Sociometric triads as multi‐variate systems†

Binary choices (choose v. not choose) among three persons may be viewed as variables and the possible choices in a triad as a 64 celled contingency table, amenable to analysis in terms of log linear effects. Fifteen non‐redundant effects occur, of which four appear consistently in a data bank of 384 sociograms. Consequently, it is claimed one may reproduce the triad frequencies in most sociograms by the effects implied by four propositions: (A) P is more likely to choose O when O chooses P, net of all other variables; (B) P is more likely to choose O when X chooses O. This association is particularly strong when imitation produces transitivity; (C) when X chooses O (O chooses X), P tends to choose both or neither; and (D) P tends to choose an X who favors P's choices. P tends to not choose an X who favors P's non‐choices.     

Critique of probabilistic models: Application of the Semi‐Markov model to migration

The role of probabilistic models, with special reference to application of the Semi‐Markov model to the analysis of internal migration, is discussed. Advantages of probabilistic models over more conventional methods based on regression analysis are detailed. Probabilistic models have stood apart from the rest of the literature, in migration as well as other areas of application, because they have no substantive content. It is argued that unless their parameters are related to the causal structure and exogenous determinants of the migration process, probabilistic models will be of little practical and scientific use. A strategy for integrating probabilistic models with theoretical and empirical analysis is sketched, to be carried out in the next article.     

Query and construction of multi‐attribute social accounts

This paper surveys methods for query of systems of social accounts that are constructed from collections of intersecting data sets. Such query methods are used to ascertain, e.g., the number of people who possess certain attribute characteristics not explicitly provided by an original account or survey. Three approaches to the query problem are considered: (1) a generalized inverse solution suggested by Ijiri (1965); (2) a row reduced echelon matrix formulation devised by Hellerman and Cavallo (1977); and (3) a Boolean matrix operation introduced by Homer (1974). The latter two methods are extended to provide a general approach for using existing multi‐attribute information for the construction of new systems of social accounts.     

A unified framework for pull control mechanisms in multi‐stage manufacturing systems

This paper presents a unified framework for pull production control mechanisms in multistage manufacturing systems. A pull production control mechanism in a multistage manufacturing system is a mechanism that coordinates the release of parts into each stage of the system with the arrival of customer demands for final products. Four basic pull production control mechanisms are presented: Base Stock, Kanban, Generalized Kanban, and Extended Kanban. It is argued that on top of any of these basic coordination mechanisms, a local mechanism to control the workinprocess in each stage may be superimposed. Several cases of basic stage coordination mechanisms with stage workinprocess control are presented, and several production control systems that have appeared in the literature are shown to be equivalent to some of these cases.     

Comparison of the performance of a time‐dependent short‐interest rate model with time‐independent models

The coefficients in the stochastic differential equation that the short interest rate follows are of vital importance in the subsequent modelling of bond prices and other interest rate products. Empirical tests have previously been performed by various authors who compare a variety of popular short‐rate models. Most recently, Ahn and Gao compared their model with affine‐drift models and showed that their model with a non‐linear drift function outperforms the others. This paper compares the model developed by Goard, which is a time‐dependent generalization of the Ahn–Gao model, with the Ahn–Gao model itself. It is found that the time‐dependent model using a second‐order Fourier series in time, outperforms the Ahn–Gao model for all data sets considered.     

Solving a multi periodic stochastic model of the rail–car fleet sizing by two-stage optimization formulation

We propose a formulation and solution procedure for optimizing the fleet size and freight car allocation under uncertainty demands. There are important interactions between decisions on sizing a rail–car fleet and utilizing that fleet. Consequently, the optimum use of empty rail–cars for demands response in the length of the time periods one of advantages the proposed model. The model also provides rail network information such as yard capacity, unmet demands, and number of loaded and empty rail–car at any given time and location. Consequently, the model helping managers or decision makers of any train company for planning and decision making. We propose two-stage solution procedure for solve rail–car fleet sizing problem. Numerical examples are given to illustrate the model and solution methodology.     

