973 resultados para mathematical functions


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The Xinli mine area of Sanshandao mine is adjacent to the Bohai Sea and its main exploitable ore deposit occurs in the undersea rock mass. The mine is the biggest undersea gold mine of China after production. The mine area faces a latent danger of water bursting, even sudden seawater inrush. There is no mature experience in undersea mining in China so far. The vein ore deposit is located in the lower wall of a fault; its possible groundwater sources mainly include bittern, Quaternary pore water and modern seawater. To ensure the safety of undersea mining, to survey the flooding conditions of the ore deposit using proper measures and study the potential seawater inrush pattern are the key technical problems. With the Xinli mine area as a case study, the engineering geological conditions of the Xinli mine area are surveyed in situ, the regional structural pattern and rock mass framework characteristics are found out, the distribution of the structural planes are modeled by a Monte Carlo method and the connectivity coefficients of rock mass structural planes are calculated. The regional hydro-geological conditions are analyzed and the in-situ hydro-geological investigation and sampling are performed in detail, the hydrochemistry and isotopes testing and groundwater dynamic monitoring are conducted, the recharge, runoff, discharge conditions are specified and the sources of flooding are distinguished. Some indices are selected from the testing results to calculate the proportion of each source in some water discharge points and in the whole water discharge of the Xinli mine area. The temporal and spatial variations of each water source of the whole ore deposit flooding are analyzed. According to the special project conditions in the Xinli mine area, the permeability coefficient tensors of the rock mass in Xinli mine area are calculated based on a fracture geometry measurement method, in terms of the connectivity and a few hydraulic testing results, a modified synthetic permeability coefficient are calculated. The hydro-geological conceptual and mathematical model are established,the water yield of mine is predicted using Visual Modflow code. The spreading law of surrounding rock mass deformation and secondary stress are studied by numerical analysis; the intrinsic mechanism of the faults slip caused by the excavation of ore deposit is analyzed. The results show that the development of surrounding rock mass deformation and secondary stress of vein ore deposit in the lower wall of a fault, is different from that in a thick-big ore deposit. The secondary stress caused by the excavation of vein ore deposit in the lower wall of a fault, is mainly distributed in the upper wall of the fault, one surface subsidence center will occur. The influences of fault on the rock mass movement, secondary stress and hydro-geological structures are analyzed; the secondary stress is blocked by the fault and the tensile stress concentration occurs in the rock mass near the fault, the original water blocking structure is destructed and the permeable structure is reconstructed, the primary structural planes begin to expand and newborn fissures occur, so the permeability of the original permeable structure is greatly enhanced, so the water bursting will probably occur. Based on this knowledge, the possible water inrush pattern and position of the Xinli mine area are predicted. Some computer programs are developed using object-oriented design method under the development platform Visual Studio.Net. These programs include a Monte Carlo simulation procedure, a joint diagrammatizing procedure, a structural planes connectivity coefficient calculating procedure, a permeability tensor calculating procedure, a water chemical formula edit and water source fixture conditions calculating procedure. A new computer mapping algorithm of joint iso-density diagram is raised. Based on the powerful spatial data management and icon functions of Geographic Information System, the pit water discharge dynamic monitoring data management information systems are established with ArcView.

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Since C.L. Hearn presented the concept of flow unit in 1984, its generation mechanisms and controlling factors have been studied in many aspects using different methods by researchers. There are some basic methods to do the research, and there are several concepts and classification standards about flow unit. Based on previous achievements and using methodologies from sedimentary geology, geophysics, seismic stratigraphy, and reservoir engineering, the author systemically studies the factors controlling flow unit, puts forward a series of methods for recognition, classification and evaluation of flow unit. The results obtained in this paper have important significance not only for understanding the flow unit, but also for revealing the distribution of remaining oil. As a case, this paper deals with the reservoir rocks in Guantao Group of Gudong Oilfield. Zhanhua Sag, Jiyang Depression in Bohaiwan Basin. Based on the study of stratigraphic, depositional and structural characteristics, the author establishes reservoir geological models, reveals the geological characteristics of oil-bearing reservoir of fluvial facies, points out the factors controlling flow unit and geological parameters for classification of flow unit. and summarizes methods and technologies for flow unit study when geological, well-logging and mathematical methods are used. It is the first attempt in literatures to evaluate reservoir by well-logging data constrained by geological conditions, then a well-logging evaluation model can be built. This kind of model is more precise than ever for calculating physical parameters in flow unit. In a well bore, there are six methods to recognize a flow unit. Among them, the activity function and intra-layer difference methods are the most effective. Along a section, the composition type of flow unit can be located according amplitude and impedance on seismic section. Slice method and other methods are used to distinguish flow unit. In order to reveal the distribution laws of flow unit in space, the author create a new method, named combination and composition of flow unit. Based on microscopic pore structure research, the classification methods of flow unit are developed. There are three types of flow unit in the reservoir of fluvial facies. They have their own lithology, petrophysics and pore structure character. Using judgement method, standard functions are built to determine the class of flow unit of fluvial facies. Combining reservoir engineering methods, the distribution laws of remaining oil in different types, or in different part of a flow unit are studied. It is evident that the remaining oil is controlled by the type of flow unit. The author reveals the relationship between flow unit and remaining oil distribution, builds the flowing models, predicts the variation of reservoir parameters in space, put forward different methods developing remaining oil in different flow unit. Especially, based on the results obtained in this paper, some suggestions for the adjustment of the developing flow units have been applied in Districts No.4 and No.7, and good results have been yielded. So, the results of this paper can guide oil field development. They are useful and significant for developing the remaining oil and enhancing the oil recovery efficiency.

