基于灰色数学的洗胃液量的软测量

鉴于洗胃液量实时在线检测与求解的困难,提出利用灰色数学的累加生成方法,把液量作为主导变量,管路二处压力差的累积压力作为二次变量,根据二者之间的一一映射关系,仿真实验研究洗胃液量的软测量技术,给出了实验结果,为液量的工程检测提供了一种数学方法.     

Generalized nets in neurology: an example of mathematical modelling

The purpose of this paper is to explain the basic theory of generalized nets (GNs) and their applications in the context of the differential diagnosis of neurological diseases. We define formally the concepts of a GN and transitions of a GN and also outline some remarks on their theory. The work here constructs an example which aims to trace the process of diagnosing different signs and symptoms in neurology. This will enable the interested reader to see the scope of nets in general as tools for the modelling, simulation, optimization and control of real processes.     

Pedagogical challenges in making mathematics relevant for Indigenous Australians

After the invasion and occupation of their land by Europeans, Indigenous Australians were expected to benefit from a Western education system based on that of the dominant Europeans. Gradually educators realized that Aboriginal children learn differently and that Indigenous culture and pedagogy has validity and strength. Of course, educators also need to be acutely aware of the diversity of Indigenous cultures in Australia and that there is not a monolithic sense of Aboriginal identity or Aboriginal pedagogy. Dispossession and alienation, poor health and few employment opportunities must also affect educational interest, attendance, application and performance. In this paper the characteristics of Indigenous learners are examined and pedagogical strategies to assist in both students' learning and teachers' delivery are explored. The message conveyed in this paper has particular relevance for teaching mathematics to Aboriginal learners. It is also of considerable value in teaching mathematics to nonAboriginal students, in Australia and elsewhere.     

Liquid hydridosilane precursor prepared from cyclopentasilane via sonication at low temperatures without the action of light

We report on a liquid hydridosilane precursor ink prepared via the ultrasonically induced ring-opening polymerisation of cyclopentasilane (Si₅H₁₀) without irradiation by ultraviolet light. The sonication is carried out in N₂ atmosphere at temperatures between 20 and 75 °C. We use size exclusion chromatography (SEC) to show polymer growth and estimate molecular mass with increasing sonication time. In combination with UV–vis transmission measurements, further SEC analysis is used to compare solutions subjected to either purely thermal or ultrasonic treatment at the same process temperature and for the same duration. Our findings provide strong evidence showing that the initiation of the polymerisation is sonocatalytic in nature and not thermic due to the macroscopic temperature of the solution. The liquid precursor is used to produce homogeneous hydrogenated amorphous silicon (a-Si:H) thin films via spin coating and pyrolytic conversion. The optoelectronic properties of the films are subsequently improved by hydrogen radical treatment. Fourier transform infrared spectroscopy (FTIR) is used to determine a compact film morphology and electrical conductivity measurements show that the layers attain a light-to-dark photosensitivity ratio of 2 × 10³ making them suitable for application in optoelectronic devices.     

杰出人物论微积分

摘编14位杰出人物对微积分的精辟论述。     

Evolving a three-world framework for solving algebraic equations in the light of what a student has met before

In this paper we consider data from a study in which students shift from linear to quadratic equations in ways that do not conform to established theoretical frameworks. In solving linear equations, the students did not exhibit the ‘didactic cut’ of Filloy and Rojano (1989) or the subtleties arising from conceiving an equation as a balance (Vlassis, 2002). Instead they used ‘procedural embodiments’, shifting terms around with added ‘rules’ to obtain the correct answer (Lima & Tall, 2008). Faced with quadratic equations, the students learn to apply the formula with little success. The interpretation of this data requires earlier theories to be seen within a more comprehensive framework that places them in an evolving context. We use the developing framework of three worlds of mathematics (Tall, 2004, Tall, 2013), based fundamentally on human perceptions and actions and their consequences, at each stage taking into account the experiences that students have ‘met-before’ (Lima and Tall, 2008, McGowen and Tall, 2010). These experiences may be supportive in new contexts, encouraging pleasurable generalization, or problematic, causing confusion and even mathematical anxiety. We consider how this framework explains and predicts the observed data, how it evolves from earlier theories, and how it gives insights that have both theoretical and practical consequences.     

Expanding conceptions of utility: middle school students’ perspectives on the usefulness of mathematics

This research explores how adolescents conceptualize the usefulness of mathematics. Integrating sociocultural theory with the study of utility value, this study uses open-ended survey items and interview tasks to examine conceptions of usefulness among a group of predominantly Latinx middle school students. Findings reveal that students primarily conceptualized the usefulness of mathematics in two ways. First, students considered the applicability of mathematics content, focusing on applications of mathematics in everyday life and future jobs/careers. Second, students considered the usefulness of features of the learning experience, such as the form of interaction and structure of the activity. Both conceptions are compared to existing conceptions of usefulness in the literature, and implications for classroom practice and future research are discussed.