In mathematics, especially order theory, a weak ordering is a mathematical formalization of the intuitive notion of a ranking of a set, some of whose...

ordered set then f induces a total ordering on X by setting x1 ≤ x2 if and only if f(x1) ≤ f(x2). The lexicographical order on the Cartesian product of a family...

contained in some total order. Stochastic dominance – Partial order between random variables Strict weak ordering – strict partial order "<" in which the relation...

therefore no additional safety net is required for weak ordering. In order to maintain weak ordering, write operations prior to a synchronization operation...

to weak ordering. They must label synchronization accesses as acquires or releases, not just as synchronization accesses. Similar to weak ordering, Release...

processes can observe only one consistent state. The original paper on weak ordering: M. Dubois, C. Scheurich and F. A. Briggs, Memory Access Buffering in...

as lex order by r {\displaystyle r} . The set of permutations on n items can be given the structure of a partial order, called the weak order of permutations...

every non-empty subset of S has a least element in this ordering. The set S together with the ordering is then called a well-ordered set (or woset). In some...

other just by renaming of elements. Two strictly weaker notions that relate to order isomorphisms are order embeddings and Galois connections. The idea of...

f\!\left(y\right)} .) To avoid ambiguity, the terms weakly monotone, weakly increasing and weakly decreasing are often used to refer to non-strict monotonicity...

memory location must be seen by all processors in the same order. Similar to weak ordering, the release consistency model allows reordering of all memory...

Weak Hero (Korean: 약한영웅) is a South Korean television series written and directed by Yoo Soo-min with Kim Jin-seok and Park Dan-hee, starring Park Ji-hoon...

consistent with reachability. This ordering on the weak components can alternatively be interpreted as a weak ordering on the vertices themselves, with...

nonempty subsets. A weak ordering may be obtained from such a partition by choosing one of k ! {\displaystyle k!} total orderings of its subsets. Therefore...

{\displaystyle \mathbb {Z} [x]} is dense. On the other hand, the linear ordering on the integers is not dense. Georg Cantor proved that every two non-empty...

and relations of a partial ordering. These are graph drawings where the vertices are the elements of the poset and the ordering relation is indicated by...

} is an equivalence; in that case " < {\displaystyle <} " is a strict weak order. The resulting preorder is connected (formerly called total); that is...

right weak Bruhat orderings were studied by Björner (1984). If (W, S) is a Coxeter system with generators S, then the Bruhat order is a partial order on...

In mathematics, especially order theory, a prefix ordered set generalizes the intuitive concept of a tree by introducing the possibility of continuous...

the partial order ⊂. For example, the T1 and T2 criteria are comparable, while the T1 and sobriety criteria are not. Strict weak ordering – Mathematical...

another. Like Galois connections, order embeddings constitute a notion which is strictly weaker than the concept of an order isomorphism. Both of these weakenings...

the lattice of normal subgroups of a group. The set of first-order terms with the ordering "is more specific than" is a non-modular lattice used in automated...

such comparison operator or comparator function must guarantee strict weak ordering. Apart from these, algorithms are provided for making heap from a range...

specifically in order theory and functional analysis, an element x {\displaystyle x} of a vector lattice X {\displaystyle X} is called a weak order unit in X...

refer to orderings that describe human preferences for one thing over an other. In mathematics, preferences may be modeled as a weak ordering or a semiorder...

variants of the theorem can be expressed in subsystems of second-order arithmetic much weaker than the subsystems where they can be proved. This was first...

In order theory, a branch of mathematics, a semiorder is a type of ordering for items with numerical scores, where items with widely differing scores are...

In mathematics, specifically order theory, a well-quasi-ordering or wqo on a set X {\displaystyle X} is a quasi-ordering of X {\displaystyle X} for which...

Sorting refers to ordering data in an increasing or decreasing manner according to some linear relationship among the data items. ordering: arranging items...

transitive, total, trichotomous, a partial order, total order, strict weak order, total preorder (weak order), or an equivalence relation, then so too...