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

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

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

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

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

Stochastic Gronwall's inequality in random time horizon and its application to BSDE

In this paper, we introduce and prove a stochastic Gronwall's inequality in (unbounded) random time horizon. As an application, we prove a comparison theorem for backward stochastic differential equation (BSDE for short) with random terminal time under stochastic monotonicity condition

Existence and Solution-representation of IVP for LFDE with Generalized Riemann-Liouville fractional derivatives and nn terms

This paper provides the existence and representation of solution to an initial value problem for the general multi-term linear fractional differential equation with generalized Riemann-Liouville fractional derivatives and constant coefficients by using operational calculus of Mikusinski's type. We prove that the initial value problem has the solution of if and only if some initial values should be zero.Comment: 15 pages, ver 5 corrected 4 typos in ver 4; this version to appear in FCAA Vol.17, No.1, 2014 with the title "Operation Method for Solving Multi-Term Fractional Differential Equations with the Generalized Fractional Derivatives

Suppression of DC term in Fresnel digital holography by sequence subtraction of holograms

An experimental method for suppression of DC term in the reconstructed images from Fresnel digital holograms is presented. In this method, two holograms for the same object are captured sequentially and subtracted. Since these two holograms are captured at different moments, they are slightly different from each other for fluctuations of noises. The DC term is suppressed in the image reconstructed from the subtraction hologram, while the two virtual and real images are successfully reconstructed. This method can be potentially used for the improvement of image quality reconstructed from Fresnel digital holograms