Distributions of Points in <Emphasis Type="Italic">d</Emphasis> Dimensions and Large <Emphasis Type="Italic">k</Emphasis>-Point Simplices

We consider a variant of Heilbronn’s triangle problem by investigating for a fixed dimension d≥2 and for integers k≥2 with k≤d distributions of n points in the d-dimensional unit cube [0,1] ^d , such that the minimum volume of the simplices, which are determined by (k+1) of these n points is as large as possible. Denoting by Δ _k,d (n), the supremum of this minimum volume over all distributions of n points in [0,1] ^d , we show that c _k,d ⋅(log n)^1/(d−k+1)/n ^k/(d−k+1)≤Δ _k,d (n)≤c _k,d ′/n ^k/d for fixed 2≤k≤d, and, moreover, for odd integers k≥1, we show the upper bound Δ _k,d (n)≤c _k,d ″/n ^{k/d+(k−1)/(2d(d−1))}, where c _k,d ,c _k,d ′,c _k,d ″>0 are constants. A preliminary version of this paper appeared in COCOON ’05.     

Linear magnetization dependence of the intrinsic anomalous Hall effect

The anomalous Hall effect is investigated experimentally and theoretically for ferromagnetic thin films of Mn5Ge3. We have separated the intrinsic and extrinsic contributions to the experimental anomalous Hall effect and calculated the intrinsic anomalous Hall conductivity from the Berry curvature of the Bloch states using first-principles methods. The intrinsic anomalous Hall conductivity depends linearly on the magnetization, which can be understood from the long-wavelength fluctuations of the spin orientation at finite temperatures. The quantitative agreement between theory and experiment is remarkably good, not only near 0 K but also at finite temperatures, up to about approximately 240 K (0.8TC).     

Link invariants of electromagnetic fields

The cross-helicity integral is known in fluid dynamics and plasma physics as a topological invariant which measures the mutual linkage of two divergence-free vector fields, e.g., magnetic fields, on a three-dimensional domain. Generalizing this concept, a new topological invariant is found which measures the mutual linkage of three closed two-forms, e.g., electromagnetic fields, on a four-dimensional domain. The integral is shown to detect a separation of the cross helicity between two of the fields with the help of the third field. It can be related to the triple linking number known in knot theory. Furthermore, it is shown that the well-known three-dimensional cross helicity and the new four-dimensional invariant are the first two examples of a series of topological invariants which are defined by n-1 field strengths F=dA on a simply connected n-dimensional manifold M(n).     

Applications of Synthetic Peptides

Peptide chemists are increasingly concerned with the synthesis of polypeptides of biological and medical interest. This article describes several important applications of synthetic peptides in biochemistry, molecular biology, immunology, and medicine. Synthetic peptides may be useful in structure-function studies of polypeptides, as peptide hormones and hormone analogues, in the preparation of cross-reacting antibodies, and in the design of novel enzymes. Peptide chemists can actively contribute to progress in these fields if they are aware of the current problems in the life sciences.     

Monochromatic Vs multicolored paths

Letl andk be positive integers, and letX={0,1,...,l ^k?1}. Is it true that for every coloring δ:X×X→{0,1,...} there either exist elementsx ₀<x ₁<...<x _l ofX with δ(x ₀,x ₁)=δ(x ₁,x ₂)=...=δ(x _l?1,x _l), or else there exist elementsy ₀<y ₁<...<y _k ofX with δ(y _i?1,y _i) ∈ δ(y _j?1,y _j) for all 1<-i<j≤k? We prove here that this is the case if eitherl≤2, ork≤4, orl≥(3k)^2k . The general question remains open.     

Interior Schwarzschild Problem and Its Integration

The interior Schwarzschild metric for a static,spherically symmetric perfect fluid can be parametrizedwith two independent functions of the radial coordinate.These functions are easily expressed in terms of (radial) integrals involving the fluidenergy density and pressure. The pressure is, however,not independent, but is determined in terms of thedensity by one of Einstein's equations, theOppenheimer–Volkov (OV) equation. An approximate integral to theOV equation is presented which is accurate for slowlyvarying, realistic, densities, and exact in theconstant-density limit. It makes it possible to findcompletely integrated accurate solutions to the interiorSchwarzschild metric in terms of the density only. Somepost-Newtonian consequences of the solution are given aswell as the resulting general relativistic pressure for an energy densityr^-1/2.     

