The Quarterly Journal of Pure and Applied Mathematics, Volumen47

J.W. Parker, 1916

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Página 139 - The irregularities of the path are so numerous and so rapid that it is impossible to follow them, and the recorded path is far simpler and shorter than the true path.
Página 347 - A. (1846, 1856). [On some analytical formulae, and their application to the theory of spherical coordinates.
Página 197 - ... where the real value of log (—y) is to be taken when y is negative, and the logarithm is rendered one- valued by the stipulation that the variable is not to cross the real axis at any point on the positive side of the origin. Since sin TTZ this result can be written in the form This theorem is valid for all values of z — in contrast to that found in the next article, which is true only for restricted values of the variable. Example l.
Página 87 - Jo j where h(s,t)=(l — a)t + — , t^ (lt)s + ~, t> *P and ^(0 is continuous in the interval 0^<^1, can be expanded in an absolutely and uniformly convergent series of the...
Página 140 - ... been done by Victor Henri, Conandon or de Broglie, so as to cinematograph the motion. In the same way it is quite impossible to fix a tangent, even approximately, at any point of the trajectory. This is a case where it is really natural to think of those continuous functions which have no differential coefficients, imagined by mathematicians, and regarded quite wrongly as simple mathematical curiosities. Nature suggests them just as much as she does the functions which have differential coefficients.
Página 347 - Catalogue of Current Mathematical Journals , etc. with the names of the Libraries in which they may be found.
Página 158 - oo (here we just use the fact that the limit of the sum is the sum of the limits and the limit of the product is the product of limits.
Página 297 - The point, however, to which I wish to draw attention is that this need of rest is a psychological factor of the utmost importance in relation to the question of the extension of the line for which the French are pressing. It is my deliberate opinion, as the result of a most careful study of the question, that, if the Army is compelled at the present time to...
Página 375 - A Proof by elementary methods , without complex quantities, that every algebraic function (with real coefficients) has factors of the form...
Página 103 - Calculation of Eighteen More, Fifty in all, Eulerian Numbers from Central Differences of Zero.

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