On Necessary Optimality Conditions with Higher-Order Complementarity Slackness for Set-Valued Optimization Problems

Set-Valued and Variational Analysis - We aim to establish Karush-Kuhn-Tucker multiplier rules involving higher-order complementarity slackness under Hölder metric subregularity. These rules...     

Convergence estimates of Galerkin-wavelet solutions to a Cauchy problem for a class of periodic pseudodifferential equations

A class of Cauchy problems for interesting complicated periodic pseudodifferential equations is considered. By the Galerkin-wavelet method and with weak solutions one can find sufficient conditions to establish convergence estimates of weak Galerkin-wavelet solutions to a Cauchy problem for this class of equations.

     

Reactions de photoaddition de benzo[b]selenophenes avec l'acetylene dicarboxylate de methyle et avec le dichloro-1,2 ethylene

Photoirradiated in presence of acetophenone, benzo[b]selenophene and its 3-methyl derivative add to dimethyl acetylenedicarboxylate. In each ease, the primary reaction product is unstable and has not been isolated. Photoexeited in its triplet state (the energy of which is in the neighbourhood of 69 $\text{kcal}\text{mole}$) benzo[b]selenophene and its 2- and 3-methyl, 2,3 dimethyl, 3 acetoxy and 2-methyl-3-acetoxy derivatives add to 1,2 dichloroethylene leading to cyclobutanes. Neither cyclo-addition occurs in absence of photosensitiser. Single-crystal X-ray analysis gave the structures of the two adducts of 3-acetoxybenzo[b]selenophene with trans-1,2-dichloroethylene. In both compounds the chlorine atoms are trans.     

New labdane-type diterpenoids from Leonurus heterophyllus SW

Five new natural labdane-type diterpenoids (5-9), designated leoheteronins A-E, together with four known diterpenoids (1-4), two phytosterols as a mixture of beta-sitosterol and stigmasterol, and the flavone genkwanin (10) were isolated from the aerial parts of Leonurus heterophyllus SW. (Lamiaceae) collected in northern Vietnam. Compound 1 was isolated for the first time from a Leonurus species, and 10 is considered to be a chemotaxonomic marker of the Leonurus genus. Their structures were determined using spectroscopic analyses.     

Theoretical and experimental reevaluation of the basicity of lambda3-phosphinine

We have investigated the basicity of phosphinine (C5H5P, phosphabenzene) in reevaluating its proton affinity (PA) and gas-phase basicity (GB) and the pK(a) value of its protonated form. As a necessary step, we have first determined its gas-phase proton affinity. Using both mass spectrometric and quantum chemical methods, we have obtained the values PA(C5H5P) = 195.8 +/- 1.0 kcal mol(-1) and GB(298)(C5H5P) = 188.1 +/- 1.0 kcal mol(-1), in good agreement with previous results. We then derived a value of pK(a)(C5H6P+) = -16.1 +/- 1.0 in aqueous solution using three different approaches: the latter markedly differs from the currently available value of -10. The reason for such a discrepancy in the pK(a) of protonated phosphinine in solution is discussed. In the theoretical determination of PAs, evaluation of the basis set superposition error (BSSE) showed that this effect is quite small, being 0.1-0.2 kcal mol(-1) for phosphinine, when a density functional theory (DFT) method in conjunction with a large basis set were used.     

On a class of graphs with prescribed mean curvature

We study a class of quasilinear elliptic equations on the unit ball of ℝ ⁿ in the divergence form ∑ _j=1 ⁿ D _j{G(|x|²,|Du|²)D _j u} =H(|x|) and get estimates on the boundary by using a modified barrier-function technique of Bernstein. We establish a maximum principle for the gradients of solutions and get a global gradient estimate. We prove that solutions with constant boundary condition must be radial. Finally, we apply these results to graphs {(x,u(x)):x∈H ⁿ } whereu:H ⁿ →ℝ is a smooth map of then-hyperbolic spaceH ⁿ =B(0,1) with the metric to get the existence of graphs with radial prescribed mean curvature.     

Solutions of logarithmic type for elliptic and hypoelliptic equations

LetK be an algebraically closed field withp:=char (K)>0 andX a bielliptic curve over Spec(K) with genus≥6 and such that the canonical model ofX is ordinary. In this paper we determine all the possible gap sequences of Weierstrass points on such curves.     

Experimental analysis of floc size distributions in a 1-L jar under different hydrodynamics and physicochemical conditions

This study focuses on the relation among hydrodynamics, physicochemical conditions, and floc size. During ortho-kinetic flocculation, the floc size is controlled by a balance between hydrodynamic stress and aggregate strength. Special attention was paid to the influence of a hydrodynamic sequencing on both the aggregate strength and the flocculation processes. Experimental research was conducted in a 1-L jar for two different pH values. The hydrodynamic sequencing was made up of successive slow and rapid mixing periods, and different slow mixing intensities were studied. First, the large floc size was shown to decrease with increasing velocity gradient (G), with an expected trend (d proportional variant epsilon(-1/4)). Then, the aggregate strength was shown to depend on two main factors: the flocculation history and the physicochemical conditions, which control the cohesion forces between primary particles. Finally, flocculation processes are discussed in terms of aggregation and breakup phenomena, with relation to local hydrodynamics and physicochemical conditions.     

Effect of carbon nanotubes on the crystallization and properties of polypropylene

The effect of different concentrations of single‐walled carbon nanotubes (SWNTs) on the nonisothermal crystallization kinetics, morphology, and mechanical properties of polypropylene (PP) matrix composites obtained by melt compounding was investigated by means of X‐ray diffraction, differential scanning calorimetry, optical and scanning electron microscopy, and dynamic mechanical thermal analysis. Microscopy showed well‐dispersed nanotube ropes together with small and large aggregates. The modulus was found to increase by about 75% at a level of 0.5 wt % nanotubes. The SWNTs displayed a clear nucleating effect on the PP crystallization, favoring the α crystalline form rather than the β form. The crystallization kinetics analysis showed a significant increase in activation energy on incorporating nanotubes. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 2445–2453, 2005     

Cytotoxic diterpenoids from Vietnamese medicinal plant Croton tonkinensis GAGNEP

Six new ent-kaurane-type diterpenoids were isolated from the leaves of the endemic Vietnamese medicinal plant Croton tonkinensis GAGNEP. (Euphorbiaceae) together with three known ent-11alpha-acetoxy-7beta,14alpha-dihydroxykaur-16-en-15-one (1), ent-kaur-16-en-15-one 18-oic acid (5) and ent-18-hydroxykaur-16-ene (7). Their structures were determined by spectroscopic analyses to be ent-7beta-acetoxy-11alpha-hydroxykaur-16-en-15-one (2), ent-18-acetoxy-11alpha-hydroxykaur-16-en-15-one (3), ent-11alpha-acetoxykaur-16-en-18-oic acid (4), ent-15alpha,18-dihydroxykaur-16-ene (6), ent-11alpha,18-diacetoxy-7beta-hydroxykaur-16-en-15-one (8), and ent-(16S)-1alpha,14alpha-diacetoxy-7beta-hydroxy-17-methoxykauran-15-one (14). ent-Kaurane-type diterpenoids from Croton tonkinensis 2-4, 6, and 9-13, were tested for toxicity in the brine shrimp lethality assay. Compounds 9, 10, and 12 demonstrated significant activity, compounds 2, 3, 6, and 11 showed weak activity, and compounds 4 and 13 were inactive.