Central role

In a number of classic papers Hohenberg, Kohn and Sham established a theoretical framework for justifying the replacement of die many-body wavefiinction by one-electron orbitals [15, 20, 21]. In particular, they proposed that die charge density plays a central role in describing the electronic stnicture of matter. A key aspect of their work was the local density approximation (LDA). Within this approximation, one can express the exchange energy as... 

Conservation laws at a microscopic level of molecular interactions play an important role. In particular, energy as a conserved variable plays a central role in statistical mechanics. Another important concept for equilibrium systems is the law of detailed balance. Molecular motion can be viewed as a sequence of collisions, each of which is akin to a reaction. Most often it is the momentum, energy and angrilar momentum of each of the constituents that is changed during a collision if the molecular structure is altered, one has a chemical reaction. The law of detailed balance implies that, in equilibrium, the number of each reaction in the forward direction is the same as that in the reverse direction i.e. each microscopic reaction is in equilibrium. This is a consequence of the time reversal syimnetry of mechanics. 

The tliree conservation laws of mass, momentum and energy play a central role in the hydrodynamic description. For a one-component system, these are the only hydrodynamic variables. The mass density has an interesting feature in the associated continuity equation the mass current (flux) is the momentum density and thus itself is conserved, in the absence of external forces. The mass density p(r,0 satisfies a continuity equation which can be expressed in the fonn (see, for example, the book on fluid mechanics by Landau and Lifshitz, cited in the Furtlier Reading)... 

In the most connnonly employed mean-field models [25] of electronic structure theory, the configuration specified for study plays a central role in defining the mean-field potential. For example, the mean-field... 

The examples described above are only a small selection out of a tremendous number of investigations of LB films aird SAMs. This number is still increasing aird it is expected tlrat ultrathin orgairic films will play a central role in botlr fundamental aird applied sciences in tire future. 

The concept of two-state systems occupies a central role in quantum mechanics [16,26]. As discussed extensively by Feynmann et al. [16], benzene and ammonia are examples of simple two-state systems Their properties are best described by assuming that the wave function that represents them is a combination of two base states. In the cases of ammonia and benzene, the two base states are equivalent. The two base states necessarily give rise to two independent states, which we named twin states [27,28]. One of them is the ground state, the other an excited states. The twin states are the ones observed experimentally. 

Shapes of atomic orbitals play central roles in governing the types of directional bonds an atom can form. 

Whereas most chemists focused their attention on speculation about atoms and the question of atomic weights, the constant multiplicity in compounds occupied an increasingly central role. The new concept of substitution, i.e., the replacement of one element by another in a compound, started to make a major impact on chemistry in the 1840s. It was probably Dumas, who in the 1830s at the request of his father-in-law (who was the director of the famous Royal Sevres porcelain factory) resolved an event that upset a royal dinner party at the Tuil-... 

I do not wish to go into further discussion of the only too well-known close interrelationship of chemistry and biology, which some these days like to call chemical biology instead of biological chemistry. The interface of chemistry and physics can be equally well called chemical physics or physical chemistry, depending on from which side one approaches the field. What is important to realize is that chemistry occupies a central role between physics and biology. Chemistry is a truly central, multifaceted science impacting in a fundamental way on other sciences, deriving as much as it contributes to them. 

I strongly believe in the central role multifaceted chemistry plays in bridging other sciences and the ways it affects all aspects of onr life. In a gnest editorial for the jonrnal Science in December 1995 I wrote ... 

Our purpose in this introduction is not to trace the history of polymer chemistry beyond the sketchy version above, instead, the objective is to introduce the concept of polymer chains which is the cornerstone of all polymer chemistry. In the next few sections we shall introduce some of the categories of chains, some of the reactions that produce them, and some aspects of isomerism which multiply their possibilities. A common feature of all of the synthetic polymerization reactions is the random nature of the polymerization steps. Likewise, the twists and turns the molecule can undergo along the backbone of the chain produce shapes which are only describable as averages. As a consequence of these considerations, another important part of this chapter is an introduction to some of the statistical concepts which also play a central role in polymer chemistry. 

Of the various parameters introduced in the Eyring theory, only r—or j3, which is directly proportional to it-will be further considered. We shall see that the concept of relaxation time plays a central role in discussing all the deformation properties of bulk polymers and thus warrants further examination, even though we have introduced this quantity through a specific model. 

Emulsifying agents which are soaps or detergents play a central role in the emulsion polymerization process. 

