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=|z|(cosθ+jsinθ), where the magnitude (aka modulus or absolute...
On the infinitesimal rigidity of homogeneous varieties Let XP be a variety (respectively an open subset of an analytic submanifold) and let x∈X be a point where all integer valued differential invariants are l... JM Landsberg - 《Compositio Mathematica》 被引量: 54发表: 1999年 ...
We present numerical algorithms for efficient and highly accurate computations of Fresnel’s sine and cosine integralsS(z) andC(z) for real (z=x) and complex (z=x+iy) arguments. The algorithms are based on series expansion for small values of |z|, expansion in Chebyshev subinterval polynomi...
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 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
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
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...
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 ...
we must find several Gaussians whose sum matches these profiles closely. 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 ...
Hecke Algebras of Classical Groups over p-adic Fields II In the previous part of this paper, we constructed a large family of Hecke algebras on some classical groups G defined over p -adic fields in order to unde... JL Kim - 《Compositio Mathematica》 被引量: 22发表: 2001年 ...