Wiener amalgams have been introduced by the author in 1980 ([F1,2]). The concept was aimed at the possibility of describing local and global properties of a function or distribution independently (allowing to speak of increasing smoothness at infinity . . . ). For a very readable survey of ‘ordinary’ amalgams, built up on local Land using global l-spaces, see the article by J. J. Fournier and J...

Introduced in 1947, the Wiener index W (T ) = ∑ {u,v}⊆V (T ) d(u, v) is one of the most thoroughly studied chemical indices. The extremal structures (in particular, trees with various constraints) that maximize or minimize the Wiener index have been extensively investigated. The Harary index H(T ) = ∑ {u,v}⊆V (T ) 1 d(u,v) , introduced in 1993, can be considered as the “reciprocal analogue” of ...

This paper presents a two-dimensional Wiener model in spatial domain for a class of laser electrophotographic printers, and embeds it into a framework of model-based digital halftoning. The Wiener model comprises an FIR filter followed by a nonlinear static mapping. The nonlinear static mapping is synthesized using a fuzzy system to maximize its capability to approximate nonlinearity of high de...

We say that Wiener’s property holds for the exponent p > 0 if we have that whenever a positive definite function f belongs to L(−ε, ε) for some ε > 0, then f necessarily belongs to L(T), too. This holds true for p ∈ 2N by a classical result of Wiener. Recently various concentration results were proved for idempotents and positive definite functions on measurable sets on the torus. These new res...

We generalise the Clark-Ocone formula for functions to give analogous representations for differential forms on the classical Wiener space. Such formulae provide explicit expressions for closed and co-closed differential forms and, as a by-product, a new proof of the triviality of the L de Rham cohomology groups on the Wiener space, alternative to Shigekawa’s approach [15] and the chaos-theoret...

Algorithmic randomness is most often studied in the setting of the fair-coin measure on the Cantor space, or equivalently Lebesgue measure on the unit interval. It has also been considered for the Wiener measure on the space of continuous functions. Answering a question of Fouché, we show that Khintchine’s law of the iterated logarithm holds at almost all points for each Martin-Löf random path ...

In this paper the problem of on-line identification and adaptive control of Neutralization reactor is studied. It is used the fact that this process can be modeled as a Wiener type system. An recursive identification algorithm for Wiener systems is proposed whose linear and nonlinear parts are modeled using a Laguerre and Piecewise Linear basis functions, respectively. The model obtained is use...

This paper considers feedforward control of a system which is described by transfer functions with marginally stable inverses. We present three different feedforward control strategies. Two of them relies on an ‘ideal’ design which is derived in the noise-free case, whereas the third is based on Wiener filtering theory. The control strategies are compared and evaluated for different signal mode...

A new method is introduced,for the identification of Wiener model. The Wiener model consists of a linear,dynamic! block followed by a static nonlinearity. The nonlinearity and the linear dynamic part in the model are identified by using radial basis functions neural network (RBFNN) and autoregressive moving average (ARMA) model, respectively. The new algorithm makes use of the well known mappin...

Fourier-based regularisation is considered for the support vector machine classification problem over absolutely integrable loss functions. By invoking the modest assumption that the decision function belongs to a Paley-Wiener space, it is shown that the classification problem can be developed in the context of signal theory. Furthermore, by employing the Paley-Wiener reproducing kernel, namely...