多集值信息表中的多粒度模糊决策论粗糙集

多粒度粗糙集和决策论粗糙集是Pawlak粗糙集的重要推广,目前已成为人工智能研究的热点.然而,它们大多处理的都是单值信息系统中的问题.而实际生活中绝大多数都是处理多值问题,为了解决这一问题,在多集值信息表中将多粒粗糙集与模糊决策论粗糙集相结合进行研究,提出了其在乐观,悲观情形下的上下近似,研究了一些相关性质并给出了多集值信息表中的多粒度模糊决策论粗糙集精度、粗度的概念,最后通过一个具体例子验证其有效性.     

Mechanics of atoms interacting with a carbon nanotorus: optimal configuration and oscillation behaviour

In this paper, we investigate a carbon nanotorus as a caged molecular structure interacting with an atom. Assuming that the atom is located along the central axis perpendicular to the torus, the interaction energy of the system is determined using the continuum approximation together with the Lennard-Jones potential. This approach avoids the intensive computational calculations that are involved in other modelling approaches. Numerical results are presented in terms of dimensionless variables. The results show that the optimal major radius of the torus has a linear relationship with its minor radius when the atom is symmetrically situated along the torus axis. When the atom is offset from this axis, the minimum energy location shifts away from the centre as the ratio of the major and minor radii exceeds the value of 0.90. Finally, the oscillatory behaviour for the carbon atom is investigated. Our findings predict a novel nano-oscillator which can produce frequencies in the gigahertz range.     

类氖氩离子能级及碰撞强度的计算

利用扭曲波波恩近似方法及AUTOSTRUCTURE (AS)程序，快速精确地计算了类氖Ar8+离子2s22p6、2s22p53s、2s22p53p、2s22p53d、2s2p63s、2s2p63p和2s2p63d组态的能级以及当电子碰撞能量为75.0、125.0、175.0、250.0 (Ry)时，从j能态到i能态的碰撞强度.并且与已有的研究成果进行了对比.结果表明，采用扭曲波波恩近似并结合AUTOSTRUCTURE (AS)程序的研究方法，可以成为研究原子或离子碰撞强度的有效途径。     

A higher resolution edge‐based finite volume method for the simulation of the oil–water displacement in heterogeneous and anisotropic porous media using a modified IMPES method

In this article, we present a higher‐order finite volume method with a ‘Modified Implicit Pressure Explicit Saturation’ (MIMPES) formulation to model the 2D incompressible and immiscible two‐phase flow of oil and water in heterogeneous and anisotropic porous media. We used a median‐dual vertex‐centered finite volume method with an edge‐based data structure to discretize both, the elliptic pressure and the hyperbolic saturation equations. In the classical IMPES approach, first, the pressure equation is solved implicitly from an initial saturation distribution; then, the velocity field is computed explicitly from the pressure field, and finally, the saturation equation is solved explicitly. This saturation field is then used to re‐compute the pressure field, and the process follows until the end of the simulation is reached. Because of the explicit solution of the saturation equation, severe time restrictions are imposed on the simulation. In order to circumvent this problem, an edge‐based implementation of the MIMPES method of Hurtado and co‐workers was developed. In the MIMPES approach, the pressure equation is solved, and the velocity field is computed less frequently than the saturation field, using the fact that, usually, the velocity field varies slowly throughout the simulation. The solution of the pressure equation is performed using a modification of Crumpton's two‐step approach, which was designed to handle material discontinuity properly. The saturation equation is solved explicitly using an edge‐based implementation of a modified second‐order monotonic upstream scheme for conservation laws type method. Some examples are presented in order to validate the proposed formulation. Our results match quite well with others found in literature. Copyright © 2016 John Wiley & Sons, Ltd.     

On log-normal convolutions: An analytical–numerical method with applications to economic capital determination

We put forward an efficient algorithm for approximating the sums of independent and log-normally distributed random variables. Namely, by combining tools from probability theory and numerical analysis, we are able to compute the cumulative distribution functions of the just-mentioned sums to a high precision and in a relatively short computing time. We illustrate the effectiveness of the new method in the contexts of the individual and collective risk models, aggregate economic capital determination, and economic capital allocation.     

Multistrain edge‐based compartmental model on networks

Multistrain diseases, which are infected through individual contacts, pose severe public health threat nowadays. In this paper, we build competitive and mutative two‐strain edge‐based compartmental models using probability generation function (PGF) and pair approximation (PA). Both of them are ordinary differential equations. Their basic reproduction numbers and final size formulas are explicitly derived. We show that the formula gives a unique positive final epidemic size when the reproduction number is larger than unity. We further consider competitive and mutative multistrain diseases spreading models and compute their basic reproduction numbers. We perform numerical simulations that show some dynamical properties of the competitive and mutative two‐strain models.