Periodicity and convergence for xn+1=|xn−xn−1|

Each solution {x_n} of the equation in the title is either eventually periodic with period 3 or else, it converges to zero—which case occurs depends on whether the ratio of the initial values of {x_n} is rational or irrational. Further, the sequence of ratios {x_n/x_n−1} satisfies a first-order difference equation that has periodic orbits of all integer periods except 3. p-cycles for each p≠3 are explicitly determined in terms of the Fibonacci numbers. In spite of the non-existence of period 3, the unique positive fixed point of the first-order equation is shown to be a snap-back repeller so the irrational ratios behave chaotically.     

Applications of surfactant-modified clays to synthetic organic chemistry

Two triphase catalysts (SLL) have been developed for organic phase-aqueous phase reactions catalyzed by suitable modified clay (solid phase). These triphase catalysts have been applied to nucleophilic displacement on activated (benzylic) as well as unactivated organic halides and provide a convenient and effective method of preparation of the corresponding products. Other useful transformations to, which these triphase catalysts have been successfully applied are the synthesis of 9,9-dichloro bicyclo[6.1.0]nonane, O-alkylation and C-alkylation of β-naphthol.     

Potential Mechanisms of Photodynamic Inactivation of Virus by Methylene BlueI. RNA–Protein Crosslinks and Other Oxidative Lesions in Qβ Bacteriophage

A spectrum of oxidative lesions was observed in a bacteriophage-based model system that is very sensitive to the photodynamic activity of selected dyes. When suspensions of the intact bacteriophage Qβ were exposed to methylene blue plus light (MB+L), inactivating events, or "hits" occurred that were oxygen-dependent and that were associated with the formation of several specific lesions: (1) carbonyl moieties on proteins, (2) 8-oxo-7,8-dihydroguanine (8-oxoGua), and (3) single-strand breaks (ssb) in the RNA genome and (4) RNA-protein crosslinks. Formation of carbonyl groups associated with protein in the Qβ phage preparation correlated positively with photoinactivation of the phage with increasing doses of either of the sensitizers MB or rose bengal. Strand breaks in the Qβ genomic RNA were observable at high MB concentrations but appeared not to be significant at the lower concentrations of MB, as full-length Qβ RNA was observable well beyond the 99% inactivation point in MB dosage. It was shown that the number of 8-oxoGua lesions were unlikely to be sufficient to account for the number of lethal events. Following exposure to MB+L, crosslink formation between Qβ RNA and protein was observed by virtue of the location of RNA at the interface of phenol-aqueous extractions of phage suspensions. A significant increase over background of RNA-protein complexes (including full-length Qβ RNA) was observed at the lowest concentration of MB tested (0.5 μ M ), which corresponded roughly to an average of 2 lethal hits per phage or approximately 13% survival compared to the zero MB control (100% survival). Due to its close correlation with Qβ inactivation and its expected lethality, RNA-protein crosslink formation may be important as an inactivating lesion in bacteriophage Qβ following MB+L exposure.     

1H NMR Metabolomics of Chinese Human Milk at Different Stages of Lactation among Secretors and Non-Secretors

Human milk is an intricate, bioactive food promoting infant health. We studied the composition of human milk samples collected over an 8-month lactation using ¹H NMR metabolomics. A total of 72 human breast milk samples were collected from ten Chinese mothers at eight different time points. The concentrations of ten human milk oligosaccharides (HMOs), fucose and lactose were quantified. Six of the mothers were classified as Lewis-positive secretors (Se⁺Le⁺) and four as Lewis-positive non-secretors (Se⁻Le⁺) based on the levels of 2′-fucosyllactose (2′-FL), lacto-N-fucopentaose (LNFP) II, lactodifucotetraose (LDFT) and lacto-N-neotetraose (LNnT). Acetate, citrate, short/medium-chain fatty acids, glutamine and urea showed a time-dependent trend in relation to the stage of lactation. The concentrations of 2′-FL, 3-FL (3-fucosyllactose), 3′-SL (3′-sialyllactose), LDFT, LNFP I, LNFP II, LNFP III, LNnT, LNT (lacto-N-tetraose), and fucose were statistically different between secretors and non-secretors. A temporal difference of approximately 1–2 months between the development of non-secretor and secretor HMO profiles was shown. The results highlighted the importance of long-term breastfeeding, especially among non-secretors.     

Inhibitory effect of safranal and crocin,two principle compounds of <Emphasis Type="Italic">Crocus sativus</Emphasis>, on fibrillation of lysozyme

A key feature in more than twenty amyloid-related diseases is the aggregation of intra-and/or extracellular misfolded proteins as amyloid fibrils. Therefore, preventing or reversing amyloid aggregation by using of small molecules is considered as useful approaches to the treatment of these diseases. We have evaluated the ability of safranal and crocin, to inhibit amyloid self-assembly of hen egg white lysozyme (HEWL), as an in vitro model system. Structural properties of HEWL in the presence of these compounds were investigated individually using thioflavin T, anilinonaphthalene-8-sulfonic acid fluorescence assays, far-UV circular dichroism and scanning electron microscopy as well as docking method. Our results showed that incubation of HEWL with either crocin or safranal at various concentrations leads a significant inhibition in the rate of amyloid formation. Docking analysis revealed crocin and safranal interact with the central hydrophobic region of lysozyme through van der Waals interaction. Hydroxyl group in crocin through hydrogen bonds connected to the several hydrophilic amino acids of lysozyme, while in safranal there are just one aldehyde group that through hydrogen bonds connected to aspartic acid in lysozyme. It can be concluded that both hydrophobic and hydrophilic groups contribute to lower lysozyme fibril accumulation.     

