Nachbin (1965) A triple is said to be a topological ordered space, where is a partially ordered set and is a topological space. Definition 2.32 McCartan (1968) A topological ordered space is called: (i) Lower (Upper) -ordered if for each in X, there is an increasing (resp. a decrea...
By the definition of the ordered Ramsey number, there is an edge coloring c of the complete ordered graph on vertex set [r] containing no monochromatic copy of H with the given ordering. We will construct a coloring of the complete ordered graph on N=sr vertices with no monochromatic copy...
Ordered Pair | Definition & Examples from Chapter 7 / Lesson 15 18K What is an Ordered Pair? Learn how it's defined and how to write an ordered pair in math. See some examples for ordered pair Related to this QuestionWrite f(-2) = 4 and f(4) = 1 as ordered pairs. If f(-...
Ordered Pair | Definition & Examples from Chapter 7 / Lesson 15 42K What is an Ordered Pair? Learn how it's defined and how to write an ordered pair in math. See some examples for ordered pair Related to this QuestionWhich ordered pair is a sol...
For any cocycle solutions, the invariants are, by definition, invariant under the gauge transformation (32) and (33), and their values must be equal to roots of 1. Therefore, the values of the invariants are fixed for a given class of factor systems ω2(g1, g2). On the other hand...
Definition 1.6 An preordered metric space is a triple where (X, d) is a metric space and is a preorder on X. One of the most important hypotheses that we shall use in next section is the monotonicity of the involved mappings. Definition 1.7 Let be a binary relation on X and be a ...
Definition 3.1 We call a triple (W,S,⩽) a totally ordered similarity space if: (i) (W,S) is a finite similarity space based on (V,⊙), and (ii) ⩽ is a total order on W such that, for u,v,w∈W, u⩽v⩽w implies min(S(u,v),S(v,w))⩾S(u,w). Note ...
Introduction Identifying the ground state for interacting quantum spins on the kagome lattice is an important unresolved question in condensed matter physics, owing to the great difficulty in selecting amongst competing states that are very close in energy. Antiferromagnetic (AF) spins on this lattice ...
Definition 3.1. An L-ordered L-semihypergroup is a triple (S, ∘, R) consisting of a nonempty set S together with an L-relation R and an L-hyperoperation ∘ on S such that (1) (S, R) is an L-poset; (2) (S, ∘) is an L-semihypergroup; (3) R (x, y) ≤ R (...
Definition 2.5 ([31, 32]). A fuzzy ordered semigroup is a triple .S; e; / consisting of a nonempty set S together with a fuzzy relation e and a binary operations on S such that (1) .S; e/ is a fuzzy poset; (2) .S; / is a semigroups; (3) e.x; y/ 6 e.z x; z...