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.     

Circle actions on 4-manifolds I

Using cohomological methods it is proved that the intersection form of a closed (cohomology-) 4-manifoldM withH ₁(M)=0 which admits a non-trivial circle action is the sum of one- and two-dimensional forms provided every fixed point has a neighbourhood containing at most 4 orbit types.     

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     

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.     

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.     

Second Dissociation Constants of 4-[N-morpholino]butanesulfonic Acid and N-[2-hydroxyethyl]piperazine-N′-4-butanesulfonic Acid from 5 to 55°C

The values of the second dissociation constant, pK ₂, for the dissociation of the NH⁺ charge center of the zwitterionic buffer compounds 4-(N-morpholino)butanesulfonic acid (MOBS), and N-(2-hydroxyethyl)piperazine-N-4-butanesulfonic acid (HEPBS) have been determined from 5 to 55°C, including, 37°C at intervals of 5°C. The electromotive-force (emf) measurements have been made utilizing hydrogen electrodes and silver–silver chloride electrodes. The value of pK ₂ for MOBS was found to be 7.702 ± 0.0005, and 8.284 ± 0.0004 for HEPBS, at 25°C, respectively. The related thermodynamic quantities, G ^o, H ^o, S ^o, and C _p ^o for the dissociation processes of MOBS and HEPBS have been derived from the temperature coefficients of pK ₂. Both the MOBS and HEPBS buffer materials are useful as primary pH standards for the control of pH 7.3 to 8.6 in the region close to that of physiological fluids.