Analysis of a Joule–heating model related to resistance welding

The purpose of this work is to establish the existence of capacity solutions to the thermistor problem under certain weak assumptions on data. Also, some numerical results are shown. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

An information‐theoretic‐based (MaxEnt) approach to social dynamical systems

Jeffreys‐Jaynes’ Predictive Statistics appears to provide a promising approach for the study of general dynamical systems. We describe an application of such theory to the analysis of the dynamics of interacting social groups. For that purpose the said statistical theory is redirected towards the construction of an equivalent stochastic theory. The working of the formalism is illustrated by applying it to a simplified case of opinion forming in a two‐candidates election.     

Phase‐plane analysis of simple nonlinear autonomous systems

The aim of this paper is to encourage the teaching of phase‐plane analysis. This topic has practical applications in a wide variety of fields including national economic modelling, biology, technological innovations, sociology and modern medicine.     

Uniform stabilization to equilibrium of a nonlinear fluid–structure interaction model

We consider uniform stability to a nontrivial equilibrium of a nonlinear fluid–structure interaction (FSI) defined on a two or three dimensional bounded domain. Stabilization is achieved via boundary and/or interior feedback controls implemented on both the fluid and the structure. The interior damping on the fluid combining with the viscosity effect stabilizes the dynamics of fluid. However, this dissipation propagated from the fluid alone is not sufficient to drive uniformly to equilibrium the entire coupled system. Therefore, additional interior damping on the wave component or boundary porous like damping on the interface is considered. A geometric condition on the interface is needed if only boundary damping on the wave is active. The main technical difficulty is the mismatch of regularity of hyperbolic and parabolic component of the coupled system. This is overcome by considering special multipliers constructed from Stokes solvers. The uniform stabilization result obtained in this article is global for the fully coupled FSI model.     

Analysis of incomplete factorizations for a nine-point approximation to a convection–diffusion model problem

We study the stability of zero-fill incomplete LU factorizations of a nine-point coefficient matrix arising from a high-order compact discretisation of a two-dimensional constant-coefficient convection–diffusion problem. Nonlinear recurrences for computing entries of the lower and upper triangular matrices are derived and we show that the sequence of diagonal entries of the lower triangular factor is unconditionally convergent. A theoretical estimate of the limiting value is derived and we show that this estimate is a good predictor of the computed value. The unconditional convergence of the diagonal sequence of the lower triangular factor to a positive limit implies that the incomplete factorization process never encounters a zero pivot and that the other diagonal sequences are also convergent. The characteristic polynomials associated with the lower and upper triangular solves that occur during the preconditioning step are studied and conditions for the stability of the triangular solves are derived in terms of the entries of the tridiagonal matrices appearing in the lower and upper subdiagonals of the block triangular system matrix and a triplet of parameters which completely determines the solution of the nonlinear recursions. Results of ILU-preconditioned GMRES iterations and the effects of orderings on their convergence are also described.     

Understanding secondary mathematics: analysis of linguistic difficulties vis‐a‐vis errors

Misconceptions caused by misunderstanding mathematical language are of different types, e.g. interference of mathematical and non‐mathematical meanings, complexity or unfamiliarity of words, improper use of symbols, syntactical misunderstandings and redundancy or inadequacy of data. Fifteen mathematical words were presented to 84 students of 8th grade and the responses of students were analysed. Mathematical items of a Science Talent Search Test were also analysed from the answers of 100 candidates of 8th grade. The analysis casts light on the processes of the development of mathematical concepts which the students learn through the vicissitudes of the interaction of mathematical and non‐mathematical meanings of words which may be familiar or unfamiliar, relevant or irrelevant, and/or distinct or difficult, to the learners. Complications in understanding mathematical concepts for individual students are pointed out from these experiments. Acquaintance with such communication processes of learners can also help in detecting strategies of imparting mathematical instructions to the learners. Roles of the uses of common, mathematical, transformational, and story‐telling language have also been discussed. The paper concludes with some comments on the importance of guided discovery learning, error analysis by teachers, and the preparation of a register of mathematical language.     

