Philosophical Transactions of the Royal Society A 

About: Philosophical Transactions of the Royal Society A is an academic journal published by Royal Society. The journal publishes majorly in the area(s): Medicine & Turbulence. It has an ISSN identifier of 1364-503X. Over the lifetime, 9207 publications have been published receiving 452343 citations. The journal is also known as: Royal Society of London. Philosophical Transactions A. Mathematical, Physical and Engineering Sciences & Philosophical transactions. Series A: Mathematical and physical sciences.

The Phenomena of Rupture and Flow in Solids

Abstract: In the course of an investigation of the effect of surface scratches on the mechanical strength of solids, some general conclusions were reached which appear to have a direct bearing on the problem of rupture, from an engineering standpoint, and also on the larger question of the nature of intermolecular cohesion. The original object of the work, which was carried out at the Royal Aircraft Estab­lishment, was the discovery of the effect of surface treatment—such as, for instance, filing, grinding or polishing—on the strength of metallic machine parts subjected to alternating or repeated loads. In the case of steel, and some other metals in common use, the results of fatigue tests indicated that the range of alternating stress which could be permanently sustained by the material was smaller than the range within which it was sensibly elastic, after being subjected to a great number of reversals. Hence it was inferred that the safe range of loading of a part, having a scratched or grooved surface of a given type, should be capable of estimation with the help of one of the two hypotheses of rupture commonly used for solids which are elastic to fracture. According to these hypotheses rupture may be expected if (a) the maximum tensile stress, ( b ) the maximum extension, exceeds a certain critical value. Moreover, as the behaviour of the materials under consideration, within the safe range of alternating stress, shows very little departure from Hooke’s law, it was thought that the necessary stress and strain calculations could be performed by means of the mathematical theory of elasticity.

Principal component analysis: a review and recent developments

Abstract: Large datasets are increasingly common and are often difficult to interpret. Principal component analysis (PCA) is a technique for reducing the dimensionality of such datasets, increasing interpretability but at the same time minimizing information loss. It does so by creating new uncorrelated variables that successively maximize variance. Finding such new variables, the principal components, reduces to solving an eigenvalue/eigenvector problem, and the new variables are defined by the dataset at hand, not a priori , hence making PCA an adaptive data analysis technique. It is adaptive in another sense too, since variants of the technique have been developed that are tailored to various different data types and structures. This article will begin by introducing the basic ideas of PCA, discussing what it can and cannot do. It will then describe some variants of PCA and their application.

Colours in Metal Glasses and in Metallic Films

Abstract: The present paper contains a discussion of some optical properties of a medium containing minute metal spheres. The discussion is divided into two Parts: the first Part dealing with colours in metal glasses, in which the proportion of volume occupied by metal is small; the second Part dealing with metal films, in which this proportion may have any value from zero to unity. In Part I. the observations of Siedentopf and Zsigmondy beyond the limit of microscopic vision (‘Ann. der Phys.,’ January, 1903) are discussed. It is shown that the particles seen in a gold ruby glass are particles of gold which, when their diameters are less than 0.1μ, are accurately spherical. I have endeavoured to show that the presence of many of these minute spheres to a wave-length of light in the glass will account for all the optical properties of “regular” gold ruby glass, and that the irregularities in colour and in polarisation effects sometimes exhibited by gold glass are due to excessive distance between consecutive gold particles or to excessive size of such particles, the latter, however, involving the former. It is also shown that the radiation from radium is capable of producing in gold glass the ruby colour which is generally produced by re-heating. The method adopted enables us to predict from a knowledge of the metal present in metallic form in a glass what colour that glass will be in its “regular” state.

On Certain Integrals of Lipschitz-Hankel Type Involving Products of Bessel Functions

Abstract: This paper is concerned with the evaluation and tabulation of certain integrals of the type (* 00 I(p, v; A) = J J fa t) ) e~cttxdt. In part I of this paper, a formula is derived for the integrals in terms of an integral of a hypergeometric function. This new integral is evaluated in the particular cases which are of most frequent use in mathematical physics. By means of these results, approximate expansions are obtained for cases in which the ratio b/a is small or in which b~a and is small. In part II, recurrence relations are developed between integrals with integral values of the parameters pt, v and A. Tables are given by means of which 7(0, 0; 1), 7(0, 1; 1), 7(1, 0; 1), 7(1,1; 1), 7(0, 0 ;0), 7(1, 0;90), 7(0, 1; 0), 7(1, 1; 0), 7(0,1; - 1 ), 7(1,0; - 1 ) and 7(1,1; - 1 ) may be evaluated for 0

On the Problem of the Most Efficient Tests of Statistical Hypotheses

Abstract: The problem of testing statistical hypotheses is an old one. Its origins are usually connected with the name of Thomas Bayes, who gave the well-known theorem on the probabilities a posteriori of the possible “causes” of a given event.* Since then it has been discussed by many writers of whom we shall here mention two only, Bertrand† and Borel,‡ whose differing views serve well to illustrate the point from which we shall approach the subject.