Two-dimensional state-space discrete models for hyperbolic partial differential equations

It is shown that the finite difference technique can be used to transform some important linear distributed processes described by partial differential equations into so-called Roesser discrete state-space models. Two illustrative examples of numerical solutions are given and compared with exact solutions.     

Numerical movable-bed models for practical engineering

Numerical modelling of sediment transport phenomena is an ambitious aim, which can only be attained in the long term by first formulating simplified models. On the basis of practical experience, these may be subsequently refined to give better results. This paper describes some simplifications of the full set of governing equations associated with sedimentation processes under time-dependent flow conditions, such as those in tidal rivers. A numerical movable-bed model is presented which, although economical in its computer requirements, nevertheless simulates some of the complex three-dimensional physical effects. Results from practical applications are given and compared with both laboratory experiments and field investigations.     

基于网络分析方法的国际贸易问题研究

本文基于网络分析方法研究贸易问题.首先利用网络特征分析考察贸易规模变化以及经济主体的地位变化问题,然后提出动态指数随机图模型来研究影响因素对贸易的影响程度变化问题.结果表明:2001年-2016年国际贸易规模总体上是扩大的;美国和德国在进出口市场上长期占有主导地位,中国是贸易关系增长最快的国家,国际地位上升明显;单边贸易对双边贸易的促进作用在经济景气时更为显著, GDP对出口的促进作用变化较进口更为明显,距离对贸易的抑制作用变化程度较小.     

A comparison of the formulation for eddy diffusion in two one-dimensional stratification models

Two models for thermal stratification based on turbulent diffusion concepts are analysed and compared. The models by Henderson-Sellers; and by McCormick and Scavia, are shown to be equivalent at large values of the Richardson number, R_i. At small R_i, the simpler model reverts to specification of the turbulent diffusion as a constant value. This simplification is also demonstrated to be a realistic approximation only at low wind speeds and for deep lakes. By comparison of these model types, a (previously empirically defined by McCormick and Scavia) parameter β is related conceptually to the lake depth, H.     

New formulation of eddy diffusion thermocline models

One-dimensional thermal stratification models (for lakes, reservoirs, oceans, fjords), based on eddy diffusion concepts to represent vertical mixing of heat, have not found extensive application due to the lack of an adequate analytical representation of the neutral eddy diffusion coefficient, K_Ho. In this paper such an analytic expression is developed and shown to be in good agreement with various pieces of empirical evidence.     

Parametric scaling of mathematical models

Parametric scaling, the process of extrapolation of a modelling result to new parametric conditions, is often required in model optimization, and can be important if the effects of parametric uncertainty on model predictions are to be quantified. Knowledge of the functional relationship between the model solution (y) and the system parameters (α) may also provide insight into the physical system underlying the model. This paper examines strategies for parametric scaling, assuming that only the nominal model solution y(α) and the associated parametric sensitivity coefficients (?y/?α, ?²y/?α², etc.) are known. The truncated Taylor series is shown to be a poor choice for parametric scaling, when y has known bounds. Alternate formulae are proposed which ‘build-in’ the constraints on y, thus expanding the parametric region in which the extrapolation may be valid. In the case where y has a temporal as well as a parametric dependence, the extrapolation may be further improved by removing from the Taylor series coefficients the ‘secular’ components, which refer to changes in the time scale of y(t), not to changes in y as a function of α.     

Prediction,measurement and comparison of fluid-structure interaction using mathematical and experimental models

Without presenting all the associated mathematics this paper considers the combined use of theoretical and experimental methods in the investigation of the fluid structure interaction of rigid and articulated structures. The structures considered are the rigid body form of the Lancaster Flexible Bag (LFB) and an articulated Cockerell raft system.In the case of the LFB the Salvesen-Tuck-Faltinsen strip theory is shown to predict vertical and horizontal bending moments which are generally consistent with measured trends (almost) irrespective of whether 2D-based or 3D-based calculated hydrodynamic active and reactive coefficients are used. The non-repeatability of some of the measured results used in the comparison caused some concern and the additional required model testing is discussed.In direct comparison application difficulties were encountered when using theoretical analyses to assist with the organization of the experiments to investigate the hydrodynamic loading of articulated systems. The finite element program PAFEC 75 was used to predict the vibration frequencies of the framework used to support the Cockerell raft model and the actuator system used to force oscillate the model. The 3D diffraction programme MATTHEW provided predictions of pressure distributions over the raft to assist with sensible positioning of the pressure transducers on the physical model. The difficulties encountered in applying these prediction tools are discussed, also the current research programme is reported.     

