Derived Picard Groups of Finite-Dimensional Hereditary Algebras

Let A be a finite-dimensional algebra over a field k. The derived Picard group DPic _k (A) is the group of triangle auto-equivalences of D> ^b( mod A) induced by two-sided tilting complexes. We study the group DPic _k (A) when A is hereditary and k is algebraically closed. We obtain general results on the structure of DPic _k , as well as explicit calculations for many cases, including all finite and tame representation types. Our method is to construct a representation of DPic _k (A) on a certain infinite quiver ^irr. This representation is faithful when the quiver of A is a tree, and then DPic _k (A) is discrete. Otherwise a connected linear algebraic group can occur as a factor of DPic _k (A). When A is hereditary, DPic _k (A) coincides with the full group of k-linear triangle auto-equivalences of D^b( mod A). Hence, we can calculate the group of such auto-equivalences for any triangulated category D equivalent to D^b( mod A. These include the derived categories of piecewise hereditary algebras, and of certain noncommutative spaces introduced by Kontsevich and Rosenberg.     

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 .

     

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.     

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.     

Theoretical studies on magnetic interactions between Cu(II) ions in hydroxypyridone nucleobases

The origin of a ferromagnetic interaction between Cu²⁺ ions in the Cu²⁺–DNA system which reported by Tanaka et al. is examined by using DFT calculations. In order to consider effects of an entanglement and a dis-entanglement of the double helix chain, three types of structural disorders i.e. distance, rotation angle and discrepancy in XY-plane, are considered in the model dimer structure. All calculated results show that J_ab values are weak anti-ferromagnetic couplings. Boltzmann distribution simulation indicates that the high spin (HS) species exist 21% at 1.5 K by thermal excitation within the model structure.     

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.     

Electrochemical properties of Li symmetric solid-state cell with NASICON-type solid electrolyte and electrodes

All-solid-state phosphate symmetric cells using Li₃V₂(PO₄)₃ for both the positive and negative electrodes with the phosphate Li_1.5Al_0.5Ge_1.5(PO₄)₃ as the solid electrolyte were proposed. Amorphous Li_1.5Al_0.5Ge_1.5(PO₄)₃ was added into the electrode to increase the interface area between the active materials and the electrolyte. Any other phases were not formed at the electrode/electrolyte interface even after hot pressing at 600 °C. The discharge capacity was 92 mAh g^? 1 at 22 µA cm^? 2 at 80 °C, and 38 mAh g^? 1 at 25 °C, respectively. Symmetric cell configuration leads to simplify the fabrication process for all-solid-state batteries and will reduce manufacturing costs.