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The conceptual framework of mathematical modeling (e.g., Lesh & Doerr, 2003) is a vital area in mathematics education research, and its implementation has potential for deeply involving children in integrated and meaningful learning. In mathematical modeling learners are active agents in content-integrated, real-world problem solving. This emphasis on integrating multiple content areas to answer big questions, the pursuit of mathematical modeling, descends from Dewey’s work. We present the definition, principles, and design of modeling practices for readers who may be familiar with early childhood curriculum but less so with using modeling for learning. We explore the application of mathematical modeling to early childhood classrooms and its compatibility with early childhood pedagogies and philosophies. Young children may often be underestimated, assumed to be unable to pose big questions that can be answered through activity, experience, and data; but we discuss how young children can be engaged in problems through mathematical modeling. Finally, as preservice teacher educators, we discuss preparing preservice and in-service teachers for modeling in their classrooms. We offer examples and guidance for early childhood teachers to engage in authentic practice – meeting children where their interests are and creating integrated problem-solving experiences.

The purpose of this paper is to deal with the application of the stochastic inventory model to the three‐tier supply chain and verify the values obtained by mathematical model in physical simulation.

The paper investigates three‐stage serial supply chain with stochastic demand and fixed replenishment lead‐time. Inventory holding costs are charged at each stage, and each stage may incur a consumer backorder penalty cost charged by primary supplier to secondary supplier. The customer‐demand follows Poisson distribution. The base stock model is implemented for inventory control at both suppliers. Physical simulation is then designed in such a way that it satisfies all the assumptions for mathematical model. Simulation is run to verify the values obtained from mathematical model.

Computer simulation is designed to include all the assumptions made by mathematical model. Hence, mathematical base stock model and computer simulation model are comparable. Demand follows Poisson distribution in both cases. The backorder cost and inventory holding cost are calculated in each phase of simulation and summarized. The paper infers that the total inventory cost is optimum in phase II, in which reorder point is same as that calculated by mathematical model. In phase I, total inventory cost is more than that of phase II because of backorders. In phase III, excess inventory increased the total cost. Thus, the values obtained from mathematical model produce optimal inventory cost. Base stock model is effective when the demand is not deterministic and service factor assumed in mathematical model is 0.9, which is quite acceptable. Base stock model assumes replenishment order quantity as 1 and the total inventory cost decreases with replenishment lead time. Base stock model is beneficial for supply chains having short replenishment lead time. Computer simulation results indicate that discrete event simulations can be used to model stochastic systems like organizational supply chains and to validate the results from mathematical models.

The paper offers a review of simulation work aiming to support improvement of agility in the supply chain.

The purpose of this paper is to explore students' mathematization through a flow of lessons using the Thailand Lesson Study Incorporated Open Approach (TLSOA) to improve the excellence of instruction.

A total of 16 Grade 4 students were selected because they have been taught using the TLSOA model for four years. Six Lesson Study (LS) team members participated, and two instruments were utilized, namely student worksheets, and field notes. An ethnographic research design was employed.

The results revealed that the students' mathematical ideas were developed from the real world to the mathematical world through a flow of lessons based on the four phases of the Open Approach (OA).

Firstly, the students demonstrated their ability to represent the real world independently when the teacher posed an open-ended problem. Secondly, the students demonstrated their ability to use semi-concrete aids to develop their ideas while self-learning. Thirdly, the students showed how they developed their ideas to solve the open-ended problem using relevant objects or related concepts as part of a whole-class discussion and comparison exercise. Finally, the students demonstrated their abilities to represent the mathematical world using numbers and symbols to communicate their ideas when they were required to make a summary by connecting their mathematical ideas.

This study adds new insight to the literature on students' mathematization using the TLSOA model.

The purpose of this paper is to address a classic problem – pattern formation identified by researchers in the area of swarm robotic systems – and is also motivated by the need for mathematical foundations in swarm systems.

The work is separated out as inspirations, applications, definitions, challenges and classifications of pattern formation in swarm systems based on recent literature. Further, the work proposes a mathematical model for swarm pattern formation and transformation.

A swarm pattern formation model based on mathematical foundations and macroscopic primitives is proposed. A formal definition for swarm pattern transformation and four special cases of transformation are introduced. Two general methods for transforming patterns are investigated and a comparison of the two methods is presented. The validity of the proposed models, and the feasibility of the methods investigated are confirmed on the Traer Physics and Processing environment.

This paper helps in understanding the limitations of existing research in pattern formation and the lack of mathematical foundations for swarm systems. The mathematical model and transformation methods introduce two key concepts, namely macroscopic primitives and a mathematical model. The exercise of implementing the proposed models on physics simulator is novel.

The purpose of this paper is to build a mathematical model of men’s wear prototype, so that the computer can draw men’s wear prototype automatically.

First, the bust line, front and back center line, waist line, side seam, front chest width and back width line in the coordinate system are expressed by equations. Then, a parabola is used to establish a neckline curve, a linear equation is used to establish a shoulder oblique line, and a double ellipse is superposed to construct the armhole arc. Finally, all the garment prototype curves are built mathematical models.

The result shows that every curve of garment prototype can be expressed approximately by mathematical model.

