Given a graph G and a set X ⊆ V (G), the relative Wiener index of X in G is defined as WX(G) = ∑ {u,v}∈(X2 ) dG(u, v) . The graphs G (of even order) in which for every partition V (G) = V1+V2 of the vertex set V (G) such that |V1| = |V2| we have WV1(G) = WV2(G) are called equal opportunity graphs. In this note we prove that a graph G of even order is an equal opportunity graph if and only if it...

Die Wiener Zauberschule der Informatik (WIZIK) führt Kinder der Primarstufe an die Denkweise der Informatik heran und vermittelt ihnen erste informatische Kompetenzen. Die Kinder lernen spielerisch verschiedene Problemlösungsstrategien kennen und erhalten einen ersten Einblick in die Grundlagen logischen und prozessorientierten Denkens.

Bereg and Wang defined a new class of highly balanced d-ary trees which they call k-trees; these trees have the interesting property that the internal path length and thus the Wiener index can be calculated quite easily. A k-tree is characterized by the property that all levels, except for the last k levels, are completely filled. Bereg and Wang claim that the number of k-trees is exponentially...

This work presents a novel approach to speech enhancement by exploiting the bimodality of speech and the correlation that exists between audio and visual speech features. For speech enhancement, a visually-derived Wiener filter is developed. This obtains clean speech statistics from visual features by modelling their joint density and making a maximum a posteriori estimate of clean audio from v...

System identification is very important to technical and nontechnical areas. All physical systems are nonlinear to some extent and it is natural better to use nonlinear model to describe a real system. The Wiener and Hammerstein systems are proved to be good descriptions of nonlinear dynamic systems in which the nonlinear static subsystems and linear dynamic subsystems are separated in differen...

The paper studies weak Paley-Wiener properties for group extensions by use of Mackey’s theory. The main theorem establishes sufficient conditions on the dual action to ensure that the group has the weak Paley-Wiener property. The theorem applies to yield the weak Paley-Wiener property for large classes of simply connected, connected solvable Lie groups (including exponential Lie groups), but al...

In this paper we prove that the centered three-dimensional Wiener sausage can be strongly approximated by a one-dimensional Brownian motion running at a suitable time clock. The strong approximation gives all possible laws of iterated logarithm as well as the convergence in law in terms of process for the normalized Wiener sausage. The proof relies on Le Gall [10]’s fine L-norm estimates betwee...

We derive the transmit Wiener filter for DS-CDMA systems which depends upon the noise power at the receivers. We show that the transmit Wiener filter converges to the transmit matched filter and the transmit zero-forcing filter for low and high signal-to-noiseratio, respectively. Simulation results show the superiority of the transmit Wiener filter compared to the other two transmit filters. Mo...

The identification algorithm of Wiener-Hammerstein nonlinear model is proposed in the paper. When the nonlinearity in the Wiener-Hammerstein model is approximated by polynomial or spline function, the identification algorithms can be implemented iteratively, and the compensator for the nonlinear distortion is given by using the estimated Wiener-Hammerstein model and its inverse. A numerical sim...