Applications of Category Theory to the Area of Algebraic Specification in Computer Science

The theory of algebraic specifications – one of the most important mathematical approaches to the specification of abstract data types and software systems – is reviewed from a mathematical and a computer science point of view. The important role of category theory in this area is discussed and it is shown how the following selected problems are treated using category theory: First, a unified framework for specification logics, second compositional semantics, third partial algebras and their specification, and fourth specifications and models for concurrent systems. For the solution of two of the problems classifying categories are used. They allow to present categories of algebras as functor categories and to derive a number of important properties from well known results for functor categories.     

Developing teachers' models for assessing students' competence in mathematical modelling through lesson study

Applications and modelling have gained a prominent role in mathematics education reform documents and curricula. Thus, there is a growing need for studies focusing on the effective use of mathematical modelling in classrooms. Assessment is an integral part of using modelling activities in classrooms, since it allows teachers to identify and manage problems that arise in various stages of the modelling process. However, teachers’ difficulties in assessing student modelling work are a challenge to be considered when implementing modelling in the classroom. Thus, the purpose of this study was to investigate how teachers’ knowledge on generating assessment criteria for assessing student competence in mathematical modelling evolved through a professional development programme, which is based on a lesson study approach and modelling perspective. The data was collected with four teachers from two public high schools over a five-month period. The professional development programme included a cyclical process, with each cycle consisting of an introductory meeting, the implementation of a model-eliciting activity with students, and a follow-up meeting. The results showed that the professional development programme contributed to teachers’ knowledge for generating assessment criteria on the products, and the observable actions that affect the modelling cycle.     

Computer-oriented, n-body modelling of minimal surfaces

In this paper a new approach to the modelling of minimal surfaces is described and applied. Rather than use a continuous model, we develop a discrete, _n-body model with basic tensile interactions derived from classical molecular force formulae. Computer results are described and discussed.     

Discursive positionings and emotions in modelling activities

Mathematical modelling is suggested as an activity through which students engage in meaningful mathematics. In the current research, the modelling activity of a group of four seventh-grade students was analysed using the discursive analysis framework. The research findings show that the positionings and emotions of the group members during their participation in the modelling activity changed as the activity proceeded. Overall, it can be said that three of the four group members acted as insiders, while the fourth acted as an outsider, and only, towards the end of the group's work on the activity, he acted as an insider. Moreover, the research findings point at four factors that affected the group members’ positionings and emotions during the modelling activity: the member's characteristics, the member's history of learning experiences, the activity characteristics and the modelling phases. Furthermore, the different positionings of the group members in the different modelling phases were accompanied by different emotions experienced by them, where being an insider and a collaborator resulted in positive emotions, while being an outsider resulted in negative emotions.     

An efficacious dynamic mathematical modelling approach for creation of best collaborative groups

In many disciplines, including business, publishing, management, health, sports, arts and education, there is a population of people which should be optimally divided into multiple groups based on certain attributes to collaboratively perform a particular task. The problem becomes more complex when some other requirements are also added. They might be importance degrees of grouping criteria, homogeneity, heterogeneity or a mixture of teams, amount of consideration to the preferences of individuals, variability or invariability of group size, having moderators, aggregation or distribution of persons, overlapping level of teams, and so forth. Several researchers have addressed the problem, but they suffered from failure to satisfy all the requirements and/or developed inexact solutions and/or had very long process times. This work reveals how these problems can be mathematically formulated through a binary integer programming approach to construct an effective model which is solvable by exact methods in an acceptable time. The suggested model was validated through data obtained from collaboration of a set of learners in an online learning discussion forum grouped by means of the provided method. The achieved outcomes confirmed that the new approach is satisfactory and promising.     

A unified approach to the modelling of holonomic and nonholonomic mechanical systems

An alternative technique, called projection method, for solving constrained system problems is presented. This approach can be used to derive equations of motion of both holonomic and nonholonomic systems, and the dynamic equations can be expressed in generalized velocities and/or quasi-velocities. Compared against the other methods of classical mechanics (Lagrange's, Gibbs-Appell, Kane's,...), the present method turns out to be extraordinarily short, elementary and general. As such, it deserves to be promoted as a generally accepted method in academic and engineering applications. Three examples are reported to illustrate advantages of the technique     

Efficacy analysis of a body-mass-reduction treatment using mathematical modelling

Obesity was categorized as a chronic disease by the World Health Organization (WHO) in 1997 because the problem had reached at pandemic level and presented a serious risk factor with respect to people who have been developing type-2 diabetes, hyperdyslipidaemia and hypertension. These four risk factors tend to accelerate the development of cardiovascular diseases. As a result, obesity has also become a significant social and economic burden. An important observation with regard to the population exhibiting increased body mass is the fact that they would like to decrease their weight, although they are frequently not successful. In this paper, a modelling-and-simulation approach is used for the presentation, analysis and explanation of the reasons that have an important influence on the treatment’s efficacy. The presented modelling results are based on the observation and treatment experiences of patients in a specialized institution over a period of 15 years, where each year around 100 new patients enter the treatment programme. The introduction of the motivation principle in the model structure allows strong support for the actions of the therapeutic team in a closed-loop manner, as the checking of different scenarios for the individual patient is easily realized. The efficacy of the treatment can, in this way, be significantly improved. In the past 6 years, which mainly involved open-loop treatments, the dropout rate was 70%. After the introduction of proposed closed-loop approach, this was reduced to 27% in the past year. As a consequence, the effect on body-mass control was significantly improved.     

