whereas there is an exact linear relation between the wiener indices of kenograms and plerograms of isomeric alkanes, the respective terminal wiener indices exhibit a completely different behavior: correlation between terminal wiener indices of kenograms and plerograms is absent, but other regularities can be envisaged. in this article, we analyze the basic properties of terminal wiener indices...

We present here two approaches to the Dirichlet problem: The classical method of subharmonic functions that culminated in the works of Perron and Wiener, and the more modern Sobolev space approach tied to calculus of variations.

where 0 ≤ s ≤ t ≤ 1 and ⊗ denotes a tensor product. Lyons [17] proved that solutions of stochastic differential equations (SDEs) are continuous functions of the Brownian rough path w(s, t) = ( w(s, t)1, w(s, t)2). We give a precise definition of the Brownian rough path in the next section; see also [18] and [15]. The discontinuity of solutions of SDEs in the uniform convergence topology of w ca...

In the space of continuous functions of a real variable, the set of nowhere dilferentiable functions has long been known to be topologically "generic". In this paper it is shown further that in a measure theoretic sense (which is different from Wiener measure), "almost every" continuous function is nowhere dilferentiable. Similar results concerning other types of regularity, such as Holder cont...

the wiener polarity index wp(g) of a molecular graph g of order n is the number ofunordered pairs of vertices u, v of g such that the distance d(u,v) between u and v is 3. in anearlier paper, some extremal properties of this graph invariant in the class of catacondensedhexagonal systems and fullerene graphs were investigated. in this paper, some new bounds forthis graph invariant are presented....

In this paper we study the Wiener–Hopf factorization for a class of Lévy processes with double-sided jumps, characterized by the fact that the density of the Lévymeasure is given by an infinite series of exponential functions with positive coefficients. We express the Wiener–Hopf factors as infinite products over roots of a certain transcendental equation, and provide a series representation fo...

The plane wave diffraction by a terminated, semi-infinite parallel-plate waveguide with four-layer material loading is rigorously analyzed using the Wiener-Hopf technique. Introducing the Fourier transform for the unknown scattered field and applying boundary conditions in the transform domain, the problem is formulated in terms of the simultaneous Wiener-Hopf equations satisfied by the unknown...