Here are the key ideas and results. • The output of linear time invariant system is the convolution of its impulse response and the input. The system is bounded iff its impulse response is summable. • The transfer function is the Fourier transform of the impulse response. • A system with rational transfer function is causal if the poles are inside the unit circle. It is causally invertible if t...

Let G be a molecular graph. The Wiener index of G is defined as the summation of all distances between vertices of G. In this paper, an exact formula for the Wiener index of a new type of nanostar dendrimer is given.

We are interested in the following problem: to describe the closed translation-invariant subspaces of lp(Z). For l2 there is a complete solution due to Wiener, in terms of zeros of Fourier transform. However, the situation when p 6= 2 is much harder. In this talk we will present a proof of Malliavin’s theorem which shows the difficulty of characterizing all invariant subspaces of l1. We will us...

The classical Wiener filter, which can be implemented in O(N log N) time, is suited best for space-invariant degradation models and space-invariant signal and noise characteristics. For space-varying degradations and nonstationary processes, however, the optimal linear estimate requires O(N2) time for implementation. Optimal filtering in fractional Fourier domains permits reduction of the error...

Wiener-typed nonlinear systems with hard input constraints are ubiquitous in industrial processes. However, because of the complex structure, there are only few achievements on the control algorithm for constrained Wienertyped system. An improved dual-mode control algorithm is put forward. Firstly, Zeroin Algorithm is applied to obtain the inverse of the static nonlinear block of the Wiener-typ...

We consider a model of 2D gravity with the action quadratic in curvature and represent path integrals as over SL(2,R) invariant Gaussian functional measure. reduce these to products Wiener calculate correlation function metric first perturbative order.