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The seismic survey is the most effective geophysical method during exploration and development of oil/gas. As a main means in processing and interpreting seismic data, impedance inversion takes up a special position in seismic survey. This is because the impedance parameter is a ligament which connects seismic data with well-logging and geological information, while it is also essential in predicting reservoir properties and sand-body. In fact, the result of traditional impedance inversion is not ideal. This is because the mathematical inverse problem of impedance is poor-pose so that the inverse result has instability and multi-result, so it is necessary to introduce regularization. Most simple regularizations are presented in existent literature, there is a premise that the image(or model) is globally smooth. In fact, as an actual geological model, it not only has made of smooth region but also be separated by the obvious edge, the edge is very important attribute of geological model. It's difficult to preserve these characteristics of the model and to avoid an edge too smooth to clear. Thereby, in this paper, we propose a impedance inverse method controlled by hyperparameters with edge-preserving regularization, the inverse convergence speed and result would be improved. In order to preserve the edge, the potential function of regularization should satisfy nine conditions such as basic assumptions edge preservation and convergence assumptions etc. Eventually, a model with clear background and edge-abnormity can be acquired. The several potential functions and the corresponding weight functions are presented in this paper. The potential functionφLφHL andφGM can meet the need of inverse precision by calculating the models. For the local constant planar and quadric models, we respectively present the neighborhood system of Markov random field corresponding to the regularization term. We linearity nonlinear regularization by using half-quadratic regularization, it not only preserve the edge, and but also simplify the inversion, and can use some linear methods. We introduced two regularization parameters (or hyperparameters) λ2 and δ in the regularization term. λ2 is used to balance the influence between the data term and the transcendental term; δ is a calibrating parameter used to adjust the gradient value at the discontinuous position(or formation interface). Meanwhile, in the inverse procedure, it is important to select the initial value of hyperparameters and to change hyperparameters, these will then have influence on convergence speed and inverse effect. In this paper, we roughly give the initial value of hyperparameters by using a trend- curve of φ-(λ2, δ) and by a method of calculating the upper limit value of hyperparameters. At one time, we change hyperparameters by using a certain coefficient or Maximum Likelihood method, this can be simultaneously fulfilled with the inverse procedure. Actually, we used the Fast Simulated Annealing algorithm in the inverse procedure. This method overcame restrictions from the local extremum without depending on the initial value, and got a global optimal result. Meanwhile, we expound in detail the convergence condition of FSA, the metropolis receiving probability form Metropolis-Hasting, the thermal procession based on the Gibbs sample and other methods integrated with FSA. These content can help us to understand and improve FSA. Through calculating in the theoretic model and applying it to the field data, it is proved that the impedance inverse method in this paper has the advantage of high precision practicability and obvious effect.

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In the general case, a trilinear relationship between three perspective views is shown to exist. The trilinearity result is shown to be of much practical use in visual recognition by alignment --- yielding a direct method that cuts through the computations of camera transformation, scene structure and epipolar geometry. The proof of the central result may be of further interest as it demonstrates certain regularities across homographies of the plane and introduces new view invariants. Experiments on simulated and real image data were conducted, including a comparative analysis with epipolar intersection and the linear combination methods, with results indicating a greater degree of robustness in practice and a higher level of performance in re-projection tasks.

