A Struwe Type Decomposition Result for a Singular Elliptic Equation on Compact Riemannian Manifolds

On a compact Riemannian manifold,we prove a decomposition theorem for arbitrarily bounded energy sequence of solutions of a singular elliptic equation.     

Some Remark on Optimal Stochastic Control with Partial Information

Abstract

We are interested in the control problem of a partially observable diffusion process, which is initialized at a fixed point of ? ⁿ , and we want to characterize the associated value function. To resort to the theory of viscosity solutions depends on the possibility to translate such a problem on Hilbert spaces like L ²(? ⁿ ), and so it can not be used here. Nevertheless, a result of N. Bouleau and F. Hirsch allows us to introduce a broadened problem which fulfills the condition. The fact remains to link these two control problems.     

An Efficient Synthesis of New Substituted Spiro Pyrazolethieno,Pyrimidinethieno, and Benzodiazepinethieno Pyridazine Derivatives with Biological Activities

3-Ethyl 2-amino-4-methyl-5-phenyl thiophene carboxylate 1 was used as a starting material to synthesize 2a,b via coupling with malononitrile or acetyl acetone, respectively. When heated, under reflux in sodium ethoxide solution, 2a,b give 3a,b. On the other hand, when compounds 3a,b were heated under reflux in ethanol with hydrazine hydrate, thiourea, or 1,1-phenylenediamine hydrochloride and a catalytic amount of piperidine 4a,b, 5a,b and 6a,b, were produced, respectively. The new compounds were tested for their antimicrobial activity. Compounds 2a–6b showed antibacterial activities, and 2a,2b and 4b showed antifungal activities.

Supplemental materials are available for this article. Go to the publisher's online edition of Phosphorus, Sulfur, and Silicon and the Related Elements to view the free supplemental file.     

SOME REACTIONS OF 3-AMINO-2-CARBOETHOXY-4,6-DIMETHYLTHIENO[2,3-b]-PYRIDINE. SYNTHESIS OF SOME NEW THIENOPYRIDOPYRIMIDINES

Abstract

Thienopyridine oxazinone (1) has been prepared and explored as a precursor by its reaction with some reagents namely, ammonium acetate, aliphatic amines, aromatic amines, hydrazine hydrate, thiosemicarbazide, and ethyl glycinate to give pyridothienopyrimidines (11-VII). The pyrimidinone compound (11) was converted to the 4-chloro derivative (X) by its reaction with excess POCl₃ Interaction of the 4-chlorocompound (X) with some reagents namely, hydrazine hydrate, methyl amine, aniline, sodium thiophenolate, ethyl glycinate, thiosemicarbazide and thiourea, yielded pyridothieno-pyrimidine derivatives (XI-XVII) substituted at 4-position, respectively.     

Cationic Photocrosslinkable Polydimethylsiloxane. III. Synthesis and Photocrosslinking of Polydimethylsiloxane Bearing Oxetane Groups

Abstract

From 3-hydroxymethyl-3-methyl oxetane, we synthesized three oxetane monomers with allylic, diethoxysilane or triethoxysilane functions. These monomers allowed us to prepare different polydimethylsiloxanes bearing oxetane groups by two routes. One is hydrosilylation of allylic monomer on hydrogeno polydimethylsiloxane, with different percentages of Si-H bonds. The second route is a condensation of α,ω-dihydroxy polydimethylsiloxane with di and tri ethoxysilane monomers. By using a photocalorimeter, we studied the kinetic of cationic photopolymerization of a polydimethylsiloxane bearing 7.4% oxetane functions. Influence of temperature in the range 35 to 125°C showed a maximum conversion for 80°C due to an increase in transfer and termination reactions.     

Synthesis and reactions of 4H-3,1-benzoxazin-4-one derivative bearing pyrazolyl moiety as antimicrobial and antioxidant agents

Ring opening of 4-aryl-2-phenyloxazol-5-one 1 with 2-aminobenzoic acid in acetic acid and n-butanol gave compounds 2 and 3, respectively. The 4H-3,1-benzoxazin-4-one derivative 4 was synthesized by refluxing of compound 2 in acetic anhydride. Then it reacted with different nitrogen nucleophiles such as hydrazine hydrate, phenylhydrazine, cyclohexylamine, piperidine, ethylenediamine, ethanolamine, semicarbazide hydrochloride, cyanoacetohydrazide and methyl glycinate hydrochloride to give compounds 5–14 in order to study the behavior of these nucleophilic reagents on the performed ring system. All the structures of the newly prepared compounds were characterized by their IR, ¹H-, 13C-NMR and MS spectral data. Some of the synthesized compounds were screened for their antimicrobial and antioxidant activities. Compound 5 showed remarkable activity upon this screening.     

Synthesis and antitumor activity evaluation of some 1, 2, 4-triazine and fused triazine derivatives

Reactions of 3-hyrazino-5,6-diphenyl-1,2,4-triazine with various carbonyl compounds such as ethyl acetoacetate, acetylacetone, benzoin, isatin, phthalic anhydride, phenyl isocyanate and acetic anhydride were discussed. Its reactions with α, β unsaturated compounds such as arylidinemalononitrile, diethyl acetylenedicarboxylate, dibenzylidine hydrazine were studied. These reactions led to the formation of various triazine and fused-triazine derivatives. The antitumor activity of the synthesized compounds was tested against HePG2 and MCF-7 cell lines. Some of the tested compounds were most active, whereas other compounds exhibited little or no activity.     

Hydrogen production by steam reforming of glycerol over Ni/Ce/Cu hydroxyapatite-supported catalysts

Hydroxyapatite-supported Ni-Ce-Cu catalysts were synthesised and tested to study their potential for use in the steam reforming of glycerol to produce hydrogen. The catalysts were prepared by the deposition-precipitation method with variable nickel, cerium, and copper loadings. The performance of the catalysts was evaluated in terms of hydrogen yield at 600°C in a tubular fixed-bed microreactor. All catalysts were characterised by the BET surface area, XRD, TPR, TEM, and FE-SEM techniques. The reaction time was 240 min in a fixed-bed reactor at 600°C and atmospheric pressure with a water-to-glycerol feed molar ratio of 8: 1. It was found that the Ni-Ce-Cu (3 mass %-7.5 mass %-7.5 mass %) hydroxyapatite-supported catalyst afforded the highest hydrogen yield (57.5 %), with a glycerol conversion rate of 97.3 %. The results indicate that Ni/Ce/Cu/hydroxyapatite has great potential as a catalyst for hydrogen production by steam reforming of glycerol.