Micro-computers and mathematical software

Explaining the effect of geometric habits of mind on mathematics courses can affect how to realize the conceptual teaching. Within this scope the aim of the study is to determine the relationship between mathematics preservice teacher’s geometric habits of mind and mathematics achievement. Therefore, this study is carried out with 30 senior preservice teacher in a state university in Turkey. In this study, the relationship between preservice teacher’s geometric habits of mind achievements tests’ scores and mathematics courses’ scores are analyzed. As a result of the study, positive and statistically significant relationship is found between preservice teacher’s geometric habits of mind scores and some mathematics courses such that Geometry, Analytical Geometry 2 and Mathematical Software. It is mean that preservice teachers use geometric habits of mind while encountered problems.

This paper reports from a case study with teachers at two schools in Norway participating in developmental projects aiming for inquiry communities in mathematics teaching and learning. In the reported case study, the teachers participated in one of the developmental projects focusing on implementation and use of computer software in mathematics teaching. I study teachers’ initial orchestration of dynamic geometry software (DGS) in mathematics teaching at lower secondary school. By utilising the notion of ‘instrumental orchestration’ from the theoretical perspective known as the ‘instrumental approach’ (Drijvers et al., in Educ Stud Math 75:213–234, 2010; Trouche, in Int J Comput Math Learn 9:281–307, 2004), I examine how teachers in their initial teaching with DGS empower students’ mathematics learning with the DGS software. According to this perspective, it involves teachers’ orchestration of two interrelated processes instrumentation and instrumentalisation. Analytical findings indicate that a difference in teachers’ empowerment is evident and consequences for students’ opportunities to engage with mathematics represented by the DGS are presented.

Subjects of the research are industrial electric drives, witch maintain the operation of main actuating units of production machines and installations during the development of mineral resource deposits. The goal is to research the possibility to ensure the energy decoupling of industrial electric drives and electric grid by means of structural implementation of active rectifiers into frequency converters. The main purpose of energy decoupling is to eliminate the negative impact of low quality electric energy and changes in energy parameters on electric drive operation. In order to accomplish energy decoupling of electric drive with active rectifier, methods of mathematical and simulation modeling with mathematical application software package were used. The integrated simulation model with two electric drives, including active rectifier (energy decoupled electric drive) and diode rectifier (standard type electric drive), were created. Simulation model is provided with tools for oscillographic testing and analysis of the impact of power quality parameters on frequency converters and drive motors operation. The analysis of effectiveness of energy decoupling by means of active rectifier of frequency converter shows that drive motor completely retains the stability and controllability of rotation frequency and torque during the changes of power quality parameters in electric grid. The use of active rectifier allows to ensure the operation of electric drive in required mode in case of voltage decrease by 30 % with normative value of 5-10 %, i.e. energy decoupling provides high stability margin for voltage. Electric drive with active rectifier ensures energy decoupling in case of asymmetry of supply voltage. The control of mechanical variables of induction motor during offsets in amplitude and frequency in all phases of electric grid is ensured to be on required level.

In this paper, we consider the application of brute force computational techniques (BFCTs) for solving computational problems in mathematical analysis and matrix algebra in a floating-point computing environment. These techniques include, among others, simple matrix computations and the analysis of graphs of functions. Since BFCTs are based on matrix calculations, the program system MATLAB® is suitable for their computer realization. The computations in this paper are completed in double precision floating-point arithmetic, obeying the 2019 IEEE Standard for binary floating-point calculations. One of the aims of this paper is to analyze cases where popular algorithms and software fail to produce correct answers, failing to alert the user. In real-time control applications, this may have catastrophic consequences with heavy material damage and human casualties. It is known, or suspected, that a number of man-made catastrophes such as the Dharhan accident (1991), Ariane 5 launch failure (1996), Boeing 737 Max tragedies (2018, 2019) and others are due to errors in the computer software and hardware. Another application of BFCTs is finding good initial guesses for known computational algorithms. Sometimes, simple and relatively fast BFCTs are useful tools in solving computational problems correctly and in real time. Among particular problems considered are the genuine addition of machine numbers, numerically stable computations, finding minimums of arrays, the minimization of functions, solving finite equations, integration and differentiation, computing condensed and canonical forms of matrices and clarifying the concepts of the least squares method in the light of the conflict remainders vs. errors. Usually, BFCTs are applied under the user’s supervision, which is not possible in the automatic implementation of computational methods. To implement BFCTs automatically is a challenging problem in the area of artificial intelligence and of mathematical artificial intelligence in particular. BFCTs allow to reveal the underlying arithmetic in the performance of computational algorithms. Last but not least, this paper has tutorial value, as computational algorithms and mathematical software are often taught without considering the properties of computational algorithms and machine arithmetic.

