{cases}...