Let G and G' be multiplicative systems. A half-homomorphism of G into G' will mean a mapping a—>a' of G into C such that for all a, bEG, (ab)'=a'V or b'a'. An anti-homomorphism is a mapping such that always (ab)' = b'a'. The terms half-isomorphism, etc., are defined similarly. It will be shown that any half-homomorphism of a group G into a group G' is either a homomorphism or an anti-homomorphi...

To each finite-dimensional operator space E is associated a commutative operator algebra UC(E), so that E embeds completely isometrically in UC(E) and any completely contractive map from E to bounded operators on Hilbert space extends uniquely to a completely contractive homomorphism out of UC(E). The unit ball of UC(E) is characterized by a Nevanlinna factorization and transfer function realiz...

Combinatorial structures have been considered under various orders, including substructure order and homomorphism order. In this paper, we investigate the homomorphic image order, corresponding to the existence of a surjective homomorphism between two structures. We distinguish between strong and induced forms of the order and explore how they behave in the context of different common combinato...

We study a class of non-deterministic program schemes with while loops: firstly, augmented with a priority queue for memory; secondly, augmented with universal quantification; and, thirdly, augmented with universal quantification and a stack for memory. We try to relate these respective classes of program schemes to well-known complexity classes and logics. We study classes of structure on whic...

Muraleetharan and Thirulogasanthar (J. Math. Phys. 2018;59(10):103506, 27p.) introduced the concept of Calkin S-spectrum a bounded quaternionic linear operator. The study this spectrum is established using Fredholm operator theory. Motivated by this, we general framework element with respect to Banach algebra homomorphism. First, investigate sum two elements in means elements. Next, prove pertu...

List coloring is an NP-complete decision problem even if the total number of colors is three. It is hard even on planar bipartite graphs. We give a polynomial-time algorithm for solving list coloring of permutation graphs with a bounded total number of colors. More generally, we give a polynomial-time algorithm that solves the list-homomorphism problem to any fixed target graph for a large clas...

Suppose A is a C*-algebra and B is a Banach algebra such that it can be continuously imbedded in B(H), the Banach algebra of bounded linear operators on some Hubert space H. It is shown that if 6 is a compact algebra homomorphism from A into B, then 6 is a finite rank operator, and the range of 0 is spanned by a finite number of idempotents. If, moreover, B is commutative, then 9 has the form 8...

In this paper, some results concerning the colorings of graph powers are presented. The notion of helical graphs is introduced. We show that such graphs are hom-universal with respect to high odd-girth graphs whose (2t+1)st power is bounded by a Kneser graph. Also, we consider the problem of existence of homomorphism to odd cycles. We prove that such homomorphism to a (2k+1)cycle exists if and ...

Under what conditions does there exist a group homomorphism near an approximate group homomorphism? This question concerning the stability of group homomorphisms was posed by Ulam 1 . The case of approximately additive mappings was solved by Hyers 2 on Banach spaces. In 1950 Aoki 3 provided a generalization of the Hyers’ theorem for additive mappings and in 1978 Th. M. Rassias 4 generalized the...