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The independency relation is symmetric and irreflexive. Conversely, given any symmetric and irreflexive relation on a finite alphabet, the relation = is a dependency relation. The pair (,) is called the concurrent alphabet.
Consider the case where a distant star is motionless relative to the Sun, and the star is extremely far away, so that parallax may be ignored. In the rest frame of the Sun, this means light from the star travels in parallel paths to the Earth observer, and arrives at the same angle regardless of where the Earth is in its orbit.
Conversion (the converse), "If I wear my coat, then it is raining ." The converse is actually the contrapositive of the inverse, and so always has the same truth value as the inverse (which as stated earlier does not always share the same truth value as that of the original proposition).
In the monoid of binary endorelations on a set (with the binary operation on relations being the composition of relations), the converse relation does not satisfy the definition of an inverse from group theory, that is, if is an arbitrary relation on , then does not equal the identity relation on in general.
The converse statement is also true: If () is a Lyapunov function for all Markov chains with positive equilibrium and is of the trace-form (() = (,)) then () = (()), for some convex function f. [ 3 ] [ 4 ] For example, Bregman divergences in general do not have such property and can increase in Markov processes.
Twitter has altered the trend algorithm in the past to prevent manipulation of this type with limited success. [55] The Twitter web interface displays a list of trending topics on a sidebar on the home page, along with sponsored content (see image). Twitter often censors trending hashtags that are claimed to be abusive or offensive.
In graph theory, a star S k is the complete bipartite graph K 1,k : a tree with one internal node and k leaves (but no internal nodes and k + 1 leaves when k ≤ 1). Alternatively, some authors define S k to be the tree of order k with maximum diameter 2; in which case a star of k > 2 has k − 1 leaves. A star with 3 edges is called a claw.
The rate of energy transfer between the components is dependent on their mass ratio and luminosity ratio. In cases where the stars are in geometric contact but the thermal contact is poor, there can exist wide differences between their respective temperatures. [6] Contact binaries are not to be confused with common envelopes. Whereas the ...