We consider basic conceptual graphs, namely simple conceptual graphs (SGs), which are equivalent to the existential conjunctive positive fragment of first-order logic. The fundamental problem, deduction, is performed by a graph homomorphism called projection. The existence of a projection from a SG Q to a SG Gmeans that the knowledge represented by Q is deducible from the knowledge represented ...

We supply an upper bound on the distinguishing chromatic number of certain infinite graphs satisfying an adjacency property. Distinguishing proper n-colourings are generalized to the new notion of distinguishing homomorphisms. We prove that if a graph G satisfies the connected existentially closed property and admits a homomorphism to H, then it admits continuum-many distinguishing homomorphism...

In this paper, we introduce the idea of generalized relative order (respectively generalized relative lower order) of entire functions of two complex variables. Hence, we study some growth properties of entire functions of two complex variables on the basis of the definition of generalized relative order and generalized relative lower order of entire functions of two complex variables.

Let Fn be a free group of rank n and F n the quotient group of Fn by the subgroup [Γn(3),Γn(3)][[Γn(2),Γn(2)],Γn(2)] where Γn(k) denotes the k-th subgroup of the lower central series of the free group Fn. In this paper, we determine the group structure of the graded quotients of the lower central series of the group F n by using a generalized Chen’s integration in free groups. Then we apply it ...

Generalized Place/Transition Petri nets, called contextual nets, and processes of such nets are considered. Processes of contextual nets are represented as partial orders with some extra structure. Operations of composing processes are deened such that each process of a contextual net can be obtained by combining processes corresponding to places and transitions of this net. Matrix-like charact...

let $g = (v, e)$ be a simple graph. denote by $d(g)$ the diagonal matrix $diag(d_1,cdots,d_n)$, where $d_i$ is the degree of vertex $i$  and  $a(g)$ the adjacency matrix of $g$. the  signless laplacianmatrix of $g$ is $q(g) = d(g) + a(g)$ and the $k-$th signless laplacian spectral moment of  graph $g$ is defined as $t_k(g)=sum_{i=1}^{n}q_i^{k}$, $kgeqslant 0$, where $q_1$,$q_2$, $cdots$, $q_n$ ...

We show that certain canonical realizations of the complexes Hom(G,H) and Hom+(G,H) of (partial) graph homomorphisms studied by Babson and Kozlov are in fact instances of the polyhedral Cayley trick. For G a complete graph, we then characterize when a canonical projection of these complexes is itself again a complex, and exhibit several well-known objects that arise as cells or subcomplexes of ...

Theorem 1.1 (Popa’s Cocycle Superrigity, Special Case). Let Γ be a discrete group with Kazhdan’s property (T), let Γ0 < Γ be an infinite index subgroup, (X0,μ0) an arbitrary probability space, and let Γ (X,μ) = (X0,μ0)0 be the corresponding generalized Bernoulli action. Then for any discrete countable group Λ and any measurable cocycle α : Γ × X → Λ there exist a homomorphism : Γ → Λ and a meas...