Mathematica also uses the positive square root, but denotes it by a double-struck ⅈ instead of j. A complex quantity z = x + jy can also be represented in terms of magnitude |z| and phase angle θ by z=|z|ejθ
Volume 176, article number1, (2025) Cite this article manuscripta mathematica Si Tiep Dinh, Feng Guo, Hong Duc Nguyen& Tien Son Pham 145Accesses Explore all metrics Abstract The main goal of this paper is to present some explicit formulas for computing the Łojasiewicz exponent in the Łojas...
Real numbers can be displayed to any level of accuracy within the limits of the computer used by Mathematica. N[π, 30] 3.14159265358979323846264338328 ■ Real addition 3.0 + 5.918 8.918 ■ Real subtraction 12.583 − 25.9999 − 13.4169 ■ Real multiplication In Mathematica, a single blank space...
Prof. Romer wrote an excellent article, Jupyter, Mathematica, and the Future of the Research Paper, about his experience with open-source software. Moreover, since Python is available at no cost, a much broader audience can use the code you develop. As you’ll see a little later on in ...
Maximais a symbolic computation program, like Mathematica and Maple: you define equations and can easily combine them, integrate, take the derivative, etc. Maxima is GNU source now, and free. Trigonometry Trig formulas, tables, and other mathematical reference material can be found atDave's Math...
We can find these by discretizing the known profile and then using optimization tools (such as those available in Mathematica and MATLAB) that perform the fitting for us. These fitting functions are based on minimizing an error term. If we know a target diffusion profile R(r) ...
The efficiency of replication error repair is a critical factor governing the emergence of mutations. However, it has so far been impossible to study this efficiency at the level of individual cells and to investigate if it varies within isogenic cell po
3 Proof of the main result 3.1 The low range With the help of a simple computer program in Mathematica, we checked all the solutions to the Diophantine equation (1) in the ranges d1≠d2∈{0,1,2,…,9}, d1>0 and 1≤ℓ,m≤n≤1000. We found only the solutions stated in Theorem...
The spectral analysis of signals is currently either dominated by the speed–accuracy trade-off or ignores a signal’s often non-stationary character. Here we introduce an open-source algorithm to calculate the fast continuous wavelet transform (fCWT). T
The LoopRefineSeries function of Package X, supported by the standard Series function of Mathematica, is able to expand all the structures contributing to the impact factor, with the exception of the box-type scalar integrals D0(0, 0, m2H , q2, −s, s, m2t , m2t , m2t , m2t ) ,...