Some topological properties of support points of convex sets

It is shown, as a corollary to Trojanski’s renorming theorem, that the set of support points (of certain closed convex sets) is connected. Some connectedness properties are established for support functionals, and it is also shown that the support points form an F_σ.     

Weak* support points of convex sets inE*

Density theorems are obtained for weak* support points and support functionals of certain convex subsets of the dual of a Banach space. Supported by National Science Foundation Grant GP 378.     

Artificial Intelligence—An Overview of Similarities with O.R.

A brief outline of A.I. is provided, noting problems, techniques and objectives which are similar to those found in O.R. It is intended that this will indicate to O.R. workers which A.I. areas might be worth following up as relevant to their own work and which problems in A.I. might be attacked by the O.R. community as part of the development of intelligent support systems.     

Dentability and extreme points in Banach spaces

It is shown that a Banach space E has the Radon-Nikodym property (equivalently, every bounded subset of E is dentable) if and only if every bounded closed convex subset of E is the closed convex hull of its strongly exposed points. Using recent work of Namioka, some analogous results are obtained concerning weak¹ strongly exposed points of weak¹ compact convex subsets of certain dual Banach spaces.     

Diode Feedback Effects in Intense Relativistic Electron Beam Oscillators

The general operation of intense relativistic electron beam oscillators is described. These oscillators employ the well-known reflex triode phenomenon to plug the ends of a magnetically confined beam drift region by setting up efficient electron reflexing between the real cathode of an accelerator and a downstream virtual cathode. For a variety of magnetic traps and experimental conditions, it is shown that the inherent electron beam feedback from the drift region can be effectively utilized to reduce the electronion diode impedance and thereby permit good matching and energy transfer between the diode and a sub-ohm particle accelerator. A theoretical model is presented to interpret the observed phenomena.     

Ionic atmosphere effects on the energetics of thermal and optical electron-exchange reactions: Application to ferrocenium-ferrocene self exchange

A treatment of ionic-atmosphere effects upon symmetrical electron-transfer reactions resulting from added electrolyte is outlined. Relationships are derived on the basis of the extended Debye-Huckel model for the increase in the activation free energy, ΔG_ia*, associated with reorganization of the ionic atmosphere for homogeneous-phase reactions involving a pair of spherical reactants with varying internuclear distance R. Similar relationships apply to the energetics of symmetrical optical electron transfer, since the increase in the optical transition energy, ΔE, should equal the corresponding ionic atmosphere reorganization energy, E; under the anticipated linear response conditions, E = 4ΔG_ia*. The predicted ΔG_ia* (and hence ΔE) values increase sharply with increasing R, as a consequence of the diminished “sharing” of the ionic cloud surrounding the donor and acceptor sites under these conditions. Outer-sphere electrochemical reactions, featuring a single “near-isolated” reactant, are predicted to feature substantially larger ΔG_ia* values than for homogeneous processes proceeding with the reaction partners in contact. The influence of more specific “ionic atmosphere” effects upon ΔG_ia*, especially involving reactant-electrolyte ion pairing, is also discussed. Unlike that of the nonspecific ionic atmosphere, the nuclear reorganization process associated with counterion transport between donor and acceptor sites coupled with electron transfer is nonlinear in nature, so that E ≠ 4ΔG_ia*. Some recent experimental data for electrolyte effects upon the rate constants for ferrocenium-ferrocene self exchange and related systems are examined in the light of these considerations.     

Constant Weight Codes and Group Divisible Designs

The study of a class of optimal constant weight codes over arbitrary alphabets was initiated by Etzion, who showed that such codes are equivalent to special GDDs known as generalized Steiner systems GS(t,k,n,g) Etzion. This paper presents new constructions for these systems in the case t=2, k=3. In particular, these constructions imply that the obvious necessary conditions on the length n of the code for the existence of an optimal weight 3, distance 3 code over an alphabet of arbitrary size are asymptotically sufficient.     

Magnetic properties of bio-synthesized zinc ferrite nanoparticles

The magnetic properties of zinc ferrite (Zn-substituted magnetite, Zn_yFe_1-yFe₂O₄) formed by a microbial process compared favorably with chemically synthesized materials. A metal reducing bacterium, Thermoanaerobacter, strain TOR-39 was incubated with Zn_xFe_1−xOOH (x=0.01, 0.1, and 0.15) precursors and produced nanoparticulate zinc ferrites. Composition and crystalline structure of the resulting zinc ferrites were verified using X-ray fluorescence, X-ray diffraction, transmission electron microscopy, and neutron diffraction. The average composition from triplicates gave a value for y of 0.02, 0.23, and 0.30 with the greatest standard deviation of 0.02. Average crystallite sizes were determined to be 67, 49, and 25 nm, respectively. While crystallite size decreased with more Zn substitution, the lattice parameter and the unit cell volume showed a gradual increase in agreement with previous literature values. The magnetic properties were characterized using a superconducting quantum interference device magnetometer and were compared with values for the saturation magnetization (M_s) reported in the literature. The averaged M_s values for the triplicates with the largest amount of zinc (y=0.30) gave values of 100.1, 96.5, and 69.7 emu/g at temperatures of 5, 80, and 300 K, respectively indicating increased magnetic properties of the bacterially synthesized zinc ferrites.     

Cyclotron superradiance of a high-current electron bunch under group synchronism conditions

We have theoretically and experimentally investigated the process of induced coherent emission (superradiance) in an electron bunch rotating in a homogeneous magnetic field. We have shown that this process makes it possible to generate ultrashort microwave pulses. In this case, the optimum conditions are found under group synchronism conditions, when the translational velocity of the bunch matches the group velocity of the radiation propagating in the waveguide circuit. For experimental investigation of the superradiance, we used a RADAN accelerator with subnanosecond electron pulse sharpener. In the 35 GHz range, we obtained microwave pulses with record short duration, down to 0.4 nsec for a peak power level up to 200 kW. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 89–97, December, 1996.