The aims of this study are conducted to know: (1) the comprehension and improvement of students ability of mathematical communications after studying cooperative learning model think-pair-share type with media software Autograph, (2) the students design in answering math comprehension and communications, (3) students responds to cooperative learning model think-pair-share type with media software Autograph. This research is a classroom action research. The subject of this research is 40 students of grade XI SMK N 9 Medan. The research object is the improvement of students ability in mathematical comprehension and communication through cooperative learning model think-pair-share type with media software Autograph at discussion of transformation. The instruments are pretest, communication mathematical test, comprehension mathematical test, student note, observation sheets, and students respond. The reliable of pretest, comprehension mathematical test cycle 1 and 2 is 0,86 and the reliable of communication mathematical test is 0,88. This study consisted of 2 cycles of the first cycle consisted of 4 meetings and the second cycle consisted of 2 meetings. The result of study show that the (1) application of cooperative learning model think-pair-share type with media software Autograph can improve the ability of mathematical comprehension and mathematical communications of student, (2) the design in answering math communications and math comprehension are graphic is true and complete, the description of graphic is not complete enough, the description of graphic is true and complete, the description of graphic is not complete. (3) Students respond of cooperative learning model think-pair-share type with media software Autograph is good. Based on this conclusion it is expected that the teachers can apply cooperative learning model think-pair-share type with media software Autograph to improve the ability of mathematical comprehension and mathematical communications of student.

According to published statistics regarding pharmaceutical industries, there has been a significant increase in the demand for cosmetics and skincare products. As a result, there has also been an increase in interest by researchers to conduct experimental and theoretical studies on these industries. The outermost layer of the skin, which is the stratum corneum, plays a key role in determining the skin permeability. This layer represents the first and main barrier against dehydration and screening from external elements and pathogens. Research efforts have been made to better understand skin permeability. Experimental methodologies play a key role in pharmaceutical and dermatology studies. However, ethical standards of using animal and human models in in-vitro permeability studies are very strict in their admission process and approval time. Furthermore, the lack of available material and financial resources for setting up, operating and repeating experiments has also limited the required progress. These problems can be addressed by developing better mathematical models on skin permeability. Progress, regarding the mathematical modelling of solute transport in skin, has been achieved in the last decades. The mathematical modelling strategy is used as a skin permeability predictor tool based on common physicochemical properties of the skin and penetrated solute molecules. Many factors play an important role in the formulation of a mathematical model and in determining how reliable the predicted results are. Therefore, the more skin physiological details are included in the model, the more computational efforts are required to interpret the solute permeation mechanisms in the dermal region and simulate a drug transport in the transdermal administration. The mathematical complexities associated with formulating a mathematical model of drug transport in skin significantly limit the utilities of such models in practice. Thus, a balance between the model’s complexity and how realistic it is in describing the solute transport processes in skin has to be achieved. Therefore, a mathematical model formulated on principles familiar to the pharmaceutical scientific community could be of value. In this thesis, we have developed a novel mathematical model using a compartmental approach. The proposed model enables for simulating solute transport across the stratum corneum (SC) in a variety of exposure scenarios in percutaneous drug delivery systems. The obtained results were compared with the diffusion model outcomes – which can be considered the current ‘golden standard’ for modelling skin transport – and showed a good agreement. The mathematical foundations of the model are relatively simple and better aligned with the physiology of the stratum corneum. In addition, this work shows that performing a numerical simulation using the compartmental model is less demanding than using the diffusing model, especially for complex exposure scenarios, and can be performed using free software, such as Python. The research findings of this thesis contribute towards a better understanding of transport phenomena across the skin. Also, the compartmental model proposed in this work can be used to describe transport phenomena in the membrane. Due to the similarity between the governing equations of diffusion and heat transfer, the proposed approach also offers a mathematical framework for studying heat transfer problems in biomaterials with minimum model development or computational efforts.

Software is the object of study in software engineering and computer science. Software is an intellectual artifact that provides a solution for a repeatable computer application, which enables existing tasks to be done easier, faster, and smarter, or which provides innovative applications for the industries and daily life. This paper attempts to explore the basic characteristics of software and to search the informatics and cognitive foundations of software in supplement to theories of computer science. In this paper, the nature of software is characterized by its informatics, behavioral, mathematical, and cognitive properties. Then, the cognitive informatics foundations of software engineering are developed on the basis of the informatics laws of software and software engineering psychology.