The concept of microemulsions now holds a central role within the field of surfactant technology. Perhaps the most fundamental fact captured by the term is that, contrary to a popular saying, oil and water can mix. 

Compressible Vlow. The flow of easily compressible fluids, ie, gases, exhibits features not evident in the flow of substantially incompressible fluid, ie, Hquids. These differences arise because of the ease with which gas velocities can be brought to or beyond the speed of sound and the substantial reversible exchange possible between kinetic energy and internal energy. The Mach number, the ratio of the gas velocity to the local speed of sound, plays a central role in describing such flows. 

T-Lymphocytes (4,5) and other cellular components of the immune system also have equally wide implications in regulation of the normal immune system. The T-lymphocytes play a central role in the body s response to harmful antigens and tumor—host interaction (4). Responses involve antigens derived from vimses, bacteria, parasites, and tumors. T-ceUs also participate in the immune surveillance response, where self-antigens are recognized, but usually sequestered within the cell and, when exposed, become markers of cellular damage. 

Microfilaments and Microtubules. There are two important classes of fibers found in the cytoplasm of many plant and animal ceUs that are characterized by nematic-like organization. These are the microfilaments and microtubules which play a central role in the determination of ceU shape, either as the dynamic element in the contractile mechanism or as the basic cytoskeleton. Microfilaments are proteinaceous bundles having diameters of 6—10 nm that are chemically similar to actin and myosin muscle ceUs. Microtubules also are formed from globular elements, but consist of hoUow tubes that are about 30 nm in diameter, uniform, and highly rigid. Both of these assemblages are found beneath the ceU membrane in a linear organization that is similar to the nematic Hquid crystal stmcture. 

This frequency is a measure of the vibration rate of the electrons relative to the ions which are considered stationary. Eor tme plasma behavior, plasma frequency, COp, must exceed the particle-coUision rate, This plays a central role in the interactions of electromagnetic waves with plasmas. The frequencies of electron plasma waves depend on the plasma frequency and the thermal electron velocity. They propagate in plasmas because the presence of the plasma oscillation at any one point is communicated to nearby regions by the thermal motion. The frequencies of ion plasma waves, also called ion acoustic or plasma sound waves, depend on the electron and ion temperatures as well as on the ion mass. Both electron and ion waves, ie, electrostatic waves, are longitudinal in nature that is, they consist of compressions and rarefactions (areas of lower density, eg, the area between two compression waves) along the direction of motion. 

The compounds of this article, ie, ftve-membered heterocycles containing two adjacent nitrogen atoms, can best be discussed according to the number of double bonds present. Pyrazoles contain two double bonds within the nucleus, imparting an aromatic character to these molecules. They are stable compounds and can display the isomeric forms, (1) and (2), when properly substituted. Pyrazoles are scarce ia nature when compared to the imidazoles (3), which are widespread and have a central role ia many biological processes. 

These useful compounds have played a central role in both theoretical and practical organic chemistry since the 1840s. In 1838 quinic acid [36413-60-2] (1) was oxidized to 1,4-benzoquinone (2) with manganese dioxide (1). 

Cysteine [52-90 ] is a thiol-bearing amino acid which is readily isolated from the hydrolysis of protein. There ate only small amounts of cysteine and its disulfide, cystine, in living tissue (7). Glutathione [70-18-8] contains a mercaptomethyl group, HSCH2, and is a commonly found tripeptide in plants and animals. Coenzyme A [85-61-0] is another naturally occurring thiol that plays a central role in the synthesis and degradation of fatty acids. 

Vitamin A constitutes the most significant sector of the commercial retinoid market and is used primarily in the feed area. In the pharmaceutical area, there are several important therapeutic dermatologic agents which stmcturaHy resemble vitamin A and they are depicted in Figure 2 (see Pharmaceuticals). The carotenoids as provitamin A compounds also represent an important commercial class of compounds with P-carotene [7235-40-7] (10) occupying the central role (Fig. 3) (9). 

Because of the expanded scale and need to describe additional physical and chemical processes, the development of acid deposition and regional oxidant models has lagged behind that of urban-scale photochemical models. An additional step up in scale and complexity, the development of analytical models of pollutant dynamics in the stratosphere is also behind that of ground-level oxidant models, in part because of the central role of heterogeneous chemistry in the stratospheric ozone depletion problem. In general, atmospheric Hquid-phase chemistry and especially heterogeneous chemistry are less well understood than gas-phase reactions such as those that dorninate the formation of ozone in urban areas. Development of three-dimensional models that treat both the dynamics and chemistry of the stratosphere in detail is an ongoing research problem. 

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