We determine the encapsulation of a chloroform molecule into a D,L-Ala cyclopeptide nanotube by investigating the interaction energy between the two molecular structures. We employ the Lennard-Jones potential and a co...We determine the encapsulation of a chloroform molecule into a D,L-Ala cyclopeptide nanotube by investigating the interaction energy between the two molecular structures. We employ the Lennard-Jones potential and a continuum approach which assumes that the atoms are evenly distributed over the molecules providing average atomic densities. Our result demonstrates that the encapsulation depends on the size of the molecule and the internal diameter of the peptide nantube. In particular, the on-axis chloroform molecule is only accepted into a peptide nanotube whose internal radius is greater than 5 ?. If located near the edge of the nanotube, then it is unlikely that the chloroform molecule will enter the nanotube. This is due to the energy valley that the molecule will need to overcome to move past the edge into the open end of the nanotube.展开更多
This article addresses the problem of pricing European options when the underlying asset is not perfectly liquid.A liquidity discounting factor as a function of market-wide liquidity governed by a mean-reverting stoch...This article addresses the problem of pricing European options when the underlying asset is not perfectly liquid.A liquidity discounting factor as a function of market-wide liquidity governed by a mean-reverting stochastic process and the sensitivity of the underlying price to market-wide liquidity is firstly introduced,so that the impact of liquidity on the underlying asset can be captured by the option pricing model.The characteristic function is analytically worked out using the Feynman–Kac theorem and a closed-form pricing formula for European options is successfully derived thereafter.Through numerical experiments,the accuracy of the newly derived formula is verified,and the significance of incorporating liquidity risk into option pricing is demonstrated.展开更多
In this paper, we explore some issues related to adopting the Adomian decomposition method （ADM） to solve partial differential equations （PDEs）, particularly linear diffusion equations. Through a proposition, we s...In this paper, we explore some issues related to adopting the Adomian decomposition method （ADM） to solve partial differential equations （PDEs）, particularly linear diffusion equations. Through a proposition, we show that extending the ADM from ODEs to PDEs poses some strong requirements on the initial and boundary conditions, which quite often are violated for problems encountered in engineering, physics and applied mathematics. We then propose a modified approach, based on combining the ADM with the Fourier series decomposition, to provide solutions for those problems when these conditions are not met. In passing, we shall also present an argument that would address a long-term standing ＂pitfall＂ of the original ADM and make this powerful approach much more rigorous in its setup. Numerical examples are provided to show that our modified approach can be used to solve any linear diffusion equation （homogeneous or non-homogeneous）, with reasonable smoothness of the initial and boundary data.展开更多
In this paper, we establish a global regularity result for the optimal transport problem with the quadratic cost, where the domains may not be convex. This result is obtained by a perturbation argument,using a recent ...In this paper, we establish a global regularity result for the optimal transport problem with the quadratic cost, where the domains may not be convex. This result is obtained by a perturbation argument,using a recent global regularity of optimal transportation in convex domains by the authors.展开更多
A standard assumption when modelling linked sample data is that the stochastic properties of the linking process and process underpinning the population values of the response variable are independent of one another.T...A standard assumption when modelling linked sample data is that the stochastic properties of the linking process and process underpinning the population values of the response variable are independent of one another.This is often referred to as non-informative linkage.But what if linkage errors are informative?In this paper,we provide results from two simulation experiments that explore two potential informative linking scenarios.The first is where the choice of sample record to link is dependent on the response;and the second is where the probability of correct linkage is dependent on the response.We focus on the important and widely applicable problem of estimation of domain means given linked data,and provide empirical evidence that while standard domain estimation methods can be substantially biased in the presence of informative linkage errors,an alternative estimation method,based on a Gaussian approximation to a maximum likelihood estimator that allows for non-informative linkage error,performs well.展开更多
文摘We determine the encapsulation of a chloroform molecule into a D,L-Ala cyclopeptide nanotube by investigating the interaction energy between the two molecular structures. We employ the Lennard-Jones potential and a continuum approach which assumes that the atoms are evenly distributed over the molecules providing average atomic densities. Our result demonstrates that the encapsulation depends on the size of the molecule and the internal diameter of the peptide nantube. In particular, the on-axis chloroform molecule is only accepted into a peptide nanotube whose internal radius is greater than 5 ?. If located near the edge of the nanotube, then it is unlikely that the chloroform molecule will enter the nanotube. This is due to the energy valley that the molecule will need to overcome to move past the edge into the open end of the nanotube.
基金support for a three-year project funded by the ARC(Australian Research Council funding scheme DP170101227)with which first author’s visiting fellowship was provided for his visit to UoW between Jan 2019 and Dec 2019+1 种基金support provided by the National Natural Science Foundation of China(No.12101554)the Fundamental Research Funds for Zhejiang Provincial Universities(No.GB202103001).
文摘This article addresses the problem of pricing European options when the underlying asset is not perfectly liquid.A liquidity discounting factor as a function of market-wide liquidity governed by a mean-reverting stochastic process and the sensitivity of the underlying price to market-wide liquidity is firstly introduced,so that the impact of liquidity on the underlying asset can be captured by the option pricing model.The characteristic function is analytically worked out using the Feynman–Kac theorem and a closed-form pricing formula for European options is successfully derived thereafter.Through numerical experiments,the accuracy of the newly derived formula is verified,and the significance of incorporating liquidity risk into option pricing is demonstrated.
文摘In this paper, we explore some issues related to adopting the Adomian decomposition method （ADM） to solve partial differential equations （PDEs）, particularly linear diffusion equations. Through a proposition, we show that extending the ADM from ODEs to PDEs poses some strong requirements on the initial and boundary conditions, which quite often are violated for problems encountered in engineering, physics and applied mathematics. We then propose a modified approach, based on combining the ADM with the Fourier series decomposition, to provide solutions for those problems when these conditions are not met. In passing, we shall also present an argument that would address a long-term standing ＂pitfall＂ of the original ADM and make this powerful approach much more rigorous in its setup. Numerical examples are provided to show that our modified approach can be used to solve any linear diffusion equation （homogeneous or non-homogeneous）, with reasonable smoothness of the initial and boundary data.
基金supported by Australian Research Council (Grant Nos. FL130100118 and DP170100929)
文摘In this paper, we establish a global regularity result for the optimal transport problem with the quadratic cost, where the domains may not be convex. This result is obtained by a perturbation argument,using a recent global regularity of optimal transportation in convex domains by the authors.
文摘A standard assumption when modelling linked sample data is that the stochastic properties of the linking process and process underpinning the population values of the response variable are independent of one another.This is often referred to as non-informative linkage.But what if linkage errors are informative?In this paper,we provide results from two simulation experiments that explore two potential informative linking scenarios.The first is where the choice of sample record to link is dependent on the response;and the second is where the probability of correct linkage is dependent on the response.We focus on the important and widely applicable problem of estimation of domain means given linked data,and provide empirical evidence that while standard domain estimation methods can be substantially biased in the presence of informative linkage errors,an alternative estimation method,based on a Gaussian approximation to a maximum likelihood estimator that allows for non-informative linkage error,performs well.
