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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 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.

The purpose of this paper is to illustrate the expressive power of Wald's maximin model and the mathematical modeling effort requisite in its application in decision under severe uncertainty.

Decision making under severe uncertainty is art as well as science. This fact is manifested in the insight and ingenuity that the modeller/analyst is required to inject into the mathematical modeling of decision problems subject to severe uncertainty. The paper elucidates this point in a brief discussion on the mathematical modeling of Wald's maximin paradigm.

The apparent simplicity of the maximin paradigm implies that modeling it successfully requires a considerable mathematical modeling effort.

The paper illustrates the importance of mastering the art of mathematical modeling especially in the application of Wald's maximin model.

This paper sheds new light on some of the modeling aspects of Wald's maximin paradigm.

To develop and test three different inventory management strategies as applied to the complex emergency in south Sudan.

Quantitative modeling, simulation, and statistics.

This research identified critical system factors that contributed most significantly to inventory system performance, and identified strengths and weaknesses of each inventory management strategy.

This research represents a first step in developing inventory management systems for humanitarian relief. Future work would include modeling correlation among relief items, multiple items, and considering the impact of information.

In a domain that has seen limited application of quantitative models, this work demonstrates the performance benefits of using quantitative methods to manage inventory in a relief setting.

This research has value for relief organizations by providing a real‐world application of quantitative inventory management strategies applied to a complex emergency, and demonstrated performance advantages of quantitative versus ad hoc methods. This research has value for researchers by providing a new application of simulation and mathematical modeling (humanitarian relief).

The purpose of this paper was to solve the shortage of carrying energy in probing robot and make full use of wind resources in the Antarctic expedition by designing a four-wheel land-yacht. Land-yacht is a new kind of mobile robot powered by the wind using a sail. The mathematical model and trajectory of the land-yacht are presented in this paper.

The mechanism analysis method and experimental modeling method are used to establish a dual-input and dual-output mathematical model for the motion of land-yacht. First, the land-yacht’s model structure is obtained by using mechanism analysis. Then, the models of steering gear, servomotors and force of wing sail are analyzed and validated. Finally, the motion of land-yacht is simulated according to the mathematical model.

The mathematical model is used to analyze linear motion and steering motion. Compared with the simulation results and the actual experimental tests, the feasibility and reliability of the proposed land-yacht modeling are verified. It can travel according to the given signal.

This land-yacht can be used in the Antarctic, outer planet or for harsh environment exploration.

A land-yacht is designed, and the contribution of this research is the development of a mathematical model for land-yacht robot. It provides a theoretical basis for analysis of the land-yacht’s motion.

The purpose of this paper is establishing a general mathematical model and theoretical design rules for 3D printing of biomaterials. Additive manufacturing of biomaterials provides many opportunities for fabrication of complex tissue structures, which are difficult to fabricate by traditional manufacturing methods. Related problems and research tasks are raised by the study on biomaterials’ 3D printing. Most researchers are interested in the materials studies; however, the corresponded additive manufacturing machine is facing some technical problems in printing user-prepared biomaterials. New biomaterials have uncertainty in physical properties, such as viscosity and surface tension coefficient. Therefore, the 3D printing process requires lots of trials to achieve proper printing parameters, such as printing layer thickness, maximum printing line distance and printing nozzle’s feeding speed; otherwise, the desired computer-aided design (CAD) file will not be printed successfully in 3D printing.

Most additive manufacturing machine for user-prepared bio-material use pneumatic valve dispensers or extruder as printing nozzle, because the air pressure activated valve can print many different materials, which have a wide range of viscosity. We studied the structure inside the pneumatic valve dispenser in our 3D heterogeneous printing machine, and established mathematical models for 3D printing CAD structure and fluid behaviors inside the dispenser during printing process.

Based on theoretical modeling, we found that the bio-material’s viscosity, surface tension coefficient and pneumatic valve dispenser’s dispensing step time will affect the final structure directly. We verified our mathematical model by printing of two kinds of self-prepared biomaterials, and the results supported our modeling and theoretical calculation.

For a certain kinds of biomaterials, the mathematical model and design rules will have unique solutions to the functions and equations. Therefore, each biomaterial’s physical data should be collected and input to the model for specified solutions. However, for each user-made 3D printing machine, the core programming code can be modified to adjust the parameters, which follows our mathematical model and the related CAD design rules.

This study will provide a universal mathematical method to set up design rules for new user-prepared biomaterials in 3D printing of a CAD structure.

In this chapter, we present our ongoing efforts in developing and sustaining interdisciplinary STEM undergraduate programs at North Carolina A&T State University (NCA&T) – a state-supported HBCU and National Science Foundation (NSF) Historically Black Colleges and Universities Undergraduate Program (HBCU-UP) Institutional Implementation Project grantee. Through three rounds of NSF HBCU-UP implementation grants, a concerted effort has been made in developing interdisciplinary STEM undergraduate research programs in geophysical and environmental science (in round 1), geospatial, computational, and information science (in round 2), and mathematical and computational biology (in round 3) on NCA&T campus. We first present a brief history and background information about the interdisciplinary STEM undergraduate research programs developed and sustained at NCA&T, giving rationales on how these programs had been conceived, and summarizing what have been achieved. Next we give a detailed description on the development of undergraduate research infrastructure including building research facilities through multiple and leveraged funding sources, and engaging a core of committed faculty mentors and research collaborators. We then present, as case studies, some sample interdisciplinary research projects in which STEM undergraduate students were engaged and project outcomes. Successes associated to our endeavor in developing undergraduate research programs as well as challenges and opportunities on implementing and sustaining these efforts are discussed. Finally, we discuss the impact of well-structured undergraduate research training on student success in terms of academic performance, graduation rate and continuing graduate study, and summarize many of the learnings we have gained from implementation and delivery of undergraduate research experiences at HBCUs.

The novel bearingless switched reluctance motor (BSRM) is proposed recently, which is different from the conventional BSRM in the stator structure and suspension winding arrangement. The reduced number of suspension windings makes the novel BSRM much simpler, so that the control circuit and algorithm are greatly simplified when compared to those of the conventional BSRM. This paper for the first time proposes the novel BSRM's analytic model, including the mathematical relationships among the winding currents, rotor angle, radial forces, and motor torque, to further achieve the suspending forces and torque control. The paper aims to discuss these issues.

The magnetic equivalent circuit method is employed to obtain the self-inductances and mutual-inductances of the motor torque windings (main windings) and suspension windings (control windings). The straight flux paths are combined with the elliptical fringing flux paths to calculate the air-gap permeances, and the stored magnetic energy. Then, the mathematical expressions of radial forces and torque are derived. A novel BSRM prototype is analyzed through using the proposed analytical model and the finite element model. The results of both methods are compared to verify the proposed mathematical model.

The proposed mathematical model of the novel BSRM considering unsaturated magnetic circuits is verified by finite-element analysis results.

The mathematical model represents the situation of magnetic circuit unsaturated and is not suitable for the magnetic circuit saturation. It cannot be used to control the motor which is working in the deep magnetic circuit saturation region.

Building mathematical model is a necessary step for the motor's suspension and rotating control. The built model provides the fundamental for the preliminary control algorithm and experimental study of this novel BSRM.

For the first time, the novel BSRM's mathematical model is proposed. It provides necessary fundamental for the motor's further analysis, design, and suspending and rotating controls.

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.