PT-Symmetry, Canonical Decomposition, Perturbation Theory

Let H be any PT-symmetric Schrödinger operator of the type H=- ² +x ² +igW(x), where W is a real polynomial, odd under reflection of all coordinates, gR, acting on L ² ( R ^d ). The proof is outlined of the following statements: PH is self-adjoint and its eigenvalues coincide with the eigenvalues of (H*H). Moreover the eigenvalues of (H*H), known as the singular values of H, can be computed via perturbation theory by Borel summability.     

Rare fluctuations of native proteins sampled by equilibrium hydrogen exchange

We present a method for determining the ensembles of native protein structures that result from the large fluctuations of low probability revealed by hydrogen-exchange experiments. The measured protection factors are used to bias Monte Carlo simulations to sample the structures of the exchange competent species. The approach is illustrated by its application to the case of alpha-lactalbumin.     

Questioni di realità sulle curve trigonali reali

Sunto. In relazione a curve trigonali reali (di genere e specie assegnati) vengono svolte alcune questioni di realità, ed in particolare quella concernente il numero dei circuiti della parte reale ed il loro comportamento rispetto alla g ₃ ⁴ il che dà luogo ad una classificazione di tali curve. Sono perciò riprese od introdotte svariate considerazioni che potrebbero anche venire più largamente utilizzate.     

Metal complexes of C2-symmetric chiral bipyridine ligands. X-ray structure of [bis(nitrato)(4S,5S)-2,2-dimethyl-4,5-bis(2-pyridyl)-1,3-dioxolane cobalt(II)]

Chelating properties of C₂-symmetric chiral bipyridine ligands are discussed. In particular we report the syntheses of the cobalt(II), nickel(II), zinc(II) and copper(II) complexes of (4S,5S)-2,2-dimethyl-4,5-bis(2-pyridyl)-1,3-dioxolane. All compounds have been characterized by IR spectroscopy, and an X-ray diffraction analysis has been carried out on one of them: Co(L)(NO₃)₂. The ligand coordinates the cobalt atom by the two nitrogen donors N(1) and N(2). A seven-membered chelation ring is formed, presenting a remarkable non-crystallographic twofold pseudosymmetry around the axis connecting Co and the midpoint of the C(6)–C(7) bond. The metal also binds two monodentate nitrates, thus completing a distorted coordination tetrahedron.     

Effects of nonionic,cationic, and anionic micelles on the kinetics of the complexation reaction of nickel (II) with pyridine-2-azo-p-dimethylaniline

The stopped-flow technique has been used to study the effect of cationic (CTAN), nonionic (Triton X-100), andanionic (SDS) micelles on the rate of the reaction between nickel(II) ion and the ligand pyridine-2-azo-p-dimethylaniline (PADA) at 20.0°C and ionic strength 0.03 mol dm^?3. The complex formation reaction is markedly inhibited by both CTAN and Triton X-100 micelles. The kinetic dataare found to conform to a reaction mechanism which implies only partitioning of the ligand between water and the micellar phase, the estimated bindingconstant of PADA being significantly larger in the presence of CTAN aggregates. Anionic micelles strongly speed the complexation reaction, Which occurs in the micellar phase with the same rate and the same mechanism as in water. The extent of binding of PADA to anionic micelles is similar to that found for the cationic micellar aggregates.     

A scattering polarimeter for X-ray astronomy

Summary We describe a high sensitivity X-ray Thomson polarimeter for astrophysical research, particularly designed for the XMM mission. The efficiency, the modulation factor and the performances of this instrument have been estimated by means of a Monte Carlo simulation. The predicted sensitivity for the high eccentricity Orbit of XMM should allow the detection of the Crab Nebula polarization (3σ, (5÷11)keV) in 15 seconds only. To speed up publication, the proofs were not sent to the authors and were supervised by the Scientific Committee.     

On the rate of points in projective spaces

The rate of a standard gradedK-algebraR is a measure of the growth of the shifts in a minimal free resolution ofK as anR-module. It is known that rate(R)=1 if and only ifR is Koszul and that rate(R) ≥m(I)−1 wherem(I) denotes the highest degree of a generator of the defining idealI ofR. We show that the rate of the coordinate ring of certain sets of pointsX of the projective space P ⁿ is equal tom(I)−1. This extends a theorem of Kempf. We study also the rate of algebras defined by a space of forms of some fixed degreed and of small codimension.     

EEG Fractal Analysis Reflects Brain Impairment after Stroke

Stroke is the commonest cause of disability. Novel treatments require an improved understanding of the underlying mechanisms of recovery. Fractal approaches have demonstrated that a single metric can describe the complexity of seemingly random fluctuations of physiological signals. We hypothesize that fractal algorithms applied to electroencephalographic (EEG) signals may track brain impairment after stroke. Sixteen stroke survivors were studied in the hyperacute (<48 h) and in the acute phase (∼1 week after stroke), and 35 stroke survivors during the early subacute phase (from 8 days to 32 days and after ∼2 months after stroke): We compared resting-state EEG fractal changes using fractal measures (i.e., Higuchi Index, Tortuosity) with 11 healthy controls. Both Higuchi index and Tortuosity values were significantly lower after a stroke throughout the acute and early subacute stage compared to healthy subjects, reflecting a brain activity which is significantly less complex. These indices may be promising metrics to track behavioral changes in the very early stage after stroke. Our findings might contribute to the neurorehabilitation quest in identifying reliable biomarkers for a better tailoring of rehabilitation pathways.