Bounds for the points of spectral concentration of sturm-liouville problems

§1. Introduction. We consider the spectral function ρα(λ) associated with the Sturm–Liouville equation with the boundary conditio

The spectral function for Sturm-Liouville problems where the potential is of Wigner-von Neumann type or slowly decaying

We consider the linear, second-order, differential equation (∗) with the boundary condition (∗∗) We suppose that q(x) is real-valued, continuously differentiable and that q(x)→0 as x→∞ with q∉L1[0,∞). Our main object of study is the spectral function ρα(λ) associated with () and (). We derive a series expansion for this function, valid for λ⩾Λ0 where Λ0 is computable and establish a Λ1, also computable, such that () and () with α=0, have no points of spectral concentration for λ⩾Λ1. We illustrate our results with examples. In particular we consider the case of the Wigner–von Neumann potential

Higher derivatives of spectral functions associated with one-dimensional schrodinger operators

We investigate the existence and asymptotic behaviour of higher derivatives of the spectral function in the context of one-dimensional Schr¨odinger operators on the half-line with integrable potentials. In particular, we identify sufficient conditions on the potential for the existence and continuity of the n-th derivative, and outline a systematic procedure for estimating numerical upper bounds for the turning points of such derivatives. Explicit worked examples illustrate the development and application of the theory

Optical biosensor techniques for monitoring organic pollutants in the aquatic environment

The principal contribution of Southampton University to the BIOPTICAS project is in the realization of planar optical waveguide probes to determine the optical properties of attached sensing films. Three types of device are being investigated: surface plasmon resonance (SPR), directional coupler and chemiluminescence sensors. Techniques have been established for the deposition of compatible electrodes for electrochemical modulation of sensing reactions as an integral part of devices, and equipment has been set up for the fabrication of waveguides in glass substrates by field-assisted ion-exchange. The modelling and design stages for the devices are now close to completion, and we have begun the fabrication and evaluation of preliminary designs and verification of models. Interaction with partners has resulted in the establishment of standardised sensor chip formals and plans for comparative evaluations of the sensors developed in the project, using standardised sensing reactions are well in hand

Waveguide surface plasmon resonance biosensor for the aqueous environment

We report the fabrication and performance of gold coated waveguide surface plasmon resonance biosensors. Biotin-avidin binding reactions at the sensor surface were observed. The output power of the sensor showed a decrease of 32% on binding a dual layer of biotin-avidin

Immune Antibodies and Helminth Products Drive CXCR2-Dependent Macrophage-Myofibroblast Crosstalk to Promote Intestinal Repair.

Helminth parasites can cause considerable damage when migrating through host tissues, thus making rapid tissue repair imperative to prevent bleeding and bacterial dissemination particularly during enteric infection. However, how protective type 2 responses targeted against these tissue-disruptive multicellular parasites might contribute to homeostatic wound healing in the intestine has remained unclear. Here, we observed that mice lacking antibodies (Aid-/-) or activating Fc receptors (Fcrg-/-) displayed impaired intestinal repair following infection with the murine helminth Heligmosomoides polygyrus bakeri (Hpb), whilst transfer of immune serum could partially restore chemokine production and rescue wound healing in Aid-/- mice. Impaired healing was associated with a reduced expression of CXCR2 ligands (CXCL2/3) by macrophages (MΦ) and myofibroblasts (MF) within intestinal lesions. Whilst antibodies and helminths together triggered CXCL2 production by MΦ in vitro via surface FcR engagement, chemokine secretion by intestinal MF was elicited by helminths directly via Fcrg-chain/dectin2 signaling. Blockade of CXCR2 during Hpb challenge infection reproduced the delayed wound repair observed in helminth infected Aid-/- and Fcrg-/- mice. Finally, conditioned media from human MΦ stimulated with infective larvae of the helminth Ascaris suum together with immune serum, promoted CXCR2-dependent scratch wound closure by human MF in vitro. Collectively our findings suggest that helminths and antibodies instruct a chemokine driven MΦ-MF crosstalk to promote intestinal repair, a capacity that may be harnessed in clinical settings of impaired wound healing

An isotope dilution model for partitioning of phenylalanine and tyrosine uptake by the liver of lactating dairy cows

An isotope dilution model to describe the partitioning of phenylalanine (PHE) and tyrosine (TYR) in the bovine liver was developed. The model comprises four intracellular and six extracellular pools and various flows connecting these pools and external blood. Conservation of mass principles were applied to generate the fundamental equations describing the behaviour of the system in the steady state. The model was applied to datasets from multi-catheterised dairy cattle during a constant infusion of [1-13C] phenylalanine and [2,3,5,6-2H] tyrosine tracers. Model solutions described the extraction of PHE and TYR from the liver via the portal vein and hepatic artery. In addition, the exchange of free PHE and TYR between extracellular and intracellular pools was explained and the hydroxylation of PHE to TYR was estimated. The model was effective in providing information about the fates of PHE and TYR in the liver and could be used as part of a more complex system describing amino acid metabolism in the whole animal

Aharonov-Bohm effect in a singly connected point contact

We report the discovery of an oscillation in the low-temperature magnetoresistance of a point contact in the two-dimensional electron gas of a GaAs-AlxGa1–xAs heterostructure. The oscillation is periodic in the magnetic field and is reminiscent of the Aharonov-Bohm effect in rings, although the geometry is singly connected. A possible mechanism for this quantum interference effect is tunneling between edge states across the point contact at the potential step at the entrance and the exit of the constriction