A mathematical model, preferably based on molecular consi- [Pg.41]

One approach to a mathematically well defined performance measure is to interpret the amplitude values of a processed signal as realizations of a stochastic variable x which can take a discrete number of values with probabilities P , n = 1,2,..., N. Briefly motivated in the introduction, then an interesting quality measure is the entropy H x) of the amplitude distribu- [Pg.90]

Kreyszig, E., "Introductory Mathematical Statistics," John Wiley Sons, New York (1970). [Pg.109]

Lakestani, F., Validation of mathematical models of the ultrasonic inspection of steel components, PISC III report 6, IRC Inst. Adv. Mater., Petten, 1992. [Pg.162]

The term p is a reaction constant and is mathematically evaluated for a particular reaction by plotting log kjkQ against a. The slope of the straight lines is p, and reflects the sensitivity of the reaction under study to effects of substituents. The value of p is obviously affected by temperature, solvent changes, etc. [Pg.200]

Reservoir simulation is a technique in which a computer-based mathematical representation of the reservoir is constructed and then used to predict its dynamic behaviour. The reservoir is gridded up into a number of grid blocks. The reservoir rock properties (porosity, saturation, and permeability), and the fluid properties (viscosity and the PVT properties) are specified for each grid block. [Pg.205]

The Supplement B (reference) contains a description of the process to render an automatic construction of mathematical models with the application of electronic computer. The research work of the Institute of the applied mathematics of The Academy of Sciences ( Ukraine) was assumed as a basis for the Supplement. The prepared mathematical model provides the possibility to spare strength and to save money, usually spent for the development of the mathematical models of each separate enterprise. The model provides the possibility to execute the works standard forms and records for the non-destructive inspection in complete correspondence with the requirements of the Standard. [Pg.26]

Once the flowsheet structure has been defined, a simulation of the process can be carried out. A simulation is a mathematical model of the process which attempts to predict how the process would behave if it was constructed (see Fig. 1.1b). Having created a model of the process, we assume the flow rates, compositions, temperatures, and pressures of the feeds. The simulation model then predicts the flow rates, compositions, temperatures, and pressures of the products. It also allows the individual items of equipment in the process to be sized and predicts how much raw material is being used, how much energy is being consumed, etc. The performance of the design can then be evaluated. [Pg.1]

Ross Kinderman and J. Laurie Snell Markov fields and their applications. Contemporary Mathematics v. 1. American Mathematical Society, 1980. [Pg.120]

Theory of the fictitious temperature field allows us to analyze the problems of residual stresses in glass using the mathematical apparatus of thermoelasticity. In this part we formulate the boundary-value problem for determining the internal stresses. We will Lheretore start from the Duhamel-Neuinan relations [Pg.136]

The main obstacles which are on the way to implement this reconstruction are discussed in [6]. One of the most rigid is how to mathematically formulate the information included in functional ). [Pg.114]

After obtaining a set of fitted velocity versus time data for a particular test specimen, we can extract the contact force and depth of indentation by mathematical operations. The differentiation of the indenter velocity gives the equation for contact force while impact [Pg.241]

TTie calculation of partial fugacltles requires knowing the derivatives of thermodynamic quantities with respect to the compositions and to arrive at a mathematical model reflecting physical reality. [Pg.152]

Most constraints can be evaluated by scoping the problem with different boundaries, as illustrated in Example 6.2. If this approach cannot be applied, then mathematical programming must be used to obtain the energy target. [Pg.184]

Heisenburg uncertainty principle For small particles which possess both wave and particle. properties, it is impossible to determine accurately both the position and momentum of the particle simultaneously. Mathematically the uncertainty in the position A.v and momentum Ap are related by the equation [Pg.201]

The most informative method of expressing uncertainty in HCIIP or ultimate recovery (UR) is by use of the expectation curve, as introduced in Section 6.2. The high (H) medium (M) and low (L) values can be read from the expectation curve. A mathematical representation of the uncertainty n a parameter (e.g. STOMP) can be defined as [Pg.178]

The example of a binary mixture is used to demonstrate the increased complexity of the phase diagram through the introduction of a second component in the system. Typical reservoir fluids contain hundreds of components, which makes the laboratory measurement or mathematical prediction of the phase behaviour more complex still. However, the principles established above will be useful in understanding the differences in phase behaviour for the main types of hydrocarbon identified. [Pg.101]

Identification of the material properties as an estimation of transfer function (TF) for the black box model. In this case the problem of identification is solving according to the results of the input (IN) and output (OUT) actions. There is a transfer of notion of mathematical description of TF on characterization of the material. This logical substitution gives us an opportunity to formalize testing procedure and describe the material as a set of formulae, which can be used for quantitative and qualitative characterization of the materials. [Pg.188]

Often the a priori knowledge about the structure of the object under restoration consists of the knowledge that it contains two or more different materials or phases of one material. Then, the problem of phase division having measured data is quite actual. To explain the mathematical formulation of this information let us consider the matrix material with binary structure and consider the following potentials [Pg.116]

According to some remarks concerning the physical interaction between the incident ultrasonic wavelet and the defects [4-6], we consider that an Ascan signal, may be described as a weighted sum of few delayed and phase-shifted replicas of the ultrasonic incident wavelet j(r). We can express this mathematically as [Pg.174]

There is some uncertainty connected with testing techniques, errors of characteristic measurements, and influence of fectors that carmot be taken into account for building up a model. As these factors cannot be evaluated a priori and their combination can bring unpredictable influence on the testing results it is possible to represent them as additional noise action [4], Such an approach allows to describe the material and testing as a united model — dynamic mathematical model. [Pg.188]

A further mind-bending collection of puzzles, games and diversions by the undisputed master of recreational mathematics. [Pg.441]

Historical Slang Literary Terms Mathematics Twentieth Century History [Pg.448]

Not to overload the Statidard, three supplements are predetermined for it. The Supplement A (compulsory ) with the list of statistics is due to compulsory determination by non-destructive magnetic method of mechanical properties test. This Supplement provided the possibility to set the reasonable compromise between two opposite tendencies -to simplify utmost a body of mathematics or, on the contrary, to complicate it to such extent that it becomes inaccessible. [Pg.26]

Herman G.T. Image reconstruction from projections.. Computer Science and Applied Mathematics, New York Academic, 1980 [Pg.220]

On the other hand, some works (7) use the wavelets theory to analyze and segment the same images. In the future, we plan to develop these mathematics tools necessary for this work. [Pg.227]

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