The continuously growing computing power of modern comput ers admits to tackle numerical problems of extreme complexity This complexity carries over to the numerical methods applied to solve the problems Whereas the mathematical formulation of these methods does not raise any di culties their implementation turns out to be the bottleneck in the realization of numerical applications In the last years in order to a ord relief object oriented methods were applied to promote reusable and extensible numerical software since this kind of exibility is the key to manage complexity It be came evident that a carefully chosen modularization of the considered methods is a necessary requirement to provide exible software com ponents In this paper we give a brief review of object oriented methods to identify the key issues that support a exible software design and discuss a modularization technique based on mathematical concepts Finally the application of this concept oriented approach to boundary element methods is presented Presented at the th GAMM Seminar on Concepts of Numerical Software Christian Albrechts Universit at Kiel January th to th in press in Notes on Numerical Fluid Mechanics Vieweg

The numerical modeling of physical phenomena has become for many users a necessity. It allows both a better understanding of the studied system and a better link with the purpose and policy makers. We discuss mathematical models, which attempts to represent the physical phenomenon of groundwater flow by mathematical expressions using different software to facilitate the design models. Coupled with GIS software model has become possible, through a database synthesized to introduce geographic data such as boundary conditions, wells, recharge areas, who see themselves as the fuel of the model, but the role of this software is limited to a part in the preparation of data for use in software hydrogeological modeling and secondly, in view of the results obtained by them, hence the need for a customized GIS application. The user of GIS in the field of hydraulic modeling groundwater is brought to the exercise of his profession to reproduce a large number of both transactions; similar processing where it needs personalized treatments. The automation of these processing in the ArcMap environment using Java ArcObjetcs and has led to significant time savings and ease in handling input data and output results.

We can only test software effectively if we under- stand how it is intended to behave. For some categories of programs, such as scientific models, it is not obvious what the output of the software should be. New techniques are needed to help domain experts, such as scientists, gather the knowledge they need to construct suitable tests and oracles. This paper introduces a new interactive tool for iterative test suite construction that is based upon the scientific method paradigm that scientists are familiar with. We apply our technique to a deterministic mathematical model, used to predict the spread of disease, and show how it helps scientists uncover situations they had not yet considered. Of the 15 hypotheses originally created by modellers, our technique found discrepancies in all but one, allowing us to refine them into a more rigorous test suite. Scientific software is particularly difficult to test, because its correct behaviour is not normally known in advance. The software is developed to investigate new research questions and the perceptions of researchers change as their hypotheses are explored (5). If we already knew the answers to these questions, there would be no need to create the software in the first place. Intrinsic difficulties occur in evaluating the output of scientific software, due to the stochasticity and uncertain- ties in the underlying model. Scientific software frequently incorporates complex models with nonlinear dynamics that are difficult to test. Each numerical approximation has the potential to introduce new errors (5), inaccuracies may arise due to the way in which experimental data are collected, and then when the model is implemented on a finite precision computer, some further accuracy is inevitably lost.

The use of a mixed biometric model for breeding evaluation of small cattle has been discussed in the article. This model of breeding evaluation involves a large number of matrix operations. At the same time, the volumes of the formed matrices are directly proportional to the number of animals in the evaluated sample as well as to the number of their off spring. An algorithm for generating matrices of estimated effects that have a large dimension has been presented in the paper. This task is the most time-consuming when using a mixed biometric model. Currently, there are the large number of mathematical packages that provide ample opportunities for performing calculations. A special place in this series is occupied by the integrated mathematical package MATLAB has been designed specifically for performing matrix operations. The authors rely on the use of this package in their work. At the same time the algorithm presented in this paper has the property of universality and can be applied by users in any other software product. Since the matrices of the estimated effects consist of zeros and ones we propose the two-step procedure for forming these matrices. At the first stage, a zero matrix of the required dimension is created. At the second stage, in accordance with the data on the number of evaluated animals, the number of herds for which off spring are distributed, the number and affiliation of evaluated animals to genetic groups, the elements of the matrix are determined, in which zeros are replaced by ones. The advantage of the proposed algorithm is its versatility, and the representation of the algorithm in the form of a block diagram will allow you to design it as a separate proceduresubroutine.

