若干图类的Wiener指数的极值

一个图的Wiener指数是指这个图中所有点对的距离和.Wiener指数在理论化学中有广泛应用. 本文刻画了给定顶点数及特定参数如色数或团数的图中Wiener指数达最小值的图, 同时也刻画了给定顶点数及团数的图中Wiener指数达最大值的图.     

On the Reverse Wiener Indices of Unicyclic Graphs

We determine the maximum values of the reverse Wiener indices of the unicyclic graphs with given cycle length, number of pendent vertices and maximum degree, respectively, and characterize the extremal graphs. We also determine the unicyclic graphs of given cycle length and diameter with minimum Wiener index.      

A Wiener Lemma for the discrete Heisenberg group

Monatshefte für Mathematik - This article contains a Wiener Lemma for the convolution algebra $$\ell ^1({{\mathrm{\mathbb {H}}}},{{\mathrm{\mathbb {C}}}})$$ and group $$C^*$$ -algebra...     

A Nonlinear Deformation of Wiener Space

Based on the complex hyperbolic geometry associated with discrete series of SU(1, 1), we construct a quasi-invariant and ergodic measure on infinite product of Poincaré disc and a hyperbolic analogue of numerical Wiener space which turns out to be a nonlinear deformation of the Wiener space. An integration by parts formula is established. We also investigate the orthogonal decomposition of the L ²-holomorphic functions which is an analogue of the Wiener–Itô–Segal decomposition. In the zero-curvature and large spin limit, we recover the linear Wiener space.     

Wiener Algebra for the Quaternions

We define and study the counterpart of the Wiener algebra in the quaternionic setting, both for the discrete and continuous case. We prove a Wiener–Lévy type theorem and a factorization theorem. We give applications to Toeplitz and Wiener–Hopf operators.     

Degree theory for Wiener maps

Degree theory is developed for a class of Wiener maps, as well as a few interesting tools, such as partitions of unity and Sard's theorem.     

Wiener measure for Heisenberg group

We build Wiener measure for the path space on the Heisenberg group by using of the heat kernel corresponding to the sub-Laplacian and give the definition of the Wiener integral. Then we give the Feynman-Kac formula.     

A Wiener process model with truncated normal distribution for reliability analysis

The use of degradation model to perform the reliability analysis has drawn much attention due to the fact that the performance of numerous highly reliable systems degrades over time. To describe the unit-to-unit variability for a population of systems, the random effect has been incorporated into the degradation model that plays an important part in assessing the reliability of deteriorating systems. In the existing literature, the normal distribution is commonly adopted to represent the random effect, but the assumption can be unsuitable for some practical applications, such as the degradation process of train wheels. In this paper, we present a degradation modeling and reliability estimation approach by using truncated normal distribution to characterize the unit-to-unit variability. A Wiener process with truncated normal distribution is firstly applied to model the degradation process of the deteriorating system, and the analytical expressions of probability density function and reliability function are derived. Expectation maximization algorithm is then used to estimate the model parameters. The effectiveness and feasibility of the presented approach are illustrated through a numerical example and practical case studies for laser devices and train wheels. The results indicate that the presented approach can obtain better reliability estimation results by considering the truncated normal distribution when the unit-to-unit variability has significant difference.     

A martingale approach for detecting the drift of a Wiener process

Lerchez (Ann. Statist. 14, 1986b, 1030–1048) considered a sequential Bayes-test problem for the drift of the Wiener process. In the case of a normal prior an o(c)-optimal test could be constructed. In this paper a new martingale approach is presented, which provides an expansion of the Bayes risk for a one-sided SPRT. Relations to the optimal Bayes risk are given, which show the o(c)-optimality for suitable nonnormal priors.     

A Wiener Chaos Approach to Hyperbolic SPDEs

We construct generalized weighted Wiener chaos solutions for hyperbolic linear SPDEs driven by a cylindrical Brownian motion. Explicit conditions for the existence, uniqueness, and regularity of generalized (Wiener Chaos) solutions are established in Sobolev spaces. An equivalence relation between the Wiener Chaos solution and the traditional one is established. The Heath–Jarrow–Morton (HJM) forward rate model is used as an example to illustrate the general construction.     

A Wiener process in a curvilinear strip

One investigates the representation of the probabilities of nonexit of a Brownian motion from a curvilinear strip in the form of an expansion with respect to a system of eigenfunctions. It is shown that the coefficients of this series satisfy a Volterra integral equation in ₂. For thin strips, with bounded first derivatives of the boundaries, the successive iterations of the equation determine a complete asymptotic expansion of the nonexit probabilities.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 4, pp. 561–563, April, 1990.     

Moment sequences for ultradistributions

Supported by DAAD, West Germany     

Quadrature Formulas for the Wiener Measure

We present a new method for the approximation of Wiener integrals and provide an explicit error bound for a class of smooth integrands. The purely deterministic algorithm is a sequence of quadrature formulas for the Wiener measure, where the knots are piecewise linear functions. It uses ideas of Smolyak, as well as the multiscale decomposition of the Wiener measure due to Lévy and Ciesielski. For the class we obtain n()max(1, 2⁻⁴), where n() is the number of integrand evaluations needed to guarantee an error at most for f .     

Malliavin calculus for two-parameter Wiener functionals

Summary In this paper we apply the Malliavin Calculus to deduce the existence and smoothness of density for the solution of stochastic differential equations with respect to a multidimensional two-parameter Wiener process.