Unilaterally competitive games

The authors acknowledge valuable discussions with Jonathan Hamilton and Mamoru Kaneko as well as very detailed comments of two referees.     

Local solution for the Kadomtsev-Petviashvili equation with periodic conditions

In this article we prove a local existence and uniqueness theorem for the Kadomtsev-Petviashvili Equation (u _t +u _xxx +uu _x ) _x −u _yy =0) in the Sobolev spaces of orders≥3, with initial values in the same spaces, and periodic boundary conditions. This theorem improves previous results based upon the application of singular perturbation techniques.     

Below-bandgap refractive index of AlAs/GaAs multiple quantum wells

Precision reflection measurements were performed on GaAs/AlAs superlattices of the same composition but different layer spacings. Nonlinear-least-squares fits to the data were performed to a single layer. Measurements were extracted for the superlattice thickness, thickness of a disturbed interface layer between the superlattice and substrate, the uniformity in composition and/or spacing and the composition. It was demonstrated that these nondestructive measurements in the infrared region (3000 to 12 000 cm^–1) in conjunction with a simple single layer model are capable of accurately yielding the above quantities with high precision.     

Barrier Discharge The Transferred Charge and Ozone Synthesis

We have undertaken an experimental investigation of the influence of the conditions of barrier discharge implementation such as: the discharge gap value, the type of gas, and the polarity and dielectric permittivity of the dielectric electrode on the value of charge transferred in a micro-discharge. It is shown that the increase in the specific capacitance of the electrodes leads to proportional increase in the transferred charge value, reaching 100–200 nC in a discharge gap 1 mm, in air. In this case the amplitude and duration of a current pulse in the microdischarge reach, respectively, 10 to 15 A and 40 ns. It is also demonstrated that in air with increase in the discharge gap value one can observe a decrease in the efficiency of the ozone synthesis whereas in oxygen there exists a more complicated dependence: the maximum of efficiency is observed at a discharge gap value of 0.7 to 1.0 mm.     

Deposition of amorphous hydrogenated semiconductors by magnetron assisted silane decomposition

Magnetron assisted silane decomposition (MASD) is proposed as a method for deposition of a-Si:H and its alloys. In this method a silane containing gas mixture is passed through the magnetron plasma near a target and decomposed there. The deposition rate in the case of the c-Si target is increased 3 times compared to magnetron sputtering and film properties are changed. a-SiSn:H is obtained with a Sn target.     

Theory of main chain nematic polymers with spacers of varying degree of flexibility

Main chain liquid crystal polymers are modelled as either worms or jointed rods. In reality they are composed of mesogenic units (rods) linked by spacers with varying degrees of flexibility. We present a molecular model to describe non-homogeneous nematic polymers. The model takes account of molecular parameters, such as the lengths of the mesogenic group and the spacer units, and the interactions between them. The spacers are found to have an order differing from the mesogenic units. If the spacer is not very long and thus in effect is inflexible, one end of the spacer can retain to some extent the orientation of the other end, allowing orientational correlation between spacers mediated by the intermediate mesogenic unit. This is important in giving the chain a global rod-like behaviour as the nematic field becomes strong or the temperature low. The nematic order of the two components (mesogens and spacers), the nematic-isotropic transition as well as the latent entropy are examined. Furthermore, the anisotropic conformations of the polymers are investigated, which show either rod-like or random walk behaviour. Comparison of our results with experiment is found to be satisfactory.     

Architectural issues related to the optical implementation of an EGS network based on embedded control

Free-space optical implementations of switching networks have been proposed to circumvent many of the system-level problems that may be encountered in systems that require many high-density, high-bandwidth connections. The details of a new class of switching network (the EGS network), that is well-suited to free-space implementations, is described. The common control injection problem that plagues most free-space photonic networks, i.e. how can control information from an electronic source be injected into the network for applications that require relatively high network reconfiguration rates, is examined. A new technique for control injection, called embedded control, which permits network operation even with relatively high network reconfiguration rates is also proposed.     

Mössbauer spectroscopic study of Prussian Blue from different provenances

Ferric ferrocyanides synthesized from different sources of ferric cations and ferrocyanide anions and those derived from ferrous ferricyanide, ferrous ferrocyanide and ferric ferricyanide have been studied using Mössbauer and XRD techniques. Structural information of the effect of the provenance on the properties of the final compound is obtained. Significant correlations between isomer shift and quadrupole splitting of inner and outer iron cations have been observed.     

Path integrals over the group manifolds

Particle motion in the SU(2) manifold is quantized by path integrals. It is shown that the Poschl-Teller, Wood-Saxon, and Rosen-Morse potentials are solved by relating their propagators to the path integrations over the SU(2) manifold. Examples with some other groups are mentioned.     

Uniformization and the diversity of Whitehead groups

Techniques of uniformization are used to prove that it is not consistent that the Whitehead groups of cardinality ℵ₁ are exactly the strongly ℵ₁-free groups. Some consequences of the assumption that every strongly ℵ₁-free group of cardinality ℵ₁ is Whitehead are derived. Other results about uniformization are also proved. Research partially supported by NSERC grant #9848. Research partially supported by the BSF. The authors thank Rutgers University for its support. Publication #441.