This research lays the foundation for the automation and intelligence of garment pattern-making.

This paper aims to propose an innovative building information modelling (BIM)-based framework for multi-objective and dynamic temporary construction site layout design (SLD), which uses a hybrid approach of systematic layout planning (SLP) and mathematical modelling.

The hybrid approach, which follows a step-by-step process for site layout planning, is designed to facilitate both qualitative and quantitative data collection and processing. BIM platform is usedto facilitate the determination of the required quantitative data, while the qualitative data are generated through knowledge-based rules.

The multi-objective layout model represents two important aspects: layout cost and adjacency score. The result shows that the model meets construction managers’ requirements in not only saving cost but also assuring the preferences of temporary facility relationships. This implies that the integration of SLP and mathematical layout modelling is an appropriate approach to deliver practical multi-objective SLD solutions.

The proposed framework is expected to serve as a solution, for practical application, which takes the advantage of technologies in data collection and processing. Besides, this paper demonstrates, by using numerical experimentation and applying Microsoft Excel Solver for site layout optimisation, how to reduce the complexity in mathematical programming for construction managers.

The original contribution of this paper is the attempt of developing a framework in which all data used for the site layout modelling are collected and processed using a systematic approach, instead of being predetermined, as in many previous studies.

The purpose of this paper is to carry out a theoretical study of the stability of the mathematical models defined in a class of systems. Furthermore, it will be supposed that the models have been obtained from experimental data and by means of the application of a methodology. The studies carried out in this paper are, on one hand, the theoretical framework for an analysis of the sensitivity and stability of a type of systems; on the other hand, they supplement the studies carried out by the authors, in which, using a computational program, the sensitivity of the mathematical models is analyzed with respect to a type of perturbation.

Initially, a class of systems is considered that are denominated quantifiable systems, in which model systems are defined that are determined by a set and a family of relationships. An initial study of the sensitivity of the mathematical models to perturbations in the experimental data lead to a concept of sensitive and stable models that forms the basis of the theory of stability developed in this paper. Furthermore, this permits a definition of the stability function for the set of the perturbations and, consequently, a determination of stable models according to the defined theoretical structure.

An analysis of the sensitivity and stability of mathematical models in quantifiable systems from a systems theory perspective will be fundamental for the determination of mathematical model stability in environmental systems.

The studies carried out in this paper supposes an advance in the study and modeling of a type of systems that the authors have denominated as quantifiable systems, applicable to the study of environmental systems and supplementing the numeric studies carried out by the authors.

The purpose of this paper is to establish the nature of mathematical modeling of systems within the framework of the object-semantic methodology.

The initial methodological position of the object-semantic approach is the principle of constructing concepts of informatics proceeding from fundamental categories and laws. As the appropriate foundation, this paper accepts the system-physical meta-ontology is being developed in this paper.

The genesis of system modeling is considered in the aspect of the evolution of language tools in the direction of objectification. A new conception of formalized knowledge is being put forward as the mathematical form of fixing time-invariant relations of the universe, reflecting regularity of the dynamics of natural or anthropogenic organization. Object knowledge is considered as a key component of the mathematical model, and the solving of system information problems with its use is characterized as “work of knowledge.” The establishment of the meta-ontological essence of modern mathematical modeling allows us to formulate its fundamental limitations.

The establishment of system-physical limitations of modern mathematical modeling outlines the boundaries from which it is necessary to proceed in the development of future paradigms of cognition of the surrounding world, which presuppose convergence, synthesis of causal (physicalism) and target (elevationism) determination.

This paper aims to present a mathematical model of the dynamics of the unmanned aerial vehicle (UAV) vertical take-off and landing (VTOL). It will be used to develop control laws to a multirotor that is inherently unstable. Also, the model will be used to design algorithms to estimate the attitude of an object.

The physical model of UAV assumes that it is a rigid body with six degrees of freedom acted by forces generated by the propellers, motors, aerodynamic forces, gravity and disturbance forces. The mathematical model was described by differential equations. However, drive system (propeller, BLDC motor and BLDC motor controller) was described by six transfer functions. These transfer functions were demarcated with Matlab/Simulink identification toolbox from data received from a specially designed laboratory stand. Moments of inertia of the platform have been analytically determined and compared with empirical results from the pendulum. The mathematical model was implemented in Matlab/Simulink.

The paper confirms the need of designing mathematical models. Moreover, mathematical models show that some parts of the object are better to be replaced by experimental results than by equations, which is proved by the data. The paper also shows advantages of using Matlab/Simulink. What is more the simulation of the model proves that multirotor is an unstable object.

The test results show that drive units are strongly dependent on ambient conditions. An additional problem is the different response of the drive set to increasing and decreasing the control signal amplitude. Next tests will be done at different temperatures and air densities of the environment, also it is need to explore drag forces.

The mathematical model is a simplification of the physical model expressed by means of equations. The results of simulation like accelerations and angular rate are noise-free. However, available sensors always have their errors and noise. To design control loops and attitude estimation algorithms, there is a need for identification of sensors’ errors and noise. These parameters have to be measured.

The paper describes a solution of correct identification of drive unit, which is a main component of the UAV.