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The quality of the Klincewicz method is not superior to older methods, especially the method of Ambrose [2] gives somewhat better results as stated by the original authors and by Reid et al. [3] The advantage of the Klincewicz method is that it is less complex.
It was used in the world record calculations of 2.7 trillion digits of π in December 2009, [3] 10 trillion digits in October 2011, [4] [5] 22.4 trillion digits in November 2016, [6] 31.4 trillion digits in September 2018–January 2019, [7] 50 trillion digits on January 29, 2020, [8] 62.8 trillion digits on August 14, 2021, [9] 100 trillion ...
In effect, the Tax Reform Act changed § 163 from a general rule for deduction into one of non-deduction with six discreet exceptions. [3] These exceptions, listed in § 163(h)(2), include exceptions for active business interest, taxable investment interest, passive activity business interest, estate tax interest, and education loan interest ...
This means j provides a bijection from the set of elliptic curves over C to the complex plane. [2] As a Riemann surface, the fundamental region has genus 0, and every modular function is a rational function in j; and, conversely, every rational function in j is a modular function. In other words, the field of modular functions is C(j).
Supreme Court of the United States 38°53′26″N 77°00′16″W / 38.89056°N 77.00444°W / 38.89056; -77.00444 Established March 4, 1789 ; 235 years ago (1789-03-04) Location Washington, D.C. Coordinates 38°53′26″N 77°00′16″W / 38.89056°N 77.00444°W / 38.89056; -77.00444 Composition method Presidential nomination with Senate confirmation Authorised by ...
In 1820, the French engineer A. Duleau derived analytically that the torsion constant of a beam is identical to the second moment of area normal to the section J zz, which has an exact analytic equation, by assuming that a plane section before twisting remains planar after twisting, and a diameter remains a straight line.
In physics, the Bethe ansatz is an ansatz for finding the exact wavefunctions of certain quantum many-body models, most commonly for one-dimensional lattice models.It was first used by Hans Bethe in 1931 to find the exact eigenvalues and eigenvectors of the one-dimensional antiferromagnetic isotropic (XXX) Heisenberg model.
In the section "Calculations of yields in the monitoring of reactions" in the 1996 4th edition of Vogel's Textbook of Practical Organic Chemistry (1978), the authors write that, "theoretical yield in an organic reaction is the weight of product which would be obtained if the reaction has proceeded to completion according to the chemical ...