Transactions of the Cambridge Philosophical SocietyUniversity Press, 1912 |
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الصفحة 241
... function of the series is upper ( lower ) semi - continuous , and that such ... monotone non - increasing sequence of non - negative continuous functions ... function is upper.
... function of the series is upper ( lower ) semi - continuous , and that such ... monotone non - increasing sequence of non - negative continuous functions ... function is upper.
الصفحة 242
... monotone increasing ( decreasing ) functions of x , then such invisible points of non - uniform oscillation are absent . Thus at a point at which the upper ( lower ) function is upper ( lower ) semi - continuous , the oscillation above ...
... monotone increasing ( decreasing ) functions of x , then such invisible points of non - uniform oscillation are absent . Thus at a point at which the upper ( lower ) function is upper ( lower ) semi - continuous , the oscillation above ...
الصفحة 248
... monotone decreasing sequence of continuous , nowhere negative , functions of any number of variables x , whose limiting function is f ( x ) , then the series αfo ( x ) + α2 fi ( x ) + ... .. ( 3 ) oscillates uniformly both above and ...
... monotone decreasing sequence of continuous , nowhere negative , functions of any number of variables x , whose limiting function is f ( x ) , then the series αfo ( x ) + α2 fi ( x ) + ... .. ( 3 ) oscillates uniformly both above and ...
الصفحة 250
... functions of any number of variables , denoted by x , and ƒ 。( x ) > f1 ( x ) > ... be a monotone decreasing sequence of continuous , never negative , functions of the variables x , whose limiting function is f ( x ) , then at any ...
... functions of any number of variables , denoted by x , and ƒ 。( x ) > f1 ( x ) > ... be a monotone decreasing sequence of continuous , never negative , functions of the variables x , whose limiting function is f ( x ) , then at any ...
الصفحة 251
... functions Si , si , fi and fi + 1 are continuous . Letting the region Q shrink up to the point x , we then have , by the definition of the peak function ... monotone non - increasing sequence whose limit is the upper limit mQ of the ...
... functions Si , si , fi and fi + 1 are continuous . Letting the region Q shrink up to the point x , we then have , by the definition of the peak function ... monotone non - increasing sequence whose limit is the upper limit mQ of the ...
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عبارات ومصطلحات مألوفة
a₁ absolutely convergent applied asymptotic B₁ bounded function bracket C₂ CAMBRIDGE concomitant consider continuous function convergent corresponding cos² curve denote differential coefficient differential equation dx² elastic equal expression factor finite follows formula ƒ x Hence impact infinite integrand irreducible k₁ Lebesgue integral Lemma linear monotone monotone function obtain operator oscillation P₁ plastic positive pressure prove R₁ reciprocant repeated integrals respect result s₁ satisfied sequence shew solution summable suppose symbols theorem theory transformation U₂ uniformly uniformly convergent unique limit upper V₁ values variables velocity W. H. Young w₁ zero α₁ ах дг ди др ду дх მყ
مقاطع مشهورة
الصفحة 280 - We know, however, that this integral is also equal to the sum of the residues at the poles of the integrand /
الصفحة 286 - The sum of the residues at the poles of the last factor, which occurs in (13.18) is therefore equal to minus the sum of the residues at the poles of the other factors.
الصفحة 358 - Since the modulus of a sum is not greater than the sum of the moduli...
الصفحة 96 - In support of such an hypothesis we may remark that as the crystalline grains are built up from their various centres, there will in general be a certain number of molecules to spare between their surfaces ; and these molecules will evidently be distributed in the spaces between the grains with relatively small density, ie, in such a fluid or serai-fluid condition, as would just account for the viscous reaction required.
الصفحة 140 - ... the same properties as the forms upon which they effectively operate, and that the forms which are invariant and the operators are properly to be regarded as one system of forms possessing the same properties.
الصفحة 312 - A geometrical progression is a series in which the ratio of any term to the preceding term is the same for all terms of the series.
الصفحة 126 - Plemelj's canonical form for the principal part of the solving function of an integral equation of the second kind in the neighbour hood of a pole.
الصفحة 48 - would prove independent of the length of the rods, provided the velocity and other conditions of the impact were kept unchanged. This was found to be the case, so that, by plotting duration of impact against length of rods, a straight line was obtained, whose slope gave the required value of the wave-velocity. * " On the Effects of Momentary Stresses in Metals,
الصفحة 348 - Rules for determining when the process of reversing the order of integration in a repeated integral is allowable.
الصفحة 100 - We are concerned here with the variation of integral forms, or more specially with their invariance, under the action of an operator which is an extension of the hydrodynamical operator in Enler's equations.