Short review of Yasuda-Shimada theorem and related topics

In this paper, we will present the past and the present situation of a very controversial topic in Finsler geometry: the necessary and sufficient conditions for a Randers space to be of constant curvature. The research on this subject started more than a quarter of century ago, but its final act was played only two years ago. Moreover, the history of Yasuda-Shimada theorem and few words on the life of Professor Yasuda are added. Finally miscellaneous topics studied by the Japanese group of Finsler geometers are reviewed.     

High speed parallel synthesis of banana-shaped molecules and phase transition behaviour of 4-bromo-substituted derivatives

Novel derivative series of the well known bent-shaped P-n-O-PIMB liquid crystal mesogens, referred to as '4Br-P-n-O-PIMB', '4Cl-P-n-O-PIMB' and '5Cl-P-n-O-PIMB', having halogen atoms substituted on the phenyl ring in the central core, were synthesized by solution phase parallel synthesis based on a combinatorial approach. The mesomorphic behaviour and physical properties of all the new compounds were studied by means of optical microscopy, differential scanning calorimetry, X-ray and circular dichroism spectroscopy. We found interesting transitional behaviour for the 4Br-P-n-O-PIMB homologous series. The homologues with alkyl tails having carbon numbers of n=3-10, 12, 14 exhibit rather complicated mesomorphic behaviour, which is strongly sensitive to n. The chiral fluid smectic B2 phase with SmC_AP_A structure and unidentified smectic Bx phase were observed in the homologues with n=9, 10, 12, 14 and n=3-5, respectively. Interestingly, every member exhibits frustrated and/or helical ordered phases at low temperatures, designated as X1, X2, and X3 phases, which result from a spontaneous escape from a macroscopic polarization. The mesomorphic behaviour and mesophase structures differ remarkably from those of the parent P-n-O-PIMB homologues, suggesting that substitution of the halogen atoms at the central core essentially creates a particular interaction between molecules.     

Electroless Nickel Plating under Continuous Ultrasonic Irradiation to Fabricate a Near-Field Probe Whose Metal Coat Decreases in Thickness toward the Tip

This paper describes a size-dependent electroless plating method to fabricate a new type of probe with a locally decreasing thickness of metal and a tiny tip size for a combined high resolution shear-force and near-field optical microscope. In this method, the tip size and decreasing thickness profile, which affect the resolution capabilities of the microscopes, are controlled by adding a continuous ultrasonic wave with a frequency of 1 MHz to a nickel plating bath. The probe with a tip radius of curvature of 25 nm was successfully fabricated at an ultrasonic power density of 1.6 W cm⁻², its metal thickness gradually decreased from 850 to 20 nm toward the distal tip.     

Facile Hydrogenation of Acenapthylenes and Azulenes on the Face of a Triruthenium Carbonyl Moiety: Discovery of Specific Reactions on the Cluster Framework Providing Unique Insight for Cluster Catalysis

Summary.  Activation of molecular hydrogen by triruthenium carbonyl clusters bearing acenaphthylene or aceanthrylene as the face-capping ligand results in partial hydrogenation of these polyaromatic ligands, giving the corresponding hydride carbonyl clusters bound to hydrogenated acenaphthylene or aceanthrylene. The first isolation of 4,5-dihydroacenaphthylene or 4,5-dihydroaceanthrylene was achieved by treatment of the resulting hydride carbonyl clusters with CO. Similarly, triruthenium carbonyl species bearing substituted azulenes as the face-capping moiety gives the corresponding hydride carbonyl cluster bearing partially hydrogenated azulenes at room temperature; the corresponding partial hydrogenation of azulenes does not occur with di- or tetraruthenium homologues. Hydrogenation of di-, tri-, and tetraruthenium carbonyl clusters bearing substituted azulenes at elevated temperatures furnishes hydrogenative cluster fragmentation to mononuclear ruthenium hydrides; the stereochemistry of these complexes suggests that the reaction takes place through the activation of H₂ by the multinuclear species. The roles of the acenaphthylene or azulene ligands as hemilabile μ₃-ligands for triruthenium carbonyl clusters are discussed. Received April 28, 2000. Accepted May 9, 2000     

Bayesian and non-bayesian analysis of gamma stochastic frontier models by Markov Chain Monte Carlo methods

Summary  This paper considers simulation-based approaches for the gamma stochastic frontier model. Efficient Markov chain Monte Carlo methods are proposed for sampling the posterior distribution of the parameters. Maximum likelihood estimation is also discussed based on the stochastic approximation algorithm. The methods are applied to a data set of the U.S. electric utility industry. The authors are grateful to two anonymous referees for their useful comments, which improved an earlier version of the paper. The first author also thanks the financial support by the Japanese Ministry of Education, Culture, Sports, Science and Technology under the Grant-in-Aid for Scientific Research No.14730022.     

