Convergent sentence example

convergent
  • Note that the funnel in Figure 4 is also a convergent nozzle.
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  • The mean brightness varies as .51; and the integral f J02(z)zdz is not convergent.
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  • The general continued fraction al is evidently equal, convergent by convergent, to the continued fraction X 2 b 2 X2X3b3 x3%4b4 a1+ A2a2 + X + X
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  • Every even convergent is greater than every odd convergent; every odd convergent is less than, and every even convergent greater than, any following convergent.
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  • Every convergent is a nearer approximation to the value of the whole fraction than any fraction whose denominator is less than that of the convergent.
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  • The difference between the continued fraction and the nth convergent is less than, and greater than a n+2 These limits qn may be replaced by the following, which, though not so close, are simpler, viz.
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  • If we suppose alb to be converted into a continued fraction and p/q to be the penultimate convergent, we have aq-bp= +1 or -1, according as the number of convergents is even or odd, which we can take them to be as we please.
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  • In this case the sum to n terms of the series is equal to the nth convergent of the fraction.
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  • The two legs of a parabolic branch may converge to ultimate parallelism, as in the conic parabola, or diverge to ultimate parallelism, as in the semi-cubical parabola y 2 = x 3, and the branch is said to be convergent, or divergent, accordingly; or they may tend to parallelism in opposite senses, as in the cubical parabola y = x 3 .
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  • Man and monkeys alone possess parallel and convergent vision of the two eyes, while a divergent, and consequently a very widely extended, vision is a prerogative of the lower mammals; squirrels, for instance, and probably also hares and rabbits, being able to see an object approaching them directly from behind without turning their heads.
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  • There is nearly always an arrangement to observe the preparation first in convergent light and then in parallel polarized light.
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  • Convergent beam electron diffraction In many materials, the crystal structure of minority phases is not known.
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  • The acute bisectrix of the optic axes never deviates from the normal to the basal plane by more than a degree or two, hence a cleavage flake of mica will always show an optic figure in convergent light when placed on the stage of a polarizing microscope.
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  • Molar series strongly convergent behind (see Prairie-Marmot).
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  • If a is zero, we may regard as the first convergent, and precede the series by and °-.
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  • Standard intelligence tests measure convergent thinking, which is the ability to come up with a single correct answer.
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  • The Japanese attack was convergent, but there was no room for envelopment; the Russian position moreover was " all-round " and presented no flanks, and except for the enfilade fire of the Japanese and Russian gunboats in the shallow bays on either side the battle was locally at every point a frontal attack and defence.
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  • On the 25th of August the 2nd and 4th Armies from Haicheng and the 1st Army from the Yin-tsu-ling and Yu-shu-ling began the last stage of their convergent advance.
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  • It follows from this property of the function that we cannot have for log x a series which shall be convergent for all values of x, as is the case with sin x and cos x, for such a series could only represent a uniform function, and in fact the equation log(I +x) =x -",, x2 +3x 3 -4x 4 + is true only when the analytical modulus of x is less than unity.
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  • The resemblance shows various grades of completeness; and the convergent mimics may be themselves noxious, or edible and innocuous.
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  • The outermost hyphae may even put forth thinner hyphae, radiating into the soil like root-hairs, and the convergent tips may be closely appressed and so divided by septa as to resemble the root-apex of a higher plant (Armillaria mellea).
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  • It is doubtful whether the convergent action of the streams has been the sole agency in the erosion of these striking cavities, or whether snow and glacier-ice have had a share in the work.
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  • If then the objective tube is directed to any star, the convergent beam from the object-glass is received by the plane mirror from which it is reflected upwards along the polar axis and viewed through the hollow upper pivot.
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  • Every convergent is nearer to the value of the whole fraction than any preceding convergent.
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  • In the case of a recurring continued fraction which represents N, where N is an integer, if n is the number of partial quotients in the recurring cycle, and pnr/gnr the nr th convergent, then p 2 nr - Ng2nr = (- I) nr, whence, if n is odd, integral solutions of the indeterminate equation x 2 - Ny 2 = I (the so-called Pellian equation) can be found.
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  • We may require to represent the infinite convergent power series ao+alx+ a2x 2 + ...
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  • Its n th convergent is not equal to the sum to n terms of the series.
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  • Lambert for expressing as a continued fraction of the preceding type the quotient of two convergent power series.
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  • The optic figure seen in convergent polarized light through a section cut parallel to the plane of symmetry of a borax crystal is symmetrical only with respect to the central point.
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  • But, while Robertson was in some measure the initiator of a movement, Prescott came to his task when the range of information was incomparably wider and when progress in sociologic theory had thrown innumerable convergent lights upon the progress of events.
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  • When the waves are convergent and the recipient screen is placed so as to contain the centre of convergency - the image of the original radiant point, the calculation assumes a less complicated form.
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  • This being so, it would be premature to disregard the convergent lines of historical evidence which tell against A.D.
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  • A continued fraction may always be found whose n th convergent shall be equal to the sum to n terms of a given series or the product to n factors of a given continued product.
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  • By separation of real and imaginary parts, C =M cos 27rv 2 +N sin 27rv2 1 S =M sin 27rv 2 - N cos 27rv2 where 35+357.9 N _ 7rv 3 7r 3 v 7 + 1.3 1.3.5.7 1.3.5.7.9.11 These series are convergent for all values of v, but are practically useful only when v is small .
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  • It is not the quantity but the quality of the anatomical and bionomic characters which determines their taxonomic value, and a few fundamental characters are better indications of the affinities of given groups of birds than a great number of agreements if these can be shown to be cases of isomorphism or heterophyletic, convergent analogy.
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  • When we can solve this equation we have an expression for the n th convergent to the fraction, generally in the form of the quotient of two series, each of n terms. As an example, take the fraction (known as Brouncker's fraction, after Lord Brouncker) I I 2325 2 72 2 + 2 + 2 + 2 + ...
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  • It is always possible to find the value of the n th convergent to a recurring continued fraction.
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  • The tests for convergency are as follows: Let the continued fraction of the first class be reduced to the form dl+d2 +d3+d4+ then it is convergent if at least one of the series.
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