Comment on double exponential formula.

On Approximating Hard Integrals with the Double-Exponential Formula

Approximating I#PART = ́ 1 0 ∏ n k=1 cos (xkπt) dt to within an accuracy of 2 −n where the input integers {xk} n k=1 are given in binary radix, is equivalent to counting the number of equal-sum partitions of the integers {xk} and is thus a #P problem. Similarly, integrating this function from zero to infinity and deciding whether the result is either zero or infinity is an NP-Complete problem. E...

A Double Exponential Formula for the Fourier Transforms

In this paper, we propose a new and efficient method that is applicable for the computation of the Fourier transform of a function which may possess a singular point or slowly converge at infinity. The proposed method is based on a generalization of the method of the double exponential (DE) formula; the DE formula is a powerful numerical quadrature proposed by H. Takahasi and M. Mori in 1974 [1...

Comment on "The Landau-Zener formula".

J. Phys. Chem. B 2005, 109 (17), 8428−8430. DOI: 10.1021/jp040627u T Landau−Zener formula was derived in 1932 and since then has remained an important tool in molecular dynamics and spectroscopy. In 2005, C. Witting proposed a simple derivation of the formula; it looks very useful and probably will be widely used. In this Comment, a new derivation of the Landau−Zener formula is proposed. Severa...

Double Exponential

Exponential Formula for Bedload Transport

An exponential formula that does not involve the concept of the critical shear stress is derived in this study for computing bedload transport rates. The formula represents well various experimental data sets ranging from the weak transport to high shear conditions. Comparisons of the present study are also made with many previous bedload formulas commonly cited in the literature.