Ince's limits for confluent and double-confluent Heun equations

We find pairs of solutions to a differential equation which is obtained as a special limit of a generalized spheroidal wave equation (this is also known as confluent Heun equation). One solution in each pair is given by a series of hypergeometric functions and converges for any finite value of the independent variable $z$, while the other is given by a series of modified Bessel functions and converges for $|z|>|z_{0}|$, where $z_{0}$ denotes a regular singularity. For short, the preceding limit is called Ince's limit after Ince who have used the same procedure to get the Mathieu equations from the Whittaker-Hill ones. We find as well that, when $z_{0}$ tends to zero, the Ince limit of the generalized spheroidal wave equation turns out to be the Ince limit of a double-confluent Heun equation, for which solutions are provided. Finally, we show that the Schr\"odinger equation for inverse fourth and sixth-power potentials reduces to peculiar cases of the double-confluent Heun equation and its Ince's limit, respectively.Comment: Submitted to Journal of Mathmatical Physic

Electron transport in gated InGaAs and InAsP quantum well wires in selectively-grown InP ridge structures

The purpose of this work is to fabricate ribbon-like InGaAs and InAsP wires embedded in InP ridge structures and investigate their transport properties. The InP ridge structures that contain the wires are selectively grown by chemical beam epitaxy (CBE) on pre-patterned InP substrates. To optimize the growth and micro-fabrication processes for electronic transport, we explore the Ohmic contact resistance, the electron density, and the mobility as a function of the wire width using standard transport and Shubnikov-de Haas measurements. At low temperatures the ridge structures reveal reproducible mesoscopic conductance fluctuations. We also fabricate ridge structures with submicron gate electrodes that exhibit non-leaky gating and good pinch-off characteristics acceptable for device operation. Using such wrap gate electrodes, we demonstrate that the wires can be split to form quantum dots evidenced by Coulomb blockade oscillations in transport measurements.Comment: 5 pages, 4 figures, additional references and improved Fig. 4c, MSS-14 conference, submitted to Physica

PREDICTING THE SUMMER TEMPERATURE OF SMALL STREAMS IN SOUTHWESTERN WISCONSIN 1

One of the biggest challenges in managing cold water streams in the Midwest is understanding how stream temperature is controlled by the complex interactions among meteorologic processes, channel geometry, and ground water inflow. Inflow of cold ground water, shade provided by riparian vegetation, and channel width are the most important factors controlling summer stream temperatures. A simple screening model was used to quantitatively evaluate the importance of these factors and guide management decisions. The model uses an analytical solution to the heat transport equation to predict steady-state temperature throughout a stream reach. The model matches field data from four streams in southwestern Wisconsin quite well (typically within 1°C) and helps explain the observed warming and cooling trends along each stream reach. The distribution of ground water inflow throughout a stream reach has an important influence on stream temperature, and springs are especially effective at providing thermal refuge for fish. Although simple, this model provides insight into the importance of ground water and the impact different management strategies, such as planting trees to increase shade, may have on summer stream temperature.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/74032/1/j.1752-1688.2005.tb03714.x.pd

Functional mechanisms underlying pleiotropic risk alleles at the 19p13.1 breast-ovarian cancer susceptibility locus

A locus at 19p13 is associated with breast cancer (BC) and ovarian cancer (OC) risk. Here we analyse 438 SNPs in this region in 46,451 BC and 15,438 OC cases, 15,252 BRCA1 mutation carriers and 73,444 controls and identify 13 candidate causal SNPs associated with serous OC (P=9.2 × 10-20), ER-negative BC (P=1.1 × 10-13), BRCA1-associated BC (P=7.7 × 10-16) and triple negative BC (P-diff=2 × 10-5). Genotype-gene expression associations are identified for candidate target genes ANKLE1 (P=2 × 10-3) and ABHD8 (P<2 × 10-3). Chromosome conformation capture identifies interactions between four candidate SNPs and ABHD8, and luciferase assays indicate six risk alleles increased transactivation of the ADHD8 promoter. Targeted deletion of a region containing risk SNP rs56069439 in a putative enhancer induces ANKLE1 downregulation; and mRNA stability assays indicate functional effects for an ANKLE1 3′-UTR SNP. Altogether, these data suggest that multiple SNPs at 19p13 regulate ABHD8 and perhaps ANKLE1 expression, and indicate common mechanisms underlying breast and ovarian cancer risk

3-M syndrome: a growth disorder associated with IGF2 silencing

3-M syndrome is an autosomal recessive disorder characterised by pre- and postnatal growth restriction, facial dysmorphism, normal intelligence and radiological features (slender long bones and tall vertebral bodies). It is known to be caused by mutations in the genes encoding Cullin 7, Obscurin like-1 and Coiled-Coil Domain Containing 8. The mechanisms through which mutations in these genes impair growth are unclear. The aim of this study was to identify novel pathways involved in the growth impairment in 3-M syndrome. RNA was extracted from fibroblast cell lines derived from four 3-M syndrome patients and 3 control subjects, hybridised to Affymetrix HU 133 plus 2.0 arrays with quantitative real time PCR used to confirm changes found on microarray. IGF-II protein levels in serum and conditioned cell culture medium were measured by ELISA. Of the top 10 downregulated probesets 3 represented IGF2 while H19 was identified as the 23rd most upregulated probeset. QRT-PCR confirmed upregulation of H19(p&lt;0.001) and downregulation of IGF2 (p&lt;0.001). Levels of IGF-II secreted into conditioned cell culture medium were higher for control fibroblasts than for 3-M fibroblasts (10.2 ± 2.9ng/ml v 0.6 ± 0.9ng/ml, p&lt;0.01). 3-M syndrome is associated with a gene expression profile of reduced IGF2 expression and increased H19 expression similar to that found in Silver Russell syndrome. Loss of autocrine IGF-II in the growth plate may be associated with the short stature seen in children with 3-M syndrome

A generalized optimization model of microbially driven aquatic biogeochemistry based on thermodynamic, kinetic, and stoichiometric ecological theory

AbstractWe have developed a mechanistic model of aquatic microbial metabolism and growth, where we apply fundamental ecological theory to simulate the simultaneous influence of multiple potential metabolic reactions on system biogeochemistry. Software design was based on an anticipated cycle of adaptive hypothesis testing, requiring that the model implementation be highly modular, quickly extensible, and easily coupled with hydrologic models in a shared state space. Model testing scenarios were designed to assess the potential for competition over dissolved organic carbon, oxygen, and inorganic nitrogen in simulated batch reactors. Test results demonstrated that the model appropriately weights metabolic processes according to the amount of chemical energy available in the associated biochemical reactions, and results also demonstrated how simulated carbon, nitrogen, and sulfur dynamics were influenced by simultaneous microbial competition for multiple resources. This effort contributes an approach to generalized modeling of microbial metabolism that will be useful for a theoretically and mechanistically principled approach to biogeochemical analysis