Tutorial on estimating the limit of detection using LC-MS analysis,part I: Theoretical review

A large body of literature exists on the limit of detection (LOD), but there is still a lot of confusion about this important validation parameter. This confusion mainly stems from its statistically complex background. The goal of this two-part tutorial is to discuss and clarify the topic of LOD for practitioners. The two main conclusions of this tutorial are: (1) the choice of how to estimate LOD should be based on the purpose of the analytical method that is being validated (e.g. considerable effort should not be made to estimate LOD for a method that is not used for detecting traces in the vicinity of LOD), and (2) LOD estimates are strongly dependent on different assumptions and the approach used, and therefore caution must be exercised when using the estimate or when comparing different estimates.     

Separation of selected metal-binding proteins with capillary zone electrophoresis

Several metal-binding proteins, including albumin, carbonic anhydrase, conalbumin, cytochrome c, ferritin, hemoglobin, myoglobin, plasma amine oxidase, superoxide dismutase and transferrin were separated with capillary zone electrophoresis (CZE) in uncoated and coated capillaries. Phosphate and tetraborate buffers achieved complementary separation selectivities. Optimised pre-wash protocols for uncoated capillaries using 0.1 M HCl as a rinsing solution for the borate buffer and a combination of 0.1 M NaOH and 0.1 M HCl for the phosphate system improved the stability of migration times considerably with coefficients of variation between 0.10 and 0.77% (n=7) instead of up to 2.92% with inappropriate rinsing conditions. Capillaries coated with poly(vinyl alcohol) and equipped with a 150 μm i.d. bubble cell increased the signal-to-noise ratio by a factor three, additionally improving the resolution. For commercial protein standards, which gave several peaks in CZE with UV detection, MS data proved the presence of proteinaceous contaminants. Molecular weights (M_r) of proteins experimentally determined from MS data showed deviations from theoretical M_r as small as 0.002-0.021%. Applicability of the developed separation for clinical samples is shown for human serum.     

On the general transformation from molecular geometric parameters to cartesian coordinates

This article presents a general method and accurate algorithm for calculating the Cartesian coordinates (x_a, y_a, z_a) from an arbitrary triple of distances r(a,i), angles, θ(a,j,k), or dihedral angles ?(a,l,m,n), specifying the position of the nucleus a relative to nuclei i, ?, n with known Cartesian coordinates. There is a brief discussion of the requirements on the 3N-6 geometric parameters in order for them to determine the shape of an N-atomic molecule.     

Capillary zone electrophoretic determination of hydroxymetabolites of atrazine in potable water using solid-phase extraction with Amberchrom resins

A CZE-separation system for hydroxyatrazine, desisopropylhydroxyatrazine, desethylhydroxyatrazine and ammeline is presented that allows their determination in environmental waters in the subgL^–1 domain after solid-phase extraction/enrichment with styrene-divinylbenzene and methacrylate macroporous (Amberchrom) resins. The CZE separation and determination system uses the stacking effect and an increased light path for UV-detection (bubble cell). The etching of the bubble cell was done in our laboratory. A ruggedness check of the CZE-system revealed the resolution of theN-dealkylated metabolites to be sensitive to pH, temperature and current variations as well as to changes of capillary dimensions. Fine-tuning of the separation is performed by variation of the current intensity in the constant-current mode. Recoveries from fortified tap-water samples were 95% for hydroxyatrazine, 70% for desethylhydroxyatrazine and approximately 20% for desisopropylhydroxyatrazine at the 0.2 g L^–1 concentration level. Due to its high polarity, ammeline is only slightly adsorbed on Amberchrom resins and cannot be enriched using these materials.