By adapting the notion of chirality group, the duality group of H can be defined as the the minimal subgroup D(H) E Mon(H) such that H/D(H) is a self-dual hypermap (a hypermap isomorphic to its dual). Here, we prove that for any positive integer d, we can find a hypermap of that duality index (the order of D(H)), even when some restrictions apply, and also that, for any positive integer k, we c...

This paper provides a unification-based implementation of Binding Theory (BT) for the English language in the framework of feature-based lexicalized tree-adjoining grammar (LTAG). The grammar presented here does not actually coindex any noun phrases, it merely outputs a set of constraints on coand contraindexation that may later be processed by a separate anaphora resolution module. It improves...

Let G = (V,E), V {1,2,...,n}, be a simple connected graph of order n, size m with vertex degree sequence d1 ? d2 ... dn > 0, di d(vi). The geometric-arithmetic topological index is defined as GA(G) i~j 2? didj/di+dj, whereas the coindex GA?(G) i~/j 2 didj/di+dj . New lower bounds for and in terms some parameters other invariants are obtained.

We prove a semi-Riemannian version of the celebrated Morse Index Theorem for geodesics in semi-Riemannian manifolds; we consider the general case of both endpoints variable on two submanifolds. The key role of the theory is played by the notion of the Maslov index of a semi-Riemannian geodesic, which is a homological invariant and it substitutes the notion of geometric index in Riemannian geome...

Abstract A topological descriptor is a mathematical illustration of molecular construction that relates particular physicochemical properties primary structure as well its depiction. Topological co-indices are usually applied for quantitative actions relationships (QSAR) and structures property (QSPR). descriptors which considered the noncontiguous vertex set. We study accompanying some renowne...

Let G = (V, E), V {v1, v2,..., vn}, be a simple graph without isolated vertices, with the sequence of vertex degrees d1 ? d2 ?...? dn > 0, di d(vi). If vertices vi and vj are adjacent in G, we write i ~ j, otherwise ~/ j. The inverse degree topological index is defined to ID(G) ?ni=1 1/di i~j (1/d2i + 1/d2j), coindex ?ID(G) i~/j(1/d2i 1/d2j). We obtain number inequalities which determine bou...

A numeric parameter which studies the behaviour, structural, toxicological, experimental, and physicochemical properties of chemical compounds under several graphs’ isomorphism is known as topological index. In 2018, Ali Trinajsti? studied first Zagreb connection index Z ...

We introduce the notion of coupled embeddability, defined for maps on products topological spaces. use known results nonsingular biskew and bilinear to generate simple examples nonexamples embeddings. study genericity properties embeddings smooth manifolds, extend Whitney embedding theorems statements about we discuss a Haefliger-type result relate embeddability Z / 2 $\mathbb{Z}/2$ -coindex sp...