The de Schipper formula and squares of Riesz spaces

In this paper we introduce and study the square mean and the geometric mean in Riesz spaces. We prove that every geometric mean closed Riesz space is square mean closed and give a counterexample to the converse. We define for positive a, b in a square mean closed Riesz space E an addition via the formulaab=sup {(cos x)a + (sin x)b: 0 x 2π},which goes back to a formula by de Schipper. In case that E is geometric mean closed this turns the mldeflying set of the positive cone of E into a lattice ordered semigroup, which in turn is the positive cone ofa Riesz space E^□. We prove, under the additional condition that E is geometric mean closed, that E^□ is Riesz isomorphic to the square of E as introduced earlier by Buskes and van Rooij.     

Spectroscopic characterization and theoretical simulation of 1,4-diallylquinoxaline-2,3-dione self dimer

Room temperature UV-vis absorption and emission spectra of the 1,4-diallylquinoxaline-2,3-dione (DAQX) are measured in solution at different concentrations. Even at very low concentration (approximately 10(-7)M), DAQX is shown to form ground state van der Waals dimers and excited dimers. These later species do not seem to rearrange into an excimer geometry. The theoretical simulation of the dimer, performed using the analytical atom-atom pair potential described below, predicts a non sandwich face-to-reverse slipped structure with head-to-tail orientation. The allowed absorption transitions, calculated using ZINDO/S package, reproduce satisfactory the experimental spectrum for both the monomer and the simulated dimer.     

Hydrolysis of mefenpyrdiethyl: an analytical and DFT investigation

The hydrolysis of the herbicide safener mefenpyrdiethyl (1-(2, 4-dichlorophenyl)-4, 5-dihydro-5-methyl-1H-pyrazole-3,5-dicarboxylic acid diethyl ester) was investigated in aqueous solutions in the pH range from 2 to 9 and the temperature range from 298 to 323 K. The kinetics of hydrolysis were pseudo first order and were found to be strongly pH and temperature dependent. While near-constant in acidic medium, the hydrolysis rates strongly increased in alkaline pH, and total hydrolysis was observed at pH 11. Two main hydrolysis products, mefenpyrethyl (monoester) and mefenpyr (dicarboxylic acid) were isolated by ultrahigh-pressure liquid chromatography (UHPLC) and characterized using high-resolution Fourier transform ion cyclotron resonance mass spectroscopy (ICR-FT/MS) as well as ¹H, ¹³C and 2D NMR analyses. Additionally, a density functional theory (DFT) investigation explained the stability of the pesticide at pH 7 and the high reactivity of the pesticide in alkaline medium. The key nucleophilic reaction partner is hydroxyl ions instead of neutral water molecules. Furthermore, the calculated activation barrier for hydrolysis in alkaline medium is in agreement with the extrapolated and experimentally determined activation barrier at pH 14.     

Experimental and theoretical push‐pull Chemo‐ and regioselectivity in 1,3‐Dipolar cycloaddition reactions: the case of benzotriazepin‐5‐one with mesitylnitrile oxide

A novel heterocyclic compound 3‐mesityl‐5‐methyl‐4,5,11,11a‐tetrahydro‐6H‐[1,2,4]oxadiazolo [5,4‐b][1,3,4]benzotriazépin‐6‐one 4 has been synthesised by a 1,3 dipolar cycloaddition (13DC) reaction of 1,3,4‐benzotriazepin‐5‐one 1 with mesitylnitrile oxide 3 . The reaction, beside its synthetic interest, has shown to be completely chemo‐ and regioselective. The structure of the compound was determined by X‐ray crystallography and analysed by spectral methods (NMR and mass spectrometry). The molecular mechanism for the reaction has been studied using quantum mechanical calculations at the B3LYP/6‐31G* theory level. Two mechanisms are possible for the formation of the cycloadduct 4 . The first one involves a 13DC reaction between 1 , as dipolarophile and 3 , as dipole. Analysis of the results indicates that it takes place along asynchronous concerted bond‐formation process with a very low polar character. The regioselectivity obtained from the calculations are in complete agreement with the unique formation of the cycloadduct 4 . The second mechanism is initiated by the nucleophilic attack of the N3 nitrogen of the tautomer form of 2 , to the C5 carbon of the nitrile oxide 3 to yield an amidoxime. However, the large energy involved in this addition prevents this mechanism. The large energy difference between the tautomers 1 and 2 , makes that only the C?N site of benzotriazepin‐5‐one 1 could act as a dipolarophile site. This fact makes the 13DC reaction to be chemoselective. The analysis of global electrophilicity of the reagents allows explaining the low polar character of these 13DC reactions. Copyright © 2007 John Wiley & Sons, Ltd.     

