A few simple examples

The trivial chemical example that is usually given in the literature on emergence since the early times of the British emergentists is water being formed from its atomic components. The collective properties of water are not present in hydrogen and oxygen so the properties of water can be viewed as emergent ones. 

This kind of simple argument can be generalized to encompass all cases in which a molecule is formed from its atomic components, e.g., CH4, CO2, HCl, NH3, and so on. In each case, obviously, the properties of the resulting molecule are not present in the initial components and can be seen as emergent properties. 

One question that can be posed after analysing these few examples is whether, and to what extent, the emergent properties can be interpreted in terms of the elements of the lower level, or, more generally, what is the relation between the emergent properties and the properties of the more basic level. 

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It is clearly evident from Che extremely simple example of the synthesis of Isovaleralde-hyde that a fully systematic approach to antithesis is not very useful. Chemists are not interested in encyclopedic catalogues of synthetic routes. We shall now discuss a few simple examples, where availability and price of starting materials are considered. This restriction generally reduces long lists of alternative target molecules and precursors to a few proposals. 

We will have more to say about both of these two possibilities later. In the remaining paragraphs of this section, we introduce (and remind ourselves of) some basic terminology, outline the LST for one dimensional systems and provide a few simple examples of its use. The section concludes with a brief discussion of some subtleties needed to define a LST for systems with dimension d > 1. 

Note Only a few simple examples of the metal complexes formed by quinoxaline oxides and dioxides are given here. 

Let us illustrate the concept of "tree-like" with a few simple examples. Suppose G is tree-like with entry node e and there is a direct connection from n to m. Situations (1), (2) and (3) below are permissible ... 

Esters can be recognized by the designation -ate in their names. Here are a few simple examples ... 

At the cellular level, the various types of receptor, transporter, enzyme and ion charmel are all chiral in form. Thus although the enantiomers of a drug may have identical physicochemical properties, the way in which they may interact with chiral targets at the level of the cell will give rise to different pharmacod)mamic and pharmacokinetic properties. A few simple examples will illustrate how taste and olfactory receptors can differentiate between enantiomers. Thus R-carvone tastes like spearmint whereas the S-isomer tastes like caraway. Similarly, R-limolene smells like lemon whereas the S-enantiomer tastes of orange. 

A specialized system of nomenclature has been developed, principally by Smith,16 for naming skeletons consisting of aromatic residues linked in various ways by saturated bridges. Those skeletons containing benzene residues only are termed cyclophanes, and names for heteroaromatic analogues are based on the name of the heterocycle with the termination -ophane. The numbers of atoms in the bridges are indicated in square brackets, and the orientation of substitution on the aromatic residue(s) is shown in parentheses. A few simple examples are given (149-151), with alternative names. 

Isospin is a useful concept in that it is conserved in processes involving the strong interaction between hadrons. The use of isospin can help us to understand the structure of nuclei and forms the basis for selection rules for nuclear reactions and nuclear decay processes. While a detailed discussion of the effects of isospin upon nuclear structure, decay, and reactions is reserved for later chapters, a few simple examples will suffice to demonstrate the utility of this concept. 

Because it takes some practice to be able to use the recipes for calculating entropy changes in the system and surroundings, a few simple examples are presented here. 

We start by acknowledging that our goals are modest as we confront such a vast field as multinuclear NMR. In Section 3.7, we have seen the impact of other nuclei that possess a magnetic moment (especially those with spin one-half) on proton spectra. We will briefly examine the NMR spectrometry of four spin one-half nuclei, which were selected for their historic importance in organic chemistry (and related natural products and pharmaceutical fields), biochemistry, and polymer chemistry. These four nuclei, l5N, 19F, 29Si, and 31P, are presented with a few simple examples and a brief consideration of important experimental factors and limitations. 

In this section we discuss first in general the techniques used to simulate the chemical reactions with relatively high activation barriers. After that we provide a more detailed discussion of the constrained dynamics approach. Special emphasis will be put on MD along the intrinsic reaction coordinate (IRC), illustrated by a few simple examples.33... 

