Advancing Mathematical Activity: A Practice-Oriented View of Advanced Mathematical Thinking

The purpose of this article is to contribute to the dialogue about the notion of advanced mathematical thinking by offering an alternative characterization for this idea, namely advancing mathematical activity. We use the term advancing (versus advanced) because we emphasize the progression and evolution of students' reasoning in relation to their previous activity. We also use the term activity, rather than thinking. This shift in language reflects our characterization of progression in mathematical thinking as acts of participation in a variety of different socially or culturally situated mathematical practices. For these practices, we emphasize the changing nature of students' mathematical activity and frame the process of progression in terms of multiple layers of horizontal and vertical mathematizing.     

Two novel FMCDM methods for alternative-fuel buses selection

In this paper, we consider the problem of alternative-fuel buses selection using two novel fuzzy multiple criteria decision-making (MCDM) methods. Several types of fuels are considered as fuel modes, i.e., electricity, fuel cell (hydrogen), and methanol. For the purpose of determining appropriate fuel buses, many factors including quantitative and qualitative ones such as efficiency, price, and capability must be taken into account. In the first proposed method, linguistic variables are used to assess the ratings and weights for factors. These linguistic ratings can be expressed in trapezoidal or triangular fuzzy numbers. Then, a hierarchical MCDM method based on fuzzy-sets theory is proposed to deal with the fuel buses selection problem. To simultaneously determine the ranking order of all alternatives based on the concept of the TOPSIS by calculating the distances to the both fuzzy positive-ideal solution (FPIS) and fuzzy negative-ideal solution (FNIS), a closeness coefficient is defined. In the second presented method we extend preference selection index (PSI) method for fuzzy environment. In this method performance ratings of criteria evaluate by linguistic variable which can be expressed in trapezoidal fuzzy numbers. Finally, an example is shown to highlight the procedure of the proposed methods and compare the results of these methods with each other.     

Defining as a mathematical activity: A framework for characterizing progress from informal to more formal ways of reasoning

The purpose of this paper is to further the notion of defining as a mathematical activity by elaborating a framework that structures the role of defining in student progress from informal to more formal ways of reasoning. The framework is the result of a retrospective account of a significant learning experience that occurred in an undergraduate geometry course. The framework integrates the instructional design theory of Realistic Mathematics Education (RME) and distinctions between concept image and concept definition and offers other researchers and instructional designers a structured way to analyze or plan for the role of defining in students’ mathematical progress.     

A robust parameter design for multi-response problems

Most real world search and optimization problems naturally involve multiple responses. In this paper we investigate a multiple response problem within desirability function framework and try to determine values of input variables that achieve a target value for each response through three meta-heuristic algorithms such as genetic algorithm (GA), simulated annealing (SA) and tabu search (TS). Each algorithm has some parameters that need to be accurately calibrated to ensure the best performance. For this purpose, a robust calibration is applied to the parameters by means of Taguchi method. The computational results of these three algorithms are compared against each others. The superior performance of SA over TS and TS over GA is inferred from the obtained results in various situations.     

Drug Release Study of Systems Containing the Tragacanth and Collagen Composite: Release Characterization and Viscoelastic Measurements

The kinetics of water penetration and pentoxifilline release from both Tragacanth gum and Tragacanth/Collagen matrices has been examined in pure deionised water. The rheological oscillatory measurements of their gel layer obtained by swelling of the imprinted pentoxifilline-filled polymer matrix with water have been performed. To qualify a polymer for application in drug formulation, appropriate gel stiffness is required. The aqueous solution of Tragacanth does not seem to acquire the actual strength that a hydrogel must retain for this purpose. Thus, along with Tragacanth, gelatin, CaCl₂ and 1, 8 octandiamine curing agent were individually blended in a mixture with Tragacanth gum to improve the gel behavior and drug delivery of the system. The strength of the gel at the body temperature (37 °C) was studied using a cone and plate rheometer. It was found that gelatin could enhance the gel strength of Tragacanth by forming a porous composite. The drug release to an aqueous solution at room temperature was analyzed to be slower for a composite of 1:2 Tragacanth/Collagen.     

A review on the applications of micro-/nano-encapsulated phase change material slurry in heat transfer and thermal storage systems

Journal of Thermal Analysis and Calorimetry - In modern heat transfer systems, thermal storage not only causes the balance between demand and supply, but also improves the heat transfer efficiency...     

Scheduling open shops with parallel machines to minimize total completion time

This paper explores scheduling a realistic variant of open shops with parallel machines per working stage. Since real production floors seldom employ a single machine for each operation, the regular open shop problem is very often in practice extended with a set of parallel machines at each stage. The purpose of duplicating machines in parallel is to either eliminate or to reduce the impact of bottleneck stages on the overall shop efficiency. The objective is to find the sequence which minimizes total completion times of jobs. We first formulate the problem as an effective mixed integer linear programming model, and then we employ memetic algorithms to solve the problem. We employ Taguchi method to evaluate the effects of different operators and parameters on the performance of memetic algorithm. To further enhance the memetic algorithm, we hybridize it with a simple form of simulated annealing as its local search engine. To assess the performance of the model and algorithms, we establish two computational experiments. The first one is small-sized instances by which the model and general performance of the algorithms are evaluated. The second one consists of large-sized instances by which we further evaluate the algorithms.     

Interfacing DNA and Polydopamine Nanoparticles and Its Applications

Polydopamine (PDA) is polymerized from dopamine under oxidative and basic conditions. PDA is a biocompatible material with great versatility for coating various surfaces and it can also form nanoparticles. DNA oligonucleotides are highly stable, and they can recognize a diverse range of molecules from complementary nucleic acids, proteins to small molecules and metal ions. To enhance the molecular recognition function of PDA, it is interfaced with DNA and the conjugates have achieved a wide range of applications in biomedical and analytical science. In this review, the chemistry of some catecholamines, including dopamine and PDA, is first briefly introduced and variables in the PDA synthesis are highlighted. Strategies to promote DNA adsorption on PDA are then discussed including the use of low pH and polyvalent metal ions. In addition, covalent attachment of DNA to PDA can be achieved by using amino or thiol-modified DNA, forming highly stable conjugates. The specific applications of PDA–DNA conjugate are also delineated, including DNA extraction, biosensing, intracellular delivery, and DNA origami. Finally, some problems in the field are discussed, along with a few future research opportunities.     

A hypothetical learning trajectory for conceptualizing matrices as linear transformations

In this paper, we present a hypothetical learning trajectory (HLT) aimed at supporting students in developing flexible ways of reasoning about matrices as linear transformations in the context of introductory linear algebra. In our HLT, we highlight the integral role of the instructor in this development. Our HLT is based on the ‘Italicizing N’ task sequence, in which students work to generate, compose, and invert matrices that correspond to geometric transformations specified within the problem context. In particular, we describe the ways in which the students develop local transformation views of matrix multiplication (focused on individual mappings of input vectors to output vectors) and extend these local views to more global views in which matrices are conceptualized in terms of how they transform a space in a coordinated way.