Differential Galois Theory of Linear Difference Equations

We present a Galois theory of difference equations designed to measure the differential dependencies among solutions of linear difference equations. With this we are able to reprove Hoelder's Theorem that the Gamma function satisfies no polynomial differential equation and are able to give general results that imply, for example, that no differential relationship holds among solutions of certain classes of q-hypergeometric functions.Comment: 50 page

A simple theory of molecular organization in fullerene containing liquid crystals

Systematic efforts to synthesise fullerene containing LCs have produced a variety of successful model compounds. We present a simple molecular theory relating the self-organisation observed in these systems to their molecular structure. The interactions are modelled by dividing each molecule into a number of sub-molecular blocks to which specific interactions are assigned. Three types of blocks are introduced, corresponding to fullerene units, mesogenic units, and non-mesogenic linkage units. The blocks are constrained to move on a rectangular 3-dimensional lattice and molecular flexibility is allowed by retaining a number of representative conformations within the block representation of the molecule. Calculations are presented for a variety of molecular architectures including twin mesogenic branch mono-adducts of C60, twin dendro-mesogenic branch mono-adducts and conical (badminton shuttlecock) multi-adducts of C60. In spite of its many simplifications, the theory accounts remarkably well for the phase behaviour of these systems.Comment: 22 pages, 9 figure

Eurasian house mouse (Mus musculus L.) differentiation at microsatellite loci identifies the Iranian plateau as a phylogeographic hotspot

Background: The phylogeography of the house mouse (Mus musculus L.), an emblematic species for genetic and biomedical studies, is only partly understood, essentially because of a sampling bias towards its most peripheral populations in Europe, Asia and the Americas. Moreover, the present-day phylogeographic hypotheses stem mostly from the study of mitochondrial lineages. In this article, we complement the mtDNA studies with a comprehensive survey of nuclear markers (19 microsatellite loci) typed in 963 individuals from 47 population samples, with an emphasis on the putative Middle-Eastern centre of dispersal of the species. Results: Based on correspondence analysis, distance and allele-sharing trees, we find a good coherence between geographical origin and genetic make-up of the populations. We thus confirm the clear distinction of the three best described peripheral subspecies, M. m. musculus, M. m. domesticus and M. m. castaneus. A large diversity was found in the Iranian populations, which have had an unclear taxonomic status to date. In addition to samples with clear affiliation to M. m. musculus and M. m. domesticus, we find two genetic groups in Central and South East Iran, which are as distinct from each other as they are from the south-east Asian M. m. castaneus. These groups were previously also found to harbor distinct mitochondrial haplotypes. Conclusion: We propose that the Iranian plateau is home to two more taxonomic units displaying complex primary and secondary relationships with their long recognized neighbours. This central region emerges as the area with the highest known diversity of mouse lineages within a restricted geographical area, designating it as the focal place to study the mechanisms of speciation and diversification of this species

X-Ray Scattering Study of the Smectic−A1Smectic-A_1 to Smectic−A2Smectic-A_2 Transition

X-ray scattering measurements are reported for critical $smectic-A_2$ fluctuations along a line of second-order transitions between the $smectic-A_1$ and $smectic-A_2$ phases in mixtures of hexylphenyl cyanobenzoyloxy benzoate $(DB_6)$ and terephthal-bis-butylaniline (TBBA). The measured exponents $\gamma = 1.46 \pm 0.05$ and $\nu_{\parallel} = \nu_{\perp}= 0.74 \pm 0.03$ are constant along the second-order line and agree with recent heat-capacity measurements and the scaling law, $3\nu + \alpha =2$. They disagree with current theoretical expectations.Engineering and Applied Science

X-Ray Studies of Transitions between Nematic, Smectic−A1,−A2,and−AdSmectic-A_1, -A_2, and -A_d Phases

