Some remarks on projectively flat complex Finsler metrics

In this paper, we hall discuss the projective flatness of complex Finsler metrics by investigating the geometry of projective bundles associated with a holomorphic vector bundle.     

Determination of trace moisture in hydrogen chloride gas by Karl Fischer titration

Moisture of several ppm in hydrogen chloride gas has been accurately determined by a new method using the Karl Fischer reagent, which hitherto had a limitation in accuracy because of a partial reaction with hydrogen chloride when direct titration was employed.The moisture in the sample gas was collected in a cold trap kept at about ?80 °C while the hydrogen chloride gas passed through and the frozen moisture was dissolved by pyridine-methanol (1:1) solvent. a KF Reagent of factoe: 0.35 mg H₂O/ml.Titration by the Karl Fischer reagent having the equivalency factor of, e.g., 0.5 mg H₂O/ml was carried out and the concentration of the moisture was calculated from the sample volume used.     

The structures of macbecin I and II : New antitumor antibiotics

Macbecin I 1, C₃₀H₄₂N₂O₈, and macbecin II 2, C₃₀H₄₄N₂O₈, were shown to be 2,6-disubstituted benzoquinone and hydroquinone derivatives by an oxidation-reduction relationship, UV. ¹H and ¹³C NMR spectra. Alkaline methanolysis of 1 gave a 2-aminobenzoquinone derivative 5, suggesting an ansa-structure for 1, and acid hydrolysis of 1 gave decarbamoyl products 9,10 and 11, indicative of the location of carbamoyloxy group in allylic position. Spin decoupling studies on 1,3 and 5clarified the partial structures [A], [B], [C] and [D]. From their mutual disposition two structures 1a and 1b, were proposed out of which 1a has been selected for the structure of 1 on the basis of the structure of oxidative degradation product 12. X-Ray analysis of the bromoacetyl derivative of 1 confirmed the above proposed structure and determined the absolute stereochemistry of 1 and 2.     

Low-lying states in112In

Low-lying states below 500 keV excitation in¹¹²In have been investigated via the¹¹²Cd(p, nγ) reaction. New levels have been established atE ^x=206.5keV and 456.1 keV from the measuredγ-ray excitation functions,γ?γ coincidences and the precision measurements of the (p, n) threshold energy of the ground state and of the 206.5 keV state of¹¹²In. Spins and parities of the 206.5 keV state (2⁺) and the 456.1 keV state (3⁺) and multipolarities and mixing ratios of the deexcitationγ-rays have been determined from the angular distributions and linear polarizations of the deexcitation γ-rays as well as the excitation functions of the residual levels. Possible configurations of the newly-found levels are discussed. Half-lives of two states have been remeasured:T _1/2=15.2±0.1 min for the ground state andT _1/2=20.9±0.1 min for the 156.4 keV (4⁺) state. The ground stateQ-value for the¹¹²Cd(p, n)¹¹² In reaction has been measured to be ?3.376±0.006 MeV.     

Pricing Lookback Options with Knock‐out Boundaries

In the last decade, many kinds of exotic options have been traded and introduced in the financial market. This paper describes a new kind of exotic option, lookback options with knock‐out boundaries. These options are knock‐out options whose pay‐offs depend on the extrema of a given securities price over a certain period of time. Closed form expressions for the price of seven kinds of lookback options with knock‐out boundaries are obtained in this article. The numerical studies have also been presented.