Synthesis of isocorrole and the higher homologues

Bis(azafulvene) derivative of gem-dimethyldipyrrylmethane reacted with 2,2′-bipyrrole under neutral conditions without catalyst to give a mixture of expanded isocorroles in ca. 50% total yields. GPC separation gave eleven porphyrinoids containing 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, and 44 units of pyrrole.     

Studies on antibacterial agents. III. Synthesis and antibacterial activities of substituted 1,4-dihydro-8-methyl-4-oxoquinoline-3-carboxylic acids

A series of substituted 4-oxoquinoline-3-carboxylic acids having a methyl group at the 8-position was prepared and tested for their antibacterial activity. 7-(trans-3-Amino-4-methyl-1-pyrrolidinyl)-1-cyclopropyl-1,4-dihydro-6- fluoro-8-methyl-4-oxoquinoline-3-carboxylic acid (21) exhibited highly potent antibacterial activity against both gram-positive and gram-negative bacteria, including Pseudomonas aeruginosa.     

Effects of Motion, Implied Direction and Displacement of a Large-Visual-Stimulus on Postural Control

Effects of motion, implied direction in a static stimulus and displacement on postural control were examined independently. In Experiment 1, rotation of a random-dot stimulus was presented. In Experiments 2 and 3, photographic slides of natural scenes were used; participants closed their eyes during stimulus rotation to eliminate motion information. In Experiment 2, the stimulus was presented upright initially, then presented again with a tilt. In Experiment 3, the order was reversed to separate the effects of implied direction and displacement. Results showed that all information of motion, implied direction, and displacement had some effect on postural control, although visual information of motion has been presumed to have a principal effect on postural control. Results suggested that the effects of implied direction might reflect an immediate processing of information. The effects of displacement and motion might reflect a continuous processing of information.     

Photoanodic and photocathodic behaviour of La5Ti2CuS5O7 electrodes in the water splitting reaction

The particulate semiconductor La₅Ti₂CuS₅O₇ (LTC) with a band gap energy of 1.9 eV functioned as either a photocathode or a photoanode when embedded onto Au or Ti metal layers, respectively. By applying an LTC/Au photocathode and LTC/Ti photoanode to, respectively, photoelectrochemical (PEC) water reduction and oxidation concurrently, zero-bias overall water splitting was accomplished under visible light irradiation. The band structures of LTC/Au and LTC/Ti calculated using a semiconductor device simulator (AFORS-HET) confirmed the critical role of the solid/solid junction of the metal back contact in the charge separation and PEC properties of LTC photoelectrodes. The prominently long lifetime of photoexcited charge carriers in LTC, confirmed by transient absorption spectroscopy, allowed the utilization of both photoexcited electrons and holes depending on the band structure at the solid/solid junction.     

Deterministic random walks on finite graphs

The rotor‐router model, also known as the Propp machine, is a deterministic process analogous to a random walk on a graph. Instead of distributing tokens to randomly chosen neighbors, the Propp machine deterministically serves the neighbors in a fixed order by associating to each vertex a “rotor‐router” pointing to one of its neighbors. This paper investigates the discrepancy at a single vertex between the number of tokens in the rotor‐router model and the expected number of tokens in a random walk, for finite graphs in general. We show that the discrepancy is bounded by O (mn) at any time for any initial configuration if the corresponding random walk is lazy and reversible, where n and m denote the numbers of nodes and edges, respectively. For a lower bound, we show examples of graphs and initial configurations for which the discrepancy at a single vertex is Ω(m) at any time (> 0). For some special graphs, namely hypercube skeletons and Johnson graphs, we give a polylogarithmic upper bound, in terms of the number of nodes, for the discrepancy. © 2014 Wiley Periodicals, Inc. Random Struct. Alg., 46,739–761, 2015     

On waiting time distributions associated with compound patterns in a sequence of multi-state trials

In this article, waiting time distributions of compound patterns are considered in terms of the generating function of the numbers of occurrences of the compound patterns. Formulae for the evaluation of the generating functions of waiting time are given, which are very effective computational tools. We provide several viewpoints on waiting time problems associated with compound patterns and develop a general workable framework for the study of the corresponding distributions. The general theory is employed for the investigation of some examples in order to illustrate how the distributions of waiting time can be derived through our theoretical results. This research was partially supported by the ISM Cooperative Research Program (2006-ISM·CRP-2007).     

A latent process model for the pricing of corporate securities

We propose a structural model with a joint process of tangible assets (marker) and firm status for the pricing of corporate securities. The firm status is assumed to be latent or unobservable, and default occurs when the firm status process reaches a default threshold at the first time. The marker process is observable and assumed to be correlated with the latent firm status. The recovery upon default is a fraction of tangible assets at the time of default. Our model can evaluate both the corporate debt and equity to fit their market prices in a unified framework. When the two processes are perfectly correlated, our model is reduced to the seminal Black–Cox model. Numerical examples are given to support the usefulness of our model. A previous version of this paper was presented at the Tsukuba–Stanford workshop held at Stanford University on March 2006. The authors are grateful to participants of the workshop for helpful discussions.