Copper(II)-selective fluorimetric bulk optode membrane based on a 1-hydroxy-9,10-anthraquinone derivative having two propenyl arms as a neutral fluorogenic ionophore

A new optical chemical sensor has been developed for the selective determination of copper(II) ions in aqueous solutions. The reversible sensing system was prepared by incorporating 1-hydrpxy-2-(prop-2'-enyl)-4-(prop-2'-enyloxy)-9,10-anthraquinone (AQ) as a neutral Cu2+-selective fluoroionophore in the plasticized PVC membrane with potassium tetrakis(p-chlorophenyl borate) as an anionic additive. The response of the sensor is based on the fluorescence quenching of AQ by Cu2+ ions. At a pH 5.5, the proposed sensor displays a calibration response for Cu2+ over a wide concentration rang of 1.0 x 10(-2) to 1.0 x 10(-6) M, with a relatively fast response of less than 40 s. In addition to high stability and reproducibility, the sensor shows a unique selectivity towards Cu2+ ion with respect to common co-existing cations. The proposed fluorescence optode was applied successfully to the determination of copper(II) in black tea samples.     

Synthesis, Characterization, Spectroscopy and Study of Antimicrobial Properties of Two New Substituted Trichloroaluminate（Ⅲ） Complexes [AlCl3X]- （X = SCN-, CN-）

The synthesis and characterization of two new aluminate(Ⅲ) complexes with general formula K[AlCl3X] are reported. These compounds derived from aluminate trichloride and related salts. Potassium trichlorothiocyanoaluminate, PCTA, and potassium trichlorocyanatoalu-minate, PCCA, are two new ionic aluminate complexes. They can be easily synthesized in a nearly quantitative yield by using the direct reaction of AlCl3 and KX. The complexes were characterized by physico-chemical and spectroscopic methods. Theoretical calculations have been used for the extraction of structural and spectroscopic data of these new synthesized complexes. The antibacterial activities of such compounds were studied against the Staphylococcus aureus, Escherichia coli, Staphylococcus Epidermidis, Estreptococo B and Shigella.     

Development of a new fluorimetric bulk optode membrane based on 2,5-thiophenylbis(5-tert-butyl-1,3-benzexazole) for nickel(II) ions

A highly sensitive and selective fluorimetric optode membrane for the determination of ultra trace amounts of Ni²⁺ ions was prepared. The plasticized PVC-membrane incorporating potassium tetrakis(p-chlorophenyl)borate (KTpClPB) and 2,5-thiophenylbis(5-tert-butyl-1,3-benzexazole) (TTBB), as a highly fluorescent chromoionophore, displays a calibration response for Ni²⁺ ions over a wide concentration range of 1.0×10⁻³ to 1.0×10⁻⁸ M. It has a relatively fast response of <40 s. In addition to high stability and reproducibility, and relatively long working lifetime, the sensor possesses good selectivity for nickel ions over several common diverse ions. The fluorescence signal of the optode membrane can be easily recovered by immersion in EDTA solution. The optode was applied successfully to the determination of traces of Ni²⁺ ion in edible oil and a wastewater sample from nickel electroplating industries.     

Macrocyclic host cyclophosphazenes from aminolysis of N3P3CI6 by bis-(2-ortho-aminophenoxyethyl)ether

Aminolysis of N₃P₃CI₆ by an oxodiamine, bis-(2-ortho-aminophenoxyethyl) ether, has been carried out under various experimental conditions and new products with different architectures have been obtained. The reaction in diethyl ether when using a Na₂CO₃-water interface process gives the mono-BINO as major product. Reaction on Al₂O₃/KOH leads to the spirocyclic compound, while, when the reaction is carried out in toluene in the presence of NEt₃, a mixture of mono- and di-BINO products are obtained. These new products have been characterized by IR, ¹H and ³¹P NMR spectroscopy.      

A Facile Room Temperature Synthesis of Zinc Oxide Nanostructure and Its Influence on the Flame Retardancy of Poly Vinyl Alcohol

In this work, poly vinyl alcohol–ZnO nanocomposites were synthesized via two different in situ and ex-situ methods. In ex-situ, at first zinc oxide nanostructures were synthesized by one-step precipitation reaction between zinc acetate and sodium hydroxide. The effect of different surfactants such as poly vinyl pyrrolidone, poly vinyl alcohol and poly ethylene glycol on the morphology of ZnO nanostructures was investigated. Nanostructures were characterized by X-ray diffraction, scanning electron microscopy. The influence of ZnO nanostructures on the flame retardancy of the poly vinyl alcohol matrix was studied using underwriter laboratories UL-94 analysis.