A solid sphere is considered, with a uniformly distributed infinity of points. Two points being pseudorandomly chosen, the analytical probability density that their separation have a given value is computed, for three types of the underlying geometry: E 3 , H 3 and S 3. Figures, graphs and histograms to complement this short note will be soon provided.
In a circle (an S 1) with circumference 1 assume m objects distributed pseudo-randomly. In the univeral covering manifold R 1 assume the objects replicated accordingly , and take an interval L > 1. In this interval, make the normalized his-togram of the pair separations which are not an integer. The theoretical (expected) such histogram is obtained in this… (More)
All orientation preserving isometries of the hyperbolic three-space are studied, and the probability density of conjugate pair separations for each isometry is presented. The study is relevant for the cosmic crystallography, and is the theoretical counterpart of the mean histograms arising from computer simulations of the isome-tries.
A flat membrane with given shape is displayed; two points in the membrane are randomly selected; the probability that the separation between the points have a specific value is sought. A simple method to evaluate the probability density is developed, and is easily extended to spaces with more dimensions.
Exact expressions for probability densities of conjugate pair separation in euclidean isometries are obtained, for the cosmic crystallography. These are the theoretical counterparts of the mean histograms arising from computer simulation of the isometries. For completeness, also the isometries with fixed points are examined, as well as the orientation… (More)
In this work we design data-driven soft sensors of downhole pressure for gas-lift oil wells. We employ a two-step procedure. First, discrete-time (N)ARX models are identified offline from historical data. Second, recursive predictions of these multiple models are combined with current measured data (of variables other than the downhole pressure) by means of… (More)
In gas-lifted oil wells the monitoring of downhole pressure plays an important role. However, the permanent downhole gauge (PDG) sensor often fails. Because maintenance or replacement of PDGs is usually unfeasible, soft-sensors are promising alternatives to monitor the downhole pressure in the case of sensor failure. In this paper, a data-driven soft-sensor… (More)
In this work an object-oriented approach for implementing soft sensor components, encapsulated as dynamic-link-library (DLL), is proposed. A variety of models used for the estimation of a specific unmeasured process variable and implemented as DLL components is integrated to the soft sensor main component by simply following the interface described in this… (More)
A practical control algorithm for stabilizing flow in risers and oil production wells should meet several requirements. i) be simple, ii) able to operate with low-cost measurements and possibly contaminated with noise and iii) stabilize the flow without setting a value for the bottom pressure. An algorithm has been proposed which does not fix any reference… (More)