Matchings and radon transforms in lattices. I. Consistent lattices

An element in a lattice is join-irreducible if x=ab implies x=a or x=b. A meet-irreducible is a join-irreducible in the order dual. A lattice is consistent if for every element x and every join-irreducible j, the element xj is a join-irreducible in the upper interval [x, î]. We prove that in a finite consistent lattice, the incidence matrix of meet-irreducibles versus join-irreducibles has rank the number of join-irreducibles. Since modular lattices and their order duals are consistent, this settles a conjecture of Rival on matchings in modular lattices.     

Supramolecular Metal Complex with Ferrocene-conjugated Macrocyclic Triaza Crown Ether as Ligand and Its Electrochemical Property

LigandscontainingelectrochemicallyresponsivecentrearegoodsubjectsforthestUdyofintfamolecularandhost-guestillteraction.Forthisreason,tYemendousamoulltsofsuchligandsandtheircomplexeshavebeensynthesized.'-'AnobservationfromthestudiesofthesecomPlexesisthattheguestionhasapermrbationonthehostcelltre.2'7-9Forexample,itwasdocumelltedthatintroductionofCo(II)ionontoN-ferrocenylmethyl-l,4,7-triazacyclononane(fcmtacn)causesapositiveshiftintheredoxpotentialofferrocenylgroupfromthatofferrocenegroupinfree…     

Direct evidence of oxidized gold on supported gold catalysts

Supported gold catalysts have drawn worldwide interest due to the novel properties and potential applications in industries. However, the origin of the catalytic activity in gold nanoparticles is still not well understood. In this study, time-of-flight secondary ion mass spectroscopy (TOF-SIMS) has been applied to investigate the nature of gold in Au (1.3 wt %)/gamma-Al2O3 and Au (2.8 wt %)/TiO2 catalysts prepared by the deposition-precipitation method. The SIMS spectrum of the supported gold catalysts presented AuO-, AuO2-, and AuOH- ion clusters. These measurements show direct evidence for oxidized gold on supported gold catalysts and may be helpful to gaining better understanding of the origin of the catalytic activity.     

INTERACTIONS AMONG PHOTOSYNTHETIC ANTENNA EXCITED STATES

Abstract. The data of Kung and DeVault (1978) showing high-order fluorescence from chromatophores of photosynthetic bacteria are analyzed in relation to other data on first-order fluorescence of photosynthetic systems, particularly that of Monger and Parson (1977). The wavelengths of emission observed (down to 445 nm) require energy equivalent to two lowest singlet-excited states. The dependence on excitation intensity is best explained by any of the following third-order processes: (a) 3 S ₁→3 S ₀; (b) 2 S ₁+ T , → 2 S ₀+ T ₁; (c) S ₁+ 2 T ₁→ 3 S ₀. However, (c) is ruled out because it predicts heavy T ₁-destruction which is not observed. Contribution from the second order process: 2 S ₁→ S ₀ is probable, but even the data of Monger and Parson show that it is insufficient by itself. Two-photon absorption: S ₀+ hv ₁→ S ₁; S ₁+ hv ₁→ S _n; S _n S ₀+ hv ₂ could also account for the high-order fluorescence and its dependence on excitation intensity. [ S ₀, S ₁ S _n are ground, first excited and a higher excited singlet states, respectively, of antenna bacteriochlorophyll, T _t is the lowest triplet state, c/v , is the exciting wavelength (694 or 868 nm) and c/v ₂ the wavelength of the high-order fluorescence (445, 535. or 600 nm), where c = velocity of light.] Maximum values are estimated for some of the rate constants.     