Syntactic approach to constructions of generic models

A syntactic approach is described to constructing generic models which generalizes the known semantic one. A sufficient condition of a generic model being homogeneous is specified. It is shown that, within the syntactic approach, any countable homogeneous model is generic. Criteria and a sufficient condition are given for the generic models created in syntactic constructions to be saturated. Supported by RFBR grant No. 05-01-00411, and by the Council for Grants (under RF President) and State Aid of Fundamental Science Schools via project NSh-4787.2006.1. __________ Translated from Algebra i Logika, Vol. 46, No. 2, pp. 244–268, March–April, 2007.     

对偶的Hom型拟Hopf代数的余表示和范畴实现

In this paper, we introduce the dual Hom-quasi-Hopf algebra and prove that the comodules category of a(braided) dual Hom-quasi-bialgebra is a monoidal category. Finally,we give a categorical realization of dual Hom-quasi-Hopf algebras.     

An approach to modelling industrial unit processes: application to a spiral concentrator for minerals

A suite of computer models which simulate process operations in common use in the minerals processing industry is being developed. Application of the models is described with reference to a particular process device, the spiral concentrator. The paper sets out to explain the basic strategy behind the unit process modelling approach and discusses in detail the overall model structure adopted. The model aims to provide a set of equations, with sufficient physical significance to give a reasonable fit to any specific data set, and which can be systematically adjusted (through auxiliary models, user judgement and experience) to provide meaningful performance predictions over a broad range of operating conditions. The approach is thought to be applicable to a wide variety of processes. The model has been tested using a variety of ores, separated on plant-scale equipment and practical examples are given. The scope and limitations of the method are reported, drawing on the results of parallel experimental work. The extent to which this kind of approach can be used as a predictive tool in process design applications and in the day-to-day running of mineral processing plant is discussed.     

Mathematical modelling of social obesity epidemic in the region of Valencia,Spain

In this article, we analyse the incidence of excess weight in 24- to 65-year-old residents in the region of Valencia, Spain, and predict its behaviour in the coming years. In addition, we present some possible strategies to prevent the spread of the obesity epidemic.

We use classical logistic regression analysis to find out that a sedentary lifestyle and unhealthy nutritional habits are the most important causes of obesity in the 24- to 65-year-old population in Valencia. We propose a new mathematical model of epidemiological type to predict the incidence of excess weight in this population in the coming years. Based on the mathematical model sensitivity analysis, some possible general strategies to reverse the increasing trend of obesity are suggested.

The obese population in the region of Valencia is increasing (11.6% in 2000 and 13.48% in 2005) and the future is worrisome. Our model predicts that 15.52% of the population in Valencia will be obese by 2011. Model sensitivity analysis suggests that obesity prevention strategies (healthy advertising campaigns) are more effective than obesity treatment strategies (physical activity) involving the obese and overweight subpopulation in controlling the increase of adulthood obesity in the region of Valencia.     

Sets and indices in linear programming modelling and their integration with relational data models

LP models are usually constructed using index sets and data tables which are closely related to the attributes and relations of relational database (RDB) systems. We extend the syntax of MPL, an existing LP modelling language, in order to connect it to a given RDB system. This approach reuses existing modelling and database software, provides a rich modelling environment and achieves model and data independence. This integrated software enables Mathematical Programming to be widely used as a decision support tool by unlocking the data residing in corporate databases.     

The delay-time modelling of preventive maintenance of plant given limited PM data and Selective repair at PM

This paper presents a maintenance-modelling case study of aplant manufacturing brake linings. A delay–time modelis developed and applied to model and optimize preventive maintenance(PM). A key subsystem in the plant is used to illustrate themodelling process and management reaction. Defects identifiedat PM may not all be removed. This incomplete response to PMis a feature which has not been modelled before. The parametervalues of the delay-time process are estimated from objectivedata from maintenance records of failures, using the methodof maximum likelihood. This is aided by a theorem extendingresults on the NHPP arival rate of failures in a perfect-inspectioncase to the non-perfect-inspection case. Problems of parameterestimation given inadequate data collected at PMs are discussed,and the necessity to augment objective data with subjectiveassessments highlighted. Based upon the estimated model parametersand delay-time distribution, an inspection model is constructedto describe the relationship between the total unit downtimeand the PM interval. The response of management is discussed.     

First principles versus artificial neural network modelling of a solar desalination system with experimental validation

ABSTRACT

The present study mainly focuses on enhancing the performance of solar still unit using solar energy through cylindrical parabolic collector and solar panels. A 300 W solar panel is used to heat saline water by thermal elements outside the solar still unit. Solar panels are cooled during the hot hours of the day; thus, reducing their temperature may lead to an increase in solar panel efficiency followed by an increase in the efficiency of the solar still unit. The maximum amount of freshwater used in the experiment was 2.132 kg/day. The experiments were modelled using ANNs. Based on neural network simulation results, there is a significant correlation between experimental data and neural network modelling. This paper compares experimental data with data obtained from mathematical modelling and ANNs. As a conclusion, the artificial neural network prediction has been more accurate than the simplified first principles model presented.     

Mathematical modelling and dynamic simulation of multi-effect falling-film evaporator for milk powder production

Multiple-effect evaporators are widely used in dairies and food industries because they are appropriately suited for concentrating food solutions. Some mathematical models for multi-effect evaporators are reported in previous studies. But most of them are steady-state models, and there are no extensive studies on the dynamic behaviour of these evaporators. In this paper, two types of dynamic model, lumped and distributed, are developed for an industrial four-effect falling-film evaporator which is used to concentrate whole milk. These models are validated with data from an industrial unit. The results show that the distributed model has slightly better predictions than the lumped model, but the lumped model has comparable performance because its structure is simple and the needed simulation time is short in comparison with the distributed model.