Electro‐optical behavior of ferroelectric liquid crystalline polyphenylene derivatives

Liquid crystalline (LC) polyphenylene derivatives, such as poly(para‐phenylene) (PPP), poly(meta‐phenylene) (PMP), poly(meta‐biphenylene) (PBP), and poly (meta‐terphenylene) (PTP) derivatives, were synthesized through substitution of fluorine‐containing chiral LC groups into side chains, with an aim to develop ferroelectric LC (FLC) conjugated polymers. All the polymers, except PTP, showed enantiotropic liquid crystallinities, where several types of mesophases were observed in both heating and cooling processes. Among them, PPP and PMP derivatives showed chiral smectic C (S_C*) phases responsible for ferroelectricity. In fact, they exhibited quick response to electric field, in spite of high viscosities inherent to polymers, giving rise to switching times of less than 1 s between two S_C states with reversely directed alignment. Hysteresis loops between the polarization and electric field were also observed for PPP and PMP. The spontaneous polarization (P_S) of PMP remained unchanged even after the electric field became zero, affording the residual polarization (P_R) whose value was the same as that of P_S. This indicates that PMP has a prospective memory function based on FLC nature. The present study is the first report for realizing a quick switching in macroscopic alignment using electric field and also for generating a potential memory function in π‐conjugated polymers. It is elucidated that unusual polymer main chains such as polyphenylenes can be used to prepare new ferroelectric polymers. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 3591–3610, 2008     

Photocyclization reactions. Part 1. Synthesis of dihydrobenzofuranols using photocyclization of 2-alkoxybenzaldehydes, 2′-alkoxyacetophenones, 2-formylphenoxyacetic acids and 2-acetylphenoxyacetic acids

Photocyclization reactions were carried out on 2-alkoxybenzaldehydes 1a-f , 2′-alkoxyacetophenones 2a-h , 2-formylphenoxyacetic acids 1i-l and 2-acetylphenoxyacetic acids 2i-m . Irradiation of 1a-f and 2a-h in acetonitrile gave the corresponding dihydrobenzofuranols 3, 5 and dihydroisobenzofuranols 4, 6 . Using carboxylic acids 1i-1, 2i-m as starting materials, decarboxylation occurred immediately to give the corresponding ethers 1a-d, 2a-e . Further irradiation of the solution afforded dihydrobenzofuranols 3, 5 and dihydroisobenzofuranols 4, 6 . Substituent effects on photocyclization and reaction pathways are discussed.     

Aharonov-Bohm scattering by vortices of dimensionally-reduced Yang-Mills field

If two dimensions of six-dimensional space-time are compactified, a topological configuration of Yang-Mills gauge field appears as a cosmic string in four dimensions, whose thickness is of the same order as the size of the compact space. We consider scattering of low-energy fermions by this object.     

On a Normal Integral Basis Problem over Cyclotomic Zp-extensions, II

Let p be an odd prime number, K an imaginary abelian field with ζ_p∈K^×, and K_∞/K the cyclotomic Z_p-extension with its nth layer K_n. In the previous paper, we showed that for any n and any unramified cyclic extension L/K_n of degree p, LK_n+1/K_n+1 does have a normal integral basis (NIB) even if L/K_n has no NIB, under the assumption that p does not divide the class number of the maximal real subfield K⁺ (and some additional assumptions on K). In this paper, we show that similar but more delicate phenomena occur for a certain class of tamely ramified extensions of degree p.     

The structure of lipopeptin a

The structure of lipopeptin A, an antifungal peptolide antibiotic was determined as $\text{1}$ on the basis of chemical and spectroscopic evidence.     

Joint distributions associated with patterns,successes and failures in a sequence of multi-state trials

Let {Z _t ,t≥1} be a sequence of trials taking values in a given setA={0, 1, 2,...,m}, where we regard the value 0 as failure and the remainingm values as successes. Let ε be a (single or compound) pattern. In this paper, we provide a unified approach for the study of two joint distributions, i.e., the joint distribution of the numberX _n of occurrences of ε, the numbers of successes and failures inn trials and the joint distribution of the waiting timeT _r until ther-th occurrence of ε, the numbers of successes and failures appeared at that time. We also investigate some distributions as by-products of the two joint distributions. Our methodology is based on two types of the random variablesX _n (a Markov chain imbeddable variable of binomial type and a Markov chain imbeddable variable of returnable type). The present work develops several variations of the Markov chain imbedding method and enables us to deal with the variety of applications in different fields. Finally, we discuss several practical examples of our results. This research was partially supported by the ISM Cooperative Research Program (2002-ISM·CRP-2007).     

Polymerization of vinyl chloride with half‐titanocene/methylaluminoxane catalysts

The polymerization of vinyl chloride (VC) with half‐titanocene /methylaluminoxane (MAO) catalysts is investigated. The polymerization of VC with the Cp*Ti(OCH₃)₃/MAO catalyst (Cp* = η⁵‐pentamethylcyclopentadienyl) afforded high‐molecular‐weight poly(vinyl chloride) (PVC) in good yields, although the polymerization proceeded at a slow rate. With the Cp*TiCl₃/MAO catalyst, the polymer was also obtained, but the polymer yield was lower than that with the Cp*Ti(OCH₃)₃/MAO catalyst. The polymerization of VC with the Cp*Ti(OCH₃)₃/MAO catalyst was influenced by the MAO/Ti mole ratio and reaction temperature, and the optimum was observed at the MAO/Ti mole ratio of about 10. The optimum reaction temperature of VC with the Cp*Ti(OCH₃)₃/MAO catalyst was around 20 °C. The stereoregularity of PVC obtained with the Cp*Ti(OCH₃)₃/MAO catalyst was different from that obtained with azobisisobutyronitrile, but highly stereoregular PVC could not be synthesized. From the elemental analyses, the ¹H and ¹³C NMR spectra of the polymers, and the analysis of the reduction product from PVC to polyethylene, the polymer obtained with Cp*Ti(OCH₃)₃/MAO catalyst consisted of only regular head‐to‐tail units without any anomalous structure, whereas the Cp*TiCl₃/MAO catalyst gave the PVC‐bearing anomalous units. The polymerization of VC with the Cp*Ti(OCH₃)₃/MAO catalyst did not inhibit even in the presence of radical inhibitors such as 2,2,6,6,‐tetrametylpiperidine‐1‐oxyl, indicating that the polymerization of VC did not proceed via a radical mechanism. © 2002 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 248–256, 2003     

Examples of stationary Euler flows

We construct concrete solutions of the incompressible Euler equation in a domain of the cylinder type, and the compressible Euler equation outside a ball (or a rotationary symmetric body) with a constant speed at infinity along the axis of symmetry.