the eccentricity connectivity index of a molecular graph g is defined as (g) = av(g)deg(a)ε(a), where ε(a) is defined as the length of a maximal path connecting a to othervertices of g and deg(a) is degree of vertex a. here, we compute this topological index forsome infinite classes of dendrimer graphs.

An infinitesimal theory for bending and earthquaking in onedimensional dynamics is developed. It is shown that any tangent vector to Teichmuller space is the initial data for a bending and for an earthquaking ordinary differential equation. The discussion involves an analysis of infinitesimal bendings and earthquakes, the Hilbert transform, natural bounded linear operators from a Banach space o...

In Fourier spectroscopy a tilting of the wavefront while the interferogram is being recorded gives rise to false structure in the computed spectrum. It is desirable to automatically tilt compensate the interferometer. One of the compensation schemes is to form a Mobius band through the interferometer. This paper discusses details of the construction of a Mcibius interferometer and test results ...

In topological data analysis, two-parameter persistence can be studied using the representation theory of 2d commutative grid, tensor product two Dynkin quivers type A. a previous work, we defined interval approximations restrictions to essential vertices intervals together with Mobius inversion. this consider homological resolutions, and show that resolution global dimension is finite for pose...

The Möbius function for a group G was introduced in 1936 by Hall in order to count ordered generating sets of G. In this paper we determine the Möbius function of the simple small Ree groups, R(q) = G2(q) where q = 3 for m > 0, using their 2-transitive permutation representation of degree q + 1. We also describe their maximal subgroups in terms of this representation. We use this to enumerate s...

Let 〈P〉 ⊂ N be a multiplicative subsemigroup of the natural numbers N= {1, 2, 3, . . .} generated by an arbitrary set P of primes (finite or infinite). We give an elementary proof that the partial sums ∑ n∈〈P〉:n≤x (μ(n))/n are bounded in magnitude by 1. With the aid of the prime number theorem, we also show that these sums converge to ∏ p∈P (1− (1/p)) (the case where P is all the primes is a we...

We study a poset of compositions restricted by part size under a partial ordering introduced by Björner and Stanley. We show that our composition poset Cd+1 is isomorphic to the poset of words A ∗ d. This allows us to use techniques developed by Björner to study the Möbius function of Cd+1. We use counting arguments and shellability as avenues for proving that the Möbius function is μ(u,w) = (−...