Coupling of a one-dimensional river routing model and a three-dimensional ocean model to predict overbank flows in a complex river–ocean system

River–ocean coupled models were developed to calculate overbank flows in a complex river–coastal ocean system comprising the Wu River and the adjacent coastal ocean of central Taiwan. The hydrodynamic quantities were exchanged between one-dimensional and three-dimensional domains during runtime to resolve the real-time exchange and interaction between the coastal waters and the river system. The coupled model was calibrated and verified with the observed water levels using data from three typhoon events. The results indicate a reasonable agreement between the model simulations and the observed data. The model was then used to calculate hydrographs of the overbank flow caused by Typhoon Kalmaegi, which occurred in 2008. The simulated overbank flows quantitatively agreed with the reported information. We also demonstrated that most of the overbank flows occurred at the upper reaches of the tributaries of the Wu River system, except for the tributary in the Fazi River.     

A new approach to the stabilization of a fluid–structure interaction model

This article is a continuation of our work on a linear fluid–structure interaction model [Grobbelaar-Van Dalsen, On a fluid–structure model in which the dynamics of the structure involves the shear stress due to the fluid, J. Math. Fluid Mech. 10(3) (2008), pp. 388–401; Grobbelaar-Van Dalsen, Strong stability for a fluid––structure model, Math. Methods Appl. Sci., 32(2009) pp. 1452–1466]. The model describes the interaction between a 3-D incompressible fluid and a 2-D plate, the interface, which coincides with a flat flexible part of the surface of the vessel containing the fluid. The mathematical model comprises the Stokes equations and the equations for the longitudinal deflections of the plate with the inclusion of the shear stress that the fluid exerts on the plate. A dissipative damping mechanism of Kelvin–Voigt type is applied to the interior of the plate. While our earlier work shows that weak solutions in a space of finite energy are strongly asymptotically stable under no-slip transmission conditions at the interface with uniform exponential stability only attainable under an additional domination condition, the present research is directed at achieving uniform exponential stability of weak solutions without imposing the domination condition. Using energy methods we establish uniform exponential decay under a modified transmission condition at the interface. This condition entails that the fluid velocity at the interface is coupled to a linear combination of the plate velocity and displacement.     

A dynamic stochastic version of the pitcher‐hamblin‐miller model of “collective violence*

The central equation of the deterministic diffusion model of Pitcher, Hamblin, and Miller (1978) is formulated as a time‐inhomogeneous stochastic process. It will be shown that the stochastic process leads to a negative binomial distribution. The deterministic diffusion function can be derived from the stochastic model and is identical to the expected value as a function of time. Therefore the deterministic model is supported in terms of the underlying stochastic process. Moreover the stochastic model allows the prediction of the distribution for any point in time and the construction of prediction intervals.     

Harvesting of a phytoplankton–zooplankton model

Considering that some phytoplankton and zooplankton are harvested for food, a phytoplankton–zooplankton model with harvesting is proposed and investigated. First, stability conditions of equilibria and existence conditions of a Hopf-bifurcation are established. Our results indicate that over exploitation would result in the extinction of the population and an appropriate harvesting strategy should ensure the sustainability of the population which is in line with reality. Furthermore, the existence of bionomic equilibria and the optimal harvesting policy are discussed. The present value of revenues is maximized by using Pontryagin’s maximum principle subject to the state equations and the control constraints. We discussed the case of optimal equilibrium solution. It is found that the shadow prices remain constant over time in optimal equilibrium when they satisfy the transversality condition. It is established that the zero discounting leads to the maximization of economic revenue and that an infinite discount rate leads to complete dissipation of economic rent. Finally, some numerical simulations are given to illustrate our results.