UNILATERAL EIGENVALUE PROBLEMS FOR NONLINEARLY ELASTIC PLATES： AN APPROACH VIA PSEUDO-MONOTONE OPERATORS

gi.TheTOpologicalDegreeforGeneralizedMonotoneOperatorsMonotoneoperatortheoryisoftenanefficienttoolforprovingtheexistenceofsolutionstononlinearProblems.Inparticular,thepseudo-monotoneoperatorsintroducedbyBrezis[2]areveryusefulforstudyingnonlinearellipticproblems.Weconsiderherethefollowingclassesofmappingsofgeneralizedmonotonetype.(QM)=theclassofquasi-mollotoneoperators,(S )=theclassofoperatorsoftype(S ),(PM)=theclassofpseudthmonotoneoperators,(LS)=theclassofLeray-Schauderoperators(compac…     

Hydrating the Bispropionate Notch in Malaria Pigment: A New Structural Motif in the Iron(III)(deuteroporphyrin) Dimer

Treating deuterohemin, chloro(deuteroporphyrinato)iron(III), with a non-coordinating base in DMSO/methanol allows for the isolation of [(deuteroporphyrinato)iron(III)]₂, deuterohematin anhydride (DHA), an analogue of malaria pigment, the natural product of heme detoxification by malaria. The structure of DHA obtained from this solvent system has been solved by X-ray powder diffraction analysis and displays many similarities, yet important structural differences, to malaria pigment. Most notably, a water molecule of solvation occupies a notch created by the propionate side chains and stabilizes a markedly bent propionate ligand coordinated with a long Fe−O bond, and a carboxylate cluster associated with water molecules is generated. Together, these features account for its increased solubility and more open structure, with an increased porphyrin–porphyrin separation. The IR spectroscopic signature associated with this structure also accounts for the strong IR band at 1587 cm⁻¹ seen for many amorphous preparations of synthetic malaria pigment, and it is proposed that stabilizing these structures may be a new objective for antimalarial drugs. The important role of the vinyl substituents in this biochemistry is further demonstrated by the structure of deuterohemin obtained by single-crystal X-ray diffraction analysis.     

One-sided Littlewood-Paley theory

In this article we develop the theory of one-sided versions of the g function of Littlewood and Paley, the area function S of Lusin and the\(g_\lambda ^* \) that admit weighted norm estimates with weights belonging to the classes A _p ⁺ of Sawyer. In Sections 1 and 2 we give definitions and some lemmas that shall be needed. Section 3 is devoted to the study of the one-sided version of the functions g and S. In Section 4 we obtain a good λ estimate for the one-sided\(g_\lambda ^* \) function, and in Sections 5 and 6 we apply the results already obtained to fractional integrals and multiplier operators.     

Electrochemistry of α, α'-dibromoketones: Reduction of 2,4-dibromo-1,5-diphenyl-1,4-pentadien-3-one (α,α'-dibromo-dibenzylidene acetone) at the mercury electrode

2,4-Dibromo-1,5-diphenyl-1,4-pentadien-3-one (VIII (PhCH=CBrCOCBr=CHPh, α, ga'-dibromodibenzylidene acetone) is electroreduced in “aprotic” dimethylformamide at the mercury electrode; E_1/2 of the first step is ?0.97 V vs. SCE; two electrons/molecule of VIII were transferred (c.p.e.) and two Br^?/molecule of VIII were released. The product was identified as cis-1,5-diphenyl-1-penten-4-yn-3-one(PhCH=CHCOC=CPh), which is the rearrangement product of an unstable dimethylenecyclopropanone. In MeOH solutions, electroreduction of VIII follows a different path, the first two-electron step being substituted by a four-electron step (c.p.e.), which furnishes 3,4-diphenyl-cyclopent-2-enone, XIII. XIII seems to be a rearrangement product of a cyclic precursor. Subsequent two-step reduction of this intermediate in MeOH affords finally 1,5-diphenylpentan-3-one(α, α'-dibenzylacetone).     