Mathematical models of competitive processes in the economy using known universal models that describe the behavior of counterparties in the market are found in this article. The object of research is to build mathematical models of competitive processes in a pair – secondhand dealer, and to process and convert the economic parameters that are necessary for the models. The methods of research use analysing and solving equations for the known and improved universal models that describe the behaviour of contractors in the market. Mathematical package for construction of schedules of dependences is used. The goals are to construct and research the modified model on the basis of mathematical model by Lotka- Volterra and its further development, and to create software product for statistical processing the economic information. Results – the mathematical model manufacturer – secondhand dealer is created, its modified version is received, and with the help of mathematical package Mathcad, researches of models were done. Prospects of the further improvement of models are revealed. The software product is developed, allowing to process the statistical economic information. On the basis of mathematical model by Lotka-Volterra and its further development a mathematical model of several producers and one middleman is created. Its modified version is studied using mathematical package Mathcad. The nonstable behavior of the counterparties is found. For this model some prospects for further improvements is identified.

This paper uses the mathematical software Maple for the auxiliary tool to study three types of integrals. We can obtain the infinite series forms of these three types of integrals by using integration term by term theorem. In addition, we propose some examples to do calculation practically. The research methods adopted in this study involved finding solutions through manual calculations and verifying these solutions using Maple.

This paper uses the mathematical software Maple for the auxiliary tool to study three types of definite integrals. The closed forms of these definite integrals can be obtained using Parseval’s theorem. In addition, we propose some definite integrals to do calculation practically. The research methods adopted in this study is to find solutions through manual calculations and verify these solutions using Maple.

Objective To find a new method for evaluating the left ventricular relaxation time constant Tau with aortic regurgitation by continuous wave Doppler. Methods Twelve Beagle dogs were included in the study. The dog aortic regurgitation model was produced under ultrasound guiding by carotid artery puncture. Aortic pressure was measured by pressure catheter and left ventricular pressure was measured by Millar catheter which was introduced into the left ventricular through cardiac apex. Then microspheres were injected into the left coronary artery under the guidance of ultrasound to induce acute ischemic left ventricular dysfunction, when left ventricular end-diastolic pressure increased more than 5 mmHg (1 mmHg=0.133 kPa). Dobutamine or esmolol was infused to alter left ventricular function. Aortic regurgitation velocity spectrum was recorded by the continuous-wave Doppler echocardiography in different hemodynamic status. At the same time, left ventricular pressure, dp/dt, aortic pressure and continuous ECG tracing were displayed on the multi-channel physiological recorder. Measurement was recorded of –dp/dtmax in the dp/dt tracings and the pressure at the time of –dp/dtmax in the left ventricular pressure tracings. Tau =-P/(dp/dtmax), Tau was the catheter-derived time constant (Taucatheter). Aortic regurgitation spectrum of original audio data was post-processed with MATLAB mathematical software. The spectral lines refresh time of about 300 μs was chosen to form a new Doppler spectrum. Three points: (t1,1 m/s), (t2, 2 m/s) and (t3, 3 m/s) were selected in aortic regurgitation velocity spectrum and t1, t2 and t3 was put into the corresponding Tau formula: Tau=(t2-t1)/ln[(ADP-C-4)/(ADP-C-16)], Tau=(t3-t1)/ln[(ADP-C-4)/(ADP-C-36)]. Tau was the aortic regurgitant time constant (Tauultrasound). The difference between Taucatheter and Tauultrasound was compared by paired t test. The correlation between Taucatheter and Tauultrasound was analyzed by Pearson correlation analysis. Results Twelve dogs were successfully produced aortic regurgitation model. Two dogs died of ventricular fibrillation during the procedure of acute ischemic left ventricular diastolic dysfunction. The range of the Taucatheter was between 27.12 ms and 86.88 ms with an average of (48.973±14.667) ms; the range of the Tauultrasound was between 28.13 ms and 90.18 ms with an average of (51.236±15.146) ms. The difference was not statistically significant (t=1.841, P>0.05). Pearson correlation analysis showed that Taucatheter was positively correlated with Tauultrasound (r=0.89, P=0.000). Conclusion Choosing three points: (t1, 1 m/s), (t2, 2 m/s) and (t3, 3 m/s) in aortic regurgitant velocity spectrum and putting into the corresponding formula, we can calculate Tau, which had a good correlation with the catheter-derived Tau. Key words: Left ventricular relaxation time constant; Continuous wave Doppler; Aortic valve insufficiency