We develop a Legendre quadrilateral spectral element approximation for the Black-Scholes equation to price European options
with two underlying assets. A weak formulation of the equations imposes the boundary conditions naturally along the boundaries
where the equation becomes singular. As examples, we apply the method to price European rainbow and basket options. We compare
the efficiency for fully implicit and IMEX integration of the equations in time, three iterative solvers and two diagonal
preconditioners. Of the choices, we find that GMRES with a fully implicit approximation in time, preconditioned with the mass
matrix is the most efficient. 相似文献
The two-layer and multi-layer Cr/CrxN coatings were fabricated on 316 L stainless steel (316 L SS) substrates by the arc ion plating technique. The two-layer Cr/CrxN coating was a typical CrN coating with an adhesive Cr layer. And the multi-layer Cr/CrxN coating design was in two dimensions. In the first dimension, the multi-layer Cr/CrxN coating consisted of alternative Cr/CrN layers with the thickness ratio of 1:5; in the second dimension, the alternative Cr2N layers with the thickness of 10 nm were inserted in CrN layers. This design was expected to increase transverse interfaces in a smaller scale. The microstructures, mechanical, corrosion and tribocorrosion performances of both Cr/CrxN coatings were systematically investigated. The results showed that the special multi-layer design of Cr/CrxN coatings improved mechanical, anti-corrosion and anti-tribocorrosion performances. Compared with the two-layer Cr/CrxN coating, the reduced tribocorrosion damage of the muti-layer Cr/CrxN coating was closely related to the inhibited synergistic effect between electrochemical corrosion and mechanical wear. In conclusion, the multi-layer Cr/CrxN coating was more suitable to work as the surface protective coating than the two-layer Cr/CrxN coating in seawater. 相似文献
Practical assessment of subgrade settlement induced by train operation requires developing suitable models capable of describing permanent deformation characteristics of subgrade filling under repeated dynamic loading. In this paper, repeated load triaxial tests were performed on coarse-grained soil (CGS), and the axial permanent strain of CGS under different confining pressures and dynamic stress amplitudes was analysed. Permanent deformation behaviors of CGS were categorized based on the variation trend of permanent strain rate with accumulated permanent strain and the shakedown theory. A prediction model of permanent deformation considering stress state and number of load cycles was established, and the ranges of parameters for different types of dynamic behaviors were also divided. The results indicated that the variational trend of permanent strain rate with accumulated permanent strain can be used as a basis for classifying dynamic behaviors of CGS. The stress state (confining pressure and dynamic stress amplitude) has significant effects on the permanent strain rate. The accumulative characteristics of permanent deformation of CGS with the number of load cycles can be described by a power function, and the model parameters can reflect the influence of confining pressure and dynamic stress amplitude. The study’s results could help deepen understanding of the permanent deformation characteristics of CGS.
Thermodynamic equilibrium calculations were performed to reveal effects of interactions among Cl, S, P and other minerals on Cu migration. Our results showed that HCl(g), SO2(g) and (P2O5)2(g) were released from the sewage sludge co-incineration. Cl was found to weaken adsorption of Cu by Al2O3, CaO and Fe2O3, while S delayed reactions of Fe2O3 and Al2O3 with Cu, with P having no effect on reactions between the minerals and Cu. Among the coupled systems of Cl, S and P, the co-existences of Cl and S, and Cl, S and P were determined to inhibit Cu volatilization, and the co-existence of Cl and P had an enhancing effect. Cu migration was affected only by S in the S and P system. With the SiO2, CaO and Al2O3 system, both Cl alone and Cl and P led to failed reactions between the minerals and Cu. In the systems of S, S and Cl, S and P, and S, Cl and P, the migration behavior of Cu was mainly affected by S at low temperatures and by Cl at high temperatures, whereas P had no effect on Cu migration during the entire process. 相似文献
Employing the coherent state ansatz and the time-dependent variational principle, we obtain a partial differential equation of motion from Hamiltonian in inharmonic molecuIar crystals. By using the method of multiple scales. we reduce this equation into the envelope function and find that the amplitude function satisfied a nonlinear Schrodinger equation. Introducing the inverse scattering transformation, we gain the single-, twry and N- soliton solutions. The energy and the spatial configurations of the system are given. We also acquire the periodic wave solution and analyze its stability. 相似文献