The classical result on singularities for the 3D Navier-Stokes equations says that the 1-dimensional Hausdorff measure of the set of singular points is zero. For a stochastic version of the equation, new results are proved. For statistically stationary solutions, at any given time t, with probability one the set of singular points is empty. The same result is true for a.e. initial condition with respect to a measure related to the stationary solution, and if the noise is sufficiently non degenerate the support of such measure is the full energy space.
We study a probabilistic generalization of Lowen's approach spaces. Such a probabilistic approach space is defined in terms of a probabilistic distance which assigns to a point and a subset a distance distribution function. We give a suitable axiom scheme and show that the resulting category is isomorphic to the category of left-continuous probabilistic topological convergence spaces and hence is a topological category. We further show that the category of Lowen's approach spaces is isomorphic to a simultaneously bireflective and bicoreflective subcategory and that the category of probabilistic quasi-metric spaces is isomorphic to a bicoreflective subcategory of the category of probabilistic approach spaces.
The pullout response of a short fiber embedded in matrix depends on both the bond between the two materials and on the inclination angle and embedded length of the fiber. Fibers placed and oriented randomly in 3D space bridge matrix cracks with certain inclination angles and embedded lengths. With a pullout law available in analytical form, a statistical description of the force per fiber depending on crack opening can be evaluated for a uniformly loaded crack bridge in a short fiber reinforced composite by integrating the powers of all possible fiber responses multiplied by their probabilities of occurrence. This information is utilized to probabilistically evaluate the crack bridging force by computing the sum of a random number of random contributions; the random number of contributions to be summed is the number of bridging fibers, and the independent random contributions are the single fiber responses. and Obsahuje seznam literatury
During the last decade we have introduced probabilistic mixture models into image modelling area, which present highly atypical and extremely demanding applications for these models. This difficulty arises from the necessity to model tens thousands correlated data simultaneously and to reliably learn such unusually complex mixture models. Presented paper surveys these novel generative colour image models based on multivariate discrete, Gaussian or Bernoulli mixtures, respectively and demonstrates their major advantages and drawbacks on texture modelling applications. Our mixture models are restricted to represent two-dimensional visual information. Thus a measured 3D multi-spectral texture is spectrally factorized and corresponding multivariate mixture models are further learned from single orthogonal mono-spectral components and used to synthesise and enlarge these mono-spectral factor components. Texture synthesis is based on easy computation of arbitrary conditional distributions from the model. Finally single synthesised mono-spectral texture planes are transformed into the required synthetic multi-spectral texture. Such models can easily serve not only for texture enlargement but also for segmentation, restoration, and retrieval or to model single factors in unusually complex seven dimensional Bidirectional Texture Function (BTF) space models. The strengths and weaknesses of the presented discrete, Gaussian or Bernoulli mixture based approaches are demonstrated on several colour texture examples.
In the Czech Republic numerous existing structures are made of different types of masonry. Decisions concerning upgrades of these structures should be preferably based on the reliability assessment, taking into account actual material properties. Due to inherent variability of masonry information on its mechanical properties has to be obtained from tests. Estimation of masonry strength from measurements may be one of key issues in the assessment of existing structures. The standard technique provided in the Eurocode EN 1996-1-1 is used to develop the probabilistc model of masonry strength taking into account uncertainties in basic variables. In a numerical example characteristic and design values of the masonry strength derived using principles of the Eurocode are compared with corresponding fractiles of a proposed probabilistic model. It appears that the characteristic value based on the probabilistic model is lower than that obtained by the standard technique. To the contrary, the partial factor for masonry recommended in EN 1966-1-1 seems to be rather conservative. and Obsahuje seznam literatury
A model of vortex filaments based on stochastic processes is presented. In contrast to previous models based on semimartingales, here processes with fractal properties between $1/2$ and $1$ are used, which include fractional Brownian motion and similar non-Gaussian examples. Stochastic integration for these processes is employed to give a meaning to the kinetic energy.
In this paper, we propose an extension of a periodic GARCH (PGARCH) model to a Markov-switching periodic GARCH (MS-PGA RCH), and provide some probabilistic properties of this class of models. In particular, we address the question of strictly periodically and of weakly periodically stationary solutions. We establish necessary and sufficient conditions ensuring the existence of higher order moments. We further provide closed-form expressions for calculating the even-order moments as well as the autocovariances of the powers of a MS-PGARCH process. We thus show how these moments and autocovariances can be used for estimating model parameters using GMM method.
In this paper we formulate a general model of the continuous double auction. We (recursively) describe the distribution of the model. As a useful by-product, we give a (recursive) analytic description of the distribution of the process of the best quotes (bid and ask).
Bayesian networks became a popiilar framework for reasoning with
uncertainty. Efficient methods have been developed for probabilistic reasoning with new evidence. However, when new evidence is nncertain or imprecise, different methods have been proposed. The original contribution of this paper are guidelines for the treatment of different types of uncertain evidence, the rules for combining evidence from different sources, and the model revision with nncertain evidence.
This paper describes the probabilty analysis of reinforced concrete containment structure of NPP with the reactor VVER V-230 under high internal overpressure. The summary of calculation models and calculation methods for the probability analysis of the structural integrity in the case of the loss of coolant accident (LOCA) is showed. The probabilistic structural analysis (PSA) level 2 aims at an assessment of the probability of the concrete structure failure under excessive overpressure. In the non-linear analysis of the concrete structures a layered approximation of the shell elements with various material properties have been included. The uncertainties of longtime temperature and dead loads, material properties (concrete cracking and crushing, reinforcement, and liner) and model uncertainties were taken into account in the 106
direct MONTE CARLO simulations. The results of the probability analysis of the containment failure under excessive overpressure show that in the case of the LOCA accident at overpressure of 122,7 kPa the probability is smaller than the required 10-4 for design resistance. and Obsahuje seznam literatury