Vibrational structure in kinetic energy spectra of O+ ions from electron impact dissociative ionization of O2: Predissociation of the B 2Σg− state of O2+

Structure has been observed in the ≈ 0.8 eV kinetic energy O⁺ ion peak produced by electron impact dissociative ionization of O₂. The spacing between the features observed is approximately 0.08 eV which is consistent with their originating through predissociation of the B ²Σ_g^? state of O⁺.     

Synthesis of 8,9-dihydrodipyrazolo[3,4-b:4′,3′-f][1,5]diazocin-10(1H)-one. A new ring system

8,9-Dihydrodipyrazolo[3,4-b:4′,3′-f][1,5]diazocin-10(1H)-ones 7 were prepared by cyclization of 1-ethyl-N,3-dimethyl-4-acetamido-N-(1-R₁-3-R₂-1H-pyrazol-5-yl)-1H-pyrazole-5-carboxamides 6 by a Bischler-Napieralski cyclization. A complete assignment of the chemical shifts to the carbon atoms of compound 7 was performed by different nmr experiments, such as DEPT and XHDEPT for one? bond C? H correlations and COLOC experiments for long-range C-H correlations.     

Hydrogen-carbon,carbon-carbon double rearrangement induced by proximity effects. 1–formation of methoxybenzyl ions in the electron impact mass spectra of substituted 1,1-bis(dimethoxyphenyl)methanes

The 75 eV electron impact mass spectra of 1,1-bis(dimethoxyphenyl)methanes bearing o-methoxy groups are dominated by intense peaks corresponding, at least formally, to benzyl ions [(CH₃O)₂C₆H₃CH₂]⁺ (b). They arise from ions [((CH₃O)₂C₆H₃)₂CH]⁺ (a), which are in turn formed from molecular ions by loss of an alkyl radical through benzylic cleavage. The analysis of compounds labelled with ²H or ¹³C at methoxy groups led to the determination of the mechanism. Hydrogen migration, as hydride, followed by electrophilic substitution by the methylene carbon of the phenyl methylene ether cation through a six-centred transition state is responsible for the formation of benzylic ions b.     

Deactivation of H3PW12O40/TiO2 catalyst used in the production of camphene

Summary The deactivation of the H3PW12O40 (HPW) catalyst supported on TiO2 used in the isomerization reaction of a-pinene and its regeneration were studied. The regeneration of the deactivated catalyst was carried out with an air flow at 300 and 500ºC, with an ozone-enriched oxygen flow at 150ºC and by extraction with solvent and acid treatment. Only the last treatment permitted to recover its activity restoring it in 48% of its initial value.     

Ring opening reaction of 1,2-diaryl-3-methyl-1,4,5,6-tetrahydropyrimidinium salts with metal hydride complexes

The reaction of a series of 1,2-diaryl-3-methyl-1,4,5,6-tetrahydropyrimidinium iodides 1 with reducing agents acting by hydride ion transfer was studied. With excellent yields alkaline borohydrides readily reacted to form N'-aryl-N-benzyl-N-methyltrimethylenediamines 3 by reductive cleavage of the intermediate hexahydropyrimidine 2 . Ring opening is explained by the formation of a stabilized iminium ion, which also accounts for the cyclic aminal 2 hydrolysis observed in alcoholic solution after gradual addition of borohydride. Reactions with lithium aluminum hydride or with borane failed to render satisfactory results due to insolubility of the salt in solvents commonly employed. Comparisons are made with the behaviour of 1H-4,5-dihydroimidazolium salts which were studied in an earlier paper.     

Ring-closing metathesis for the synthesis of benzo-fused bicyclic compounds

Ring-closing metathesis (RCM) was used to synthesise five 4H-chromenes, a naphthol and an indenol. These are the first examples of RCM applied to the synthesis of such benzo-fused bicyclic compounds.