China
Africa
Explore chapters and articles related to this topic
A tool for modeling systems
Published in William L. Chapman, A. Terry Bahill, A. Wayne Wymore, Engineering Modeling and Design, 2018
William L. Chapman, A. Terry Bahill, A. Wayne Wymore
The results of many systems are the same, or they can be made to look the same with a transformation. A homomorphism is a function that translates three sets from one system into another system: the set of states (SZ), the set of inputs (IZ), and the set of outputs (OZ). An important use of a homomorphism is for translating the results of a model into a real world application. Homomorphisms to change Z1 into Z 2 use the following syntax: HS = {(SZ1 ,SZ2)}, where HS isa function mapping SZ1 onto SZ2.HI = {(IZ1 ,IZ2)}, where HI is a function mapping IZ1 onto IZ2.HO = -((0Z1 ,0Z2)}, where HO is a function mapping 0Z1 onto 0Z2.
Symmetries and Group Theory
Published in Mattias Blennow, Mathematical Methods for Physics and Engineering, 2018
The final general concept that we will discuss before having a look at different useful groups is that of group homomorphisms. a homomorphism is a mapping h from a group G to a group H that preserves the structure of the group operation, i.e., () h(ab)=h(a)h(b),
Graph Morphology in Image Analysis
Published in Edward R. Dougherty, Mathematical Morphology in Image Processing, 2018
In this section, by graph we always mean a nonoriented graph without loops and multiple edges. A graph G is a mathematical structure consisting of a set of vertices V and edges E. We denote this as G = (V, E). Since edges are supposed to be simple, they may be represented as a pair of vertices (v, w), denoting that v and w are neighbors. Our assumption that G is undirected can be made explicit by putting (v, w) = (w, v). Let G = (V, E) and G′ = (V′, E′) be two graphs. We say that G is a subgraph of G′ if V ⊆ V’ and E ⊆ E′. In literature, the word subgraph is often used in a more restricted sense [2]. By a homomorphism from G to G′ we mean a one-to-one mapping 0 : V → V’ with the property that (v, w) ∈ E implies that (θ(V), θ(w)) ∈ E′. In that case we say that G and G′ are homomorphic and write G ⊂ G′. If the homomorphism θ is onto (and hence a bijection), it is called an isomorphism. The graphs G and G′ are called isomorphic if they are related by an isomorphism. We denote this as G ≃ G′. An isomorphism from the graph G to itself is called a symmetry of G. We denote by Sym(G) the family of all symmetries of G. Obviously, this family forms a group called the symmetry group of G. The identity mapping id, defined by id(V) = v, is contained in Sym(G) and is called the trivial symmetry of G (see Figure 1).
A variety of algebras closely related to subordination algebras
Published in Journal of Applied Non-Classical Logics, 2022
Let and be subordination algebras. A subordination algebra morphism (Bezhanishvili, Bezhanishvili, Sourabh, et al., 2017) from to is a Boolean homomorphism h such that for all A strong subordination algebra morphism from to is a subordination algebra morphism h from to that in addition satisfies for all that The category whose objects are the subordination algebras and whose morphisms are the subordination algebra morphisms is introduced in Bezhanishvili, Bezhanishvili, Sourabh, et al. (2017), where a topological duality is provided. We will later arrive at this duality as a byproduct of the duality for one of the two categories of pseudo-subordination algebras that we define in the sequel. We will consider also the subcategory of with the same objects and morphisms the strong subordination algebra morphisms.
One-sided topological conjugacy of normal subshifts and gauge actions on the associated C*-algebras
Published in Dynamical Systems, 2021
For and the groupoid homomorphism defined in (5), we define one-parameter unitaries on by setting As in [20], the one-parameter unitaries satisfy the condition for , the family gives rise to an action of on the -algebra by The automorphism is often writen as for the groupoid homomorphism . We then have the following proposition.
Observables on lexicographic MV-algebras
Published in International Journal of General Systems, 2019
There is also a categorical equivalence of the category of strongly -perfect MV-algebras. Let be the category of strongly -perfect MV-algebras whose objects are triplets , where is a strongly -perfect MV-algebra, is a retractive ideal of M such that , and is an isomorphism of MV-algebras. If and are objects of , then a morphism in is a homomorphism of MV-algebras such that It is easy to verify that is a category. In addition, the triplet is an object of the category , where is a retractive ideal of and given by , .