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