Modeling sexual transmission of HIV/AIDS in Jiangsu province,China

HIV transmission by sexual activities exhibits a substantial increase and has become a primary transmission mode in China recently. A mathematical model is formulated so as to identify the key processes and parameters that could explain the quick increase in the proportion of heterosexual transmission and further to assist in suggesting control measures urgently. On the basis of surveillance data on a number of people living with HIV/AIDS in Jiangsu province, we parameterize the model and estimate the reproduction number by using the least squares method. The basic reproduction number was estimated to be R₀ = 3.52 for the therapy scenario of heterosexual transmission. The model predicts that the epidemic will peak in 2020. New infections are sensitive to the transmission coefficient, dependent on condom use rate, and the risky activities during the early period, whereas are sensitive to the recruitment rate in the late period of the transmission respectively. Antiviral therapy can either increase or decrease the new infections depending on both the extended life span of treated individuals and the infectiousness of the treated individuals. Hence, effective control measures during different transmission periods can be suggested, and antiretroviral therapy is a contentious issue for disease control. Copyright © 2012 John Wiley & Sons, Ltd.     

Analysis of a map-based neuronal model

ABSTRACT

Subthreshold oscillations in neurons are those oscillations which do not attain the critical value of the membrane's voltage needed for triggering an action potential (a spike). Their contribution to the forming of action potentials in neurons is a current field of research in biology. The present work approaches this subject using tools from mathematical modelling, more exactly, a neuronal non-smooth map-based model is proposed and studied. The behaviour of the model in a noisy medium is also studied.     

Pattern formation of a diffusive predator-prey model with herd behavior and nonlocal prey competition

In this paper, we study the influence of the nonlocal interspecific competition of the prey population on the dynamics of the diffusive predator-prey model with prey social behavior. Using the linear stability analysis, the conditions for the positive constant steady state at which undergoes Hopf bifurcation, T-H bifurcation (Turing-Hopf bifurcation) are investigated. The Turing patterns occur in the presence of the nonlocal competition and cannot be found in the original system. For determining the dynamical behavior near T-H bifurcation point, the normal form of the T-H bifurcation has been used. Some graphical representations are provided to illustrate the theoretical results.     

Semi-elliptic computation of an axi-symmetric transonic nozzle flow

A newly developed, semi-elliptic computational algorithm is employed to predict the transonic flow inside an axisymmetric, convergent-divergent nozzle featuring small wall radius of curvature at the throat. The predictions obtained are compared against flow measurements for this nozzle, which have been reported elsewhere. Good agreement between the corresponding measurements and predictions is revealed, thus validating the computational algorithm and demonstrating its value as a design tool.     

Modeling of the Interphase of Polymer-Matrix Composites: Determination of Its Structure and Mechanical Properties

In this work, a model is developed which allows one to determine the thickness and properties of the interphase layer in unidirectional and filled composites, assuming that the materials of the interphase, matrix, and fillers may have a fractal structure, and to predict the properties of composites with interphases. Using a set of computer programs elaborated, the corresponding calculations are carried out for glass-epoxy composites, epoxy carboplastics, and graphite-filled epoxy polymers.     

Design of feedback controllers by two-stage methods

When the eigenvalues of linear, time-invariant discrete systems are widely separated in absolute value, it is shown that the design of state or output feedback controllers can be best approached by two-stage methods. In these methods, the feedback gain matrices are computed by separately placing slow and fast eigenvalues at desired locations. Applications to the problem of independently controlling the speed and torque of petrol engine/dynamometer test rig have demonstrated the potential of the two-stage feedback design methods.     

Computer simulation of stable structures in crystal substances

Mathematical methods and algorithms used to design an automated system for predicting the properties of substances with a given crystal-chemical formula are described.     

Random effects logistic regression model for default prediction of technology credit guarantee fund

Korean government has been funding the small and medium enterprises (SME) with superior technology based on scorecard. However high default rate of funded SMEs has been reported. In order to effectively manage such governmental fund, it is important to develop accurate scoring model for SMEs. In this paper, we provide a random effects logistic regression model to predict the default of funded SMEs based on both financial and non-financial factors. Advantage of such a random effects model lies in the ability of accommodating not only the individual characteristics of each SME but also the uncertainty that cannot be explained by such individual factors. It is expected that our study can contribute to effective management of government funds by proposing the prediction models for defaults of funded SMEs.     

六关节机械臂运动路径设计

就关节式机械臂指尖在任意两点间移动、沿固定曲线移动、机械臂绕开障碍物执行任务以及参数优化等问题展开研究.首先确定了自由度组合到指尖空间位置的映射,建立了求解上述问题的最小二乘模型、泛函条件极值模型,并给出了数值解法.最后,结合图像处理等技术,对各参数的优化设计提出了改进措施.     

Comparison of Mechanical Properties and Effects in Micro- and Nanocomposites with Carbon Fillers (Carbon Microfibers,Graphite Microwhiskers,and Carbon Nanotubes)

The mechanical properties and effects in fibrous composite materials are compared. The materials are based on the same matrix (EPON-828 epoxy resin) and differ in the type of fibers: Thornel-300 carbon microfibers, graphite microwhiskers, carbon zigzag nanotubes, and carbon chiral nanotubes. Two material models are considered: a model of elastic medium (macrolevel model) and a model of elastic mixture (micro-nanolevel model). Mechanical constants of 40 materials (4 types + 10 modifications) are calculated and compared. The theoretical ultimate compression strength along the fibers is discussed. The effects accompanying the propagation of longitudinal waves in the fiber direction are investigated.     