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In this paper, we bound the generalization error of a class of Radial Basis Function networks, for certain well defined function learning tasks, in terms of the number of parameters and number of examples. We show that the total generalization error is partly due to the insufficient representational capacity of the network (because of its finite size) and partly due to insufficient information about the target function (because of finite number of samples). We make several observations about generalization error which are valid irrespective of the approximation scheme. Our result also sheds light on ways to choose an appropriate network architecture for a particular problem.

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A large computer program has been developed to aid applied mathematicians in the solution of problems in non-numerical analysis which involve tedious manipulations of mathematical expressions. The mathematician uses typed commands and a light pen to direct the computer in the application of mathematical transformations; the intermediate results are displayed in standard text-book format so that the system user can decide the next step in the problem solution. Three problems selected from the literature have been solved to illustrate the use of the system. A detailed analysis of the problems of input, transformation, and display of mathematical expressions is also presented.

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This report develops a conceptual framework in which to talk about mathematical knowledge. There are several broad categories of mathematical knowledge: results which contain the traditional logical aspects of mathematics; examples which contain illustrative material; and concepts which include formal and informal ideas, that is, definitions and heuristics.

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"The Structure and Interpretation of Computer Programs" is the entry-level subject in Computer Science at the Massachusetts Institute of Technology. It is required of all students at MIT who major in Electrical Engineering or in Computer Science, as one fourth of the "common core curriculum," which also includes two subjects on circuits and linear systems and a subject on the design of digital systems. We have been involved in the development of this subject since 1978, and we have taught this material in its present form since the fall of 1980 to approximately 600 students each year. Most of these students have had little or no prior formal training in computation, although most have played with computers a bit and a few have had extensive programming or hardware design experience. Our design of this introductory Computer Science subject reflects two major concerns. First we want to establish the idea that a computer language is not just a way of getting a computer to perform operations, but rather that it is a novel formal medium for expressing ideas about methodology. Thus, programs must be written for people to read, and only incidentally for machines to execute. Secondly, we believe that the essential material to be addressed by a subject at this level, is not the syntax of particular programming language constructs, nor clever algorithms for computing particular functions of efficiently, not even the mathematical analysis of algorithms and the foundations of computing, but rather the techniques used to control the intellectual complexity of large software systems.

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P-glycoprotein (P-gp), an ATP-binding cassette (ABC) transporter, functions as a biological barrier by extruding cytotoxic agents out of cells, resulting in an obstacle in chemotherapeutic treatment of cancer. In order to aid in the development of potential P-gp inhibitors, we constructed a quantitative structure-activity relationship (QSAR) model of flavonoids as P-gp inhibitors based on Bayesian-regularized neural network (BRNN). A dataset of 57 flavonoids collected from a literature binding to the C-terminal nucleotide-binding domain of mouse P-gp was compiled. The predictive ability of the model was assessed using a test set that was independent of the training set, which showed a standard error of prediction of 0.146 +/- 0.006 (data scaled from 0 to 1). Meanwhile, two other mathematical tools, back-propagation neural network (BPNN) and partial least squares (PLS) were also attempted to build QSAR models. The BRNN provided slightly better results for the test set compared to BPNN, but the difference was not significant according to F-statistic at p = 0.05. The PLS failed to build a reliable model in the present study. Our study indicates that the BRNN-based in silico model has good potential in facilitating the prediction of P-gp flavonoid inhibitors and might be applied in further drug design.

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A multi-plate (NIP) mathematical model was proposed by frontal analysis to evaluate nonlinear chromatographic performance. One of its advantages is that the parameters may be easily calculated from experimental data. Moreover, there is a good correlation between it and the equilibrium-dispersive (E-D) or Thomas models. This shows that it can well accommodate both types of band broadening that is comprised of either diffusion-dominated processes or kinetic sorption processes. The MP model can well describe experimental breakthrough curves that were obtained from membrane affinity chromatography and column reversed-phase liquid chromatography. Furthermore, the coefficients of mass transfer may be calculated according to the relationship between the MP model and the E-D or Thomas models. (C) 2004 Elsevier B.V. All rights reserved.

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Douglas, Robert; Cullen, M.J.P., (2002) 'Large-Amplitude nonlinear stability results for atmospheric circulations', The Quarterly Journal of the Royal Meteorological Society 129 pp.1969-1988 RAE2008

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Gohm, Rolf; Dey, S., 'Characteristic function for ergodic tuples', Integral Equations and Operator Theory 58(1) pp.43-63 RAE2008