Non-uniqueness of the source for singular gauge fields

We show that the singular Wu-Yang solution for SU(2) gauge fields may be interpreted as due to a point source at the origin. However, the electric or magnetic nature of the source depends on whether one approaches the singularity by means of a “smeared” potential or a “smeared” field strength.     

Twisted loop groups and their affine flag varieties

We develop a theory of affine flag varieties and of their Schubert varieties for reductive groups over a Laurent power series local field k((t)) with k a perfect field. This can be viewed as a generalization of the theory of affine flag varieties for loop groups to a “twisted case”; a consequence of our results is that our construction also includes the flag varieties for Kac–Moody Lie algebras of affine type. We also give a coherence conjecture on the dimensions of the spaces of global sections of the natural ample line bundles on the partial flag varieties attached to a fixed group over k((t)) and some applications to local models of Shimura varieties.     

Representations of generalized inverses via full-rank QDR decomposition

Numerical Algorithms - In this paper, novel representations of generalized inverses of rational matrices are developed. Therefore, a unified approach for the computation of {1,2,3} and {1,2,4}...     

Temporal dynamics of receptor-induced apoptosis in an affinity microdevice

The temporal dynamics of Fas-induced apoptosis is elucidated. Jurkat cells are captured on the affinity surface of a microdevice coated with anti-CD95, an antibody known to induce apoptosis in cells via the extrinsic (caspase 8) pathway. The timing of apoptosis induction is controlled by the binding of the cells to the surface. Once bound, the cells are continuously stained with the caspase probe, l-bisaspartic acid rhodamine 110 (D₂R), and the fluorescence of the cells was monitored for 6 h by light microscopy. This approach normalizes the temporal dynamics for each cell, as the binding event is also the start of apoptosis. In addition to providing the number of apoptotic cells over time, the fluorescence of individual cells can be monitored, providing information about the timing of caspase activity in each cell. The rate of caspase cleavage of D₂R in each cell is also measured and shows good agreement between the cells in a given population. The effects of the caspase inhibitor, z-VAD-FMK, on the timing of caspase activity are also investigated and are shown to dramatically slow the apoptotic process. In the future, other caspase probes could be used to provide additional information about the temporal dynamics of caspase activation. Additional techniques, such as fluorescence correlation spectroscopy, can be coupled to these methods to provide faster temporal response and help to elucidate the heterogeneity of the apoptosis process.     

Response Surface Methodology to Optimize the Isolation of Dominant Volatile Compounds from Monofloral Greek Thyme Honey Using SPME-GC-MS

This study aimed at an experimental design of response surface methodology (RSM) in the optimization of the dominant volatile fraction of Greek thyme honey using solid-phase microextraction (SPME) and analyzed by gas chromatography-mass spectrometry (GC-MS). For this purpose, a multiple response optimization was employed using desirability functions, which demand a search for optimal conditions for a set of responses simultaneously. A test set of eighty thyme honey samples were analyzed under the optimum conditions for validation of the proposed model. The optimized combination of isolation conditions was the temperature (60 °C), equilibration time (15 min), extraction time (30 min), magnetic stirrer speed (700 rpm), sample volume (6 mL), water: honey ratio (1:3 v/w) with total desirability over 0.50. It was found that the magnetic stirrer speed, which has not been evaluated before, had a positive effect, especially in combination with other factors. The above-developed methodology proved to be effective in the optimization of isolation of specific volatile compounds from a difficult matrix, like honey. This study could be a good basis for the development of novel RSM for other monofloral honey samples.     

Integral Grothendieck–Riemann–Roch theorem

We show that, in characteristic zero, the obvious integral version of the Grothendieck–Riemann–Roch formula obtained by clearing the denominators of the Todd and Chern characters is true (without having to divide the Chow groups by their torsion subgroups). The proof introduces an alternative to Grothendieck’s strategy: we use resolution of singularities and the weak factorization theorem for birational maps.     

Standardization for oxygen isotope ratio measurement - still an unsolved problem

Numerous organic and inorganic laboratory standards were gathered from nine European and North American laboratories and were analyzed for their delta(18)O values with a new on-line high temperature pyrolysis system that was calibrated using Vienna standard mean ocean water (VSMOW) and standard light Antartic precipitation (SLAP) internationally distributed reference water samples. Especially for organic materials, discrepancies between reported and measured values were high, ranging up to 2 per thousand. The reasons for these discrepancies are discussed and the need for an exact and reliable calibration of existing reference materials, as well as for the establishment of additional organic and inorganic reference materials is stressed. Copyright 1999 John Wiley & Sons, Ltd.