Random and stochastic disturbances on the input flow in chemostat models with wall growth

In this paper, we analyze a chemostat model with wall growth where the input flow is perturbed by two different stochastic processes: the well-known standard Wiener process, which leads into several drawbacks from the biological point of view, and a suitable Ornstein-Uhlenbeck process depending on some parameters which allow us to control the noise to be bounded inside some interval that can be fixed previously by practitioners. Thanks to this last approach, which has already proved to be very realistic when modeling other simplest chemostat models, it will be possible to prove the persistence and coexistence of the species in the model without needing the theory of random dynamical systems and pullback attractors needed when dealing with the Wiener process. This is an advantage since the theoretical framework in this paper is much less complicated and provides us much more information than the other.     

Reliability and availability analysis of stochastic degradation systems based on bivariate Wiener processes

It is still a challenge to study the degradation mechanisms of complex systems with multiple performance characteristics. This paper develops a two-stage stochastic degradation model. The degeneration processes of two correlated performance characteristics are described by a correlated bivariate Wiener process in the first stage, in which neither of the degradation levels of performance characteristics reaches their thresholds. When one of the degradation levels of performance characteristics reaches its threshold, the system operates defectively in the second stage, and the system degradation process is described by the other performance characteristic which is modeled by a univariate Wiener process. The system fails completely when both the degradation levels of performance characteristics reach their thresholds. Explicit expressions of the system reliability and availabilities are given based on different inspection and maintenance policies. Simulation is also presented, and it shows that the analytical results and the simulation results are in good agreement. Finally, a detailed case study of the rail track geometry degradation is given to demonstrate the results obtained in the paper.     

混合范数条件下平移不变信号的非均匀平均采样

L~p平移不变子空间中的采样研究通常要求生成函数属于一个不依赖于p的Wiener amalgam空间,此条件因不能控制p而显得太强.本文主要讨论生成函数属于混合范数空间时,非衰减平移不变空间中的非均匀平均采样与重构.生成函数属于混合范数空间的条件弱于Wiener amalgam空间且依赖于参数p.基于混合范数空间中的一些引理,针对两种平均采样泛函建立了采样稳定性,并给出了对应的具有指数收敛的迭代重构算法.     

Normal convergence using Malliavin calculus with applications and examples

We prove the chain rule in the more general framework of the Wiener–Poisson space, allowing us to obtain the so-called Nourdin–Peccati bound. From this bound, we obtain a second-order Poincaré-type inequality that is useful in terms of computations. For completeness we survey these results on the Wiener space, the Poisson space, and the Wiener–Poisson space. We also give several applications to central limit theorems with relevant examples: linear functionals of Gaussian subordinated fields (where the subordinated field can be processes like fractional Brownian motion or the solution of the Ornstein–Uhlenbeck SDE driven by fractional Brownian motion), Poisson functionals in the first Poisson chaos restricted to infinitely many “small” jumps (particularly fractional Lévy processes), and the product of two Ornstein–Uhlenbeck processes (one in the Wiener space and the other in the Poisson space). We also obtain bounds for their rate of convergence to normality.     

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.     

由几何反演导出的分形几何

本文介绍了由几何反演而导出的自反分形概念.构造了一个对称的,分叉自反分形曲线和一个自反分形尘集.推广了分形密切的概念而且提出了一个新的概念——分形包络.最后给出了“肥皂”和“鸡蛋”的两个自反分形的实例.     

Representation theory of finite groups in Wiener–Hopf factorization problem

We consider the Wiener–Hopf factorization problem for a matrix function that is completely defined by its first column: the succeeding columns are obtained from the first one by means of a finite group of permutations. The symmetry of this matrix function allows us to reduce the dimension of the problem. In particular, we find some relations between its partial indices and can compute some of the indices. In special cases, we can explicitly obtain the Wiener–Hopf factorization of the matrix function.     

Analysis of estimation accuracy of the first moments of a Monte Carlo solution to an SDE with Wiener and Poisson components

In this paper, the estimation accuracy of the first moments of a numerical solution to an SDE with Wiener and Poisson components is investigated by a generalized explicit Euler method. Exact expressions for the mathematical expectation and variance of a test SDE solution are obtained. These expressions allow us to investigate the estimation accuracy obtained by a Monte Carlo method versus the SDE parameters, the integration step, and the size of the ensemble of simulated trajectories of the solution. The results of test numerical experiments are presented.     

一类随机利率下的破产时罚金折现期望

本文在经典风险模型下, 引进带有一种随机利率的破产时罚金折现期望的概念, 其利率的随机性通过标准Wiener过程和Poisson过程来描述. 给出破产时罚金折现期望所满足的更新方程, 并利用这个更新方程给出破产时罚金折现期望的渐近公式.     

Various topologies in the Wiener space and Lévy's stochastic area

Summary In this paper, we observe how Lévy's stochastic area looks when we see it through various topologies in the Wiener space. Our theorem implies that it is quite natural from the viewpoint of topology to define a distinct skeleton of Lévy's stochastic areaS(w) for each distinct topology in the Wiener space, or equivalently, for each distinct abstract Wiener space on which the Wiener measure andS(w) are realized. Thus we cannot determine its intrinsic skeleton in the theory of abstract Wiener spaces.     