CUDA parallel programming for simulation of epidemiological models based on individuals

Mathematical models are of great value in epidemiology to help understand the dynamics of the various infectious diseases, as well as in the conception of effective control strategies. The classical approach is to use differential equations to describe, in a quantitative manner, the spread of diseases within a particular population. An alternative approach is to represent each individual in the population as a string or vector of characteristic data and simulate the contagion and recovery processes by computational means. This type of model, referred in the literature as MBI (models based on individuals), has the advantage of being flexible as the characteristics of each individual can be quite complex, involving, for instance, age, sex, pre‐existing health conditions, environmental factors, social habits, etc. However, when it comes to simulations involving large populations, MBI may require a large computational effort in terms of memory storage and processing time. In order to cope with the problem of heavy computational effort, this paper proposes a parallel implementation of MBI using a graphics processor unit compatible with CUDA. It was found that, even in the case of a simple susceptible–infected–recovered model, the computational gains in terms of processing time are significant. Copyright © 2015 John Wiley & Sons, Ltd.     

回归分析法在建立岩爆数学模型上的应用

本通过实践与理论对岩爆进行了分析与研究，探讨了直接影响岩爆的几个主要因素，首次利用回归分析法对岩爆的有关数学模型进行了一些探讨，取得了一些结果，并且通过实践验证了所得结果的正确性，速对今后多方面进一步研究岩爆具有一定的指导意义。     

Lot‐sizing policies for deterioration items under two‐level trade credit with partial trade credit to credit‐risk retailer and limited storage capacity

The main purpose of this article is to investigate the optimal wholesaler's replenishment decisions for deterioration items under two levels of the trade credit policy and two storage facilities in order to reflect the supply chain management situation within the economic order quantity framework. In this study, each of the following assumptions have been made: (1) The own warehouse with limited capacity always is not sufficient to store the order quantity, so that a rented warehouse is needed to store the excess units over the capacity of the own warehouse; (2) The wholesaler always obtains the partial trade credit, which is independent of the order quantity offered by the supplier, but the wholesaler offers the full trade credit to the retailer; (3) The wholesaler must take a loan to pay his or her supplier the partial payment immediately when the order is received and then pay off the loan with the entire revenue. Under these three conditions, the wholesaler can obtain the least costs. Furthermore, this study models the wholesaler's optimal replenishment decisions under the aforementioned conditions in the supply chain management. Two theorems are developed to efficiently determine the optimal replenishment decisions for the wholesaler. Finally, numerical examples are given to illustrate the theorems that are proven in this study, and the sensitivity analysis with respect to the major parameters in this study is performed. Copyright © 2016 John Wiley & Sons, Ltd.     

The OWA-based consensus operator under linguistic representation models using position indexes

When using linguistic approaches to solve decision problems, we need linguistic representation models. The symbolic model, the 2-tuple fuzzy linguistic representation model and the continuous linguistic model are three existing linguistic representation models based on position indexes. Together with these three linguistic models, the corresponding ordered weighted averaging operators, such as the linguistic ordered weighted averaging operator, the 2-tuple ordered weighted averaging operator and the extended ordered weighted averaging operator, have been developed, respectively. In this paper, we analyze the internal relationship among these operators, and propose a consensus operator under the continuous linguistic model (or the 2-tuple fuzzy linguistic representation model). The proposed consensus operator is based on the use of the ordered weighted averaging operator and the deviation measures. Some desired properties of the consensus operator are also presented. In particular, the consensus operator provides an alternative consensus model for group decision making. This consensus model preserves the original preference information given by the decision makers as much as possible, and supports consensus process automatically, without moderator.     

