Conformal metrics with prescribed Q-curvature on S n

In this paper we prescribe a fourth order conformal invariant on the standard n-sphere, with n????5, and study the related fourth order elliptic equation. We prove new existence results based on a new type of Euler?CHopf type formula. Our argument gives an upper bound on the Morse index of the obtained solution. We also give a lower bound on the number of conformal metrics having the same Q-curvature.     

Implementation of a continuation method for normal maps

This paper presents an implementation of a nonsmooth continuation method of which the idea was originally put forward by Alexander et al. We show how the method can be computationally implemented and present numerical results for variational inequality problems in up to 96 variables. The research reported here was sponsored by the Air Force Office of Scientific Research, Air Force Materiel Command, USAF, under grant numbers F49620-93-1-0068 and F49620-95-1-0222, by the U.S. Army Research Office under grant number DAAH04-95-1-0149, and by the National Science Foundation under grant number CCR-9109345. The U.S. Government has certain rights in this material, and is authorized to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright notation thereon. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of the sponsoring agencies or the U.S. Government.     

Solubility study of sodium, potassium and calcium sulfates and chlorides, in ammonia

Solubility of sodium, potassium and calcium sulfates and chlorides in 28% ammonia solution was determined through monitoring conductivity measurements and kinetics of solids dissolution as a function of temperature and stirring time. The major findings of the present study show that Na₂SO₄ and K₂SO₄ solutions conductivity follow straight linear segments with different slopes. However, in case of NaCl, KC1, CaCl₂ and CaSO₄ · 2H₂O, conductivity curves were continuous, monotonous and reach constants maximum values. The hypothesis of complex formation or dissolution via intermediaries such as NaNH₄SO₄ and KNH₄SO₄ salts seams to be true, through X-ray diffraction study of resulting deposits. Furthermore, the dissolution rates at 25°C of potassium and calcium chlorides in ammonia solution are higher than that reported in the literature for water. In fact, ammonia significantly reduces the solubility of K₂SO₄; conversely, a slight increase in this parameter was observed for CaSO₄.     

Chemoselective preparation of disymmetric bistriazoles from bisalkynes

Best of both worlds, molecules bearing two alkyne groups, activated and unactivated, can selectively react on the activated one in a copper-free version of Huisgen’s reaction to form a first triazole ring, with a good selectivity toward the 1,4-isomer, which is solely isolated by a simple trituration procedure. The other alkyne function is then submitted to the selective reaction using a polymer-supported copper(I) catalyst to form a second triazole ring. This gave access to disymmetric bistriazoles without the need of protection using simple, easy, and fast procedures.     

Glaucasides A-C, three saikosaponins from Atriplex glauca L. var. ifiniensis (Caball) Maire

From the roots of Atriplex glauca L. var. ifiniensis (Caball) Maire (syn. of Atriplex parvifolia Lowe var. genuina Maire), three new saikosaponins designated as glaucasides A-C (1-3) were isolated together with the known 3-O-β-D-glucopyranosyl-(1 → 2)-β-D-galactopyranosyl-saikogenin F (4). The structures of the new compounds were elucidated by extensive analysis of one-dimensional and two-dimensional NMR spectroscopy, FABMS, HR-ESIMS and chemical evidence as 13β,28-epoxy-16β,21β-dihydroxyolean-11-en-3β-yl O-β-D-[2-O-sulfate]-glucopyranosyl-(1 → 2)-α-L-arabinopyranoside (1), 13β,28-epoxy-16β,21β-dihydroxyolean-11-en-3β-yl O-β-D-[2-O-sulfate]-glucopyranosyl-(1 → 2)-α-L-arabinopyranosyl 21-O-{4-(secbutylamido)-butanoyl ester} (2) and 3-O-β-D-glucopyranosyl-(1 → 2)-β-D-galactopyranosyl saikogenin G (3). The cytotoxic activities of these compounds were evaluated against the HT-29 and HCT 116 human colon cancer cell lines.     

Existence and Properties of Radial Solutions of a Sub-linear Elliptic Equation

A non lipschitzian nonlinear elliptic equation is reviewed and results of existence, uniqueness, positivity and classification are proved using direct methods derived from the equation.     

Cytotoxicity of new secondary metabolites,fatty acids and tocols composition of seeds of Ducrosia anethifolia (DC.) Boiss

Two new monoterpene Ducrosin A (1) and sesquiterpene Ducrosin B (2) were isolated along with three known compounds, stigmasterol (3) and two furanocoumarins (4 and 5), from the dichloromethane extract of the seeds of Ducrosia anethifolia (DC.) Boiss. Their structures were determined using extensive 1D and 2D NMR, (ES)-HRMS and IR spectroscopic analyses and by comparison with literature data. Gas chromatography analysis of the fatty acids (FAs) of D. anethifolia seed oils (DAOs) showed high percentages of elaidic acid (C18:1 Δ9t) 65% and oleic acid (C18:1 Δ9c) 15%. The total tocopherol (tocols) content in DAOs was found to be 164 mg/100 g. The cytotoxic effect of the isolates was also evaluated using the MTT assay against the HCT-116 and SKOV-3 cell lines. The results showed that compound 2 was the most cytotoxic agent followed by compounds 1 and 4, which has an epoxide moiety that most likely contributes to its activity.     

Nauplathizine, a new unusual O-heteroside from Nauplius aquaticus (L)

A novel O-heteroside, (3RS,4RS)-3,4-dihydroxy-4-(2-hydroxy-5-acetylphenyl)-2-[(beta-O-glucopyranosyl)methyl]-but-1-ene (1), named nauplathizine, and a previously known compound, acetophenone-4-O-glucoside (2), were isolated from the antibacterial acetone extract of the aerial parts of Nauplius aquaticus (L) (Asteraceae, Inulae). The structure of 1 was established via its acetylated derivative by means of spectroscopic and chemical data.