Similarities and Differences of the Active Sites in Basic and Advanced MgCl2‐Supported Ziegler‐Natta Propylene Polymerization Catalysts

Though preparation procedures of heterogeneous Ziegler‐Natta catalysts for propylene polymerization are sophisticated, it is uncertain whether the nature of the active sites is similar or different for different preparation procedures. In this study, the effects of preparation procedures on the nature of the active sites were investigated by stopped‐flow polymerization in combination with microstructure analysis of polymers. Both basic and advanced types of catalysts showed the same two kinds of isospecific active site, which indicated little influence of the preparation method on the active site structure. On the contrary, the ratios of the two kinds of isospecific sites were not the same, resulting in variation of average polymer properties.

     

Design and synthesis of phthalimide-based fluorescent liver x receptor antagonists

Based on our structure-activity relationship study of liver X receptor (LXR) ligands, we designed and synthesized fluorescent LXR antagonists containing an unsubstituted or substituted amino group on a phthalimide unit.     

Transverse mode control by manipulating gain distribution in a Yb:YAG ceramic thin disk

We demonstrated that transverse mode can be controlled by manipulating gain distribution in a Yb:YAG ceramic thin disk. Several elongated higher order transverse modes of a Hermite-Gaussian beam were observed when a straight-line-shaped gain region was created by using a diode laser output from an optical fiber. An orthogonally crossing pair of straight-line-shaped gain regions created with an additional optical fiber output resulted in the generation of a doughnut-shaped Laguerre-Gaussian beam. This implies that easy and quick switching of Hermite-Gaussian and Laguerre-Gaussian beams is possible without mechanical handling.     

Quandle homology and complex volume

We introduce a new homology theory of quandles, called simplicial quandle homology, which is quite different from quandle homology developed by Carter et al. We construct a homomorphism from a quandle homology group to a simplicial quandle homology group. As an application, we obtain a method for computing the complex volume of a hyperbolic link only from its diagram.     

Peptidehelicenes in solution and gel: chiral discrimination through interactions between two types of helixes

Helical [5]thiaheterohelicene 5HM, which rapidly interconverts between P and M enantiomers in solution, was connected to helical l-phenylalanine oligomers with an ester linkage to give peptidehelicenes (5Fn, where n: number of bonded phenylalanines). The characteristics of 5F4 and 5F5 with two types of helixes in a molecule were investigated, particularly in comparison with those of 5F1–5F3 with an incomplete coil of a peptide moiety. l-Phenylalanine peptide chains induced a shift in the equilibrium between the P and M helixes of 5HM toward the P side for all the 5Fns examined. The enantiomeric excess (ee) of the P form increased with a decrease in temperature, together with an elongation of the peptide chains. 5F4 and 5F5 in hot solutions of some solvents formed a gel at room temperature, whereas 5F1–5F3 showed no such behavior. In this gel, the stable helical form of the 5HM moiety in 5F4 and 5F5 was observed to be the M form in contrast to that in their solutions.     

Low Power Penalty Operation of a Wide Input Dynamic Range Cross-Phase Modulation Wavelength Converter

We successfully demonstrated low power penalty operation of a cross-phase modulated (XPM) wavelength converter using a semiconductor optical amplifier (SOA) power equalizer. We also clarified the SOA equalizing level for more adaptive wavelength conversion and achieved a power penalty of less than 1 dB over the wide input dynamic range of 15 dB.     

A Regularly Preemptive Model and its Approximations

A regularly preemptive model D,MAP/D ₁,D ₂/1 is studied. Priority customers have constant inter-arrival times and constant service times. On the other hand, ordinary customers' arrivals follow a Markovian Arrival Process (MAP) with constant service times. Although this model can be formulated by using the piecewise Markov process, there remain some difficult problems on numerical calculations. In order to solve these problems, a novel approximation model MAP/MR/1 with Markov renewal services is proposed. These two queueing processes become different due to the existence of idle periods. Thus, a MAP/MR/1 queue with a general boundary condition is introduced. It is a model with the exceptional first service in each busy period. In particular, two special models are studied: one is a warm-up queue and the other is a cool-down queue. It can be proved that the waiting time of ordinary customers for the regular preemption model is stochastically smaller than the waiting time of the former model. On the other hand, it is stochastically larger than the waiting time of the latter model.