Complexity of linear programming

The complexity of linear programming is discussed in the “integer” and “real number” models of computation. Even though the integer model is widely used in theoretical computer science, the real number model is more useful for estimating an algorithm's running time in actual computation.Although the ellipsoid algorithm is a polynomial-time algorithm in the integer model, we prove that it has unbounded complexity in the real number model. We conjecture that there exists no polynomial-time algorithm for the linear inequalities problem in the real number model. We also conjecture that linear inequalities are strictly harder than linear equalities in all “reasonable” models of computation.     

High-resolution X-ray photoelectron spectroscopy of chlorine-terminated GaAs(111)A surfaces

Oxide-terminated and Cl-terminated GaAs(111)A surfaces have been characterized in the As and Ga 3d regions by high-resolution, soft X-ray photoelectron spectroscopy. The Cl-terminated surface, formed by treatment with 6 M HCl(aq), showed no detectable As oxides or As(0) in the As 3d region. The Ga 3d spectrum of the Cl-terminated surface showed a broad, intense signal at 19.4 eV and a smaller signal at 21.7 eV. The Ga 3d peaks were fitted using three species, one representing bulk GaAs and the others representing two chemical species on the surface. The large peak was well-fitted by the bulk GaAs emission and by a second doublet, assigned to surface Ga atoms bonded to Cl, that was shifted by 0.34 eV from the bulk GaAs 3d emission. The smaller peak, shifted by 2.3 eV in binding energy relative to the bulk GaAs Ga 3d signal, is assigned to Ga(OH)3. The data confirm that wet chemical etching allows for the formation of well-defined, Cl-terminated GaAs(111)A surfaces free of detectable elemental As, that can provide a starting point for further functionalization of GaAs.     

NH4NO3 extractable trace element contents of soil samples prepared for proficiency testing – a stability study

In view of its intended use as a sample for proficiency testing or as a reference material the stability of the extractable trace element contents of a soil from an irrigation field was tested using the extraction with 1 mol/L ammonium nitrate solution according to DIN 19730. Therefore, changes of the extractability of sterilized and non sterilized soil samples stored at different temperatures were evaluated over a period of 18 months. Sets of bottles were kept at –20?°C, +4?°C, about +20?°C and +40?°C, respectively. The NH₄NO₃ extractable contents of Cd, Cr, Cu, Ni, Pb and Zn were determined immediately after bottling and then after 3, 6, 12 and 18 months with ICP-AES or ETAAS. Appropriate storage conditions are of utmost importance to prevent deterioration of soil samples prepared for the determination of NH₄NO₃ extractable trace element contents. Temperatures above +20?°C must be avoided. The observed changes in the extractability of the metals (especially for Cr and Cu) most likely could be related to thermal degradation of the organic matter of the soil. There is no need to sterilize dry soil samples, because microbiological activity in soils with a low moisture content appears to be negligible with regard to trace element mobilization.     

High-resolution laser ablation inductively coupled plasma mass spectrometry used to study transport of metallic nanoparticles through collagen-rich microstructures in fibroblast multicellular spheroids

We have efficiently produced collagen-rich microstructures in fibroblast multicellular spheroids (MCSs) as a three-dimensional in vitro tissue analog to investigate silver (Ag) nanoparticle (NP) penetration. The MCS production was examined by changing the seeding cell number (500 to 40,000 cells) and the growth period (1 to 10 days). MCSs were incubated with Ag NP suspensions with a concentration of 5 μg mL⁻¹ for 24 h. For this study, laser ablation inductively coupled plasma mass spectrometry (LA-ICP-MS) was used to visualize Ag NP localization quantitatively. Thin sections of MCSs were analyzed by LA-ICP-MS with a laser spot size of 8 μm to image distributions of ¹⁰⁹Ag, ³¹P, ⁶³Cu, ⁶⁶Zn, and ⁷⁹Br. A calibration using a NP suspension was applied to convert the measured Ag intensity into the number of NPs present. The determined numbers of NPs ranged from 30 to 7200 particles in an outer rim of MCS. The particle distribution was clearly correlated with the presence of ³¹P and ⁶⁶Zn and was localized in the outer rim of proliferating cells with a width that was equal to about twice the diameter of single cells. Moreover, abundant collagens were found in the outer rim of MCSs. For only the highest seeding cell number, NPs were completely captured at the outer rim, in a natural barrier reducing particle transport, whereas Eosin (⁷⁹Br) used as a probe of small molecules penetrated into the core of MCSs already after 1 min of exposure.

Fibroblast MCS could build up the barrier only for nanoparticles

     

On coloring box graphs

We consider the chromatic number of a family of graphs we call box graphs, which arise from a box complex in n$n$-space. It is straightforward to show that any box graph in the plane has an admissible coloring with three colors, and that any box graph in n$n$-space has an admissible coloring with n+1$n+1$ colors. We show that for box graphs in n$n$-space, if the lengths of the boxes in the corresponding box complex take on no more than two values from the set {1,2,3}$\{1,2,3\}$, then the box graph is 3$3$-colorable, and for some graphs three colors are required. We also show that box graphs in 3-space which do not have cycles of length four (which we call “string complexes”) are 3$3$-colorable.     

High-resolution soft X-ray photoelectron spectroscopic studies and scanning auger microscopy studies of the air oxidation of alkylated silicon(111) surfaces

High-resolution soft X-ray photoelectron spectroscopy was used to investigate the oxidation of alkylated silicon(111) surfaces under ambient conditions. Silicon(111) surfaces were functionalized through a two-step route involving radical chlorination of the H-terminated surface followed by alkylation with alkylmagnesium halide reagents. After 24 h in air, surface species representing Si(+), Si(2+), Si(3+), and Si(4+) were detected on the Cl-terminated surface, with the highest oxidation state (Si(4+)) oxide signal appearing at +3.79 eV higher in energy than the bulk Si 2p(3/2) peak. The growth of silicon oxide was accompanied by a reduction in the surface-bound Cl signal. After 48 h of exposure to air, the Cl-terminated Si(111) surface exhibited 3.63 equivalent monoleyers (ML) of silicon oxides. In contrast, after exposure to air for 48 h, CH(3)-, C(2)H(5)-, or C(6)H(5)CH(2)-terminated Si surfaces displayed <0.4 ML of surface oxide, and in most cases only displayed approximately 0.20 ML of oxide. This oxide was principally composed of Si(+) and Si(3+) species with peaks centered at +0.8 and +3.2 eV above the bulk Si 2p(3/2) peak, respectively. The silicon 2p SXPS peaks that have previously been assigned to surface Si-C bonds did not change significantly, either in binding energy or in relative intensity, during such air exposure. Use of a high miscut-angle surface (7 degrees vs < or =0.5 degrees off of the (111) surface orientation) yielded no increase in the rate of oxidation nor change in binding energy of the resultant oxide that formed on the alkylated Si surfaces. Scanning Auger microscopy indicated that the alkylated surfaces formed oxide in isolated, inhomogeneous patches on the surface.