If (R,M) and (S,N) are quasilocal (commutative integral) domains and f : R → S is a (unital) ring homomorphism, then f is said to be a strong local homomorphism (resp., radical local homomorphism) if f (M) = N (resp., f (M) ⊆ N and for each x ∈ N , there exists a positive integer t such that xt ∈ f (M)). It is known that if f : R→ S is a strong local homomorphism where R is a pseudovaluation do...

In this paper we find a secure routing protocol for computer networks, which finds minimum optimum path using homomorphic encryption schemes. We briefly look into the existing homomorphic encryption algorithms. We make use of ElGamal encryption, Elliptic Curve encryption and a privacy homomorphism, which exhibits the property of homomorphism in our new routing protocol. Elliptic curve exhibits ...

For digraphs G and H , a homomorphism of G to H is a mapping f : V (G)→V (H) such that uv ∈ A(G) implies f(u)f(v) ∈ A(H). In the minimum cost homomorphism problem we associate costs ci(u), u ∈ V (G), i ∈ V (H) with the mapping of u to i and the cost of a homomorphism f is defined ∑ u∈V (G) cf(u)(u) accordingly. Here the minimum cost homomorphism problem for a fixed digraph H , denoted by MinHOM...

In this paper, we introduce some properties of an intuitionistic normal fuzzy m-subgroup of m- group with m-homomorphism and isomorphism. We study he image, the pre-image and the inverse mapping of the intuitionistic normal fuzzy m-‎subgroups.‎

We extend certain homomorphisms defined on the higher Torelli subgroups of the mapping class group to crossed homomorphisms defined on the entire mapping class group. In particular, for every k ≥ 2, we construct a crossed homomorphism ǫk which extends Morita’s homomorphism τ̃k to the entire mapping class group. From this crossed homomorphism we also obtain a crossed homomorphism extending the kt...

We discuss resonance properties in three-body systems, with examples on $$^{12}{\mathrm C}$$ and $$^{24}\mathrm{Mg}$$ . use a microscopic cluster model, where the generator coordinate is defined hyperspherical formalism. The nucleus described by an $$\alpha +\alpha $$ structure, whereas considered as $$^{16}\mathrm{O}+\alpha system. essentially pay attention to resonances. review various techni...