Quantify, defined

Because of the appearance of terms q p " (k) in the above expressions, this approach is known as q p perturbation theory. The quantifies defined in Eq. (3.44) are elements of a two-index matrix (n and n y, the diagonal matrix elements are simply the expectation value of the momentum operator in state We can... 

The life cycle is first defined and the complete resource requirements (materials and energy) quantified. This allows the total environmental emissions associated with the life cycle to be quantified by putting together the individual parts. This defines the life-cycle inventory. 

This energy region is that which corresponds to the electron energy states of the molecules, which are quantified and so can have only well-defined discrete values. 

Unlike the solid state, the liquid state cannot be characterized by a static description. In a liquid, bonds break and refomi continuously as a fiinction of time. The quantum states in the liquid are similar to those in amorphous solids in the sense that the system is also disordered. The liquid state can be quantified only by considering some ensemble averaging and using statistical measures. For example, consider an elemental liquid. Just as for amorphous solids, one can ask what is the distribution of atoms at a given distance from a reference atom on average, i.e. the radial distribution function or the pair correlation function can also be defined for a liquid. In scattering experiments on liquids, a structure factor is measured. The radial distribution fiinction, g r), is related to the stnicture factor, S q), by... 

A major potential drawback with cluster analysis and dissimilarity-based methods f selecting diverse compounds is that there is no easy way to quantify how completel one has filled the available chemical space or to identify whether there are any hole This is a key advantage of the partition-based approaches (also known, as cell-bas( methods). A number of axes are defined, each corresponding to a descriptor or son combination of descriptors. Each axis is divided into a number of bins. If there are axes and each is divided into b bins then the number of cells in the multidimension space so created is ... 

Stress relaxation time, obtained from rheograms based on viscometric flows, is used to define a dimensionless parameter called the Deborah number , which quantifies the elastic character of a fluid... 

Other techniques that work well on small computers are based on the molecules topology or indices from graph theory. These fields of mathematics classify and quantify systems of interconnected points, which correspond well to atoms and bonds between them. Indices can be defined to quantify whether the system is linear or has many cyclic groups or cross links. Properties can be empirically fitted to these indices. Topological and group theory indices are also combined with group additivity techniques or used as QSPR descriptors. 

The significant thing about these and numerous other side reactions that could be described for specific systems is the fact that they lower the efficiency of the initiator in promoting polymerization. To quantify this concept we define the initiator efficiency f to be the following fraction ... 

Reliability. The rehabiUty of a system is defined as the probabiUty that the system will perform its intended function satisfactorily for a specified interval of time when operating under stated environmental conditions. It has to be realized that supposedly identical products fail at different times, thus rehabihty can be quantified only as a probabiUty. For any product there is some underlying function that describes this success pattern. Typical reUabiUty functions are shown in Figure 1 for two different products. These products can be compared at the same rehabihty level R or the rehabihty levels can be compared for any selected time period, t. ... 

The molecules in a gas-hquid interface are in tension and tend to contract to a minimum surface area. This tension may be quantified by the surface tension, which is defined as the force in the plane of the surface per unit length. Jasper" has made a critical evaluation of experimental surface tension data for approximately 2200 pure chem-ic s. He correlates surface tension C (mN/m = dyn/cm) with temperature T (°C) over a specified temperature range as... 

Before setting about the task of developing such a model, the product development process requires definition along with an indication of its key stages, this is so the appropriate tools and techniques can be applied (Booker et al., 1997). In the approach presented here in Figure 5.11, the product development phases are activities generally defined in the automotive industry (Clark and Fujimoto, 1991). QFD Phase 1 is used to understand and quantify the importance of customer needs and requirements, and to support the definition of product and process requirements. The FMEA process is used to explore any potential failure modes, their likely Occurrence, Severity and Detectability. DFA/DFM techniques are used to minimize part count, facilitate ease of assembly and project component manufacturing and assembly costs, and are primarily aimed at cost reduction. 

Static sampling systems are defined as those that do not have an active air-moving component, such as the pump, to pull a sample to the collection medium. This type of sampling system has been used for over 100 years. Examples include the lead peroxide candle used to detect the presence of SO2 in the atmosphere and the dust-fall bucket and trays or slides coated with a viscous material used to detect particulate matter. This type of system suffers from inability to quantify the amount of pollutant present over a short period of time, i.e., less than 1 week. The potentially desirable characteristics of a static sampling system have led to further developments in this type of technology to provide quantitative information on pollutant concentrations over a fked period of time. Static sampling systems have been developed for use in the occupational environment and are also used to measure the exposure levels in the general community, e.g., radon gas in residences. 

The most accurate - and most popular - method of quantifying matrix effects is to analyze the unknown sample with a similar sample of known composition. The relationship between measured intensity and the content of each sample is, usually, defined by the relative sensitivity factor (RSF) ... 

The first step is to define the objectives of the flow model, and to identify those flow aspects that are relevant for the performance of the reactor. Then, the engineer must identify and quantify the various times and space scales involved, as well as the geometry of the system. These actions allow the problem to be represented by a mathematical model. Creating this model accurately is the most crucial task in the flow modeling project. 

GO is suited for many PSA applications with boundary conditions well-defined by. i system schematic and other design documents to quantify the components. 

Techniques for quantifying Techniques used were basically from NUREG/CR-1278 or PRA Procedun s Guide, Chapter 4. (l)THERP (1980 version NUREG/CR-1278 with appropriate factors for a tree was used in procedure defined events. (2) A time dependent modeling approach was used to quantify operator actions during a sequence. THERPmethixlr. were ii ,cd as described in WASH- Id ... 

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