This paper deals with pricing formulae for a European call option and an exchange option in the case where underlying asset price processes are represented by stochastic delay differential equations with jumps (hereafter “SDDEJ”). We introduce a new model in which Poisson jumps are added in stochastic delay differential equations to capture behaviors of an underlying asset process more precisely. We derive explicit pricing formulae for the European call option and the exchange option by proving a Lemma on the conditional expectation. Finally, we show that our “SDDEJ” model is meaningful through some numerical experiments and discussions.

Thick coatings of tetrahedral amorphous carbon (ta-C) have great existing and potential commercial importance for components such as automobile accessories. We confirmed the feasibility of depositing thick ta-C coating on Si wafer, WC, stainless steel (STS), and Al alloy substrates by a home-made filtered cathode vacuum arc. A ta-C coating of 800 nm thickness was successfully deposited over 20 min continuous coating. Interestingly, coatings with thicknesses exceeding 1 μm were easily delaminated by thermal and internal stress effects when the coating time exceeded 20 min. Varying the bias (0 V ↔ 500 V) was highly effective in controlling the internal stress relaxation of the ta-C. This method showed significant improvements in the stress relaxation of the ta-C coatings. By applying multicycle coating, the thickness and hardness of the ta-C coating could reach 9.3 μm and 45 GPa, respectively, at a coating speed of 3.0 μm/h on a fixed substrate.

Ti-Si-N nanocomposite coatings have been investigated using a hybrid coating system. The elimination of macro particles and the control of Si content should be accompanied to realize high quality of coating layer since macro particles induce corrosive reaction and the Si content of Ti-Si-N coating affects the mechanical properties such as hardness and friction coefficient. We introduced the hybrid coating system which consists of double bending filtered vacuum arc system (DBFVAS) and magnetron sputter cathode to solve two problems such as the macro particles and the control of Si content in Ti-Si-N coatings. The DBFVAS and magnetron sputter equipped with Ti cathode and Si cathode target, respectively. Ar and N2 are used for discharge and reaction gas and operating pressure is 0.6 mTorr. We confirmed that the DBFVAS reduced macro particles effectively and the Si content could be changed by controlling the applied power on magnetron sputtering cathode. The properties of Ti-Si-N coating layer are estimated by X-ray diffraction, X-ray photoelectron spectroscopy, wear test and nano indentation. And we compared Si content with Si emission (594.84 nm) of process chamber using an optical emission spectroscopy.

Nb-doped Bi4Ti3O12 (Nb-BIT) ferroelectric thin films were prepared in the presence of a nonionic surfactant (pluronic P123) added as an additive to the sol solution and by rapid thermal annealing (RTA). The film annealed at the relatively low temperature of 600 °C was well crystallized and showed good ferroelectricity. The switching charge of capacitors with polarization reversal rapidly increased with a large amplitude and low frequency of the applied pulse, and gradually decreased with a small amplitude and high frequency. The remanent polarization (2Pr) after subjecting the Nb-BIT capacitors to 108 read/write cycles was 46 μC/cm2, which is remarkably higher than 20 μC/cm2 observed in the initial state. These phenomena seem to appear by the presence of space charges trapped after heat treatment by the RTA process.

The photocatalytic properties of TiO2 rutile powder with acicular primary particles were characterized using the photocatalytic reaction in aqueous 4-chlorophenol (4CP) solution and compared to those of TiO2 anatase with almost the same surface area of approximately 200 m2g. The characteristics of commercial P-25 TiO2 powders with the surface area of approximately 55 m2/g were also compared to rutile and anatase powders. The rutile phase powders surpassed both anatase and P-25 ones in decomposition rate for 4CP. The excellent photo-oxidative ability of the powder was dependent on the specific powder-preparation method, which led to a direct crystallization in aqueous solution, regardless of the crystalline structures of the powders.