In this paper we introduce a ten-parameter family of Lévy processes for which we obtain Wiener-Hopf factors and distribution of the supremum process in semi-explicit form. This family allows an arbitrary behavior of small jumps and includes processes similar to the generalized tempered stable, KoBoL and CGMY processes. Analytically it is characterized by the property that the characteristic exp...

We elucidate the relation between the two ways of formulating causality in nonlocal quantum field theory: using analytic test functions belonging to the space S (which is the Fourier transform of the Schwartz space D) and using test functions in the Gelfand-Shilov spaces S α. We prove that every functional defined on S 0 has the same carrier cones as its restrictions to the smaller spaces S α. ...

The Wiener matrix and the hyper-Wiener number of a tree (acyclic structure), higher Wiener numbers of a tree that can be represented by a Wiener number sequence W, W,W.... whereW = W is the Wiener index, and R W k K    ,.... 2 , 1 is the hyper-Wiener number. The concepts of the Wiener vector and hyper-Wiener vector of a graph are introduced for the molecular graph of bi-phenylene. Moreover, ...

Distribution functions for random variables that depend on a parameter are computed asymptotically for ensembles of positive Hermitian matrices. The inverse Fourier transform of the distribution is shown to be a Fredholm determinant of a certain operator that is an analogue of a Wiener-Hopf operator. The asymptotic formula shows that up to the terms of order o(1), the distributions are Gaussian.

In this paper we provide sufficient conditions for the solvability of the standard H∞suboptimal control problem for linear, time invariant, infinite-dimensional systems with finite-dimensional input and output spaces. The sufficient conditions are formulated in terms of the existence of two J-lossless factorizations. For the Wiener algebra class of the transfer functions an algorithm for solvin...

A new method for identifying Hammerstein/Wiener models is proposed, where the parameters of a piecewise linear characteristic and a linear transfer function are estimated by recursive least-squares (RLS). Using smooth validity functions and an adaptive algorithm for optimal partitioning of the local linear models an efficient and accurate model can be identified.

One of the most widely known topological index is the Wiener index. The Wiener Index Conjecture states that all positive integer numbers except a finite set are the Wiener indices of some trees. We explore the Wiener indices of the binary trees. We present efficient algorithms for generating the Wiener indices of the binary trees. Based on experiments we strengthen the conjecture for the class ...

6. Spectral Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 Random processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 Random variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 Random vectors . . . . . . . . . . ....