The dual of a finitely generated multiplication module

This paper is based on the M. Sc. thesis written by the third author under the supervision of the first two authors. It was submitted to the University of Baghdad in 1986.     

High-pressure effect on the crystal and magnetic structure of LuMnO3: Correlation between a distortion of the triangular lattice and the symmetry of the magnetic state in hexagonal frustrated manganites

The effect of a high pressure (up to 6 GPa) on the crystal and magnetic structure of the hexagonal manganite LuMnO₃ is studied by neutron diffraction in the temperature range 10–295 K. It is found that, as the pressure increases, the ordered magnetic moment of Mn ions at T = 10 K decreases noticeably from 2.48 (0 GPa) to 1.98 μ_B (6 GPa). This decrease is due to an enhancement of the geometrical frustration effects on the triangular lattice. At the same time, the symmetry of the triangular antiferromagnetic state (the irreducible representation Γ₂) remains unchanged. A correlation is revealed between the distortion parameter of the triangular lattice formed by Mn ions and the symmetry of the antiferromagnetic state of hexagonal manganites RMnO₃. Based on this correlation, a generalized magnetic phase diagram of these compounds is constructed. The obtained phase diagram provides an explanation for the changes observed in the magnetic state of hexagonal manganites caused by high pressure and chemical substitution.     

Self-assembly of a linear mesoscale tetramer with electrical connectivity

Capillary interaction-based self-assembly of block-shaped mesoscale components into an electrically interconnected 1-D tetramer is reported. Low melting point solder droplets, selectively patterned on the faces of the blocks, were employed to drive the sequential alignment, registration, linking and electrical interconnection of each block. The solder patterns were designed so that successful assembly would only occur when the solder patterns on one block face were correctly aligned with those on the face of an adjacent block. For assembly, the blocks were agitated in a flask containing KBr solution. At 60 °C the solder was molten, and collisions between blocks enabled the solder menisci to easily interact. To minimize interfacial free energy, the menisci coalesced and quickly drove the interacting blocks to form a stable, registered and aligned assembly. When agitation was terminated and the solution cooled, the self-aligned, linear tetrameric arrangement of blocks was permanently captured by solder solidification, a process that provided good mechanical bonding and electrical interconnection between each block. PACS 81.16.Dn; 68.03.Cd; 85.40.-e     

Influence of focusing depth on the microfabrication of waveguides inside silica glass by femtosecond laser direct writing

We studied the influence of focusing depth on the index change threshold and damage threshold of silica glass irradiated by a focused 120 fs laser beam. Both thresholds increased with the focusing depth. The aspect ratio of the waveguide cross section can be selected by changing the focusing depth. A 5 mm long waveguide was written at the depth of 2100 μm, which was single mode at 632.8 nm and exhibited propagation loss of 0.56 dB/cm. The refractive index change was calculated to be ∼2.47×10^-3. The influence of the focusing depth should be considered in multi-layer devices as shown in the fabrication of a 3×3 waveguide array. PACS 42.62.-b; 42.82.Et; 81.05.Kf     

The measurement of beta asymmetries at UNISOR/NOF using external plastic scintillator detectors

The performance of two external plastic scintillator detectors has been tested in an off-line mode using a source of¹⁰⁶RuFe at UNISOR/NOF. The measurement of beta asymmetries at various temperatures has resulted in the reproduction of the previously-determined magnetic dipole moment for the 1⁺ ground state of¹⁰⁶Rh and in addition the conclusion that the sign of this moment is positive.     

Consistency of decisions in a hierarchy of games

Translated from Vychislitel'nye Kompleksy i Modelirovanie Slozhnykh Sistem, pp. 98–106, Moscow State University, 1989.     

Limits of parallelism in explicit ODE methods

Numerical methods for ordinary initial value problems that do not depend on special properties of the system are usually found in the class of linear multistage multivalue methods, first formulated by J.C. Butcher. Among these the explicit methods are easiest to implement. For these reasons there has been considerable research activity devoted to generating methods of this class which utilize independent function evaluations that can be performed in parallel. Each such group of concurrent function evaluations can be regarded as a stage of the method. However, it turns out that parallelism affords only limited opportunity for reducing the computing time with such methods. This is most evident for the simple linear homogeneous constant-coefficient test problem, whose solution is essentially a matter of approximating the exponential by an algebraic function. For a given number of stages and a given number of saved values, parallelism offers a somewhat enlarged set of algebraic functions from which to choose. However, there is absolutely no benefit in having the degree of parallelism (number of processors) exceed the number of saved values of the method. Thus, in particular, parallel one-step methods offer no speedup over serial one-step methods for the standard linear test problem. Although the implication of this result for general nonlinear problems is unclear, there are indications that dramatic speedups are not possible in general. Also given are some results relevant to the construction of methods.Work supported in part by National Science Foundation grants DMS 89 11410 and DMS 90 15533 and by US Department of Energy grant DOE DEFG02-87ER25026. Work of the second author was completed while at the University of Illinois.     

FT-EPR and HPLC study of the mechanism of 4-chlorophenol photolysis

The mechanism of 4-chlorophenol (4CP) photolysis was investigated with the aid of Fourier Transform Electron Paramagnetic Resonance (FT-EPR) and pulsed-laser photolysis combined with High Performance Liquid Chromatography (HPLC) detection-of stable (diamagnetic) products. With FT-EPR transient free radicals produced by pulsed-laser excitation of solutions of 4CP in alcohols could be identified. Time profiles of the FT-EPR spectra provided information on reaction kinetics and Chemically Induced Dynamic, Electron Polarization (CIDEP) effects. It was found that 4CP photolysis in alcohols leads to the simultaneous formation of the phenoxyl radical and radicals produced by hydrogen abstraction from the solvent. CIDEP patterns establish that these radicals are formed in a reaction sequence involving a triplet state precursor and radical pair intermediate. Results of earlier transient optical absorption measurements indicate that the triplet precursor must be the carbene 4-oxocyclohexa-2,5-dienylidene. This assignment is supported by the finding that photolysis of quinone diazide in a hydrogen-donating solvent gives the same free radical products as those obtained from 4CP. The formation of the phenoxyl radical intermediate accounts for the finding that photolysis of deoxygenated solutions of 4CP in alcohols gives phenol as stable diamagnetic product. By contrast, photolysis of aerated and deoxygenated aqueous solutions of 4CP produces benzoquinone and hydroquinone as primary products, respectively.