Mayberry-Murasugi's formula for links in homology 3-spheres

We prove the Mayberry-Murasugi formula for links in homology 3-spheres, which was proved before only for links in the 3-sphere. Our proof uses Franz-Reidemeister torsions.

     

Mapping Properties of a Projection Related to the Helmholtz Equation

We study the continuity properties of a projection derived from a recent characterization of Herglotz Wave Functions in the plane. Herglotz Wave Functions are the entire solutions of the Helmholtz equation which have L²-Far-Field-Pattern. The behavior of this projection is reminiscent of the Disc Multiplier Operator on both L^p and mixed L^p-normed spaces. In particular a Kakeya type set plays a central role in our analysis. As a consequence we answer a question posed by Alvarez, Folch-Gabayet and Pérez-Esteva.     

Laser stabilitron

We consider a new method for producing intensity stabilization of cw lasers. This method incorporates negative feedback from a nonlinear saturable absorber to provide wideband noise-reduction and may produce an output beam for which shot noise is below the quantum limit. This new method can be used with a large variety of cw lasers and is particularly applicable to frequency-stabilized lasers which are locked to absorption lines.Permanent address: Institute of Laser Physics, Novosibirsk 630090, Russia     

Synthesis and thermal crosslinking of oxazolidine‐functionalized polyurethanes

A new oxazolidine derivative was obtained from phenol, 2‐amino‐2‐methylpropane‐1,3‐diol and paraformaldehyde. The reaction of this novel oxazolidine diol with phenylisocyanate lead to a urethane model compound which can be polymerized thermally by oxazolidine ring opening to give a Mannich bridge structure. Linear segmented polyurethanes were prepared by reaction of different ratios of oxazolidine diol and commercial polyethylenglycol (M_w ～ 400) with 4,4′‐methylenbis (cyclohexylisocyanate) (HMDI, 90% isomers mixture). The polyurethanes were thermally characterized and crosslinked by oxazolidine ring opening to obtain materials which showed improved thermal stability. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 4965–4973, 2007     

A transportable gamma spectroscopy system applied to the measurement of fission products

Normally, gamma-ray spectroscopy is performed by equipment positioned in the SLOWPOKE-2 Facility at the Royal Military College; however, there have occasionally been requirements for analyses externally. A transportable gamma spectroscopy system was thus assembled by acquiring a commercially available multichannel analyzer, analysis program and detector, and by designing and constructing a transportable shielding castle. It was then used to take measurements of fission product concentrations at several research reactors.     

Rheological and diffusion properties of a dextran-con A polymer in the presence of Insulin and Magnesium

Previous work carried out in our laboratories has focused on the formation and investigation of a dextran and concanavalin A (con A) based gel, which has the ability to alter its conformational structure in the presence and absence of free and terminal glucoses such that a gel–sol phase transition occurs. Here we report the diffusion and rheological investigations in to the effects of the addition of insulin and varyingconcentrations of magnesium chloride hexahydrate (Mg₂Cl₂6H₂O) at 20 and 37 °C. Rheological examination of glucose-sensitive (dextran-con A) gels were conducted using a cone and plate viscometer used in continual rotation and oscillatory modes. The results are interpreted in terms of the structure of the gel network and suggest rheological assessment provides an effective method of assessing the properties of gel systems. The subsequent testing of such formulations in in-vitro diffusion experiments revealed a reduction in the rate of diffusivity in the insulin marker, poly R-478 dye. The performance of this self-regulating drug delivery system has been examined and the addition of insulin and magnesium chloride may alter the way in which the gel operates as a drug delivery device and in the delivery of insulin. This may have implications for other ligands.     

Partition Lattice q-Analogs Related to q-Stirling Numbers

We construct a family of partially ordered sets (posets) that are q-analogs of the set partition lattice. They are different from the q-analogs proposed by Dowling [5]. One of the important features of these posets is that their Whitney numbers of the first and second kind are just the q-Stirling numbers of the first and second kind, respectively. One member of this family [4] can be constructed using an interpretation of Milne [9] for S[n, k] as sequences of lines in a vector space over the Galois field F _q. Another member is constructed so as to mirror the partial order in the subspace lattice.