The convenient route to cd fragment for the synthesis of vitamin D3 relatives

The efficient degradation of $\text{1}$ to the α-methylene ketone $\text{4}$ is described. Compound $\text{4}$ was then converted to the allylic alcohol $\text{8a}$ - the precursor of vitamin D³ relatives.     

Some analytical semigroups occurring in probability theory

One-parameter semigroups occurring in operator-limit distributions are investigated. The topological-algebraic background of the relevant monoids is discussed and Lie semigroup theory is applied to the Urbanik Decomposability Semigroup.     

Correction procedure for the electron microprobe analysis of porous materials

A correction method is proposed for the quantitative determination of stoichiometric ratios in porous materials by electron microprobe analysis. Analysis of this kind of material is complicated by an imperfect surface that can only be improved to some extent. The correction is based on a linear dependence (different for each element) of the analyses on a sum of weight concentrations of oxides. With this correction it is possible to use analyses affected by the imperfection of the surface with much better confidence compared to common normalisation. An example is presented for a series of ceramic superconductors Bi_2.1(SrCa)_2.9Cu₂O₈₊.     

(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.     

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.     

Strong Mixing and Operator-Selfdecomposability

For nonstationary, strongly mixing sequences of random variables taking their values in a finite-dimensional Euclidean space, with the partial sums being normalized via matrix multiplication, with certain standard conditions being met (an “infinitesimality” assumption, and a restriction to “full” distributions), the possible limit distributions are precisely the operator-self-decomposable laws.