On the radius continuity of the models of polytropic gas spheres which correspond to the positive solutions of the generalized Emden-Fowler equation

We completely answer the question which positive solutions of the Emden-Fowler equation , n > ½, m > ? 1, m+n > 0 induce models of polytropic gas spheres of finite radius or finite mass. We continue and complete the investigation of the radius continuity of these models initiated by van den Broek and Verhulst⁸ in connection with a numerical analysis by Hénon⁷.     

Polyfunctional pyridines from nitroacetamidine and β-diketones. A useful synthesis of substituted imidazo [4,5-b] pyridines and related compounds

Nitroacetamidine undergoes a useful cyclocondensation with β-diketones to produce substituted 2-amino-3-nitropyridines. Use of an acylpyruvate generates hitherto unreported 2-amino-3-nitropyridine-4-carboxylates. These may be converted easily to functionalized imidazo[4,5-b]pyridines and oxazolo-[5,4-b]pyridines.     

(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.     

Dendrimer-functionalized self-assembled monolayers as a surface plasmon resonance sensor surface

We report here a multistep route for the immobilization of DNA and proteins on chemically modified gold substrates using fourth-generation NH(2)-terminated poly(amidoamine) dendrimers supported by an underlying amino undecanethiol (AUT) self-assembled monolayer (SAM). Bioactive ultrathin organic films were prepared via layer-by-layer self-assembly methods and characterized by fluorescence microscopy, variable angle spectroscopic ellipsometry, atomic force microscopy (AFM), X-ray photoelectron spectroscopy (XPS), and attenuated total internal reflection Fourier transform infrared spectroscopy (ATR-FTIR). The thickness of the AUT SAM base layer on the gold substrates was determined to be 1.3 nm from ellipsometry. Fluorescence microscopy and AFM measurements, in combination with analyses of the XPS/ATR-FTIR spectra, confirmed the presence of the dendrimer/biopolymer molecules on the multilayer sensor surfaces. Model proteins, including streptavidin and rabbit immunoglobulin proteins, were covalently attached to the dendrimer layer using linear cross-linking reagents. Through surface plasmon resonance measurements, we found that sensor surfaces containing a dendrimer layer displayed an increased protein immobilization capacity, compared to AUT SAM sensor surfaces without dendrimer molecules. Other SPR studies also revealed that the dendrimer-based surfaces are useful for the sensitive and specific detection of DNA-DNA interactions. Significantly, the multicomponent films displayed a high level of stability during repeated regeneration and hybridization cycles, and the kinetics of the DNA-DNA hybridization process did not appear to be influenced by surface mass transport limiting effects.     

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.     

Numbers,scale and symbols: the public understanding of nanotechnology

Nanotechnology will be an increasing part of the everyday lives of most people in the world. There is a general recognition that few people understand the implications of the technology, the technology itself or even the definition of the word. This lack of understanding stems from a lack of knowledge about science in general but more specifically difficulty in grasping the size scale and symbolism of nanotechnology. A potential key to informing the general public is establishing the ability to comprehend the scale of nanotechnology. Transitioning from the macro to the nanoscale seems to require an ability to comprehend scales of one-billion. Scaling is a skill not common in most individuals and tests of their ability to extrapolate size based upon scaling a common object demonstrates that most individuals cannot scale to the extent needed to make the transition to nanoscale. Symbolism is another important vehicle to providing the general public with a basis to understand the concepts of nanotechnology. With increasing age, individuals are able to draw representations of atomic scale objects, but these tend to be iconic and the different representations not easily translated. Ball and stick models are most recognized by the public, which provides an opportunity to present not only useful symbolism but also a reference point for the atomic scale.     

Time resolved collapse of a folding protein observed with small angle x-ray scattering

High-intensity, "pink" beam from an undulator was used in conjunction with microfabricated rapid-fluid mixing devices to monitor the early events in protein folding with time resolved small angle x-ray scattering. This Letter describes recent work on the protein bovine beta-lactoglobulin where collapse from an expanded to a compact set of states was directly observed on the millisecond time scale. The role of chain collapse, one of the initial stages of protein folding, is not currently understood. The characterization of transient, compact states is vital in assessing the validity of theories and models of the folding process.     

Scars of the Wigner Function

We propose a picture of Wigner function scars as a sequence of concentric rings along a two-dimensional surface inside a periodic orbit. This is verified for a two-dimensional plane that contains a classical hyperbolic orbit of a Hamiltonian system with 2 degrees of freedom. The stationary wave functions are the familiar mixture of scarred and random waves, but the spectral average of the Wigner functions in part of the plane is nearly that of a harmonic oscillator and individual states are also remarkably regular. These results are interpreted in terms of the semiclassical picture of chords and centers.