Scale and time effects on mathematical models for transport in the environment

The purpose of this paper is to analyse mathematical models used in environmental modelling.Following a brief survey of the development in modelling scale-and time-dependent dispersion processes in the environment,this paper compares three similarity solutions,one of which is a solution of the generalized Feller equation(GF)with fractal parameters,and the other two for the newly-developed generalized Fokker-Planck equation(GFP).The three solutions are derived with parameters having physical significance.Data from field experiments are used to verify the solutions.The analyses indicate that the solutions of both GF and GFP represent the physically meaningful natural processes,and simulate the realistic shapes of tracer breakthrough curves.     

Bilinear markovian representation and bilinear models

An extension of the linear Markovian repsentation called the bilinear Markovian representation is introduced, and is shown to provide representations of all-diagonal bilinear time series models. Some properties of the bilinear Markovian representation are also given.     

Exchange rate uncertainty and trade growth—a comparison of linear and non‐linear (forecasting) models

A huge body of empirical and theoretical literature has emerged on the relationship between foreign exchange (FX) uncertainty and international trade. Empirical findings about the impact of FX uncertainty on trade figures are at best weak and often ambiguous with respect to its direction. Almost all empirical contributions assume and estimate a linear relationship. Possible nonlinearity or state dependence of causal links between FX uncertainty and trade has been mostly ignored yet. In addition, widely used regression models have not been evaluated in terms of ex‐ante forecasting. In this paper we analyse the impact of FX uncertainty on sectoral categories of multilateral exports and imports for 15 industrialized economies. We particularly provide a comparison of linear and non‐linear models with respect to ex‐ante forecasting. In terms of average ranks of absolute forecast errors non‐linear models outperform both, a common linear model and some specification building on the assumption that FX uncertainty and trade growth are uncorrelated. Our results support the view that the relationship of interest might be non‐linear and, moreover, lacks of homogeneity across countries, economic sectors and when contrasting imports vs exports. Copyright © 2005 John Wiley & Sons, Ltd.     

Optimization of dynamic regional models

In this paper we consider several problems concerning the optimization of Dynamic Regional Models. In particular we describe the optimization of the model of a region. Western Andalusia, in Southern Spain. Fuzzy set theory is applied because of the inherent imprecisions in the judgements about goals and its tradeoffs. Multicriteria optimization is used due to the fact that, in most cases, the search for the optimal policies must be performed taking into account non conmensurable and conflicting objectives. We present a program package which incorporates these methodologies together with simulation, optimization and sensitivity analysis routines.     

Juche in international trade

We show that in trade between two parties, one of whom has much greater endowment that the other, calculated by the Nash bargaining solution, tends to exploit the poorer party, as compared with the competitive equilibrium. This can be interpreted as saying that trade between a developed country and a developing nation, each acting on the basis of self-interest, will result in exploitation of the developing nation. This illustrates one aspect of the idea of Juche. We also show that if trade in two goods among two parties is extended to a third, one of the two parties will be worse off as a result under natural hypotheses. This can be interpreted as explaining why trade between a developing country and a developed country might make some groups in the developing country rich but other groups poor, a second aspect of Juche.     

Optimal ordering policies for perishable multi-item under stock-dependent demand and two-level trade credit

In this paper, a multi-item inventory model for perishable items is developed, where the demand rates of the items are stock dependent, two-level trade credit is adopted and the restriction of inventory capacity is also considered. The major objective is to determine the optimal cycle time and order quantities such that the total profit is maximized. The existence and uniqueness of the optimal cycle is discussed by Lagrange approach, and line search algorithms are developed to find the optimal solution of the model. Furthermore, numerical examples are given to illustrate the methods. The sensitivity of the solution to changes in the values of different parameters is also discussed.     

Facility location models for distribution planning

A strategic issue which is of interest to distribution planners is where to best site warehouses. Model formulations, and solution approaches, which address the issue vary widely in terms of mathematical and computational complexity. This paper reviews some of the significant contributions which have been made to the relevant and current state of knowledge.     

A note on the representation of parametric models for multivariate extremes

In this note, the representations of extremal Dirichlet and logistic distributions are reviewed and extended. These new representations allow exact simulations of the spectral distribution functions and an extension of the extremal logistic case to dimensions higher than two.