For digraphs D and H , a mapping f : V (D)→V (H) is a homomorphism of D to H if uv ∈ A(D) implies f(u)f(v) ∈ A(H). For a fixed digraph H , the homomorphism problem is to decide whether an input digraph D admits a homomorphism to H or not, and is denoted as HOMP(H). Digraphs are allowed to have loops, but not allowed to have parallel arcs. A natural optimization version of the homomorphism probl...

Trigraph list homomorphism problems (also known as list matrix partition problems) have generated recent interest, partly because there are concrete problems that are not known to be polynomial time solvable or NP -complete. Thus while digraph list homomorphism problems enjoy dichotomy (each problem is NP -complete or polynomial time solvable), such dichotomy is not necessarily expected for tri...

In this paper we provide a new scheme to securely forward the message in wireless mobile ad hoc networks (MANETs) by using existing homomorphic encryption schemes. This scheme is an alternative for threshold cryptography (TC) in MANETs to securely forward the message. By using homomorphic encryption schemes we remove the computational cost associated with Lagrange Interpolation scheme used in T...

The role of symmetry in ring theory is universally recognized. most directly definable universal relation a symmetric set isomorphism. This article develops certain structure bipolar fuzzy subrings, including quotient ring, homomorphism, and We define (?,?)-cut investigate the algebraic attributions this phenomenon. also support prove various important properties relating to concept. Additional...

Let $M$ be a manifold, $N$ 1-dimensional manifold. Assuming $r \neq \dim(M)+1$, we show that any nontrivial homomorphism $\rho: \text{Diff}^r_c(M)\to \text{Homeo}(N)$ has standard form: necessarily is $1$-dimensional, and there are countably many embeddings $\phi_i: M\to N$ with disjoint images such the action of $\rho$ conjugate (via product $\phi_i$) to diagonal $\text{Diff}^r_c(M)$ on $M \ti...

In this paper, we show that if an injective map  on symmetric matrices   n S C satisfies then           , , n ABA A B A A B S        C ,   Φ t f A SA S   for all   n A S C  , where f is an injective homomorphism on , is a complex orthogonal matrix and C S f A is the image of A under f applied entrywise.

We show that the commutator subgroup G ′ of a classical knot group G need not have subgroups of every finite index, but it will if G ′ has a surjective homomorphism to the integers and we give an exact criterion for that to happen. We also give an example of a smoothly knotted S n in S n+2 for all n ≥ 2 whose infinite cyclic cover is not simply connected but has no proper finite covers.

We prove that for any infinite field F , the map H3(SLn(F ), Z)→ H3(SLn+1(F ), Z) is an isomorphism for all n ≥ 3. When n = 2 the cokernel of this map is naturally isomorphic to 2 · K 3 (F ), where K n (F ) is the nth Milnor K-group of F . We deduce that the natural homomorphism from H3(SL2(F ), Z) to the indecomposable K3 of F , K3(F ), is surjective for any infinite field F .

In the study of homology cobordisms, knot concordance and link concordance, the following technical problem arises frequently: let π be a group and let M → N be a homomorphism between projective Z[π]-modules such that Zp⊗Z[π]M → Zp⊗Z[π]N is injective; for which other right Z[π]-modules V is the induced map V ⊗Z[π] M → V ⊗Z[π] N also injective? Our main theorem gives a new criterion which combin...

Let $mathcal {A} $ and $mathcal {B} $ be C$^*$-algebras. Assume that $mathcal {A}$ is of real rank zero and unital with unit $I$ and $k>0$ is a real number. It is shown that if $Phi:mathcal{A} tomathcal{B}$ is an additive map preserving $|cdot|^k$ for all normal elements; that is, $Phi(|A|^k)=|Phi(A)|^k $ for all normal elements $Ainmathcal A$, $Phi(I)$ is a projection, and there exists a posit...