Partially ordered finite monoids and a theorem of I.

Lakshmikantham, Fixed point theorems in

partially ordered metric spaces and applications, Nonlinear Anal.

A semigroup S is said to be a

partially ordered semigroup, or to be

partially ordered, if it admits a compatible ordering [less than or equal to]; that is, [less than or equal to] is a partial order on S such that ([for all] a, b [member of] S, x [member of] [S.

Partially ordered sets (a special kind of DAG) are often used in mathematics to analyze ordering, sequencing or arrangement of distinct objects which can block all routes from the maximal to the minimal nodes by killing a subset of agents in a terror network.

Appendices review

partially ordered sets, Lebesgue measure theory, and mollifications.

If P is a poset, and J(P) is the set of order ideals of P,

partially ordered by inclusion, the Fon-Der-Flaass action [PSI] maps an order ideal I [member of] J(P) to the order ideal [PSI](I) whose maximal elements are the minimal elements of P\I.

This snippet says that a possible way to explain the presence of a secret printed state in a plan is to add to the plan a

partially ordered sequence of actions implementing the attack.

COMPARATIVE STUDY OF

PARTIALLY ORDERED MATERIALS AND MATHEMATICAL SETS.

To construct a

partially ordered edge set, a

partially ordered node set is defined, since a

partially ordered edge set can be constructed by a Cartesian product of two partial ordered node sets, removing structurally unrelated node pairs from the product.

Their topics include contraction mappings, fixed point theorems in

partially ordered sets, topological fixed point theorems, variational and quasivariational inequalities in topological vectors spaces and generalized games, best approximations and fixed point theorems for set-valued mappings in topological vector spaces, degree theories for set-valued mappings, and nonexpansive types of mappings and fixed-point theorems in locally convex topological vector spaces.

In semi-crystalline plastics, these random molecules begin to form

partially ordered shapes.

Others redistribute

partially ordered lists so that each processor stores an approximately equal number of keys and all take part of the merge process during the running.