Injective resolutions of Noetherian rings and cogenerators

We give new construction of injective resolutions of complexes and bimodules. Applying this construction to an injective resolution of a Noetherian ring, we construct a -embedding cogenerator for the category of modules of projective dimension . Moreover, for a Noetherian projective -algebra , we show that satisfies the Auslander condition if and only if the flat dimension of every -module is equal to or larger than the one of the injective hull .

     

Bottom-up fabrication and piezoelectric properties of CaBi<Subscript>4</Subscript>Ti<Subscript>4</Subscript>O<Subscript>15</Subscript> micro-plateaus

CaBi₄Ti₄O₁₅ (CBTi144) micro-plateaus were fabricated on Si wafers and Pt foils using a self-assembled monolayer (SAM) and a complex metal alkoxide solution. The micro-plateaus are delineated by metal masks, which are used for shadowing against the ultraviolet (UV) irradiation for decomposition of SAM to make the surface hydrophilic. The micro-plateaus crystallized to a ferroelectric phase with random orientation. The crystallization depended on the SAM-derived ultra thin layers at the surface of the substrates. The primitive PFM measurements without any top electrodes confirmed that the micro-plateaus exhibited the piezoresponse behaviors. The piezoelectric constant, d₃₃, had some distribution, and the maximum d₃₃ was confirmed as about 45 pm/V, which is identical to the d₃₃ of the polar-axis oriented CBTi144 thin films. PACS 77.84.-s; 81.20.Fw; 77.65.-j     

Fluctuations in time intervals of financial data from the view point of the Gini index

We propose an approach to explain fluctuations in time intervals of financial markets data from the view-point of the Gini index. We show the explicit form of the Gini index for a Weibull distribution: A good candidate to describe the first passage time of foreign exchange rate. The analytical expression of the Gini index compares well with the value obtained from empirical data.     

Correlation of coming limit price with order book in stock markets

We examine the correlation of the limit price with the order book, when a limit order comes. We analyzed the Rebuild Order Book of Stock Exchange Electronic Trading Service, which is the centralized order book market of London Stock Exchange. As a result, the limit price is broadly distributed around the best price according to a power-law, and it is not randomly drawn from the distribution, but has a strong correlation with the size of cumulative unexecuted limit orders on the price. It was also found that the limit price, on the coarse-grained price scale, tends to gather around the price which has a large size of cumulative unexecuted limit orders.     

A study on the reaction between chlorine trifluoride gas and glass-like carbon

The reaction between glass-like carbon (GC) and chlorine trifluoride (ClF₃) gas was investigated with weight measurements, surface analysis, and gas desorption measurements, where the ClF₃ gas is used for the in situ cleaning of tubes in silicon-related fabrication equipment. From Auger electron spectroscopy and X-ray photoelectron spectroscopy measurements, a carbon mono-fluoride, –(CF)_n–, film near the surface of GC is considered to be grown onto the GC surface above 400 °C by the chemical reaction with ClF₃, and this thickness of the fluoride film depends on the temperature. The grown fluoride film desorbs by annealing in a vacuum up to 600 °C. Although GC is apparently etched by ClF₃ over 600 °C, the etch rate of GC is much lower than that of SiC and quartz.     

Stereoselective synthesis of trans olefins by the reaction of Wittig reagents with selenium. Formation of selenocarbonyl compounds.

Wittig reagents were successfully changed to symmetrical olefins when treated with elemental selenium. The reaction proceeds through a selenocarbonyl intermediate, which existence was confirmed by Diels-Alder reaction.     

The reaction of 1-silylcyclopropyl anions with dichloromethyl methyl ether: the efficient synthesis of cyclopropyl silyl ketones via cyclopropylidene derivatives

The reaction of 1-silylcyclopropyl anions with dichloromethyl methyl ether is described. The reaction with an excess amount of dichloromethyl methyl ether gives the corresponding cyclopropyl silyl ketones in low yields. On the other hand, the reaction under basic conditions proceeded smoothly to afford the corresponding cyclopropylidene derivatives, exclusively. The resulting cyclopropylidene compounds are subjected to hydrolysis or trapping with electrophiles easily to give the cyclopropyl silyl ketone derivatives in good yields.     

Effect of industrial water components on thermal stability of nitrocellulose

In order to prevent the spontaneous ignition of nitrocellulose (NC), NC is stabilized by washing with industrial water in its synthesis process. However, there is a possibility that the components in industrial water contribute to the thermal stability of NC. In this way, the purpose of this study is to clarify the effect of industrial water components on the thermal stability of NC. In experiments, a heat flux calorimeter was used to observe the thermal behavior of NC with the residue of vaporized industrial water. The induction period of heat release of NC with 2-mass% residues was approximately 2–5 h shorter than that of NC alone whose induction period was observed at 7 h. Those results indicate that the residue destabilized NC. On the other hand, when the additive amount of the residue was increased, the induction period gradually increased as well. Based upon these results, we assume that inorganic salts contributing to stabilization and destabilization competitively coexist in the industrial water components. The same thermal analysis was performed on NC with CaCO₃, CaSO₄, CaCl, ZnSO₄, NaCl, and CuCl. Those salts are predicted to exist in the industrial water. In the results, the induction period of NC with 2-mass% CaCO₃ was approximately 15-h longer than that of NC alone, while the induction period with the inorganic salts CaSO₄, CaCl, ZnSO₄, NaCl, and CuCl was 4–5-h shorter. Therefore, when the industrial water components accumulate in NC, the destabilization by inorganic salts such as CaSO₄, CaCl, ZnSO₄, NaCl, and CuCl and the stabilization by compounds such as CaCO₃ are thought to countervail against each other.