The Wiener index is a graphical invariant that has found extensive application in chemistry. We define a generating function, which we call the Wiener polynomial, whose derivative is a q-analog of the Wiener index. We study some of the elementary properties of this polynomial and compute it for some common graphs. We then find a formula for the Wiener polynomial of a dendrimer, a certain highly...

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Graovac and Pisanski [On the Wiener index of a graph, J. Math. Chem. 8 (1991) 53 – 62] applied an algebraic approach to generalize the Wiener index by symmetry group of the molecular graph under consideration. In this paper, exact formulas for this graph invariant under some graph operations are presented.

— We study Gibbs measures invariant under the flow of the NLS on the unit disc of R. For that purpose, we construct the dynamics on a phase space of limited Sobolev regularity and a wighted Wiener measure invariant by the NLS flow. The density of the measure is integrable with respect to the Wiener measure for sub cubic nonlinear interactions. The existence of the dynamics is obtained in Bourga...

Graphical matrices are presented. Their construction via selected sets of subgraphs and the replacement of subgraphs by numbers representing graph invariants are discussed. The last step of the procedure is to apply the method of choice for obtaining the desired double invariant from the graphical matrix in the numerical form. It is also pointed out that many so-called special graph-theoretical...

The notion of Wiener-Hopf type factorization is introduced in the abstract framework of Wiener algebras of matrix-valued functions on connected compact abelian groups. Factorizations of 2 x 2 block triangular matrix functions with elementary functions on the main diagonal are studied in detail. A conjectl,lre is formulated concerning characterization of dual groups with the property that every ...

Introduction: Block-oriented structures are useful to model a nonlinear system. Applications range from RF amplifiers over chemical processes to physiological systems [1]. A block-oriented model consists of two types of blocks: Linear Time Invariant (LTI) and static nonlinear blocks. The most simple block-oriented model structures are the Wiener (a LTI block followed by a static nonlinear block...

This work proposes a new approach to the blind inversion of Wiener systems. A Wiener system is composed of a linear time-invariant (LTI) sub-system followed by a memoryless nonlinear function. The goal is to recover the input signal by knowing just the output of the Wiener system, and the straightforward scheme to achieve this is called the Hammerstein system –– apply a memoryless nonlinear map...

Main objective of this paper is to represent an approach for biometric recognition of human faces based on KLT algorithm and Wiener filtering techniques. This approach involves registering a set of human faces to a face database, matching real time faces with already stored faces. Matlab based programs are implemented for this approach. KLT algorithm is used for create face database as well as ...