We report high-resolution x-ray scattering measurements of the critical fluctuations in mixtures of hexylphenyl cyanobenzoyloxy benzoate $(DB_6)$ and terephtal-bis-butylaniline (TBBA). The phase sequence exhibited on cooling pure $DB_6$ (or mixtures with a low concentration of TBBA), is nematic (N) to $smectic-A_d (A_d)$ to $smectic-A_2 (A_2)$. Mixtures with $\gtrsim 12$ molar percent (mol %) of TBBA have a $smectic-A_1 (A_1)$ phase between the nematic and $smectic-A_2$ phases. For each of the second-order transitions the critical-temperature dependence of the susceptibility and correlation lengths are fit to power laws of the form $t^x$ where $t=(T-T_c)/T_c$. For the $N-A_d$ transition in pure $DB_6$ the susceptibility exponent $\beta=1.29 \pm 0.05$ and the parallel and perpendicular correlation-length exponents are $\nu_{\parallel} 0.67 \pm 0.03$ and $\nu_{\perp} =0.52 \pm 0.03$, respectively. Close to the multicritical point (12 mol% TBBA) where the second-order $N-A_1$ line meets the first-order portion of the $A_1-A_2$ line, the $N-A_1$ exponents are $\beta =1.09 \pm 0.05, \mu_{\parallel} 0.57 \pm 0.03, and \nu_{\perp} =0.43 \pm 0.03$. The correlation length anisotropy $(\nu_{\parallel} \neq \nu_{\perp})$ persists along the entire $N-A_1$ line, with the observed exponents decreasing as the concentration approaches the multicritical point. The $A_1-A_2$ line has both first-order and second-order regions. All the measured exponents $(\beta, \nu_{\parallel}, \nu_{\perp})$ were invariant along the second-order portion of the $A_1-A_2$ line and the correlation-length exponents were isotropic $(\nu_{\parallel} = \nu_{\perp})$. The measured exponents were $\beta = 1.46 \pm 0.05$, and $\nu_{\parallel} = \nu_1 = 0.74 \pm 0.03$. These numbers also held close to the tricritical point where the $A_1-A_2$ transition became first order.Engineering and Applied Science

Vicariance in a generalist fish parasite driven by climate and salinity tolerance of hosts

Acanthocephalans are parasites with complex lifecycles that are important components of aquatic systems and are often model species for parasite-mediated host manipulation. Genetic characterization has recently resurrected Pomphorhynchus tereticollis as a distinct species from Pomphorhynchus laevis, with potential implications for fisheries management and host manipulation research. Morphological and molecular examinations of parasites from 7 English rivers across 9 fish species revealed that P. tereticollis was the only Pomphorhynchus parasite present in Britain, rather than P. laevis as previously recorded. Molecular analyses included two non-overlapping regions of the mitochondrial gene – cytochrome oxidase and generated 62 sequences for the shorter fragment (295 bp) and 74 for the larger fragment (583 bp). These were combined with 61 and 13 sequences respectively, from Genbank. A phylogenetic analysis using the two genetic regions and all the DNA sequences available for P. tereticollis identified two distinct genetic lineages in Britain. One lineage, possibly associated with cold water tolerant fish, potentially spread to the northern parts of Britain from the Baltic region via a northern route across the estuarine area of what is now the North Sea during the last Glaciation. The other lineage, associated with temperate freshwater fish, may have arrived later via the Rhine/Thames fluvial connection during the last glaciation or early Holocene when sea levels were low. These results raise important questions on this generalist parasite and its variously environmentally adapted hosts, and especially in relation to the consequences for parasite vicariance

Effects of habitat and livestock on nest productivity of the Asian houbara Chlamydotis macqueenii in Bukhara Province, Uzbekistan

To inform population support measures for the unsustainably hunted Asian houbara Chlamydotis macqueenii (IUCN Vulnerable) we examined potential habitat and land-use effects on nest productivity in the Kyzylkum Desert, Uzbekistan. We monitored 177 nests across different semi-arid shrub assemblages (clay-sand and salinity gradients) and a range of livestock densities (0–80 km-2). Nest success (mean 51.4%, 95% CI 42.4–60.4%) was similar across four years; predation caused 85% of those failures for which the cause was known, and only three nests were trampled by livestock. Nesting begins within a few weeks of arrival when food appears scarce, but later nests were more likely to fail owing to the emergence of a key predator, suggesting foraging conditions on wintering and passage sites may be important for nest productivity. Nest success was similar across three shrub assemblages and was unrelated to landscape rugosity, shrub frequency or livestock density, but was greater with taller mean shrub height (range 13–67 cm) within 50 m. Clutch size (mean = 3.2 eggs) and per-egg hatchability in successful nests (87.5%) did not differ with laying date, shrub assemblage or livestock density. We therefore found no evidence that livestock density reduced nest productivity across the range examined, while differing shrub assemblages appeared to offer similar habitat quality. Asian houbara appear well-adapted to a range of semi-desert habitats and tolerate moderate disturbance by pastoralism. No obvious in situ mitigation measures arise from these findings, leaving regulation and control as the key requirement to render hunting sustainable

Jean-Baptiste Bélanger, hydraulic engineer, researcher and academic

Jean-Baptiste BÉLANGER (1790-1874) worked as a hydraulic engineer at the beginning of his career. He developed the backwater equation to calculate gradually-varied open channel flow properties for steady flow conditions. Later, as an academic at the leading French engineering schools (Ecole Centrale des Arts et Manufactures, Ecole des Ponts et Chaussées, and Ecole Polytechnique), he developed a new university curriculum in mechanics and several textbooks including a seminal text in hydraulic engineering. His influence on his contemporaries was considerable, and his name is written on the border of one of the four facades of the Eiffel Tower. BÉLANGER's leading role demonstrated the dynamism of practicing engineers at the time, and his contributions paved the way to many significant works in hydraulics