The phrase "establish rank" is grammatically correct and can be used in written English.
It means to determine or solidify one's position in a hierarchy or social structure. Example: The new CEO worked hard to establish her rank among the company's top executives.
The improv contests take various messy forms, but they most resemble the spontaneous dissing that can be heard in clusters around schoolyards and bus stops, wherever kids try to establish rank by matching wits.
Now, to establish rank(X k )=1, we use the complementary slackness condition Tr(X k Z k )=0 and prove rank(Z k )=M−1.
To establish rank(G k ) ≤ 1, we use the complementarity slackness condition Tr G k Z k )=0 and prove rank(Z k )=M−1.
Contemporary documents identify the statuette as a New Year's gift an étrennes a Roman custom Charles revived to establish rank and alliances during the period of factionalism and war.
We conclude that queens of L. acervorum from Spain establish rank orders by ritualized dominance interactions, such as antennal boxing.
Given that the displacement interaction matrices had the least number of unknown dyads, there were considered most reliable to establish rank orders.
If your clique members are having a hard time realizing that you are the alpha, establish ranks.
Furthermore, there are many problems on establishing rank formulas for generalized inverses of matrix products and their applications.
Especially, a comprehensive result on establishing rank formulas of (D - CA^{ i,ldots,j }B) was given in [26].
In fact, the social structure of a clan is probably most aptly compared to that of a wolf pack; in that each member has a clearly established rank and each clan has an alpha leader.
Workers therefore play an important role in the regulation of reproduction, but presumably only after the queens themselves have established rank orders.