正变坐标系下完全深度平均湍流方程组

本文针对宽浅型水域，对三维湍流时均方程组逐项进行深度平均，推导出包含自由水面和地形影响的深度平均流动控制方程组．本文还同时获得了深度平均形式的ｋ－ε湍流模型方程组．因计入了水流的三维效应，该模型称为完全深度平均模型．考虑到天然水域几何边界复杂，本文运用较简便的方法，将上述模型方程组交换至正交坐标系下．所得控制方程组可以直接运用于对实际问题的数值模拟．     

Comparison of techniques for assessing effects of loading uncertainty upon a long term phosphorous model

This paper compares the feasibility of applying three stochastic techniques to a linear water quality model. The Monte Carlo, first order analysis, and generation of moment equation techniques are applied to a long term phosphorus model of Lake Washington. The effect of uncertainty of the phosphorus loading term on simulated phosphorus levels is analysed. The simulated concentrations of phosphorus in the water column are very responsive to uncertainty in annual phosphorus loading, but the sediment concentrations are relatively insensitive. All three stochastic techniques produced identical results, but the level of preparatory and computational effort required varies considerably. The Monte Carlo technique requires the most computation time of the three stochastic techniques examined. The first order analysis and generation of moment equation techniques are shown to be precise and efficient methods of stochastic analysis. In this application they required less than one-thousandth the computer time of the Monte Carlo technique     

Controllability of Boolean control networks with impulsive effects and forbidden states

This paper investigates the controllability of Boolean control networks (BCNs) with impulsive effects while avoiding certain forbidden states. Using semi‐tensor product of matrices, the BCNs with impulsive effects can be converted into impulsive discrete‐time systems. Then, some necessary and sufficient conditions for the controllability are obtained. It is interesting to find that impulsive effects play an important role in the controllability of BCNs. Finally, an example is given to show the efficiency of the obtained results. Copyright © 2013 John Wiley & Sons, Ltd.     

双层0.618法在某力学问题中的应用

建立了一组平行移动荷载作用下,简支桥梁挠度的数学模型;利用双层0.618法搜索梁的绝对最大挠度对应的最危险截面位置以及移动荷载最不利位置,计算该位置相应的挠度得到梁的绝对最大挠度.本文算法以计算机为工具,适用于任意有限多个平行移动荷载,对于桥梁的设计计算与安全评估,有一定的实用价值.     

An algorithm to analyze stability of gene-expression patterns

Many problems in the field of computational biology consist of the analysis of so-called gene-expression data. The successful application of approximation and optimization techniques, dynamical systems, algorithms and the utilization of the underlying combinatorial structures lead to a better understanding in that field. For the concrete example of gene-expression data we extend an algorithm, which exploits discrete information. This is lying in extremal points of polyhedra, which grow step by step, up to a possible stopping.We study gene-expression data in time, mathematically model it by a time-continuous system, and time-discretize this system. By our algorithm we compute the regions of stability and instability. We give a motivating introduction from genetics, present biological and mathematical interpretations of (in)stability, point out structural frontiers and give an outlook to future research.     

Interplay between Riccati,Ermakov, and Schrödinger equations to produce complex‐valued potentials with real energy spectrum

Nonlinear Riccati and Ermakov equations are combined to pair the energy spectrum of 2 different quantum systems via the Darboux method. One of the systems is assumed Hermitian, exactly solvable, with discrete energies in its spectrum. The other system is characterized by a complex‐valued potential that inherits all the energies of the former one and includes an additional real eigenvalue in its discrete spectrum. If such eigenvalue coincides with any discrete energy (or it is located between 2 discrete energies) of the initial system, its presence produces no singularities in the complex‐valued potential. Non‐Hermitian systems with spectrum that includes all the energies of either Morse or trigonometric Pöschl‐Teller potentials are introduced as concrete examples.     

Modelling of laminate structures in elasto-plasticity with a mixed finite element

The main advantage of the mixed finite element (displacements-stresses) is that, because of its continuity, it gives a good approximate stress field, without needing a high degree of interpolation in displacements. This degree of approximation is essential for elastic-plastic computations. However, the total continuity of stresses is too strong in a laminate structure along the interfaces. We show a method of achieving the correct level of continuity without losing the advantage of a good approximation. Some examples of laminate plane structures with plastic areas along the interfaces are given.     

Calculation of deformations in nanocomposites using the block multipole method with the analytical-numerical account of the scale effects

Local scale effects for linear continuous media are investigated as applied to the composites reinforced by nanoparticles. A mathematical model of the interphase layer is proposed that describes the specific nature of deformations in the neighborhood of the interface between different phases in an inhomogeneous material. The characteristic length of the interphase layer is determined formally in terms of the parameters of the mathematical model. The local stress state in the neighborhood of the phase boundaries in the interphase layer is examined. This stress can cause a significant change of the integral macromechanical characteristics of the material as a whole if the interphase boundaries are long. Such a situation is observed in composite materials reinforced by microparticles and nanoparticles even when the volume concentration of the inclusions is small. A numerical simulation of the stress state is performed on the basis of the block analytical-numerical multipole method with regard for the local effects related to the special nature of the deformation of the interphase layer in the vicinity of the interface.