This chapter has introduced foundational concepts of statistical thermodynamics and physical chemistry for analysis of systems involving chemical reactions, molecular transitions, and material transport. A few simple examples of applications of thermodynamic concepts to biological systems were illustrated in Section 1.7. The remainder of this book focuses on applications to the analysis of biological systems. 

In this section, we look at a few simple examples of finding the modified Onsager equations and the calculation of coefficients Ay for particular schemes of the interrelated chemical transformations that are not very complicated. 

A few simple examples should suffice to demonstrate the critical role that MD plays in chemical reactions. Conservation of momentum must be enforced. Atoms and molecular fragments in motion must maintain their motion unless some barrier or force is applied to them. Consider the reaction of m-2-butene with... 

The stoichiometric number v is defined as the number of times the rate determining step must occur, for the overall reaction to occur once. This is best explained by showing a few simple examples. For the reaction sequence shown earlier for hydrogen evolution... 

It is worthwhile to consider a few simple examples to get a feeling for the values of k. If the two dipoles have orientations in space perpendicular to each other, and if the acceptor dipole is juxtaposed next to the donor, but in the direction perpendicular... 

We will now consider a few simple examples to illustrate the flux-force relations in a number of common elemental reactions. 

Meanwhile, let us consider a few simple examples, illustrating the spatial behavior of the migrated electromagnetic fields. The first example represents the results of migration of the magnetic component of the field generated by a local horizontal electric dipole, located at some depth, zq, in the homogeneous lower half-space of conductivity ab- The current in the dipole is described by the delta-pulse ... 

Many carbonyls have been prepared containing atoms of two or more different elements, some with only CO ligands and others with ligands of various types. The special interest lies in the metal-metal bonds and in the stereochemistry of the metal atoms. We give in Table 22.9 a few simple examples of typical molecules ... 

A few simple examples demonstrate the application of the calculation of FC for each of the separate atoms ... 

Simulations are useful to understand the system under consideration and to answer what if questions. Indeed, without simulations a model is like a bicycle without a rider. In the absence of simulations, the model simply exists and can only be used for characterizing or summarizing a system. A few simple examples... 

A detailed treatment of particle flow around objects, in channels of various geometries, and so on, is beyond the scope of this book. Treatments are provided by Fuchs (1964), Hinds (1999), and Flagan and Seinfeld (1988). We will focus our analysis on a few simple examples demonstrating the important concepts. 

From the rotational or vibration-rotation spectra of a diatomic molecule such as HCl, we can calculate the internuclear distance directly from the measurement of the spacing of the lines. This simplicity is absent in polyatomic molecules except in certain special cases. We consider only a few simple examples to illustrate the difficulties. 

With spectral data, it is not uncommon to measure several thousand variables at one time. However, it is often hard for beginners to conceptualize so many variables therefore, we will begin our discussion of MVA with a few simple examples that illustrate important statistical concepts that are essential in chemometrics. The first problem is a set of pharmaceutical quality data. Measurements of density and assay have been collected for 43 lots of material. The data is shown in Table 11.2. Inspection of the data reveals that the density values are near 1.0, while the assay values are closer to 100. A goal of the data analysis is to understand the variation within the data set. It will be advantageous to have the two variables in the data set with similar magnitudes therefore, we will scale each of the two variables by its own standard deviation. 

Only a few simple examples of applications will be given. For ion-ion reactions the solvent effect, Eq. (49), is controlled by the relationship... 

A few simple examples will make this electron counting rule clearer. In Cr(CO)6 the CO groups donate two cr electrons each for a total of 12 electrons. The charge... 

The speech synthesis markup languages followed a similar philosophy, so instead of specifying that a word should be spoken at 150Hz (which would have different effects for different speakers), instead more abstract or logical instructions are used, which for instance state that a particular word is to be emphasised. A few simple examples will now be explored. 

Next we present a few simple examples that demonstrate how frequently practical computations and important theoretical problems are reduced to solving linear systems of algebraic equations (more examples are presented in Sections VLB and VII.D) (Those readers not interested in the present section may proceed to Section HI, consulting Section II as they are referred to it.)... 

Discussion of Band Structure through a Few Simple Examples 21... 

DISCUSSION OF BAND STRUCTURE THROUGH A FEW SIMPLE EXAMPLES... 

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