Motivating Example

Pressure-induced phase transformations are known to occur for a wide range of solids. Bulk Si, for example, has the diamond structure at ambient conditions but converts to the 3-tin structure at pressures around lOOkbar. Figure 2.5 shows how it is possible to use the kinds of information we have calculated in this chapter using DFT to predict the existence of pressure-induced phase transformations. It was essentially this idea that was used to make the geologically relevant predictions of the properties of minerals such as MgSi03 that were mentioned as one of the motivating examples in Section 1.2. 

Activation of the caspases requires the help of a number of cofactors that are also known as activators or adaptors. Different cofactors are involved depending on the trigger mechanism of caspase activation. A central function of the cofactors is to bring about aggregation and thus activation of the procaspases. This occurs by specific protein-protein interactions with the help of common structural motives. Examples of such motives are the death domains (DD), death effector domains (DED) and the caspase recruitment domains (CARD), which all have a similar structure of six a-heh-ces. 

Illustration 3.2.12 This example is the motivating example for the second order necessary optimality conditions ... 

Illustration 6.3.4 This example is taken from Floudas and Visweswaran (1990) and served as a motivating example for global optimization. 

This example, which corresponds to the motivating example of Gundersen and Grossmann (1990) below the pinch point, features three hot process streams, two cold streams, and a cold utility with data shown in Table 8.4. 

Let us continue with the analysis of the motivating examples introduced in Section 4.2, and present the derivation of reduced-order models for the fast and slow dynamics of the two process systems, according to the theoretical framework developed above. 

The program has been tested on several QED and QCD motivated examples such as electron g — 2 in QED, gauge independence of the electron wave function renormalization in QED, a relation between the pole and the MS mass in QCD, exponentiation of the infra-red asymptotic of the heavy fermion propagator. Many details concerning these checks and other technical aspects of our calculations can be found in Ref. [11] which the interested reader should consult. 

The series Lecture Notes in Physics reports new developments in physical research and teaching - quickly, informally, and at a high level. The type of material considered for publication includes monographs presenting original research or new angles in a classical field. The timeliness of a manuscript is more important than its form, which may be preliminary or tentative. Manuscripts should be reasonably self-contained. They will often present not only results of the author(s) but also related work by other people and will provide sufficient motivation, examples, and applications. 

From the motivating example presented so far, we derive the following requirements ... 

The CMI method assumes that the length of time between the measurement of last quantifiable concentration and the LLOQ value is small relative to the drug half-life. If there is a considerable length of time between the measurement of the last quantifiable concentration and the LLOQ value, then CMI as proposed here has to be modified to account for this. The latter is beyond the scope of this chapter. A motivating example is used to illustrate the application of CMI below. 

The aim of this chapter is to equip the pharmacometrician with sufficient theory and application to confidently approach the PK/PD-based analysis of count data and thus derive the maximum return on investment from clinical study data. Section 27.2 provides a motivating example and Section 27.3 presents relevant definitions and theory. Section 27.4 applies the theory to the example and introduces diagnostics methods. Throughout the chapter, the focus is on population approaches using nonlinear mixed effects models. Code segments of NONMEM control files are presented in the appendix. Mixed effects analysis methodology is described in detail in Chapter 4 of this text. 

In the sections that follow types of PK/PD knowledge creation, general steps in the knowledge creation process, data supplementation and the motivation for it, data supplementation procedure, nonparametric approximate Bayesian data supplementation method, structure-based multiple supplementation with a motivating example, and implications of the use of multiple data supplementation for the characterization of an unexplored region of the response are described. The emphasis in this chapter is on the use of data supplementation to characterize unexplored region of the response surface. A discussion on data synthesis, the qualitative characterization of the response surface, and the estimation of inestimable uncertainty has been elegantly presented by Williams et al. (1) and Ette and Onyiah (5). Therefore, these approaches are discussed in brief in the sections that follow. 

Data supplementation deals with the supplementation of data to enable the exploration of an aspect of the response surface that may not have been targeted for exploration in a completed trial. It also deals with the supplementation of data in preclinical animal studies where the destructive nature of the sampling design does not permit the construction of individual profiles for inaccessible tissues. A motivating example that deals with a targeted aspect of an unexplored region of the response surface is discussed next to provide clarity on the approach. Data supplementation in the preclinical animal setting is beyond the scope of this chapter. 

STRUCTURE-BASED MULTIPLE SUPPLEMENTATION A MOTIVATING EXAMPLE 835... 

Example 3. Consider the p-mapping pM, the source instance Ds, and the query Q in the motivating example. 

Example 5. Consider rewriting Q in the motivating example, repeated as follows ... 

Fig. 4.5 The motivating example (a) p-mapping for Si and M3, (b) p-mapping for Si and M4, and (c) query answers w.r.t. M and pM. Here we denote phone, hPhone by hPPhone, phone, oPhone by oPPhone, address, hAddr by hAAddr, and address, oAddr by oAAddr...

Monograph manuscripts should be reasonably self-contained and rounded off. Thus they may, and often will, present not only results of the author but also related work by other people. They may be based on specialised lecture courses. Furthermore, the manuscripts should provide sufficient motivation, examples and applications. This clearly distinguishes Lecture Notes from journal articles or technical reports which normally are very concise. Articles intended for a journal but too long to be accepted by most journals, usually do not have this lecture notes character. For similar reasons it is unusual for doctoral theses to be accepted for the Lecture Notes series, though habilitation theses may be appropriate,... 

As a motivating example, one could start with the following statement of a typical process design problem. 

They also find that the cost of learning is a consequence of censored information and shared with the consumer in the form of a higher selling price when demand uncertainty is additive. They also apply the results to three motivating examples a market research problem in which a product is introduced in a test market prior to a widespread launch a global newsvendor problem in which a seasonal product is sold in two different countries with nonoverlapping selling seasons and a minimum quantity commitment problem in which procurement resources for multiple purchases may be pooled. 

Rhee (2001) generalizes Rhee and Park (2000) by explicitly modeling a competitive impetus for a manufacturer to add a direct channel alongside its established retail channel to respond to a direct-sales-only challenger (usually Internet-based). A motivating example is Compaq s 1998 introduction of the Compaq.com online store, largely viewed as a response to the likes of Dell Computer. 

Our challenge is to teach you just a few concepts, as has been our approach throughout the book, and add maybe just one more (interest rates). Then we will present stimulating and motivating examples from everyday life and, more importantly, from situations one might encounter in chemical and bioprocess engineering. 

As an illustration of the physical content of Eq. (4) (which also serves as a motivating example for the SCM), we show in Figure 4.1 the size-evolutionary pattern of the ionization potentials (IPs) of Na/v clusters, which exhibits odd-even oscillations in the observed... 

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