The Wiener index of a graph G is defined as W(G) = 1/2∑{x,y}⊆V(G)d(x,y), where V(G) is the set of all vertices of G and for x,y ∈ V(G), d(x,y) denotes the length of a minimal path between x and y. In this paper, we first report our recent results on computing Wiener, PI and Balaban indices of some nanotubes and nanotori. Next, the PI and Szeged indices of a new type of nanostar dendrimers are c...

An original method to denoise ultrasonic images affected by speckle is presented. Speckle is modeled as a signal-dependent noise corrupting the image. Noise reduction is approached as a Wiener-like filtering performed in a shift-invariant wavelet domain by means of an adaptive rescaling of the coefficients of an undecimated octave decomposition. The scaling factor of each coefficient is calcula...

Using a stochastic representation provided by Wiener-regularized path integrals for the semigroups generated by certain Berezin-Toeplitz operators, a transformation formula for their resolvents is derived. The key property used in the transformation of the stochastic representation is that, up to a time change, Brownian motion is invariant under harmonic morphisms. This result for Berezin-Toepl...

In this paper we analyze the approximation of stable linear time-invariant systems, like the Hilbert transform, by sampling series for bandlimited functions in the Paley–Wiener space PW π . It is known that there exist systems and functions such that the approximation process is weakly divergent, i.e., divergent for certain subsequences. Here we strengthen this result by proving strong divergen...

The Volterra theory gives a characterization of nonlinear systems in terms of polynomial functionals. This theory was analysed in comparison to algorithms for the construction of invariant image features in 1] and conditions were derived so that these features remain constant if the images are transformed according to the action of a transformation group. However in general one can observe a hi...

We propose a generalization of the stochastic gauge fixing procedure for the stochastic quantization of gauge theories where not only the drift term of the stochastic process is changed but also the Wiener process itself. All gauge invariant expectation values remain unchanged. As an explicit example we study the case of an abelian gauge field coupled with three bosonic matter fields in 0+1 dim...

A Markov chain approach to identification of the Wiener, Hammerstein, and nonlinear ARX (NARX) systems is presented. The motivation of this approach comes from the fact that these classes of nonlinear systems are connected with Markov chains, and hence their asymptotical properties, such as ergodicity, stationarity, and invariant probability distribution, can be derived from the corresponding c...

In this paper we present conventional and translation-invariant (TI) wavelet-based approaches for single-trial evoked potential estimation based on intracortical recordings. We demonstrate that the wavelet-based approaches outperform several existing methods including the Wiener filter, least mean square (LMS), and recursive least squares (RLS), and that the TI wavelet-based estimates have high...

Abstract. In this paper Reverse Wiener index, Reverse Detour Wiener index, Reverse Circular Wiener index Reverse Harary index, Reverse Detour Harary index, Reverse Circular Harary index, Reverse Reciprocal Wiener index, Reverse Detour Reciprocal Wiener index, Reverse Circular Reciprocal Wiener index, Reverse Hyper Wiener index, Reverse, Detour Hyper Wiener index, Reverse Circular Hyper Wiener i...

We give an explicit computation of the Banach envelope for the Paley-Wiener type spaces E, 0 < p < 1. This answers a question by Joel Shapiro.