decreasing
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1: 10.37 Inequalities; Monotonicity
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►If
is fixed, then throughout the interval , is positive and increasing, and is positive and decreasing.
►If
is fixed, then throughout the interval , is decreasing, and is increasing.
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2: 33.23 Methods of Computation
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►On the other hand, the irregular solutions of §§33.2(iii) and 33.14(iii) need to be integrated in the direction of decreasing radii beginning, for example, with values obtained from asymptotic expansions (§§33.11 and 33.21).
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►This implies decreasing
for the regular solutions and increasing for the irregular solutions of §§33.2(iii) and 33.14(iii).
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3: 7.8 Inequalities
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►The function is strictly decreasing for .
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4: 8.13 Zeros
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►The negative zero
decreases monotonically in the interval , and satisfies
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5: 1.4 Calculus of One Variable
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►
§1.4(i) Monotonicity
… ►Similarly for nonincreasing and decreasing (strictly decreasing) functions. Each of the preceding four cases is classified as monotonic; sometimes strictly monotonic is used for the strictly increasing or strictly decreasing cases. …6: 26.12 Plane Partitions
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►A plane partition, , of a positive integer , is a partition of in which the parts have been arranged in a 2-dimensional array that is weakly decreasing (nonincreasing) across rows and down columns.
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►A strict shifted plane partition is an arrangement of the parts in a partition so that each row is indented one space from the previous row and there is weak decrease across rows and strict decrease down columns.
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7: 2.6 Distributional Methods
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►, a continuous linear functional) on the space of rapidly decreasing functions on .
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2.6.11
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2.6.12
,
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2.6.13
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2.6.16
,
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8: 19.30 Lengths of Plane Curves
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►As increases, the eccentricity
decreases and the rate of change of arclength for a fixed value of is given by
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9: 18.16 Zeros
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►Then is strictly increasing in and strictly decreasing in ; furthermore, if , then is strictly increasing in .
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►Arrange them in decreasing order:
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