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Mechanistic insights into azo compound back-isomerization from spin-flip time-dependent DFT combined with Marcus theory. [PDF]

Chem Sci
Serez A, Aleotti F, Gerbaux P, Muccioli L, Cornil J.   +4 more
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On a Formula of Inversion

SIAM Journal on Mathematical Analysis, 1982
This paper develops a formula of inversion for an integral transform of a type similar to that associated with the names of Kontorovich and Lebedev except that the kernel involves the Neumann function $Y_u (kr)$ and the variable r varies over the truncated infinite interval $a \leq r 0$.
Naylor, D., Chang, P. H.
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Chen’s inversion formula

Physical Review A, 1990
Nan-xian Chen [Phys. Rev. Lett. 64, 1193 (1990)] has generalized a formula of classical algebraic number theory to continuous variables and noted some useful consequences of the generalization. We present an alternative view of this analysis, based on the Mellin transformation and Riemann's \ensuremath{\zeta} function.
, Hughes, , Frankel, , Ninham
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Arithmetical Inversion Formulas

Canadian Journal of Mathematics, 1960
Let n and r be integers, r positive, and define the coreγ(r) of r to be the product of the distinct prime factors of r (γ(1) = 1). Let f(n,r) be a complex-valued, arithmetical function of n and r. If for all n,f﹛n,r) = f((n,r), r) then f(n, r) is called an even function (mod r), and if f(n,r) = f(γ(n, r), r) for all n, γ(n, r) = γ((n, r)), then f(n, r)
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Some Finite Inversion Formulae

The Mathematical Gazette, 1962
In a great many problems in probability, one is given one set of quantities X j expressed in terms of a second set of quantities Y k
Stanton, R. G., Sprott, D. A.
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Ramanujan’s hyperelliptic inversion formula

The Ramanujan Journal, 2023
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Arithmetical Functions and Inversion Formulae

Journal of the London Mathematical Society, 1974
For a fixed integer \(N\ge 2\) let \(\nu_N(m) = 1\) if \(m\) is an \(N\)-th power and \(0\) otherwise, and let \(\lambda_N(n)= \sum_{m\mid n} \mu(n/m)\nu_N(m)\). The authors derive the following inversion formulae, in which \(T\) runs through the \(N\)-free integers: \[ f(n)= \sum_{T\mid n} g(n/T) \Leftrightarrow g(n) = \sum_{d\mid n} \lambda(d)f(n/d),
Evelyn, C. J. A., Heath-Brown, D.
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Inversion techniques and reciprocal formulae

International Journal of Computer Applications in Technology, 2012
Combinatorics has an important role in the development of computer science. Combinatorial identity which attracts numerous mathematicians is absolutely an important branch of it. As the effective tools, all kinds of inversion techniques are often used to prove known results and find new identities.
Chuanan Wei, Dianxuan Gong
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Algorithm study of Collins formula and inverse Collins formula

Applied Optics, 2007
In the study of a diffraction field of a light wave passing through a symmetrical paraxial optical system, the Collins formula and its inverse are convenient for calculation. The algorithm study of the Collins formula demonstrates that both a single fast Fourier transform algorithm and a double fast Fourier transform algorithm can be used in ...
Junchang, Li, Chongguang, Li
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A Direct Inversion Formula for SFT

Sankhya A, 2014
The subject of the paper is the stochastic Fourier transformation, for short SFT. The paper is a continuation of the author's previous works [C. R. Acad. Sci., Paris, Sér. A 288, 359--362 (1979; Zbl 0397.60047); Japan J. Appl. Math. 2, 229--240 (1985; Zbl 0616.60056); in: Patterns and waves.
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