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Numbers, trigonometric functions and coordinate geometry
Published in Alan Jeffrey, Mathematics, 2004
In mathematics, when working with trigonometric functions the argument of the function is always in radians and never in degrees. As 2π radians are equivalent to 360 degrees, the conversion from θ degrees to x radians is accomplished by using the result xπθ180 from which it follows that the conversion from x radians to θ degrees is given by θ=180xπ.
Analyzing FROC data
Published in Dev P. Chakraborty, Observer Performance Methods for Diagnostic Imaging, 2017
Line 6 defines , that is, the figure of merit, as . Line 11 uses to read the crossed modality dataset. Lines 12–13 perform the mAs analysis using function . The first argument to this function is the . The argument (1) tells the function to average the FOM over the first modality index, that is, over the reconstruction index. The third argument passes the FOM argument and the argument requests RRFC analysis, as this is a phantom study. The results are in Section 18.5.3, where due to page-width constraints, some of the output is suppressed; the reader should run the code to view the full output.
Further concepts
Published in C.W. Evans, Engineering Mathematics, 2019
When the relationship between two variables x and y is such that given any x there corresponds at most one y, we say we have a function and write y = f(x). The set of numbers x for which f(x) is defined is called the domain of the function, and each element in the domain is called an argument of the function.
On the benefit of smart tyre technology on vehicle state estimation
Published in Vehicle System Dynamics, 2022
Victor Mazzilli, Davide Ivone, Stefano De Pinto, Leonardo Pascali, Michele Contrino, Giulio Tarquinio, Patrick Gruber, Aldo Sorniotti
The longitudinal force balance equation is: where is the longitudinal acceleration; is the vehicle mass; and is the aerodynamic drag force. The lateral force balance equation is: where is the lateral acceleration. The yaw moment balance equation is: where is the yaw mass moment of inertia, and is the self-aligning moment of the tyres. The vehicle speed and sideslip angle are given by: In (5) and the remainder, the notation ‘’ indicates the argument of a function. The dynamics of each wheel are described by a moment balance equation, which, for the rear wheels, is: where is the equivalent mass moment of inertia of the wheel, including the contribution of the powertrain components; is the angular wheel acceleration; is the transmission gear ratio; and is the transmission efficiency.
Electric line source illumination of a chiral cylinder placed in another chiral background medium
Published in Journal of Modern Optics, 2018
M. Aslam, A. Saleem, Z. A. Awan
where is the nth-order Hankel function of second kind and is the nth-order Bessel function of first kind. The prime shows the derivative with respect to the whole argument of the function. The factors and are unknown coefficients and needed to be determined. Likewise, the tangential components of total electric and magnetic fields in the region II, i.e. , , and can be found from Equations (7)–(12) by replacing by , by and also interchanging their respective derivatives. On the other hand, the electric and magnetic fields inside the chiral cylinder can be expressed as follows,
Sediment yield prediction using neural networks at a watershed in south east India
Published in ISH Journal of Hydraulic Engineering, 2018
RBNN is a supervised and feed-forward neural network. It can be considered to be a three layer network. The hidden layer of RBNN consists of a number of nodes and a parameter vector called a center, which can be considered as the weight vector. The standard Euclidean distance is used to measure how far an input vector is from the center. The Euclidean distance is determined from the point that is being evaluated to the center of each neuron, and a radial basis function is applied to the distance to compute the weight for each neuron. The radial basis function is so named because the radius distance is the argument to the function. In the RBNN, the design of neural networks is a curve-fitting problem in high-dimensional space. Training the RBNN implies finding the set of basis nodes and weights. Therefore, the learning process is to find the best fit to the training data. The transfer functions of the nodes are governed by non-linear functions, which are assumed to be approximations of the influenced data points at the center. The transfer function of RBNN is mostly built up of Gaussian rather than sigmoid functions. The Gaussian functions decrease with distance from the center. In our case Gaussian function has been used is given by . Where, σ controls the width of the RBF center referred to as spread parameter and Euclidean distance Where, Ii is the input element and vji is the cluster center.