Different reaction routes found in acid-catalyzed glycosylation of endo- and exo-glycals: competition between Ferrier rearrangement and protonation

Acid-mediated glycosylations of endo- and exo-glycals have been carried out in good to excellent yields, in which a mixture of two products is often obtained resulting from Ferrier rearrangement and protonation. The former reaction exclusively takes place with the t-butyl carbonate or hydroxyl substituent at the C3 position of endo-glycals, while the latter mainly occurs in the glycosylation of exo-glycals with allyl benzyl ether or acetate. In addition to the substituent effect, protecting groups are critical to determine the activity and favored reaction pathway. Furthermore, the method is applicable to O-, C-, and N-nucleophiles.     

Separation of Dyes from Aqueous Solutions by Paper Adsorption

Separation of the dyes methyl violet, methylene blue, and congo red from aqueous solutions by paper capillary permeation adsorption method was studied using paper. Nearly 100% of the investigated dyes could be separated under the optimum conditions. The effect of pH on the separation efficiency was studied in particular. At pH 5–9, 1.3–11, and 7–11, the maximum separation was achieved for methyl violet, methylene blue and congo red, respectively. The effects of dye concentration and some foreign ions on the separatability were examined. Moreover, the selective separation of some dyes was attempted by elution with chemical reagents.     

Synthesis of indeno-fused derivatives of quinolizinium salts, imidazo[1,2-a]pyridine, pyrido[1,2-a]indole, and 4h-quinolizin-4-one via benzannulated enyne-allenes

The benzannulated enediynyl propargylic alcohol 8 was prepared from 1-bromo-2-iodobenzene by two consecutive Sonogashira cross-coupling reactions. The subsequent transformation to mesylate 9 followed by treatment with 4-substituted pyridines 10 then furnished the benzannulated enediynes 11. On exposure of 11 to triethylamine, the indeno-fused quinolizinium salts 15 were produced in quantitative yield. Presumably the reaction proceeded through a 1,3-prototropic rearrangement to form the benzannulated enyne-allenes 12, which then underwent either a concerted Diels-Alder reaction or a two-step process involving a Schmittel cyclization reaction to form biradical 13 followed by an intramolecular radical-radical coupling to afford 14. A subsequent prototropic rearrangement then produced 15. Similarly, 21a and 21b were produced from 19a and 19b, respectively. The use of the Sonogashira reaction for cross-coupling between 1-iodo-2-(phenylethynyl)benzene (7) and 1-(2-propynyl)-1H-imidazole (25) followed by treatment of the resulting adduct with potassium tert-butoxide gave the indeno-fused imidazo[1,2-a]pyridine 24 in 98% yield. Similarly, the indeno-fused pyrido[1,2-a]indole 32 and 4H-quinolizin-4-one 35 were obtained by starting from 7 for cross-coupling with 1-(2-propynyl)-1H-indole (30) and 1-(2-propynyl)-2(1H)-pyridinone (33), respectively, followed by treatment with potassium tert-butoxide.     

Synthesis and rotational barriers of atropisomers of 1,2-bis[5-(11H-benzo[b]fluorenyl)]benzenes and related compounds

Several 1,2-bis[5-(11H-benzo[b]fluorenyl)]benzenes and related compounds were synthesized via a cascade reaction sequence of the corresponding benzannulated enyne-allene precursors. The X-ray structures showed that the two benzo[b]fluorenyl moieties attached via the C5 carbons to the adjacent carbon atoms of the central benzene ring are oriented essentially perpendicular to the central benzene ring. The rates of rotation around the carbon-carbon single bonds attaching the benzo[b]fluorenyl moieties to the central benzene ring are relatively slow, allowing several anti and syn atropisomers to be separated at ambient temperature.     

Synthesis and study of N,N‐disubstituted 4‐[(4‐aminophenyl)diazenyl]benzylidene‐4′‐alkylanilines

A series of N,N‐disubstituted‐4‐[(4‐aminophenyl)diazenyl]benzylidene‐4′‐alkylanilines (azo dyes) were synthesized from the reaction of the corresponding benzaldehyde with alkylanilines. These azo dyes exhibit nematic and SmC phases on heating. Their order parameter, photo‐stability and miscibility were studied by investigation of a representative sample.