Extensions for finite Chevalley groups II

Let be a semisimple simply connected algebraic group defined and split over the field with elements, let be the finite Chevalley group consisting of the -rational points of where , and let be the th Frobenius kernel. The purpose of this paper is to relate extensions between modules in and with extensions between modules in . Among the results obtained are the following: for 2$"> and , the -extensions between two simple -modules are isomorphic to the -extensions between two simple -restricted -modules with suitably ``twisted" highest weights. For , we provide a complete characterization of where and is -restricted. Furthermore, for , necessary and sufficient bounds on the size of the highest weight of a -module are given to insure that the restriction map is an isomorphism. Finally, it is shown that the extensions between two simple -restricted -modules coincide in all three categories provided the highest weights are ``close" together.

     

LET distributions from CR-39 plates on Space Shuttle missions STS-84 and STS-91 and a comparison of the results of the CR-39 plates with those of RRMD-II and RRMD-III telescopes

The LET distributions during the Space Shuttle missions STS-84 (altitude 270-412 km, average 375 km; inclination angle, 51.6 degrees) and STS-91 (altitude 328-397 km, average 373 km; inclination angle, 51.6 degrees) were measured using CR-39 plastic nuclear track detectors. A correction for the dip-angle dependence of the track-formation sensitivity of the CR-39 plates was applied to the data analysis. The absorbed doses and the dose equivalents around RRMD Detector Units, estimated from the LET distributions in the LET region of 4-200 keV/micrometers, fluctuated with standard deviations of +/- 21% to +/- 35% in both flight experiments. The LET distributions obtained from the CR-39 plates agreed well with that obtained from RRMD-II in STS-91. However, the particle fluxes obtained from RRMD-III in STS-84 and STS-91 were two or three times higher than those obtained from RRMD-II and the CR-39 plates. It was concluded that the LET distributions obtained from RRMD-II and the CR-39 plates in the present flight experiments did not include the contribution of target-fragmented secondary heavy particles produced by low-LET particles, such as relativistic or semi-relativistic protons and helium ions, whereas RRMD-III was able to detect these secondary particles because of its low triggering level.     

Induction in linear logic

Linear logic, introduced by Girardet al., has a great power of expression, but no method for induction. This paper proposes a method of induction using knowledge represented by linear logical formulas. In linear logic, the number of propositions is controlled by logical operators. When a background theory and a hypothesis prove an example, the number of propositions on each side must be equivalent.     

Propagating beam analysis of fiber wavelength filters with a depressed-index section

A wavelength filter consisting of single-mode and few-mode fibers is investigated numerically. A simple finite-difference beam-propagation method, in which a transparent boundary condition can be imposed, is developed for circularly symmetric waveguides. After confirming the validity of the numerical method by the mode-mismatch loss, we calculate the propagating field in the fiber wavelength filter, in which interference between LP₀₁, and LP₀₂ modes occurs. To improve the filtering operation, a depressed-index fiber is employed for the few-mode fiber. The effects of the radius and refractive index of the depressed section on the transmission power are revealed and discussed. Power is suppressed to less than 0.1% at 1.3 μm, while maintaining power transmission of more than 85% at 1.55 μm. It is also found that the filtering operation shifts to higher wavelengths as the input power is increased when we choose a self-focusing nonlinear material in the depressed section.     

Substituent effect of the coordinated pyridine in a series of pyrazolato bridged dinuclear diiron(II) complexes on the spin-crossover behavior

Two series of pyrazolato bridged dinuclear NCS and NCBH3 diiron(II) complexes with various types of 3- or 4-substituted pyridines, [{Fe(NCS or NCBH3)(X-py)}2(mu-bpypz)2], were prepared and their variable-temperature magnetic susceptibilities were measured. There were found linear correlations of the spin-crossover temperatures Tc not only between the NCS and NCBH3 complexes with the corresponding substituted pyridines, but also between the Tc and the Hammett constants, supporting the electronic substituent effect of the coordinated pyridine rather than a steric effect. The ligand field and the interelectronic repulsion parameters together with the thermodynamic data and/or cooperativity factor were discussed in relation with their spin-crossover behavior.     

Photon number squeezing of ultrabroadband laser pulses generated by microstructure fibers

To the best of our knowledge, we demonstrate for the first time the generation of photon number squeezing by spectral filtering for ultrabroadband light generated by microstructure fibers at 800 nm. A maximum squeezing of 4.6 dB is observed, corresponding to 10.3 dB after correcting for detection losses. We numerically analyzed the quantum dynamics of ultrashort laser pulse propagation through optical fibers by solving a nonlinear quantum Schr?dinger equation that included Raman scattering, especially for the quantum correlation of photon number fluctuation among frequency modes in broadband pulses.     

Chiral phosphinooxazolidine ligands for palladium- and platinum-catalyzed asymmetric Diels-Alder reactions

Cationic palladium (Pd)- and platinum (Pt)-phosphinooxazolidine catalysts 13a-c, 15a-d, 17a-c, and 19a-c were prepared from phosphinooxazolidine ligands 1-3, MCl(2) (M = Pd and Pt), and counterions, and the activities of the catalysts in the asymmetric Diels-Alder (DA) reactions of cyclic or acyclic dienes with imide dienophiles were investigated. These catalysts demonstrated high levels of catalytic activity. The cationic Pd-POZ complex 13c provided particularly excellent enantioselectivity (98% ee) in the DA reactions of cyclopentadiene with acryloyl-, crotonyl-, and fumaroyl-1,3-oxazolidin-2-ones (20a-c).