Mathematical chemistry is a branch of theoretical chemistry for discussion and prediction of the molecular structure using mathematical methods without necessarily referring to quantum mechanics. In theoretical chemistry, distance-based molecular structure descriptors are used for modeling physical, pharmacologic, biological and other properties of chemical compounds. The Wiener Polarity index ...

In this paper we present a characterization of those Wiener functionals that are the likelihood ratio for a 'signal plus independent noise' model. The characterization is expressed in terms of the representation of such functionals in a series of multiple Wiener integrals. Let {ys, 0 <s =z r} be a random process with measurable sample functions satisfying ] y, ] G K as. Let { Ws, 0 <s < T} be a...

We show that multi-window Gabor frames with windows in the Wiener algebra W (L∞, `) are Banach frames for all Wiener amalgam spaces. As a by-product of our results we prove the canonical dual of a Gabor frame with a continuous generator in the Wiener algebra also belongs to this space. Our proofs are mostly based on recent noncommutative versions of Wiener’s 1/f lemma.

The problem of distances in a graph, G, is one of the most studied questions, both from theoretical point of view and applications (the reader can consult two recent reviews ). It is connected to the Wiener number, W, or "the path number" as denominated by its initiator. In acyclic structures, Wiener number and its extension, hyper-Wiener number, can be defined as edge/path contributions, Ie/p ...

The edge versions of reverse Wiener indices were introduced by Mahmiani et al. very recently. In this paper, we find their relation with ordinary (vertex) Wiener index in some graphs. Also, we compute them for trees and TUC4C8(s) naotubes.

Let G be a connected simple (molecular) graph. The distance d(u, v) between two vertices u and v of G is equal to the length of a shortest path that connects u and v. In this paper we compute some distance based topological indices of H-Phenylenic nanotorus. At first we obtain an exact formula for the Wiener index. As application we calculate the Schultz index and modified Schultz index of this...

Some of the following problems look similar to the MAD Triangulation problem, but we have not found any deep connections: •Minimum Average Distance Spanning Subgraph in a budgeted version [2] was studied in the context of network design (minimizing average routing time). The problem is NP-complete even with unit weights. •Minimum Average Distance Spanning Tree [1]. NP-completeness is implied by...

We show that the only ow solving the stochastic di erential equation (SDE) on R dXt = 1{Xt>0}W+(dt) + 1{Xt<0}dW−(dt), where W and W− are two independent white noises, is a coalescing ow we will denote φ±. The ow φ± is a Wiener solution. Moreover, K = E[δφ±|W+] is the unique solution (it is also a Wiener solution) of the SDE K s,tf(x) = f(x) + ∫ t s Ks,u(1R+f )(x)W+(du) + 1 2 ∫ t s Ks,uf ′′(x)du...

For a one-parameter process of the form X, = X0 + & (b, d W, + & & ds, where W is a Wiener process and I+ d W is a stochastic integral, a twice continuously differentiable function f(X,) is again expressible as the sum of a stochastic integral and an ordinary integral via the Ito differentiation formula. In this paper we present a generalization for the stochastic integrals associated with a tw...

A lot of research and various techniques have been devoted for finding the topological descriptor Wiener index, but most of them deal with only particular cases. There exist three regular plane tessellations, composed of the same kind of regular polygons namely triangular, square, and hexagonal. Using edge congestion-sum problem, we devise a method to compute the Wiener index and demonstrate th...