The strength of countable saturation

We determine the proof-theoretic strength of the principle of countable saturation in the context of the systems for nonstandard arithmetic introduced in our earlier work.Comment: Corrected typos in Lemma 3.4 and the final paragraph of the conclusio

Isospectrality and heat content

We present examples of isospectral operators that do not have the same heat content. Several of these examples are planar polygons that are isospectral for the Laplace operator with Dirichlet boundary conditions. These include examples with infinitely many components. Other planar examples have mixed Dirichlet and Neumann boundary conditions. We also consider Schr\"{o}dinger operators acting in $L^2[0,1]$ with Dirichlet boundary conditions, and show that an abundance of isospectral deformations do not preserve the heat content.Comment: 18 page

The utility of NBS profiling for plant systematics: a first study in tuber-bearing Solanum species

Systematic relationships are important criteria for researchers and breeders to select materials. We evaluated a novel molecular technique, nucleotide binding site (NBS) profiling, for its potential in phylogeny reconstruction. NBS profiling produces multiple markers in resistance genes and their analogs (RGAs). Potato (Solanum tuberosum L.) is a crop with a large secondary genepool, which contains many important traits that can be exploited in breeding programs. In this study we used a set of over 100 genebank accessions, representing 49 tuber-bearing wild and cultivated Solanum species. NBS profiling was compared to amplified fragment length polymorphism (AFLP). Cladistic and phenetic analyses showed that the two techniques had similar resolving power and delivered trees with a similar topology. However, the different statistical tests used to demonstrate congruency of the trees were inconclusive. Visual inspection of the trees showed that, especially at the lower level, many accessions grouped together in the same way in both trees; at the higher level, when looking at the more basal nodes, only a few groups were well supported. Again this was similar for both techniques. The observation that higher level groups were poorly supported might be due to the nature of the material and the way the species evolved. The similarity of the NBS and AFLP results indicate that the role of disease resistance in speciation is limite

The Approximating Hamiltonian Method for the Imperfect Boson Gas

The pressure for the Imperfect (Mean Field) Boson gas can be derived in several ways. The aim of the present note is to provide a new method based on the Approximating Hamiltonian argument which is extremely simple and very general.Comment: 7 page

The Canonical Perfect Bose Gas in Casimir Boxes

We study the problem of Bose-Einstein condensation in the perfect Bose gas in the canonical ensemble, in anisotropically dilated rectangular parallelpipeds (Casimir boxes). We prove that in the canonical ensemble for these anisotropic boxes there is the same type of generalized Bose-Einstein condensation as in the grand-canonical ensemble for the equivalent geometry. However the amount of condensate in the individual states is different in some cases and so are the fluctuations.Comment: 23 page

Allele mining in solanum: conserved homologues of Rpi-blb 1 are identified in Solanum stoloniferum

Allele mining facilitates the discovery of novel resistance (R) genes that can be used in breeding programs and sheds light on the evolution of R genes. Here we focus on two R genes, Rpi-blb1 and Rpi-blb2, originally derived from Solanum bulbocastanum. The Rpi-blb1 gene is part of a cluster of four paralogues and is flanked by RGA1-blb and RGA3-blb. Highly conserved RGA1-blb homologues were discovered in all the tested tuber-bearing (TB) and non-tuber-bearing (NTB) Solanum species, suggesting RGA1-blb was present before the divergence of TB and NTB Solanum species. The frequency of the RGA3-blb gene was much lower. Interestingly, highly conserved Rpi-blb1 homologues were discovered not only in S. bulbocastanum but also in Solanum stoloniferum that is part of the series Longipedicellata. Resistance assays and genetic analyses in several F1 populations derived from the relevant late blight resistant parental genotypes harbouring the conserved Rpi-blb1 homologues, indicated the presence of four dominant R genes, designated as Rpi-sto1, Rpi-plt1, Rpi-pta1 and Rpi-pta2. Furthermore, Rpi-sto1 and Rpi-plt1 resided at the same position on chromosome VIII as Rpi-blb1 in S. bulbocastanum. Segregation data also indicated that an additional unknown late blight resistance gene was present in three populations. In contrast to Rpi-blb1, no homologues of Rpi-blb2 were detected in any material examined. Hypotheses are proposed to explain the presence of conserved Rpi-blb1 homologues in S. stoloniferum. The discovery of conserved homologues of Rpi-blb1 in EBN 2 tetraploid species offers the possibility to more easily transfer the late blight resistance genes to potato varieties by classical breeding

