Corrigendum: Remark on Algorithm 723: Fresnel Integrals

There are mistakes and typographical errors in Remark on Algorithm 723: Fresnel Integrals , which appeared in ACM Transactions on Mathematical Software 22, 4 (December 1996). This remark corrects those errors. The software provided to Collected Algorithms of the ACM was correct.

Solving a Triangle in Teaching Primary School Mathematics

The paper studies solving a triangle in primary school mathematics education. It proposes a system of problems reflecting the classification of the concept of triangle according to the sides and the angles. Each subsystem of a given main system includes a basic problem with generalized formulation and a sample solution followed by problems illustrating the basic problem. The methodological analysis encompasses some didactic components – short description, construction/drawing, sample solution, necessary component concepts, component pieces of knowledge and component problems. All drawings in the study have been made by using the mathematical software GeoGebra in order to ensure dynamism and clarity, and subsequently to achieve easier understanding of a problem and finding out its solution.

Visualization In Mathematics Teaching

In recent years, there has been an increased use of information and communication technologies and mathematical software in mathematics teaching. Numerous studies of the effectiveness of mathematical learning have shown the justification and usefulness of the implementation of new teaching aids. They also showed that learning with educational software has a great impact on students' achievement in the overall acquisition of mathematical knowledge during the school year as well as in the final exam at the end of primary education. Teaching realized by using computers and software packages is interesting for students, increases their interest and active participation. It is indisputable that the use of computers and mathematical software has great benefits that have been proven and presented in their works by many researchers of effective learning. It is also indisputable that one of the main tasks of teaching mathematics is to develop constructive thinking of students. Visualization and representation of mathematical laws are of great importance in the realization of mathematics teaching. They should be applied everywhere and whenever possible.

Phase vapor–liquid equilibrium for the solutions of diethyl selenide and diethylzinc

Using a semi-empirical Wilson’s model, the vapor-liquid equilibrium in the “diethylzinc - diethyl selenide” system is described: the activity coefficients of the solution components, the separation coefficient, the excess functions of the solution (HE, GE, TSE) are calculated, and isothermal P-X diagrams are obtained. The parameters of the Wilson’s model were calculated on the basis of our data on measuring the temperature dependence for saturated vapor pressure of high-purity samples of diethylzinc, diethyl selenide and their equimolecular solution using iterations from the mathematical software package Mathsad 14. Peculiarities of intermolecular interaction in the “diethylzinc – diethyl selenide” system and the presence of a negative deviation from Raoul's law have been found. The studied system is homogeneous in the whole concentration range. The concentration dependence of the enthalpy of mixing is alternating for the researched temperature range (280-340 K).

Turning Tool Wear Estimation Based on the Calculated Parameter Values of the Thermodynamic Subsystem of the Cutting System

Today, modern metalworking centers are not yet able to reliably assess the degree of wear of the tool used in metal cutting. Despite the fact that a large number of methods for monitoring the service life of the tool have been developed, this issue still remains a difficult task that needs to be solved. Idea: The article proposes a new, previously unused method for estimating the power of a cutting wedge in metalworking. The aim of the study is to develop a method for indirectly estimating the tool wear rate based on a consistent model of intersystem communication that describes the force, thermal and vibration reactions of the cutting process to the shaping movements of the tool. Research methods: The study consists of experiments on a measuring stand and a homemade measuring complex. It also uses the Matlab mathematical software package for processing and graphical interpretation of data obtained during experiments. The results show that the proposed method of estimating the current tool wear is applicable for the interpretation of experimental data. Statistically, the modified Voltaire operator of the second kind models the temperature more accurately; at the peak, this method is three times more accurate than the other.

Using Free Mathematical Software in Engineering Classes

There are many computational applications and engines used in mathematics, with some of the best-known arguably being Maple, Mathematica, MATLAB, and Mathcad. However, although they are very complete and powerful, they demand the use of commercial licences, which can be a problem for some education institutions or in cases where students desire to use the software on an unlimited number of devices or to access it from several of them simultaneously. In this contribution, we show how GeoGebra, WolframAlpha, Python, and SageMath can be applied to the teaching of different mathematical courses in engineering studies, as they are some of the most interesting representatives of free (and mostly open source) mathematical software. As the best way to show a topic in mathematics is by providing examples, this article explains how to make calculations for some of the main topics associated with Calculus, Algebra, and Coding theories. In addition to this, we provide some results associated with the usage of Mathematica in different graded activities. Moreover, the comparison between the results from students that use Mathematica and students that participate in a “traditional” course, solving problems and attending to master classes, is shown.

Product of κ-μ and α-μ Distributions and Their Composite Fading Distributions

In this study, product of two independent and non-identically distributed (i.n.i.d.) random variables (RVs) for κ-μ fading distribution and α-μ fading distribution is considered. The novel exact series formulas for the product of two i.n.i.d. fading distributions κ-μ and α-μ are derived instead of Fox H-function to solve the problem that Fox H function with multiple RVs cannot be implemented in professional mathematical software packages as MATHEMATICA and MAPLE. Exact close-form expressions of probability density function (PDF) and cumulative distribution function (CDF) are deduced to represent provided product expressions and generalized composite multipath shadowing models. At last, these analytical results are validated with Monte Carlo simulations, it shows that for provided κ-μ/α-μ model nonlinear parameter has more important influence than multipath component in PDF and CDF when the ratio between the total power of the dominant components and<br>the total power of the scattered waves is same. <br>