Extended iterative methods for the solution of operator equations

Summary Given an iterative methodM ₀, characterized byx ^(k+1=G ₀(x( ^k )) (k0) (x(⁰) prescribed) for the solution of the operator equationF(x)=0, whereF:XX is a given operator andX is a Banach space, it is shown how to obtain a family of methodsM _p characterized byx ^(k+1=G _p (x( ^k )) (k0) (x(⁰) prescribed) with order of convergence higher than that ofM _o. The infinite dimensional multipoint methods of Bosarge and Falb [2] are a special case, in whichM ₀ is Newton's method.Analogues of Theorems 2.3 and 2.36 of [2] are proved for the methodsM _p, which are referred to as extensions ofM ₀. A number of methods with order of convergence greater than two are discussed and existence-convergence theorems for some of them are proved.Finally some computational results are presented which illustrate the behaviour of the methods and their extensions when used to solve systems of nonlinear algebraic equations, and some applications currently being investigated are mentioned.     

Regioselective syntheses of 7-nitro-7-deazapurine nucleosides and nucleotides for efficient PCR incorporation

Substitution at the C(7) position of purine nucleotides by a potent electron-withdrawing nitro group facilitates the cleavage of glycosidic bonds under alkaline conditions. This property is useful for sequence-specific cleavage of DNA containing these analogues. Here we describe the preparation of 7-deaza-7-NO(2)-dA and 7-deaza-7-NO(2)-dG using two different approaches, starting from 2'-deoxy-adenosine and 6-chloro-7-deaza-guanine, respectively. These modified nucleosides were converted to nucleotide triphosphates, each of which can replace the corresponding, naturally occurring triphosphate to support PCR amplification. [structure: see text]     

Designed helical peptides inhibit an intramembrane protease

gamma-Secretase cleaves the transmembrane domain of the amyloid precursor protein, a process implicated in the pathogenesis of Alzheimer's disease, and this enzyme is a founding member of an emerging class of intramembrane proteases. Modeling and mutagenesis suggest a helical conformation for the substrate transmembrane domain upon initial interaction with the protease. Moreover, biochemical evidence supports the presence of an initial docking site for substrate on gamma-secretase that is distinct from the active site, a property predicted to be generally true of intramembrane proteases. Here we show that short peptides designed to adopt a helical conformation in solution are inhibitors of gamma-secretase in both cells and enzyme preparations. Helical peptides with all d-amino acids are the most potent inhibitors and represent potential therapeutic leads. Subtle modifications that disrupt helicity also substantially reduce potency, suggesting that this conformation is critical for effective inhibition. Fluorescence lifetime imaging in intact cells demonstrates that helical peptides disrupt binding between substrate and protease, whereas an active site-directed inhibitor does not. These findings are consistent with helical peptides interacting with the initial substrate docking site of gamma-secretase, suggesting a general strategy for the development of potent and specific inhibitors of intramembrane proteases.     

(Z)-3-p-tolylsulfinylacrylonitrile as a chiral dienophile: diels-alder reactions with furan and acyclic dienes

The behavior of (Z)-3-p-tolylsulfinylacrylonitrile (1) as a chiral dienophile has been evaluated from its reactions with furan and acyclic dienes. Electrostatic interactions of the cyano group with the sulfinyl one restrict the conformational mobility around the C-S bond, thus controlling the pi-facial selectivity, which is almost complete in all cases, the approach of the diene from the less-hindered face of the dienophile (that bearing the lone electron pair) in the predominant rotamer being the favored one. The regioselectivity is also completely controlled by the cyano group. Additionally, the reactivity of compound 1 as well as its endo-selectivity are both higher than those observed for the corresponding (Z)-3-sulfinylacrylates, thus proving the potential of sulfinylnitriles as chiral dienophiles.     

Syntheses of 3-Chloro-7-[(Chlorocarbonyl)Methoxy]-4-Methylcoumarin

Two efficient syntheses of 3-chloro-7-[(chlorocarbonyl)methoxy]-4-methylcoumarin are described, one utilizing traditional chemistry starting from 3-chloro-7-hydroxy-4-methylcoumarin, while the other uses a novel reagent, sulfuryl chloride/thionyl chloride, in a one-pot reaction starting from 7-(carboxymethoxy)-4-methylcoumarin.     

Narrow band quantitative and multivariate electroencephalogram analysis of peri-adolescent period

ABSTRACT: BACKGROUND: The peri-adolescent period is a crucial developmental moment of transition from childhood to emergent adulthood. The present report analyses the differences in Power Spectrum (PS) of the Electroencephalogram (EEG) between late childhood (24 children between 8 and 13 years old) and young adulthood (24 young adults between 18 and 23 years old). RESULTS: The narrow band analysis of the Electroencephalogram was computed in the frequency range of 0--20 Hz. The analysis of mean and variance suggested that six frequency ranges presented a different rate of maturation at these ages, namely: low delta, delta-theta, low alpha, high alpha, low beta and high beta. For most of these bands the maturation seems to occur later in anterior sites than posterior sites. Correlational analysis showed a lower pattern of correlation between different frequencies in children than in young adults, suggesting a certain asynchrony in the maturation of different rhythms. The topographical analysis revealed similar topographies of the different rhythms in children and young adults. Principal Component Analysis (PCA) demonstrated the same internal structure for the Electroencephalogram of both age groups. Principal Component Analysis allowed to separate four subcomponents in the alpha range. All these subcomponents peaked at a lower frequency in children than in young adults. CONCLUSIONS: The present approaches complement and solve some of the incertitudes when the classical brain broad rhythm analysis is applied. Children have a higher absolute power than young adults for frequency ranges between 0-20 Hz, the correlation of Power Spectrum (PS) with age and the variance age comparison showed that there are six ranges of frequencies that can distinguish the level of EEG maturation in children and adults. The establishment of maturational order of different frequencies and its possible maturational interdependence would require a complete series including all the different ages.