Self-repelling walk on the Sierpiński gasket

 We construct a one-parameter family of self-repelling processes on the Sierpiński gasket, by taking continuum limits of self-repelling walks on the pre-Sierpiński gaskets. We prove that our model interpolates between the Brownian motion and the self-avoiding process on the Sierpiński gasket. Namely, we prove that the process is continuous in the parameter in the sense of convergence in law, and that the order of H?lder continuity of the sample paths is also continuous in the parameter. We also establish a law of the iterated logarithm for the self-repelling process. Finally we show that this approach yields a new class of one-dimensional self-repelling processes. Received: 8 March 2001 / Revised version: 30 May 2001 / Published online: 22 August 2002     

Demonstration of Optical Isolator with CeY2Fe5O12 Guiding Layer Employing Nonreciprocal Phase Shift

A waveguide optical isolator with a CeY2Fe5O12 guiding layer employing a nonreciprocal phase shift was studied.The isolation ratio of more than 12.2 dB was achieved at a wavelength of 1.55 μm.     

Reduction of Fringe Noise in Wavelength Modulation Spectroscopy Using a One-Dimensional Focal Plane Array

In wavelength modulation spectroscopy using diode lasers, detection limit of molecular absorption is often imposed by spurious fringe noises that arise from slight reflections among optical components. In an attempt to reduce this fringe effect, we propose and demonstrate the use of a one-dimensional focal plane array. With the help of a multiplexer, a single lock-in amplifier is employed to obtain multiple-channel signals from wavelength-modulated output of an array detector. It is found that the intensity change of the molecular absorption signal is nearly proportional to the transversal beam intensity distribution, whereas that of fringe noise is much less conspicuous. These features, as well as the phase difference among the channels, contribute to separate the signal and fringe noise components from the multiplexed spectra, leading to the overall improvement in the signal-to-noise ratio.     

Hydrosilylation of olefins and dehydrogenative double silylation of conjugated dienes catalyzed by lanthanide–imine complexes

Divalent lanthanide–imine complexes and a related species catalyzed the hydrosilylation of olefins with phenyl- and diphenylsilane. On the other hand, conjugated dienes were converted to 1,4-bissilyl-2-butenes and 3-silacyclopentenes, accompanied with hydrogen evolution, under similar conditions.     

Factorization and Stochastic Decomposition Properties in Bulk Queues with Generalized Vacations

This paper considers a class of stationary batch-arrival, bulk-service queues with generalized vacations. The system consists of a single server and a waiting room of infinite capacity. Arrivals of customers follow a batch Markovian arrival process. The server is unavailable for occasional intervals of time called vacations, and when it is available, customers are served in groups of fixed size B. For this class of queues, we show that the vector probability generating function of the stationary queue length distribution is factored into two terms, one of which is the vector probability generating function of the conditional queue length distribution given that the server is on vacation. The special case of batch Poisson arrivals is carefully examined, and a new stochastic decomposition formula is derived for the stationary queue length distribution.AMS subject classification: 60K25, 90B22, 60K37     

A multiscale approach for modeling scale-dependent yield stress in polycrystalline metals

Modeling of scale-dependent characteristics of mechanical properties of metal polycrystals is studied using both discrete dislocation dynamics and continuum crystal plasticity. The initial movements of dislocation arc emitted from a Frank-Read type dislocation source and bounded by surrounding grain boundaries are examined by dislocation dynamics analyses system and we find the minimum resolved shear stress for the FR source to emit at least one closed loop. When the grain size is large enough compared to the size of FR source, the minimum resolved shear stress levels off to a certain value, but when the grain size is close to the size of the FR source, the minimum resolved shear stress shows a sharp increase. These results are modeled into the expression of the critical resolved shear stress of slip systems and continuum mechanics based crystal plasticity analyses of six-grained polycrystal models are made. Results of the crystal plasticity analyses show a distinct increase of macro- and microscopic yield stress for specimens with smaller mean grain diameter. Scale-dependent characteristics of the yield stress and its relation to some control parameters are discussed.     

Sequential Synthesis of Coordination Polymersomes

Novel organic–inorganic hybrid liposomes, so‐called coordination polymersomes (CPsomes), with artificial domains that exhibit strong lateral cohesion were prepared by a three‐step procedure that formed a coordinative interaction leading to a lipid bilayer. First, the lipophilic complex (dabco‐C₁₈)[Mn(N)(CN)₄(dabco‐C₁₈)] ( 1 ; dabco‐C₁₈⁺=1,4‐diazabicyclo[2,2,2]octane‐(CH₂)₁₇? CH₃ cation), was synthesized. 1 has a lipophilic alkyl tail part and a tetracyanometallate head group, which can be used for an expansion to two‐dimensional coordination networks. Second, 1 and 1,2‐dipalmitoyl‐sn‐glycero‐3‐phosphocholine were mixed to prepare the liposomes. Finally, CPsomes were obtained by the addition of transition‐metal ions ( M ) to form unilamellar faceted liposomes with plain CP raft domains with Mn? CN? M linkages. The concentration of 1 influences the size of the CP raft domains and the shape of the CPsomes. The synthesis of coordination polymers in lipid bilayers is a novel approach for the construction of artificial architectures as raft domains, for example, in cell membranes.     

Hetero‐Selective DNA‐Like Duplex Stabilized by Donor–Acceptor Interactions

We report on the characterization of a novel hetero‐selective DNA‐like duplex of pyrene and anthraquinone pseudo base pairs. The pyrene/anthraquinone pairs showed excellent selectivity in hetero‐recognition and even trimers were found to form a hetero‐duplex. Pyrene and anthraquinone moieties were tethered on acyclic D ‐threoninol linkers and linked to adjacent residues by using standard phosphoramidite chemistry. When pyrene and anthraquinone were incorporated at pairing positions in complementary strands of natural DNA oligonucleotides, the duplex was stabilized significantly. Moreover, a pyrene hexamer and an anthraquinone hexamer formed a stable artificial hetero‐duplex without the assistance of natural base pairs. The pyrene/anthraquinone pair was so stable that even trimers formed a hetero‐duplex under conditions in which natural DNA strands of three residues do not.     

One-pot method for α-phenylation of ketones using isoxazolidine and triphenylaluminum

The efficient one-pot umpolung α-phenylation of ketones via N-alkenylisoxazolidine is described. When the various ketones are treated with triphenylaluminum prepared from phenylmagnesium chloride and AlCl₃ in the presence of isoxazolidine, the desired products are obtained in good to moderate yield. This method is equivalent to a direct α-arylation reaction of carbonyl groups.