Temporal oscillations of the shear stress and scattered light in a shear-banding-shear-thickening micellar solution

The results of optical and rheological experiments performed on a viscoelastic solution (cetyltrimethylammonium bromide + sodium salicylate in water) are reported. The flow curve has a horizontal plateau extending between two critical shear rates characteristic of heterogeneous flows formed by two layers of fluid with different viscosities. These two bands which also have different optical anisotropy are clearly seen by direct observation in polarized light. At the end of the plateau, apparent shear thickening is observed in a narrow range of shear rates; in phase oscillations of the shear stress and of the first normal stress difference are recorded in a shearing device operating under controlled strain. The direct observation of the annular gap of a Couette cell in a direction perpendicular to a plane containing the vorticity shows that the turbidity of the whole sample also undergoes time dependent variations with the same period as the shear stress. However no banding is observed during the oscillations and the flow remains homogeneous.     

Photophysical and photochemical studies of thifensulfuron-methyl herbicide in aqueous solution

The photophysical and photochemical studies of a sulfonylurea herbicide, thifensulfuron-methyl (THM), have been investigated in a buffered aqueous solution. In the first part, the influence of pH on the spectroscopic properties was studied. This allowed the determination of the ground and excited state acidity constants, pK_a = 4 and 4.4, respectively, thus exhibiting the potential existence of a photoinduced protonation in the singlet state. In the second part, the photolysis kinetics was studied at different pH and varying oxygen concentrations, using an HPK 125 W lamp and followed up by the identification of photoproducts formed under continuous photo-irradiation. The kinetics results suggest that the photolysis process is faster in acidic (k = 3 × 10^?4 s^?1) than in basic medium (k = 9.8 × 10^?5 s^?1). The photolysis products were identified by high performance liquid chromatography HPLC-DAD, HPLC–MS and HPLC–MS–MS. In order to obtain a better understanding of the photodegradation mechanism, a laser flash photolysis study was performed. By comparing the quenching rate constant (k_q = 9.64 × 10⁸ mol^?1 l s^?1) obtained from triplet state quenching by molecular oxygen and from the Stern–Volmer relation (k_q = 0.41 × 10⁸ mol^?1 l s^?1), the role of the singlet state in the photodegradation process was demonstrated. The photoproducts originating from both singlet and triplet excited states have been identified and hypothetical photodegradation pathways of the thifensulfuron-methyl in aqueous solution are proposed.     

Dark-managed solitons in inhomogeneous cubic–quintic–septimal nonlinear media

Nonlinear Dynamics - We investigate the inhomogeneous higher-order nonlinear Schrödinger (INHLS) equation including cubic–quintic–septic (CQS) nonlinear terms and gain or loss with...     

Solitary wave solutions for high dispersive cubic-quintic nonlinear Schrödinger equation

We consider the higher-order dispersive nonlinear Schrödinger equation including fourth-order dispersion effects and a quintic nonlinearity. This equation describes the propagation of femtosecond light pulses in a medium that exhibits a parabolic nonlinearity law. By adopting the ansatz solution of Li et al. [Zhonghao Li, Lu Li, Huiping Tian, Guosheng Zhou. New types of solitary wave solutions for the higher-order nonlinear Schrödinger equation. Phys Rev Lett 2000;84:4096], we find two different solitary wave solutions under certain parametric conditions. These solutions are in the form of bright and dark soliton solutions.     

Approximate positive controllability of positive boundary control systems

This paper is devoted to the study of the approximate positive controllability for linear systems with positive boundary controls. The results are applied to an abstract transport equation and controlled flows in networks.