A Class of Trees and its Wiener Index

In this paper, we will consider the Wiener index for a class of trees that is connected to partitions of integers. Our main theorem is the fact that every integer is the Wiener index of a member of this class. As a consequence, this proves a conjecture of Lepović and Gutman. The paper also contains extremal and average results on the Wiener index of the studied class.This work was supported by Austrian Science Fund project no. S-8307-MAT.     

Analytical and numerical inversion formulas in the Gaussian convolution by using the Paley–Wiener spaces

We shall discuss the relations among sampling theory (Sinc method), reproducing kernels and the Tikhonov regularization. Here, we see the important difference of the Sobolev Hilbert spaces and the Paley–Wiener spaces when we use their reproducing kernel Hibert spaces as approximate spaces in the Tikhonov regularization. Further, by using the Paley–Wiener spaces, we shall illustrate numerical experiments for new inversion formulas for the Gaussian convolution as a much more powerful and improved method by using computers. In this article, we shall be able to give practical numerical and analytical inversion formulas for the Gaussian convolution that is realized by computers.     

城市交通拥挤问题的探讨

本文探讨了城市交通拥挤问题的解决方法．根据道路的拥挤状况引入畅通度的概念，量化了道路的拥挤程度．在道路的物理距离的基础上加入畅通因素把它转化为一种新的距离，这样使原有寻找最短路径的算法能继续适用．同时本文详细介绍了公路网络中信息的存储方法：Coordinate Storage（COO），Compressed Sparse Row（CSR），Compressed Sparse Column（CSC），Block Sparse Row，以及最短路径的搜索算法：Dijkstra算法和Bellman—ford算法，同时给出了Dijkstra算法步骤和它的最新改进算法．     

A simple PDE and Wiener‐Hopf Riccati equations

We investigate the PDE (1.1), concentrating on the case when σ < in which the boundary condition (1.1b) is not of Feller's type and we lose the minimum principle. Investigation of nonnegative solutions leads us to Wiener‐Hopf theory and to a Riccati equation. A much‐studied Markov chain analogue is developed further in the hope that it will illuminate all aspects of the PDE case. © 2005 Wiley Periodicals, Inc.     

An Introduction to Constant Curvature Spaces in the Commutative (Segre) Quaternion Geometry

It is known that complex numbers can be associated with plane Euclidean geometry and their functions are successfully used for studying extensions of Euclidean geometry, i.e., non-Euclidean geometries and surfaces differential geometry. In this paper we begin to study the constant curvature spaces associated with the geometry generated by commutative elliptic-quaternions and we show how the “mathematics” they generate allows us to introduce these spaces and obtain the geodesic equations without developing a complete mathematical apparatus as the one developed for Riemannian geometry.     

The local times and Hausdorff measure for level sets of a Wiener sheet

In this paper, we discuss the relation between the local times and the level sets of a Wiener sheet, and give moment estimates for the local times of a Wiener sheet. We show that the correct Hausdorff measure function for level sets of N-parameter Rd-valued Wiener sheet is (r)=rN-d/2(loglog1/r)d/2 if 2N＞d. This solves the problem posed by S. J. Taylor.     

Continuous dependence on the time and spatial geometry for the equations of thermoelasticity

In this paper we establish the stability of the solution of the standard initial-boundary value problem of linear anisotropic thermoelasticity under perturbations of the initial time geometry and of the spatial geometry. This is done by deriving appropriate explicit a priori inequalities which permit us to bound in particular the L₂ integral of the perturbation in terms of some well defined measure of the perturbation in the geometry.     

On Tightness and Weak Convergence in the Approximation of the Occupation Measure of Fractional Brownian Motion

In this paper we consider approximations of the occupation measure of the Fractional Brownian motion by means of some functionals defined on regularizations of the paths. In a previous article Berzin and León proved a cylindrical convergence to a Wiener process of conveniently rescaled functionals. Here we show the tightness of the approximation in the space of continuous functions endowed with the topology of uniform convergence on compact sets. This allows us to simplify the identification of the limit.     

Integral characteristics of rigid inclusions and cavities in the two-dimensional theory of elasticity

Representations of the components of the elastic-polarization matrices and the Wiener elastic capacity are obtained in terms of the coefficients of the Kolosov-Muskhelishvili complex potentials and the coefficients of the conformal representation, which define the geometry of an infinite elastic solid. A new integral characteristic of a rigid inclusion—the Roben matrix, whose components are dimensiordess, is proposed for use in applied problems. Examples of calculations, which correct formulae published previously elsewhere, are given.     

A class of infinite dimensional stochastic processes with unbounded diffusion

The paper studies Dirichlet forms on the classical Wiener space and the Wiener space over non-compact complete Riemannian manifolds. The diffusion operator is almost everywhere an unbounded operator on the Cameron–Martin space. In particular, it is shown that under a class of changes of the reference measure, quasi-regularity of the form is preserved. We also show that under these changes of the reference measure, derivative and divergence are closable with certain closable inverses. We first treat the case of the classical Wiener space and then we transfer the results to the Wiener space over a Riemannian manifold.