A construction of fractal surfaces with function scaling factors on a rectangular grid

A fractal surface is a set which is a graph of a bivariate continuous function. In the construction of fractal surfaces using IFS, vertical scaling factors in IFS are important one which characterizes a fractal feature of surfaces constructed. We construct IFS with function vertical scaling factors which are 0 on the boundaries of a rectangular grid using arbitrary data set on a rectangular grid and give a condition for an attractor of the IFS constructed being a surface. Finally, lower and upper bounds of Box-counting dimension of the constructed surface are estimated.Comment: 9 pages, 2 figure

Construction of Fractal Surfaces by Recurrent Fractal Interpolation Curves

A method to construct fractal surfaces by recurrent fractal curves is provided. First we construct fractal interpolation curves using a recurrent iterated functions system(RIFS) with function scaling factors and estimate their box-counting dimension. Then we present a method of construction of wider class of fractal surfaces by fractal curves and Lipschitz functions and calculate the box-counting dimension of the constructed surfaces. Finally, we combine both methods to have more flexible constructions of fractal surfaces.Comment: 14 pages, 2 figure

Scattering of a Single Plasmon by Three Non-equally Spaced Quantum Dots System Coupled to One-Dimensional Waveguide

Scattering properties of a single plasm on interacting with three non-equally spaced quantum dots coupled to one-dimensional surface plasmonic waveguide is investigated theoretically via the real-space approach. It is demonstrated that the transmission and reflection of a single plasmon can be switched on or off by controlling the detuning and changing the interparticle distances between the quantum dots. By controlling the transition frequencies and interparticle distances of QDs, one can construct a half-transmitting mirror with three QDs system. We also showed that controlling the transition frequencies and interparticle distances of QDs results in the complete transmission peak near the zero detuning

The Pricing of Multiple-Expiry Exotics

In this paper we extend Buchen's method to develop a new technique for pricing of some exotic options with several expiry dates(more than 3 expiry dates) using a concept of higher order binary option. At first we introduce the concept of higher order binary option and then provide the pricing formulae of $n$-th order binaries using PDE method. After that, we apply them to pricing of some multiple-expiry exotic options such as Bermudan option, multi time extendable option, multi shout option and etc. Here, when calculating the price of concrete multiple-expiry exotic options, we do not try to get the formal solution to corresponding initial-boundary problem of the Black-Scholes equation, but explain how to express the expiry payoffs of the exotic options as a combination of the payoffs of some class of higher order binary options. Once the expiry payoffs are expressed as a linear combination of the payoffs of some class of higher order binary options, in order to avoid arbitrage, the exotic option prices are obtained by static replication with respect to this family of higher order binaries.Comment: 16 pages, 3 figures, Ver. 1 was presented in the 1st International Conference of Pyongyang University of Science & Technology, 5~6, Oct, 2011, in ver. 2 added proof, in ver. 3 revised and added some detail of proofs, Ver. 4,5: latex version, Ver. 6~8: corrected typos in EJMAA Vol.1(2)2013,247-25

Using Pi-calculus to Model Dynamic Web Services Composition Based on the Authority Model

There are lots of research works on web service, composition, modeling, verification and other problems. Theses research works are done on the basis of formal methods, such as petri-net, pi-calculus, automata theory, and so on. Pi-calculus is a natural vehicle to model mobility aspect in dynamic web services composition (DWSC). However, it has recently been shown that pi-calculus needs to be extended suitably to specify and verify DWSC. In this paper, we considers the authority model for DWSC, extends pi-calculus in order to model dynamic attributes of system, and proposes a automatic method for modeling DWSC based on extended pi-calculus.Comment: 11 pages, 3 figure

The effect of Magnetic Field on Spin Injection of DMS/FM Heterostructure

We discuss spin injection efficiency as a function of Fermi energy in DMS/FM heterostructures by spin injection efficiency equation and Landauer formula. The higher electric field, the stronger spin injection efficiency, and its velocity of increase gets lower and approaches to the equilibrium state. Additionally, the higher is interface conductivity, the weaker is spin injection efficiency, and the transmission as a function of Fermi energy for spin up and spin down is different from each other. This result causes the effect of the exchange interaction term in DMS. Finally, according to the investigation of spin injection efficiency as a function of the magnetic field in the same structure, the spin injection efficiency vibrates sensitively with the magnetic field. This result allows us to expect the possibility of spintronic devices with high sensitivity to magnetic field

A generalized scheme for BSDEs based on derivative approximation and its error estimates

In this paper we propose a generalized numerical scheme for backward stochastic differential equations(BSDEs). The scheme is based on approximation of derivatives via Lagrange interpolation. By changing the distribution of sample points used for interpolation, one can get various numerical schemes with different stability and convergence order. We present a condition for the distribution of sample points to guarantee the convergence of the scheme.Comment: 11 pages, 1 table. arXiv admin note: text overlap with arXiv:1808.0156

Numerical analysis for a unified 2 factor model of structural and reduced form types for corporate bonds with fixed discrete coupon

Conditions of Stability for explicit finite difference scheme and some results of numerical analysis for a unified 2 factor model of structural and reduced form types for corporate bonds with fixed discrete coupon are provided. It seems to be difficult to get solution formula for PDE model which generalizes Agliardi's structural model [1] for discrete coupon bonds into a unified 2 factor model of structural and reduced form types and we study a numerical analysis for it by explicit finite difference scheme. These equations are parabolic equations with 3 variables and they include mixed derivatives, so the explicit finite difference scheme is not stable in general. We find conditions for the explicit finite difference scheme to be stable, in the case that it is stable, numerically compute the price of the bond and analyze its credit spread and duration.Comment: 15 pages, 12 figure

A Numerical Scheme For High-dimensional Backward Stochastic Differential Equation Based On Modified Multi-level Picard Iteration

In this paper, we propose a new kind of numerical scheme for high-dimensional backward stochastic differential equations based on modified multi-level Picard iteration. The proposed scheme is very similar to the original multi-level Picard iteration but it differs on underlying Monte-Carlo sample generation and enables an improvement in the sense of complexity. We prove the explicit error estimates for the case where the generator does not depend on control variate

A Condition for Hopf bifurcation to occur in Equations of Lotka - Volterra Type with Delay

It is known that Lotka - Volterra type differential equations with delays or distributed delays have an important role in modeling ecological systems. In this paper we study the effects of distributed delay on the dynamics of the harvested one predator - two prey model. Using the expectation of the distribution of the delay as a bifurcation parameter, we show that the equilibrium that was asymptotic stable becomes unstable and Hopf bifurcation can occur as the expectation crosses some critical values.Comment: 9 pages, in ver 2 added references and conclusion and further study, version 2 is accepted in JTP