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Basics of Fortran
Published in Caio Lima Firme, Quantum Mechanics, 2022
There are several versions of Fortran (FORmulaTRANslation), from Fortran IV to Fortran 2018 (https://wwwfortran.com/). In this book, we have used Fortran-90 to write our source codes (see examples below). Fortran presents a backward compatibility. As a compiled language that results in binary codes after compilation, Fortran has a high performance, fast debugging and testing. It has a huge number of numerical libraries and contains modern features such as OOP (object oriented programming) It also has elegant treatment of arrays and it has its own scalable parallel programming model (Fortran 2008 co-arrays for operation of Cartesian grids). Fortran is a living dinosaur of the scientific programming language and is still evolving. Moreover, the apprentices of scientific programming will see in this chapter that Fortran is very easy to learn. More information can also be found in the link. http://fortranwiki.org/fortran/show/HomePage.
Preliminaries
Published in Patrick Knupp, Stanly Steinberg, Fundamentals of Grid Generation, 2020
Patrick Knupp, Stanly Steinberg
In the next section, a standard notation is set up to describe transformations and their Jacobians. It is critical, as discussed later in this chapter, that the transformation be invertible. The connection between the invertibility of the transformation and the Jacobian is discussed in detail. Next, some classical transformations like polar coordinates are introduced and used to generate grids. At this stage the reader needs to know a scientific programming language such as FORTRAN, Pascal, basic, or C to complete the exercises. It is also important to have computer graphics software and hardware appropriate for plotting grids. Next a fast method of generating grids on simple regions, known as transfinite interpolation, is introduced. An exercise requires the reader to build a useful grid-generation code based on transfinite interpolation.
Linear Algebra for Machine Learning
Published in Richard M. Golden, Statistical Machine Learning, 2020
From a computational perspective, the Kronecker Product Operator needs to be carefully implemented. For example, suppose that A and B are 500-dimensional square matrices. Then, the Kronecker Product C = A ⊗ B is a 250, 000-dimensional square matrix. If either A or B is a sparse matrix, then taking advantage of the sparse matrix structure by using only non-zero elements of these matrices for storage and computation is essential. The scientific programming language MATLAB®, for example, has a feature to support sparse matrix construction and manipulation.
Zombies: a simple discrete model of the apocalypse
Published in International Journal of Mathematical Education in Science and Technology, 2018
This material could be employed as a supplement to a first course in chaos and complex systems, illustrating to students the following skills in applied mathematics: Formulating and changing a model to reflect various assumptions; simple population dynamics using the logistic map and various common functional responses.Numerical investigation, with a scientific programming language of choice.Chaos, strange attractors as well as other kinds of dynamical behaviour in the phase space, Lyapunov exponents, fractals in science/nature by considering the parameter space.Analysis of dynamical systems by analytically locating and determining the linear stability of fixed points.Demonstrating the practical application of mathematics to non-specialists, in medical, sociological and ecological fields.
Effects of the FIFA 11+ on ankle evertors latency time and knee muscle strength in amateur futsal players
Published in European Journal of Sport Science, 2020
Mário Lopes, João Manuel Rodrigues, Pedro Monteiro, Mário Rodrigues, Rui Costa, José Oliveira, Fernando Ribeiro
All subjects were familiarized with the trapdoor mechanism’s function and the EMG protocol. Skin preparation and electrode placement followed SENIAM recommendations (www.seniam.org). A detailed description of the procedures used in this study can be found elsewhere (Correia et al., 2016). In brief, the trapdoor mechanism used in this study was custom made with a non-slip surface to submit each ankle of the subject, in a random manner, to a sudden movement of inversion in a 30° frontal plane. The testing stopped, once each subject completed 3 valid tests in each leg. The trapdoor was released randomly to inhibit the participant from anticipating the dropping as well as to discard pre-motor activity from the muscles being tested. The real-time analysis of baseline activity was assessed to prevent potential pre-motor response (Cordova & Ingersoll, 2003). EMG muscle activity was recorded using an EMG wireless system (Myon 320, myon AG, Schwarzenberg, Switzerland), with a sampling frequency of 1000 Hz. The latency time was calculated with a specific mathematical routine implemented using GNU Octave 4.0.0 scientific programming language. The routine began by smoothing the rectified EMG signal through a 6th-order low pass Butterworth filter with a 50 Hz cut-off frequency and then estimating the baseline EMG mean and standard deviation (SD) amplitude during a time window of 250 ms before the opening of the trapdoor. This signal then passed through moving-average filter with a 25 ms sliding window, and the muscle EMG onset was determined as the instant where this average first surpassed 3 SD above the baseline mean and remained higher for at least another 25 ms. Finally, the latency time was determined as the time elapsed between the opening of the trapdoor and the start of the first window above threshold. This algorithm is analogous to previously reported onset detection methods (Correia et al., 2016; Hodges & Bui, 1996). A visual inspection of EMG trace adjacent to the zone of interest was also performed in order to prevent any errors of the EMG activity onset detection routine (Forestier & Terrier, 2011).
Environmental and Energy Improvements of LED Lamps over Time: A Comparative Life Cycle Assessment
Published in LEUKOS, 2020
Heather E. Dillon, Crysta Ross, Rachel Dzombak
The matrix calculations and inversions were performed in the scientific programming language R (R Core Team 2016). The R language has robust matrix methodology and inversion of the matrix is well established and accurate.