Author

# N. W. McLachlan

Bio: N. W. McLachlan is an academic researcher. The author has contributed to research in topics: Operational calculus & Bessel function. The author has an hindex of 7, co-authored 9 publications receiving 2987 citations.

##### Papers

More filters

•

15 Mar 2007

124 citations

•

25 Jun 2012

TL;DR: McLachlan as discussed by the authors introduced operational calculus based on the transform of f(x) defined by that is to say, the Laplace transform multiplied by p. The function p(p) so defined is identical with what Heaviside called the operational form.

Abstract: THIS book is intended as an introduction to operational calculus based upon the transform of f(x) defined by that is to say, the Laplace transform multiplied by p. The function p(p) so defined is identical with what Heaviside called the operational form. The advantage of the present treatment over Heaviside's is that the theorems of operation can be placed upon an impeccable basis without the necessity for acts of faith. The contents are : 1, the Laplace transform ; 2, rules of the operational calculus ; 3, solution of ordinary linear differential equations with constant coefficients ; 4, solution of partial linear differential equations with constant coefficients ; 5, evaluation of integrals ; 6, derivation of Laplace transforms ; 7, Laplace transform for a finite interval ; impulses.Modern Operational Calculus With Applications in Technical Mathematics. By Dr. N. W. McLachlan. Pp. xiv+218. (London: Macmillan and Co., Ltd., 1948.) 21s. net.

11 citations

##### Cited by

More filters

••

[...]

TL;DR: Various applications of f(R) theories to cosmology and gravity — such as inflation, dark energy, local gravity constraints, cosmological perturbations, and spherically symmetric solutions in weak and strong gravitational backgrounds are reviewed.

Abstract: Over the past decade, f(R) theories have been extensively studied as one of the simplest modifications to General Relativity. In this article we review various applications of f(R) theories to cosmology and gravity - such as inflation, dark energy, local gravity constraints, cosmological perturbations, and spherically symmetric solutions in weak and strong gravitational backgrounds. We present a number of ways to distinguish those theories from General Relativity observationally and experimentally. We also discuss the extension to other modified gravity theories such as Brans-Dicke theory and Gauss-Bonnet gravity, and address models that can satisfy both cosmological and local gravity constraints.

3,375 citations

••

TL;DR: In this article, the authors identify a new cosmological problem for models which solve the strong CP puzzle with an invisible axion, unrelated to the domain wall problem, and identify the energy density stored in the oscillations of the classical axion field does not dissipate rapidly; it exceeds the critical density needed to close the universe unless fa ⩽ 1012GeV wherefa is the axion decay constant.

2,557 citations

••

TL;DR: Theoretical and experimental work on radio-frequency (Paul) traps is reviewed in this paper, with a focus on ions trapped in radiofrequency traps, which are ideal for quantum-optical and quantum-dynamical studies under well controlled conditions.

Abstract: Single trapped ions represent elementary quantum systems that are well isolated from the environment. They can be brought nearly to rest by laser cooling, and both their internal electronic states and external motion can be coupled to and manipulated by light fields. This makes them ideally suited for quantum-optical and quantum-dynamical studies under well-controlled conditions. Theoretical and experimental work on these topics is reviewed in the paper, with a focus on ions trapped in radio-frequency (Paul) traps.

2,406 citations

••

TL;DR: In this paper, the production of axions in the early universe was studied and axion models which break the U(1)PQ symmetry above 1012 GeV were found to produce an unacceptably large axion energy density.

2,252 citations