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Format Statement
Published in Subrata Ray, Fortran 2018 with Parallel Programming, 2019
A real number may be printed with the 'f' descriptor. The number is printed right adjusted within the field. Leading zeros are replaced by blanks, and for positive numbers the plus sign is omitted. For a negative number, the minus sign is placed before the number. If w is equal to 0, the processor will calculate minimum number of places necessary to display the number with a leading sign, if required. Unless w is not equal to 0, d must not be greater than w. If the width is not sufficient to accommodate the number (when w>0), asterisks are displayed. real :: a a=1.236 print 200, a 200 format(f8.3)
Desktop Publishing
Published in Paul W. Ross, The Handbook of Software for Engineers and Scientists, 2018
In addition to the nonprinting uses of the em, en, and thin spaces, there are three corresponding, identical width, types of dashes: the em and en dashes and the hyphen. The em dash is the longest and is used in place of the two typewritten dashes used when writing parenthetically, for example. The en dash is used primarily for specifying ranges. For example, ten to twelve as 10-12. The hyphen is used as a single dash for hyphenating words and as a minus sign (although it is preferable to use the en dash for minus signs when not in a tabular form).
Circulatory System Based Optimization (CSBO): an expert multilevel biologically inspired meta-heuristic algorithm
Published in Engineering Applications of Computational Fluid Mechanics, 2022
Mojtaba Ghasemi, Mohammad-Amin Akbari, Changhyun Jun, Sayed M. Bateni, Mohsen Zare, Amir Zahedi, Hao-Ting Pai, Shahab S. Band, Massoud Moslehpour, Kwok-Wing Chau
The results for dimension 30 are given in Table 10 based on the mean value and standard deviation. The winning sign is defined by +, indicating the CSBO has won over the competitor algorithm in that function. In addition, the minus sign – and equity sign = show the failure and the same performance of CSBO compared to the corresponding algorithm. Total statistical results are given in Figures 4 and 5. As can be seen from the results of the first three unimodal functions and simple multimodal function F4, CSBO results are significant and superior to PSOs. On the other hand, the performance of the proposed algorithm for the last three test functions, F28, F29 and F30, which are composition test functions, is average and relatively poor compared to PSOs. CSBO scored the worst ranking of 7 for these three test functions.
Wave field in a layer with a linear background profile and multiscale random irregularities
Published in Waves in Random and Complex Media, 2022
To reduce the integral representation (4) to a form convenient for further analysis of the statistical moments of the field of waves reflected and scattered in layer (3), we make a number of approximations. Let us assume that the fluctuations are weak enough to calculate the integral over in (4) asymptotically due to the large-scale of the background medium: To do this, taking into account that in the backscattering case and , we find the point of the stationary phase in (4) from : and we expand in a power series of in the vicinity of the stationary phase point. Hence for the Green’s function from (4) we obtain where Plus/minus sign in Eqs. (13–17) corresponds to two waves (12) arriving at the observation point: after scattering, without reflection (with a lower sign, Figure 1(a)) and after scattering and reflection (with an upper sign, Figure 1(b)).
An Intrinsic Geometrical Approach for Statistical Process Control of Surface and Manifold Data
Published in Technometrics, 2021
Xueqi Zhao, Enrique del Castillo
The Laplace operator of a twice differentiable function is minus the divergence of its gradient field: and measures the difference between f(x) and the average f(x) in a neighborhood around x. Given the second derivatives, it is a measure of curvature, and can be alternatively understood as minus the trace of the Hessian of f(x). The minus sign is for consistency with Equation (4). Note how the domain of the function here is n-dimensional Euclidean space. We next extend this definition to general manifolds, obtaining the main differential-geometric operator used in the sequence, the LB operator, widely used in computer graphics and machine learning (Belkin 2003; Kimmel 2004; Levy 2006; Reuter, Wolter, and Peinecke 2006; Patané 2014).