Positive block matrices and numerical ranges

Any positive matrix M partitioned in four n-by-n blocks satisfies the unitarily invariant norm inequality $6M6\le 6M_{1,1}+M_{2,2}+\omega I6$, where ω is the width of the numerical range of $M_{1,2}$. Some related inequalities and a reverse Lidskii majorization are given.     

Genetics in primary care: a USA faculty development initiative

The Genetics in Primary Care (GPC) project is a USA national faculty development initiative with the goal of enhancing the training of medical students and primary care residents by developing primary care faculty expertise in genetics. Educational strategies were developed for the project by an executive committee with input from an advisory committee, comprising individuals with primary care, medical education and genetics expertise. These committees identified the key issues in genetics education for primary care as (1) considering inherited disease in the differential diagnosis of common disorders; (2) using appropriate counseling strategies for genetic testing and diagnosis, and (3) understanding the implications of a genetic diagnosis for family members. The group emphasized the importance of a primary care perspective, which suggests that the clinical utility of genetic information is greatest when it has the potential to improve health outcomes. The group also noted that clinical practice already incorporates the use of family history information, providing a basis for discussing the application of genetic concepts in primary care. Genetics and primary care experts agreed that educational efforts will be most successful if they are integrated into existing primary care teaching programs, and use a case-based teaching format that incorporates both clinical and social dimensions of genetic disorders. Three core clinical skills were identified: (1) interpreting family history; (2) recognizing the variable clinical utility of genetic information, and (3) acquiring cultural competency. Three areas of potential controversy were identified as well: (1) the role of nondirective counseling versus shared decision-making in discussions of genetic testing; (2) the intrinsic value of genetic information when it does not influence health outcomes, and (3) indications for a genetics referral. The project provides an opportunity for ongoing discussion about these important issues.     

Charging megadalton poly(ethylene oxide)s by electrospray ionization. A charge detection mass spectrometry study

Ions from compounds of megadalton (MDa) molecular weight were produced in an electrospray ionization source from solutions of poly(ethylene oxide) (PEO) samples with average molecular weights ranging from 1,000,000 to 7,000,000 Da. Charge detection mass spectrometry (CDMS) has been used to determine the mass of the MDa PEOs. Simultaneous measurement of the charge and velocity of individual ions allows the mass determination of the ion, after calibration of the instrument with independent samples. In addition to the mass spectra, CDMS generates charge-versus-mass plots, which allow investigation of the charging of electrosprayed ions over a broad range of masses. The experimental charging capacity of MDa PEOs is compared with a simple model based on the affinity of alkali cations for oxygen sites and on the electrostatic potential energy of the charged polymer. The charging capacity of PEOs was also investigated as a function of the concentration of and the type of alkali ions.     

Size dependence of the folding of multiply charged sodium cationized polylactides revealed by ion mobility mass spectrometry and molecular modelling

Ion mobility spectrometry coupled with mass spectrometry was used to experimentally determine the three-dimensional structure of multiply charged sodium cationized polylactides (PLA). In particular, the experiments were conducted to evaluate the influence of the charge state and the size on the gas-phase conformation of cationized PLA. The measured collision cross sections were then compared to calculated values obtained by computational chemistry methods. The most striking feature was the experimental and theoretical observation of a breaking point in the quasilinear relationship between the average collision cross sections and the number of monomer units for the triply charged cations. This breaking point was theoretically demonstrated, for the doubly and triply charged cations, to be associated with a significant folding of the polymer chains around the cationizing agents. The occurrence of such breaking points could be exploited to correlate the charge state of the most intense ion series observed upon electrospray ionization with the number-average molecular mass of a polymer.     

Commutability of homogenization and linearization at identity in finite elasticity and applications

We prove under some general assumptions on elastic energy densities (namely, frame indifference, minimality at identity, non-degeneracy and existence of a quadratic expansion at identity) that homogenization and linearization commute at identity. This generalizes a recent result by S. Müller and the second author by dropping their assumption of periodicity. As a first application, we extend their Γ-convergence commutation diagram for linearization and homogenization to the stochastic setting under standard growth conditions. As a second application, we prove that the Γ-closure is local at identity for this class of energy densities.     

Synthesis and reactivity of a phosphine-stabilized monogermanium analogue of alkynes

The synthesis of the first isolable C-phosphino-Ge-aminogermyne, stabilized by a phosphine ligand, has been achieved. X-ray diffraction analysis indicates a quite long Ge-C bond whose length is between that of a single and a double bond but consistent with the theoretically predicted values for a germyne bearing π-donating substituents. The isomerization of this germyne derivative affords a new stable N-heterocyclic germylene through migration of the original phosphine ligand from germanium to the carbon center.     

Description of the response of a fiber optic velocity sensor applied to capillary gas chromatography

This paper explores the response of a novel fiber optics sensor allowing real-time determination of the migration rate of vapor zones in capillary gas chromatography. The sensitivity is related to the gradient of the vapor zone distribution in the capillary and it is highest when vapor zones show steep variations in concentration. The expected linearity between the height of the velocity peaks and the response of a thermal conductivity detector is demonstrated experimentally. The sensor can be used to infer an approximate value of the analyte diffusion coefficient from the time response. Finally, the time evolution of the envelope of the optical signal is explained with experimental evidences.     

Three-dimensional imaging of sulfides in silicate rocks at submicron resolution with multiphoton microscopy

We report the first application of multiphoton microscopy (MPM) to generate three-dimensional (3D) images of natural minerals (micron-sized sulfides) in thick (～120 μm) rock sections. First, reflection mode (RM) using confocal laser scanning microscopy (CLSM), combined with differential interference contrast (DIC), was tested on polished sections. Second, two-photon fluorescence (TPF) and second harmonic signal (SHG) images were generated using a femtosecond-laser on the same rock section without impregnation by a fluorescent dye. CSLM results show that the silicate matrix is revealed with DIC and RM, while sulfides can be imaged in 3D at low resolution by RM. Sulfides yield strong autofluorescence from 392 to 715 nm with TPF, while SHG is only produced by the embedding medium. Simultaneous recording of TPF and SHG images enables efficient discrimination between different components of silicate rocks. Image stacks obtained with MPM enable complete reconstruction of the 3D structure of a rock slice and of sulfide morphology at submicron resolution, which has not been previously reported for 3D imaging of minerals. Our work suggests that MPM is a highly efficient tool for 3D studies of microstructures and morphologies of minerals in silicate rocks, which may find other applications in geosciences.