In this study, generalized k-order Fibonacci hybrid quaternion is defined. We give recurrence relation, generating function, the summation formula and some properties for these quaternions. Furthermore, matrix representation quaternions determined. The Q_k defined numbers given By means of another matrices, several identities are also obtained.

In this paper, we study two questions related to the problem of testing whether a function is close to a homomorphism. For two finite groups (not necessarily Abelian), an arbitrary map , and a parameter , say that is -close to a homomorphism if there is some homomorphism such that and differ on at most elements of , and say that is -far otherwise. For a given and , a homomorphism tester should ...

We survey structures endowed with natural partial orderings and prove their universality. These partial orders include partial orders on set of words, partial orders formed by geometric objects, grammars, polynomials and homomorphism order for various combinatorial objects.

We address the problem of characterizing H-coloring problems that are first-order definable on a fixed class of relational structures. In this context, we give several characterizations of a homomorphism dualities arising in a class of structure.