Hydrothermal Synthesis and Crystal Structure of a New BariumVanadium Bronze Ba1+xV8O21 with a Tunnel Structure

A barium vanadium bronze Ba_1+xV₈O₂₁ has been hydrothermally synthesized and structurally characterized. Hydrothermal treatment of a suspension of VO₂ powders in Ba(NO₃)₂ solution at 350°C yielded a fibrous brown compound having nonstoichiometric composition Ba_1+xV₈O₂₁ (x=0.13). Single-crystal X-ray diffractometry revealed the monoclinic system C2/m with a=15.144(6), b=3.596(4), c=14.972(3) Å, β=90.08(3)°, and Z=2, with the refinement based on 2021 reflections with I>3σ(I) converged to R=0.054 and R_w=0.046. A new tunnel-type bronze structure was disclosed in which VO₆ octahedra and VO₅ trigonal bipyramids form a V–O framework with a tunnel cavity running along [010]. The Ba atom partially occupies the tunnel site with more than half occupancy of 56.6%, which causes displacement of the Ba atom and further displacement of V and O atoms along the tunnel axis. Ba_1+xV₈O₂₁ is the first tunnel-type barium vanadium bronze whose structure has been fully determined.     

Cationic copolymerization behavior of epoxide and 3‐isochromanone

Cationic copolymerization of n‐butyl glycidyl ether (BGE) and 3‐isochromanone (ICM) was investigated using trifluoromethanesulfonic acid (TfOH) as an initiator at 100 °C. In the copolymerization, the reactive site of ICM with the propagating cation was completely different from that in its homopolymerization: in the former, the propagating cation reacted with the carbonyl oxygen of ICM, while in the latter, the propagating cation reacted with the aromatic ring of ICM. In spite of the potential of ICM to undergo the homopolymerization, in the present copolymerization, ICM was consumed smoothly only in the presence of epoxide. As a result, the copolymerization proceeded in a statistic manner to afford the corresponding copolymer bearing ICM‐derived ester linkages distributed in the main chain. Cationic copolymerization of bisphenol A‐diglycidyl ether and ICM was also performed to synthesize the corresponding networked polymer. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2013 , 51, 4213–4220     

Crosslinkable polyurethane bearing a methacrylate structure in the side chain

A polyurethane bearing methacrylate groups through urethane linkages was prepared by the addition of 2‐methacryloyloxyethyl isocyanate to the hydroxyl groups in poly(hydroxyurethane) prepared by the polyaddition of a bifunctional cyclic carbonate with 1,12‐diaminododecane. The urethanization proceeded quantitatively in the presence of a catalytic amount of di‐n‐butyltin dilaurate at an ambient temperature, whereas a crosslinked product was obtained from the reaction at 60 °C. The resulting linear polyurethane, bearing a methacrylate structure, was thermally crosslinkable. Its radical copolymerization with vinyl‐type monomers afforded the corresponding crosslinked polymers, whose low glass transition temperatures suggested the flexibility of the polymer chains in the crosslinked product. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 3400–3407, 2007     

Does truth-table of linear norm reduce the one-query tautologies to a random oracle?

In our former works, for a given concept of reduction, we study the following hypothesis: “For a random oracle A, with probability one, the degree of the one-query tautologies with respect to A is strictly higher than the degree of A.” In our former works (Suzuki in Kobe J. Math. 15, 91–102, 1998; in Inf. Comput. 176, 66–87, 2002; in Arch. Math. Logic 44, 751–762), the following three results are shown: The hypothesis for p-T (polynomial-time Turing) reduction is equivalent to the assertion that the probabilistic complexity class R is not equal to NP; The hypothesis for p-tt (polynomial-time truth-table) reduction implies that P is not NP; The hypothesis holds for each of the following: disjunctive reduction, conjunctive reduction, and p-btt (polynomial-time bounded-truth-table) reduction. In this paper, we show the following three results: (1) Let c be a positive real number. We consider a concept of truth-table reduction whose norm is at most c times size of input, where for a relativized propositional formula F, the size of F denotes the total number of occurrences of propositional variables, constants and propositional connectives. Then, our main result is that the hypothesis holds for such tt-reduction, provided that c is small enough. How small c can we take so that the above holds? It depends on our syntactic convention on one-query tautologies. In our setting, the statement holds for all c < 1. (2) The hypothesis holds for monotone truth-table reduction (also called positive reduction). (3) Dowd (in Inf. Comput. 96, 65–76, 1992) shows a polynomial upper bound for the minimum sizes of forcing conditions associated with a random oracle. We apply the above result (1), and get a linear lower bound for the sizes.     

Residues of codimension one singular holomorphic distributions

For a codimension one locally-free singular holomorphic distribution, we give a residue formula in terms of the conormal sheaf given by Pfaffian equations. We also prove a Baum-Bott type residue formula for singular distributions.      

A characterization of Hyers-Ulam stability of first order linear differential operators

Let X be a complex Banach space and a continuous function. Let be the linear differential operator defined by T_hu=u′+hu. We give a necessary and sufficient condition in order that the operator T_h has the Hyers-Ulam stability.     

On-line biosensors for simultaneous determination of glucose, choline, and glutamate integrated with a microseparation system

An effective microseparation system integrated with ring-disc electrodes and two microfluidic devices was fabricated for in vivo determination using a microdialysis pump. The major interference of ascorbic acid (AA) was excluded by direct oxidation with ascorbate oxidase. Glucose, glutamate, and choline were successfully determined simultaneously through the biosensors modified with a bilayer of osmium-poly(4-vinylpyridine)gel-horseradish peroxidase (Os-gel-HRP)/glucose oxidase (GOD), glutamate oxidase (GlutaOD) or choline oxidase (ChOD). To stabilize the biosensors, 0.2% polyethylenimine (PEI) was mixed with the oxidases. The cathodic currents of glucose, glutamate, and choline biosensors started to increase after the standard solutions were injected into the microseparation system. The on-line biosensors show a wide calibration range (10(-7)-10(-5) mol/L) with a detection limit of 10(-8) mol/L at the working potential of -50 mV. The variations of glucose, glutamate, and choline were determined simultaneously in a free moving rat when we perfused the medial frontal cortex with 100 micro mol/L N-methyl-D-aspartate (NMDA) solution, which is the agonist of the NMDA receptor.