Abstract The n-th order Wiener index of a molecular graph G was put forward by Estrada et al. [New J. Chem. 22 (1998) 819] as ( ) 1 ( , ) n n x W H G x where ( , ) H G x is the Hosoya polynomial. Recently Brückler et al. [Chem. Phys. Lett. 503 (2011) 336] considered a related graph invariant, ( ) 1 1 (1/ !) ( ( , )) / n n n n x W n d x H G x d x . For n=1, both W and W reduce to the ordinary W...

A novel unsymmetric square matrix, WPU , is proposed for calculating both Wiener, W , and hyper-Wiener, WW, numbers. This matrix is constructed by using single endpoint characterization of paths. Its relations with Wiener-type numbers are discussed.

Block-oriented nonlinear models are popular in nonlinear modeling because of their advantages to be quite simple to understand and easy to use. To increase the flexibility of single branch block-oriented models, such as Hammerstein, Wiener, and WienerHammerstein models, parallel block-oriented models can be considered. This paper presents a method to identify parallel Wiener-Hammerstein systems...

We consider a random walk Sk with i.i.d. steps on compact group equipped bi-invariant metric. prove quantitative ergodic theorems for the sum ? k=1Nf(Sk) Hölder continuous test functions f, including central limit theorem, law of iterated logarithm and an almost sure approximation by Wiener process, provided that distribution converges to Haar measure in p-Wasserstein metric fast enough. As exa...

the invariant factors of its state-space matrix A + BF . This result can be seen as the solution of an inverse problem; that of finding a non-singular polynomial matrix with prescribed in‐ variant factors and left Wiener–Hopf factorization indices at infinity. To see this we recall that the invariant factors form a complete system of invariants for the finite equivalence of polynomial matrices ...

Complex networks are ubiquitous in biological, physical and social sciences. Network robustness research aims at finding a measure to quantify network robustness. A number of Wiener type indices have recently been incorporated as distance-based descriptors of complex networks. Wiener type indices are known to depend both on the network's number of nodes and topology. The Wiener polarity index i...

Abstract The classes of band-dominated operators and the subclass in Wiener algebra $${\mathcal {W}}$$ W are known to be inverse closed. This paper studies extends partially results that type for one-sided generalized invertibility. Furthermore, invertibility, Fredholm property index independent underlying sp...

In this paper, we investigate the long-time behavior of stochastic reaction– diffusion equations of the type du = (Au + f (u))dt + σ(u)dW (t), where A is an elliptic operator, f and σ are nonlinear maps and W is an infinite-dimensional nuclear Wiener process.The emphasis is onunboundeddomains.Under the assumption that the nonlinear function f possesses certain dissipative properties, this equat...

In this article, we obtain a version of the noncommutative Banach Principle suitable to prove Wiener-Wintner type results for weights in W1-space. This is used ergodic theorems various types certain positive Dunford-Schwartz operators. We also study b.a.u. (a.u.) convergence some subsequential averages and moving such operators