Functional Methods for Arbitrary Densities in Curved Spacetime

This paper gives an introduction to the technique of functional differentiation and integration in curved spacetime, applied to examples from quantum field theory. Special attention is drawn on the choice of functional integral measure. Referring to a suggestion by Toms, fields are choosen as arbitrary scalar, spinorial or vectorial densities. The technique developed by Toms for a pure quadratic Lagrangian are extended to the calculation of the generating functional with external sources. Included are two examples of interacting theories, a self-interacting scalar field and a Yang-Mills theory. For these theories the complete set of Feynman graphs depending on the weight of variables is derived.     

Insights into UV-induced apoptosis: ultrastructure, trichrome stain and spectral imaging

Nuclear substructures associated with apoptosis in HeLa cells have been examined using light-microscopic morphometry, trichrome staining, spectral imaging and transmission electron microscopy. This detailed analysis reveals several sites where alterations in the normal cellular ultrastructure occur during apoptotic progression. To correlate these ultrastructural changes with the underlying molecular processes, we have characterized and quantified apoptotic cell morphology with and without inhibition of two caspases, which are key effectors of the apoptotic program. Using this analysis, early apoptotic events included: (a) the segregation of nucleolar components, a diminished granular component, and a reduction in number but increase in size of fibrillar centers, (b) an increase in the number of cytoplasmic ribosomes and (c) a very minimal increase in the amount of peripherally condensed DNA. Apoptosis progressed with: (a) an increase in the number of perichromatin granules and perichromatin fibrils, (b) a reduction in number of interchromatin granule centers concomitant with an increase in their size, (c) partial digestion and circumferential condensation of the DNA at the nuclear membrane and (d) rounding of the cytoplasm with an increase in organellar density and shrinkage in cell size. Endstage apoptotic cells showed: (a) one (or two) very large pools of incompletely digested DNA, (b) one (or two) very large interchromatin granule centers, (c) an increased number of perichromatin granules which were distanced from DNA and often closely apposed to the nucleolus, (d) formation of unusually condensed, highly coiled perinucleolar bodies and (e) blebbing of highly dense cytoplasm.In HeLa cells treated with UV and inhibitors of caspase 1 and 3, the length of time from early apoptosis to the formation of apoptotic bodies was greatly extended. Inhibiting caspase activity: (a) prevented the pooling of DNA, (b) retarded the formation of large interchromatin granule centers, (c) increased the number of perichromatin granules, (d) produced disassembly of the nucleolus, (e) prevented the formation of highly coiled perinucleolar bodies, and (f) caused vacuolization in the cell center and a unipolar blebbing of the cytoplasm.Spectral imaging in conjunction with serial section electron microscopy confirmed the staining specificities of the condensed DNA, of the large condensed interchromatin granule centers, and of the nucleoli. The results indicate that the interface between the components of the chromatin domain and the interchromatin space is a critical site of caspase activity in apoptosis, and precedes other events such as internucleosomal DNA degradation.     

Blood analysis by Raman spectroscopy

Concentrations of multiple analytes were simultaneously measured in whole blood with clinical accuracy, without sample processing, using near-infrared Raman spectroscopy. Spectra were acquired with an instrument employing nonimaging optics, designed using Monte Carlo simulations of the influence of light-scattering-absorbing blood cells on the excitation and emission of Raman light in turbid medium. Raman spectra were collected from whole blood drawn from 31 individuals. Quantitative predictions of glucose, urea, total protein, albumin, triglycerides, hematocrit, and hemoglobin were made by means of partial least-squares (PLS) analysis with clinically relevant precision (r(2) values >0.93). The similarity of the features of the PLS calibration spectra to those of the respective analyte spectra illustrates that the predictions are based on molecular information carried by the Raman light. This demonstrates the feasibility of using Raman spectroscopy for quantitative measurements of biomolecular contents in highly light-scattering and absorbing media.     

Parallel shear flows of fluids with a temperature dependent viscosity

We investigate whether parallel shear flows of an incompressible Newtonian fluid with a viscosity which depends linearly on temperature is possible in situations where the temperature changes along the flow direction. It is shown that parallel flow is possible only in planar or axisymmetric geometries. These two situations are investigated further. For either a plane channel or a circular pipe, we show that the temperature variation in the flow direction must be exponential.Received: December 16, 2003; revised: October 11, 2004     

An example of a space L on which the Hardy-Littlewood maximal operator is not bounded

We give an example of a function p such that the Hardy-Littlewood maximal operator is not bounded on the generalized Lebesgue space L^p(x).     

Filter products of C0-semigroups and ultraproduct representations for Lie groups

We provide a new approach to filter products of C₀-semigroups and prove a spectral theorem for the generator and its filter product. In a similar fashion, we construct ultraproducts of strongly continuous unitary representations of locally compact groups and study spectral theoretic connections between the representations and their ultraproducts. In the case of Lie groups, our investigations are extended to the infinitesimal representation.     

Perturbative contributions to the electroweak interface tension

The main perturbative contribution to the free energy of an electroweak interface is due to the effective potential and the tree level kinetic term. The derivative corrections are investigated with one-loop perturbation theory. The action is treated in derivative, in heat kernel, and in a multi local expansion. The massive contributions turn out to be well described by the Z-factor. The massless mode, plagued by infrared problems, is numerically less important. Its perturbatively reliable part can by calculated in derivative expansion as well. A self consistent way to include the Z-factor in the formula for the interface tension is presented.     

Positive Definite Toeplitz Completions

The problem of completing a partially prescribed Toeplitz matrixto a positive definite Toeplitz matrix is considered. The mainresult is a characterization of the patterns of specified entriesthat guarantee the existence of a positive definite Toeplitzcompletion of a partial positive definite Toeplitz matrix. Thischaracterization resolves affirmatively a conjecture of C. R.Johnson and L. Rodman.