Results from GRACE/SUSY at one-loop

We report the recent development on the SUSY calculations with the help of GRACE system. GRACE/SUSY/1LOOP is the computer code which can generate Feynman diagrams in the MSSM automatically and compute one-loop amplitudes in the numerical way. We present new results of various two-body decay widths and chargino pair production at ILC (international linear collider) at one-loop level.      

Conjugacy relationship between M-convex and L-convex functions in continuous variables

By extracting combinatorial structures in well-solved nonlinear combinatorial optimization problems, Murota (1996,1998) introduced the concepts of M-convexity and L-convexity to functions defined over the integer lattice. Recently, Murota–Shioura (2000, 2001) extended these concepts to polyhedral convex functions and quadratic functions in continuous variables. In this paper, we consider a further extension to more general convex functions defined over the real space, and provide a proof for the conjugacy relationship between general M-convex and L-convex functions.Mathematics Subject Classification (1991): 90C10, 90C25, 90C27, 90C35This work is supported by Grant-in-Aid of the Ministry of Education, Culture, Sports, Science and Technology of Japan     

Phase Conjugation in Saturable Absorbing Dye Films by Degenerate Four-Wave Mixing and Holographic Processes Using Nanosecond Pulse and CW Lasers

We report on the simultaneous generation of phase-conjugate signals by degenerate four-wave mixing (DFWM) and holographic processes using a nanosecond pulse and a CW lasers in polyvinyl alcohol (PVA) films doped with four kinds of saturable absorbing dyes. For the pulse laser, of the four kinds of dye-doped PVA films, the erythrosine B-doped PVA and uranine doped-PVA films generate PC signals only by the DFWM process, while the other dye-doped PVA films generate PC signals simultaneously by not only the DFWM process but also the holographic process. Especially, the safranin T-doped PVA film generates strong PC signals by the holographic process. In contrast, all of the dye-doped PVA films generate the two types of PC signals for the CW laser. The fading of dye molecules is found to result in the generation of the holographic component of PC signals which governs the temporal behavior of the total PC signals.     

Fast Optical Switching Using Oriented Cyanine Dye-Doped Nematic Liquid Crystal

A cyanine dye, 2-[7-（1,3-dihydro-1,3,3-trimethyl-2H-indol-2-ylidene）-1,3,5-heptatrienyl]-1,3,3-trimethyl-3H-indolium iodide （NK-125）, is doped in 4-cyano-4＇-pentylbiphenyl （5 CB）, and the mixture is sandwiched between two pieces of rubbed glass plates. The third-order nonlinear optical properties of the oriented NK-125-SCB layers are measured by the resonant femtosecond degenerate four-wave mixing （DFWM） technique at 760 nm. The third-order nonlinear optical susceptibility of one of the present samples is 5.5×10^-8 esu. The slow DFWM response of the NK-125-SCB layers due to a population grating is accelerated by the increasing laser power because of amplified spontaneous emission （ASE）. On the other hand, we do not observe a similar phenomenon for NK-125- polyethylene glycol （PEG-400）. Oriented NK-125 molecules in nematic liquid crystals must have very high ASE efficiency. Hence the population grating in a DFWM signal disappears within about 4 ps. It is expected that NK-125-SCB can be used as a material for very fast all-optical switching.     

Synthesis and properties of tricyclo[6.4.1.0]trideca-1,3(6),7,9,11-pentaene

A new cyclobutene-fused 1,6-methano[10]annulene was synthesized by pyrolysis of the sulfone and sulfinate adducts of 3,4-bis(methylene)-1,6-methano[10]annulene and its physical and chemical properties were disclosed.     

A facile non-oxidative method for synthesizing 1,3-disubstituted pyrroles from pyrrolidine and aldehydes

Reactions of pyrrolidine with 2 equiv of aldehydes without any catalyst in a pressurized vessel at 140–200 °C yielded 1,3-disubstituted pyrroles. -Branched aldehydes gave fairly good yields of the corresponding products by this method, which provides a facile non-oxidative procedure for synthesizing 1,3-dialkylpyrroles from inexpensive pyrrolidine and aldehydes.