The Heat Equation with Initial Data Corrupted by Measurement Error and Missing Data

In this work the Cauchy problem for the one-dimensional heat equation is considered. In contrast to existing literature it is assumed that the initial state f is unknown and that information regarding f is obtained by some process of measurement. To enhance realism, both measurement errors and missing data are allowed for. Under assumptions on f in the Fourier-domain first an approximation to f is derived from the data by means of a novel uncertainty principle. Then, it is studied how this perturbation in the initial state propagates with time.      

Ueber die Darstellung von Traubenzucker

Ohne Zusammenfassung     

Controlling the water content of never dried and reswollen bacterial cellulose by the addition of water-soluble polymers to the culture medium

For the modification of medically useful biomaterials from bacterially synthesized cellulose, fleeces of Acetobacter xylinum have been produced in the presence of 0.5, 1.0, and 2.0% (m/v) carboxymethylcellulose (CMC), methylcellulose (MC), and poly(vinyl alcohol) (PVA), respectively, in the Hestrin-Schramm culture medium. The incorporation of the water-soluble polymers into cellulose and their influence on the structure, crystal modifications, and material properties are described. With IR and solid-state ¹³C NMR spectroscopy of the fleeces, the presence of the cellulose ethers and an increase in the amorphous parts of the cellulose modifications (NMR results) have been detected. The incorporation is represented by a higher product yield, too. As demonstrated by scanning electron microscopy, a porelike cellulose network structure forms in the presence of CMC and MC. This modified structure increases the water retention ability (expressed as the water content), the ion absorption capacity, and the remaining nitrogen-containing residues from the culture medium or bacteria cells. The water content of bacterial cellulose (BC) in the never dried state and the freeze-dried, reswollen state can be controlled by the CMC concentration in the culture solution. The freeze-dried, reswollen BC-CMC (2.0%) contains 96% water after centrifugation, whereas standard BC has only 73%. About 98% water is included in a BC-MC composite in the wet state, and about 93% is included in the reswollen state synthesized in the presence of 0.5, 1.0, or 2.0% MC. These biomaterial composites can be stored in the dried state and reswollen before use, reaching a higher water absorption than pure, never dried BC. The copper ion capacity of BC-CMC composites increases proportionally with the added amount of CMC. BC-CMC (0.5%) can absorb 3 times more copper ions than original BC. In the case of 0.5 and 1.0% PVA additions to the culture solution, this polymer cannot be detected in the cellulose fleeces after they are washed. Nevertheless the presence of PVA in the culture medium effects a decreased product yield, a retention of nitrogen-containing residues in the material during purification, a reduced water absorption ability, and a slightly higher copper ion capacity in comparison with original BC. The water content of freeze-dried, reswollen BC-PVA (0.5%) is only 62%. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 463–470, 2004     

The convex hull property and topology of hypersurfaces with nonnegative curvature

We prove that, in Euclidean space, any nonnegatively curved, compact, smoothly immersed hypersurface lies outside the convex hull of its boundary, provided the boundary satisfies certain required conditions. This gives a convex hull property, dual to the classical one for surfaces with nonpositive curvature. A version of this result in the nonsmooth category is obtained as well. We show that our boundary conditions determine the topology of the surface up to at most two choices. The proof is based on uniform estimates for radii of convexity of these surfaces under a clipping procedure, a noncollapsing convergence theorem, and a gluing procedure.     

High-energy gamma-rays accompanying the spontaneous fission of 252Cf

The γ-ray spectrum of ²⁵²Cf(sf) was measured in the Darmstadt-Heidelberg Crystal Ball spectrometer, with a double ionization chamber mounted inside to detect the fission fragments. The measurement was aimed at a better understanding of an unusual component found in the high-energy region between 3 and 8 MeV, with fragment mass splits near symmetry. This component was proved to be predominantly emitted by the heavier fragment, to reach its highest intensity at a fragment mass split of 132:120, and to have an almost isotropic angular distribution. Calculations with the statistical code CASCADE could reproduce the main features.     

The electrical resistivity of the reentrant spin glass alloys (Fe0.65Ni0.35)1−x Mn x in the temperature range 4 to 280 K

The specific electrical resistivityp(T) was measured for the reentrant spin glass system (Fe_0.65Ni_0.35)_1–x Mn _x (0x0.102) in the temperature range 4 KT280 K. We used our own phenomenological ansatz to explain the results obtained in order to provide the fitted parameters with physical meaning. The cause of the observed minimum in the measured curves can be given by a model of local magnetism.     

An Inexpensive Laser Raman Spectrometer Based on CCD Detection

We describe an inexpensive modular Raman spectrometer system that can be assembled from commercial components for under $5000. Three typical applications are presented: a demonstration of a vibrational isotope effect, a Raman polarization experiment, and a resonance Raman experiment. This spectrometer system should make it easier to include the important topic of Raman spectroscopy in the undergraduate physical and analytical chemistry laboratory curricula.     

Diagnostic and therapy-control of inborn metabolic disorders by high-performance liquid chromatography: 2,8-dihydroxyadeninuria,xanthinuria

Summary 2,8-Dihydroxyadeninuria and xanthinuria are inborn enzyme disorders which must be under lifelong therapeutic control. Quantitative determination of 2,8-DHA and xanthine using reversed phase HPLC was performed. A new application for the separation of purines shortens analysis-time. Examples of the determination of 2,8-DHA and xanthine before and under certain therapies are shown. Long term monitoring of the patients offers the possibility of a reliable prophylaxis against stone recurrence.