For any given partial ordering ⪯ of a set χ, real-valued functions ϕ defined on χ, which satisfy (phi(x leqphi y)) whenever (xpreceq y), are variously referred to as 'monotonic', 'isotonic', or 'order-preserving'.
For the given partial order ⪯ on the set X, we will denote also by ⪯ the order on X × X given by ( x 1, y 1 ) ⪯ ( x 2, y 2 ) ⟺ x 1 ⪯ x 2 and y 1 ⪰ y 2. (4.1).
For the given partial order ⪯ on the set X, we shall denote also by ⪯ the order on (Xtimes X) given by (x_{1},y_{1} preceq(x_{2},y_{2}) quad Leftrightarrowquad x_{1}preceq x_{2}quad text{and}quad y_{1}preceq y_{2}.
The president's statement, made while Greenspan was in the hospital undergoing surgery for an enlarged prostate, was given partial credit for yesterday's modest market rally in which the Dow Jones Industrial Average and the Nasdaq both climbed by 1.9%.
To the extent that sex bias indicates function in the biased sex (Connallon and Clark 2011), purifying selection should be more efficient for male-biased genes than for female-biased genes, given partial recessivity.
Although the tariffs are given partial credit for an ongoing consolidation of domestic steel manufacturers, they contributed to a severe financial squeeze for steel-consuming industries, which have experienced significant job losses since the levies were put in place.
Jens Laerke, spokesman for the U.N. Office for the Coordination of Humanitarian Affairs, said the government had later given partial approval for the food convoy.
For a given oxygen partial pressure (PO2) there was a saturated relative density which decreased with increasing PO2 and boundary faceting.
For a given instance (partial ), the matching of the subject [9] at a location L is given by optimization equation (2) mentioned below: begin{aligned} T={T_{i,j}}_{left{ {i=1,2,ldots,n} right} {j=1,2,ldots,k}}.
However, for a given matrix stiffness, partial blocking of β1 integrins mitigates the shift in intracellular mechanical state that is invoked by switching from a 2D to 3D matrix architecture.
