Existence of conformal metrics with prescribed scalar curvature on the four dimensional half sphere

In this paper, we consider the problem of prescribing the scalar curvature under minimal boundary conditions on the four dimensional half sphere. Using dynamical and topological methods involving the study of the critical points at infinity of the associated variational structure, we prove some existence results like Bahri-Coron theorem. Furthermore, we consider the approximate subcritical problem and we construct some solutions which blow up at two different points, one of them lay on the boundary and the other one is an interior point.     

SYNTHESES A L'AIDE D'HETEROCUMULENES. 6. CYCLOADDITION DIPOLAIRE-1,3 ENTRE LA DIPHENYLNITRILIMINE ET LES ISOCYANATES D'AROXYSULFONYLE ET DE TRICHLORO-2,2,2-ETHOXYSULFONYLE

Abstract

In accordance with a [2 + 3] cycloaddition, aroxy and 2,2,2-tri-chloroethoxysulfonyl isocyanates react with diphenylnitrilimine, to furnish, in high yield, the corresponding 1,3,4-oxadiazolines and 1,2,4-triazolines. The latter are formed too by a direct addition of α-chlorobenzylidene-phenylhydrazine to these heterocumulenes, followed by a dehydrohalogenation of the intermediates.

La cycloaddition [2 + 3] des isocyanates d'aroxy et de trichloro-2,2,2-éthoxysulfonyle sur la diphénylnitrilimine, fournit les oxadiazolines-1,3,4 et les triazolines-1,2,4 correspondants avec de hauts rendements. Ces měmes hétérocycles sont obtenus par une voie différente: addition directe de l'α-chlorobenzylidène-phénylhydrazine sur ces hétérocumulènes, suivie d'une déhydrohalogénation des intermédiaires ainsi formés dans la première étape de la réaction.     

Antitumor Activity of Some Novel 1,2,5-Thiadiazole Derivatives

Some novel thiourea,1,2,4-triazole, quinazoline, thieno[2,3-d]pyrimi-dine, and thiazolidine derivatives were synthesized to evaluate their antitumor activity. Compound (3f) is nearly as active as reference drug, (Doxorubicin) as positive control.     

Substituent Effect on the Electronic Structure of Sulfines: Molecular Orbital Treatment

The electronic structure and ground state properties of the gaseous sulfine H₂CSO and some of its derivatives were studied at the RHF, MP2, and B3LYP levels. The calculations showed that the Z-isomer is more stable than the E-one and their difference in energy depends on their level of calculation, basis set, and substituent. The factors affecting the isomer stability are the electrostatic interactions, the steric factor, and π-electrons delocalization. The substituent has little effect on the geometry of the CSO moiety but greatly affects its charge distribution and polarizability. The ΔE value of the E- to Z-isomerization process via rotation of the S═O bond was calculated. The substituent has an appreciable effect on both the geometry and energy barrier of isomerization depending on its electronegativity, electrostatic attraction, and effect on π-delocalization over the molecule.     

The hyperconjugation effect on the graphene counterparts based on silicon and germanium

Bending of the A = A (A of the group IVA) double bond neighboring is rationalized by the hyperconjugation phenomenon analysis. The bending is also observed for the high sized linear, cyclic or graphene-like compounds that imply the conjugated double bonds. The electronic delocalization takes place between occupied σ(π) and unoccupied π*(σ*) orbitals especially for compound implying Si and Ge atoms. Leading to rippled structure, this phenomenon affects the silicene and germane thickness sheets and probably would have some consequences on the properties of such compounds when they will be involved in the industries in the future. However we introduce a new parameter to assess the thickness of graphenic structures when the hyperconjugation takes place in the bonding framework. The study has been undertaken at high levels of theory like B3LYP/6-311 + G(3df,2p).     

EPEC: an efficient privacy-preserving energy consumption scheme for smart grid communications

In this paper, we propose an efficient privacy-preserving energy consumption scheme with updating certificates, called EPEC, for secure smart grid communications. Specifically, the proposed EPEC scheme consists of four phases: gateways initialization, party registration, privacy-preserving energy consumption, and updating certificates. Based on the bilinear pairing, the identity-based encryption, and the strategy of updating certificates, EPEC can achieve data privacy, gateway privacy, and is robust to data replay attack, availability attack, modification attack, man-in-the-middle attack, and Sybil attack. Through extensive performance evaluations, we demonstrate the effectiveness of EPEC in terms of transmission delay performance at the HAN gateway and average delivery ratio, by implementing three types of curves including, the Barreto–Naehrig curve with modulus 256 bits, the Kachisa–Schaefer–Scott curve with modulus 512 bits, and the Barreto–Lynn–Scott curve with modulus 640 bits.     

Inclusion complex of N-nitroso,N-(2-chloroethyl), N′, N′-dibenzylsulfamid with β-Cyclodextrin: Fluorescence and molecular modeling

The inclusion complex of N-nitroso, N-(2-chloroethyl), N′, N′-dibenzylsulfamid with β-Cyclodextrin have been investigated using the spectrofluorescence technique ¹H NMR spectroscopy. The stoichiometric ratio of the complex was found to be 1:1 and the stability constant was evaluated using the Benesi-Hildebrand equation. In order to find the most favorable structure, molecular mechanics calculations were employed to study the inclusion of CENS-Dibenz in β-CD in vacuum and in the presence of water as a solvent. The driving forces for complexation are dominated by non-bonded van der Waals host-guest interactions with very little electrostatic contribution in both environments. After this stage of calculation, both the most stable complexes obtained by MM+ were re-optimized using semi-empirical and quantum mechanical calculations. It was found that the PM3 and the hybrid method ONIOM2 calculations predict the same mode of inclusion of the drug molecule in the host cavity. In the most stable conformation (i.e. Complex A), one of the two aromatic cycles is dipped within the relatively less polar cavity of β-cyclodextrin, while the other aromatic cycle as well as the active groupings (alkylating agent and nitroso group) are directed towards the exterior through the narrow rim of β-CD. This orientation is preferred because it is the most energetically favorable structure. Moreover, statistical thermodynamic calculations demonstrate that the formation of the inclusion complex is an enthalpy-driven process. A comparison between the experimental and theoretical values of ΔG⁰ proves that simulation of the complexes without an explicit treatment of the solvent leads to dubious results.     

Clay Catalysis: Stork's Alkylation and Acylation of Cyclohexanone Without Isolation of Enamine

Cyclohexanone and morpholine in the presence of KSF under azeotropic distillation gave 1-morpholinocyclohexene which is alkylated or acylated in situ without isolation of the enamine. The overall yield of these Stork's reactions are better or equivalent to those obtained by isolation of the enamine.