Error estimate in operator norm for Trotter-Kato product formula

In the present paper we study the error estimate in the operator norm for the Trotter-Kato product formula, having an intention to apply the obtained result to Schrödinger semigroups with singular potentials.     

One-Step Synthesis of Furo[2,3-d]Pyrimidine-2,4(1H,3H)-Diones Using the Can-Mediated Furan Ring Formation

The reaction of 1,3-dimethylpyrimidine-2,4,6(1H,3H,5H)-trione with various alkenes or terminal alkynes in the presence of cerium(IV) ammonium nitrate (CAN) afforded the corresponding 5,6-dihydrofuro[2,3-d]pyrimidine-2,4(1H,3H)-diones or furo[2,3-d]pyrimidine-2,4(1H,3H)-diones in moderate to good yields.     

Fluoroalkyl end‐capped oligomers possessing nonflammable characteristic in calcium carbonate nanocomposites

Calcium chloride reacted with sodium carbonate in the presence of a variety of fluoroalkyl end‐capped oligomers such as fluoroalkyl end‐capped acrylic acid oligomer (R_F‐[ACA]_n‐R_F), 2‐methacryloyloxyethanesulfonic acid oligomer (R_F‐[MES]_n‐R_F), N,N‐dimethylacrylamide oligomer (R_F‐[DMAA]_n‐R_F) and acryloylmorpholine oligomer (R_F‐[ACMO]_n‐R_F) to afford the corresponding fluorinated oligomers/calcium carbonate composites. Each fluorinated oligomer/calcium carbonate composite thus obtained is nanometer size‐controlled very fine particles (25–114 nm) possessing a good dispersibility and stability in a variety of solvents including water. Thermal stability of these fluorinated calcium carbonate nanocomposites was studied by thermogravimetic analyses measurements. Fluorinated oligomes, in which the theoretical oligomer content in the composites is 19%, were able to give no weight loss corresponding to the content of oligomer in each case even after calcination at 800 °C. On the other hand, a slight weight loss corresponding to the contents of oligomers in the composites after calcination at 800 °C was observed in R_F‐(MES)_n‐R_F/, R_F‐(DMAA)_n‐R_F/ and R_F‐(ACMO)_n‐R_F/calcium carbonate nanocomposites, in which the theoretical contents of the oligomers were 36–53%, although R_F‐(ACA)_n‐R_F/calcium carbonate nanocomposites gave a clear weight loss corresponding to the contents of oligomer under similar conditions. Fluorinated oligomers/calcium carbonate nanocomposites possessing no weight loss at 800 °C were applied to the surface modification of poly(methyl methacrylate) (PMMA) to exhibit a good oleophobicity imparted by fluorines on the surfaces. Interestingly, these fluorinated calcium carbonate nanocomposites after calcination at 800 °C were found to exhibit the similar oleophobic characteristic on the modified PMMA surfaces as well as that of the nanocomposites before calcination. Copyright © 2013 John Wiley & Sons, Ltd.     

Phase-Transfer Reactions Catalyzed by Polymer-Supported Imidazoles

Abstract

Polymer-supported imidazoles were prepared by copolymerization of vinyl monomers containing imidazole moiety, styrene, and divinylbenzene with AIBN. The resulting polymers accelerated the reaction of octyl bromide with potassium thiocyanate, and the alkylation of an active methylene compound, benzyl cyanide, under phase-transfer conditions. The latter catalytic reaction afforded monoalkylated compound exclusively, although dialkylated compound was also obtained in monomeric alkylimidazole catalyzed reaction. Further, these polymers served as phase-transfer catalysts for the reduction of acetophenone by sodium borohydride. The relationship between the structure and catalytic activity, and the factors governing these catalytic reactions were examined.