In 1918 and 1919 Daniell's papers on what is now called the Daniell integral appeared. As an application he constructed the most general finite measure of Borel sets in Euclidean space of countable dimensionality. In 1933 Kolmogorov, in his formalization of probability as measure theory, rediscovered the Daniell result in constructing measures on Euclidean space of arbitrary dimensionality. Aft...

on 11temp (G(F)) . The object of this note is to characterize the image of the map. Results of this nature are well known. The case of the Hecke algebra on G(F), which is in fact more difficult, was established in [3] and [5]. A variant of the problem for the smooth functions of compact support on a real group was solved in [4]. For the Schwartz space, one has a choice of several possible appro...

The Wiener index of a connected graph G, denoted by W(G) , is defined as ∑ ( , ) , ∈ ( ) .Similarly, hyper-Wiener index of a connected graph G,denoted by WW(G), is defined as ( ) + ∑ ( , ) , ∈ ( ) .In this paper, we present the explicit formulae for the Wiener, hyper-Wiener and reverse Wiener indices of some graph operations. Using the results obtained here, the exact formulae for Wiener, hyper...

In recent years considerable attention has been paid to the numerical solution of stochastic ordinary diierential equations (SODEs), as SODEs are often more appropriate than their deterministic counterparts in many modelling situations. However, unlike the deterministic case numerical methods for SODEs are considerably less sophisticated due to the diiculty in representing the (possibly large n...

conclusion various filters are needed to improve the image quality. in this study, seven different filters were implemented and investigated on both noisy and noise-free images. background developmental dysplasia of the hip (ddh) can be detected with ultrasonography (usg) images. however, the accuracy of this method is dependent on the skill of the radiologist. radiologists measure the hip join...

the unitary cayley graph xn has vertex set zn = {0, 1,…, n-1} and vertices u and v areadjacent, if gcd(uv, n) = 1. in [a. ilić, the energy of unitary cayley graphs, linear algebraappl. 431 (2009) 1881–1889], the energy of unitary cayley graphs is computed. in this paperthe wiener and hyperwiener index of xn is computed.

We prove that de Branges spaces of entire functions describe universality limits in the bulk for random matrices, in the unitary case. In particular, under mild conditions on a measure with compact support, we show that each possible universality limit is the reproducing kernel of a de Branges space of entire functions that equals a classical Paley-Wiener space. We also show that any such repro...

Consider a set of continuous maps from the interval [0, 1] to a domain in R. Although the topological boundary of this set in the path space is not smooth in general, by using the theory of functions of bounded variation (BV functions) on the Wiener space and the theory of Dirichlet forms, we can discuss the existence of the surface measure and the Skorokhod representation of the reflecting Orn...

− This paper deals first with the mathematical formulation of a non-linear second-order stochastic model of free irrotational ocean surface wave on deep water. Then, the case of wave motion of zero bandwidth is treated to illustrate the model. On the basis of the usual hydrodynamic equations, the formulation is made by successive applications of the harmonic decomposition and the so-called Wien...

motivated by the terminal wiener index‎, ‎we define the ashwini index $mathcal{a}$ of trees as‎ begin{eqnarray*}‎ % ‎nonumber to remove numbering (before each equation)‎ ‎mathcal{a}(t) &=& sumlimits_{1leq i‎&+& deg_{_{t}}(n(v_{j}))],‎ ‎end{eqnarray*}‎ ‎where $d_{t}(v_{i}‎, ‎v_{j})$ is the distance between the vertices $v_{i}‎, ‎v_{j} in v(t)$‎, ‎is equal to the length of the shortest path start...