Mathematicians had long understood that for non-negative functions with a limiting processes of mathematical analysis and the mathematical theory of probability it became clear that more careful approximation techniques were needed to define a suitable integral.
12.
The lady is arrogant, disdainful, haughty, although in this case the negative function entrusted to it by the very structure of the story, since it will give women an example of how these should not behave.
13.
Conversely, as shown in a theorem by Schwartz ( similar to the Riesz representation theorem ), every distribution which is non-negative on non-negative functions is of this form for some ( positive ) Radon measure.
14.
"' Non-negative functions "': Let be a non-negative measurable function on, which we allow to attain the value, in other words, takes non-negative values in the extended real number line.
15.
In 1994, proposal of the " Developmental hourglass " ( egg-timer ) concept, In 1996, link between the dominant negative function of Hox genes and a human genetic syndrome ( the type II syndactyly or synpolydactyly ) via posterior prevalence.
16.
The demand for imports, M, from the South is a positive function of per capita consumption in the North and a negative function of the terms of trade, \ theta, ( higher \ theta means relative price of primary products is high and less will be demanded ).
17.
In probability theory, a "'normalizing constant "'is a constant by which an everywhere non-negative function must be multiplied so the area under its graph is 1, e . g ., to make it a probability density function or a probability mass function.
18.
The absolute value of " f " in the conditions above can be replaced by either the positive or the negative part of " f "; these forms include Tonelli's theorem as a special case as the negative part of a non-negative function is zero and so has finite integral.
19.
This rule may be generalized by introducing a non-negative function \ textstyle p ( x ) \ leq 1 in order to define the located-dependent \ textstyle p ( x )-thinning where now the probability of a point being removed is \ textstyle p ( x ) and is dependent on where the point of \ textstyle { N } is located on the underlying space.
20.
Using a bump function on the second factor, a non-negative function " g " with compact support can be constructed such that " g " is smooth off ?, has support in a small neighbourhood of ?, and in a sufficiently small neighbourhood of ? is equal to 0 for " s " < 0 and 1 for " s " e " 0.
