Kac integral [1, 2, 3] appears as a path-wise presentation of Brownian motion and shortly becomes, with Feynman approach [4], a powerful tool to study different processes described by the wave-type or diffusion-type equations. In the basic papers [1, 4], the paths distribution was based on averaging over the Wiener measure. It is worthwhile to mention the Kac comment that the Wiener measure can...

Wiener model identification and predictive control of a pH neutralisation process is presented. Input-output data from a nonlinear, first principles simulation model of the pH neutralisation process are used for subspace-based identification of a black-box Wiener-type model. The proposed nonlinear subspace identification method has the advantage of delivering a Wiener model in a format which is...

We prove a topological Paley-Wiener theorem for the Fourier transform deened on the real hyperbolic spaces SO o (p; q)=SO o (p ? 1; q), for p; q 2 2N, without restriction to K-types. We also obtain Paley-Wiener type theorems for L-Schwartz functions (0 < 2) for xed K-types.

This paper is devoted to a general stochastic delay differential equation with infinite-dimensional diffusions in Hilbert space. We not only investigate the existence of invariant measures either Wiener process or Lévy jump process, but also obtain pullback attractor under process. In particular, we prove non-trivial stationary solution which exponentially stable and generated by composition ra...

Molecules and molecular compounds are often modeled by molecular graphs. One of the most widely known topological descriptor [6, 9] is the Wiener index named after chemist Harold Wiener [13]. The Wiener index of a graph G(V, E) is defined as W (G) = ∑ u,v∈V d(u, v), where d(u, v) is the distance between vertices u and v (minimum number of edges between u and v). A majority of the chemical appli...