Non-linear ground state representations and sharp Hardy inequalities

We determine the sharp constant in the Hardy inequality for fractional Sobolev spaces. To do so, we develop a non-linear and non-local version of the ground state representation, which even yields a remainder term. From the sharp Hardy inequality we deduce the sharp constant in a Sobolev embedding which is optimal in the Lorentz scale. In the appendix, we characterize the cases of equality in the rearrangement inequality in fractional Sobolev spaces.     

Quantised phase filters with binary low and high pass amplitude response: the effect of quantisation for scale and rotation input distortions

In the field of optical pattern recognition, there are a large number of filters that possess identification capabilities for certain kinds of input distortions. The resolution of the spectral components plays an important role in the overall processing time of a correlator that may employ such filters. In this paper, two different techniques are discussed: low pass phase filtering and high pass phase filtering. This is achieved by binarizing the amplitude information which then allows certain frequencies to pass and others to be blocked. Their response to different kinds of input distortions is presented and the effect of phase quantisation is considered in detail.     

Simultaneous Quantification of Neomycin and Bacitracin by LC-ELSD

The first simultaneous quantification of neomycin and bacitracin using liquid chromatography evaporative light scattering detection as an alternative to MS detection and pre-/post-column derivatisation, respectively, was the aim of this study. The developed method was validated for two strength of neomycin and one strength of bacitracin in sterile pharmaceutical formulation and is a fast and efficient tool for content uniformity tests in quality control. With this method the separation of neomycin from sulfate and the base line separation of the four major components of bacitracin (bacitracin A, B1, B2 and B3) was achieved. These four components are responsible for 96% of the microbiological activity. A Phenomenex Synergi POLAR analytical column (250 mm × 4.6 mm, 4 μm I.D.) in combination with 0.5% perfluoropropionic acid and acetonitrile in gradient mode, the peaks of interest could be separated with high efficiency within 14 min. The calibration was performed using a second order regression with an R ² = 0.9999 for neomycin (B and C) sulfate and R ² = 0.9996 for bacitracin A, B1, B2 and B3. The results of the accuracy evaluation were 99.2 and 99.7%, respectively, for neomycin and 100.8% for bacitracin. Injection precision results are 0.4–1.5 RSD% recorded for six injections. The established method has a high potential for routine high-throughput analyses in the pharmaceutical industry.     

Energy cost to make a hole in the Fermi sea

The change in energy of an ideal Fermi gas when a local one-body potential is inserted into the system, or when the density is changed locally, are important quantities in condensed matter physics. We show that they can be rigorously bounded from below by a universal constant times the value given by the semiclassical approximation.     

A DNA-based method for detecting homologous blood doping

Homologous (or allogeneic) blood doping, in which blood is transferred from a donor into a recipient athlete, is the easiest, cheapest, and fastest way to increase red cell mass (hematocrit) and therefore the oxygen-carrying capacity of the blood. Although thought to have been rendered obsolete as a doping strategy by the increased use of rhEPO to increased hematocrits, there is evidence that athletes are still using this potentially dangerous method to improve endurance performance. Current testing for homologous blood doping is based on identification of mixed populations of red blood cells by flow cytometry. This paper proposes that homologous blood doping could also be tested for by high-resolution qPCR-based genotyping and demonstrates that assays could be developed that would detect second populations of cells even if the “donor” blood was depleted of 99 % of the DNA-containing leukocytes. Issues of test specificity and sensitivity are discussed as well as some of the ethical considerations that would have to be addressed if athletes’ genotypes were to be used by the anti-doping authorities to prevent, or detect, the use of prohibited ergogenic practices.     

Equidivisible kleene monoids and the Elgot-Mezei theorem

Equidivisible Kleene monoids satisfy the Elgot-Mezei theorem.