Gravitational diffraction radiation

We show that if the visible universe is a membrane embedded in a higher-dimensional space, particles in uniform motion radiate gravitational waves because of spacetime lumpiness. This phenomenon is analogous to the electromagnetic diffraction radiation of a charge moving near to a metallic grating. In the gravitational case, the role of the metallic grating is played by the inhomogeneities of the extra-dimensional space, such as a hidden brane. We derive a general formula for gravitational diffraction radiation and apply it to a higher-dimensional scenario with flat compact extra dimensions. Gravitational diffraction radiation may carry away a significant portion of the particle's initial energy. This allows to set stringent limits on the scale of brane perturbations. Physical effects of gravitational diffraction radiation are briefly discussed.Comment: 5 pages, 2 figures, RevTeX4. v2: References added. Version to appear in Phys. Rev.

Spectroscopic Follow-up of X-ray Sources in the ChaMPlane Survey: Identification of a New Cataclysmic Variable

We present a multi-object optical spectroscopy follow-up study of X-ray sources in a field along the Galactic Plane (l=327.42 deg, b=2.26 deg) which is part of the Chandra Multi-wavelength Plane survey (ChaMPlane). We obtained spectra for 46 stars, including 15 likely counterparts to X-ray sources, and sources showing an H-alpha color excess. This has led to the identification of a new cataclysmic variable (CV), CXOPS J154305.5-522709, also named ChaMPlane Bright Source 7 (CBS~7), and we identified 8 X-ray sources in the field as active late-type stars. CBS~7 was previously studied in X-rays and showed a hard spectrum and two periods: 1.22+/-0.08 h and 2.43+/-0.26 h. We present here clear evidence that the source is a CV through the detection of H, HeI and HeII emission lines in its optical spectrum. The hard X-ray spectrum and the presence of the HeII 4686 in emission with a large equivalent width suggest a magnetic CV. The near-infrared counterpart is significantly variable, and we found a period consistent with the longest X-ray period at 2.39+/-0.05 h but not the shortest X-ray period. If this period is the orbital period, this would place the system in the CV period gap. The possible orbital period suggests a dM4+/-1 companion star. The distance is then estimated to be ~1 kpc. The system could be a relatively hard and X-ray luminous polar or an intermediate polar, possibly nearly-synchronous.Comment: accepted for publication in ApJ; 6 figures, 5 tables, 8 pages with emulateapj styl

Allocation of Railway Rolling Stock for Passenger Trains

For a commercially operating railway company, providing a high level of service for the passengers is of utmost importance.The latter requires a high punctuality of the trains and an adequate rolling stock capacity.Unfortunately, the latter is currently (2002) one of the bottlenecks in the service provision by the main Dutch railway operator NS Reizigers.Especially during the morning rush hours, many passengers cannot be transported according to the usual service standards due to a shortage of the rolling stock capacity.On the other hand, a more effective allocation of the available rolling stock capacity seems to be feasible, since there are also a few trains with some slack capacity.The effectiveness of the rolling stock capacity is determined mainly by the allocation of the train types and subtypes to the lines.Therefore, we describe in this paper a model that can be used to find an optimal allocation of train types and subtypes to train series.This optimal allocation is more effective than the manually planned one, which is accomplished by minimizing the shortages of capacity during the rush hours.The model is implemented in the modeling language OPL Studio 3.1, solved by CPLEX 7.0, and tested on several scenarios based on the 2001-2002 timetable of NS Reizigers.The results of the model were received positively, both by the planners and by the management in practice, since these results showed that a significant service improvement over the manually planned allocation can be achieved within a shorter throughput time of the involved part of the planning process