Notation clarifying

If there is no decimal point, assume the zeros are not significant, unless exponential notation clarifies the quantity 5300 L is assumed to have two significant figures, but 5.300X10 L has four, 5.30X10 L has three, and 5.3X10 L has two. 

This result should be compared with Eq. (8.28) for the case of the ideal mixture. It is reassuring to note that for n = 1, Eq. (8.36) reduces to Eq. (8.28). Next let us consider whether a change of notation will clarify Eq. (8.36) still more. Recognizing that the solvent, the repeat unit, and the lattice site all have the same volume, we see that Ni/N is the volume fraction occupied by the solvent in the mixture and nN2/N is the volume fraction of the polymer. Letting be the volume fraction of component i, we see that Eq. (8.36) becomes... 

Operational definitions of molecular structure are needed to clarify experimental significance. In addition, some statistical notation is needed to clarify physical meaning. All statistical definitions hinge on the minimum of potential energy in a bound electronic state, which defines the equilibrium geometry or r,-intemuclear distance type. 

To clarify the notation I will write the indexes outside the parentheses thus... 

Some synonyms in the Alphabetical index are followed by bracketed notations. These notations provide additional clarifying information about the entry such as composition, modifications to the agents (e.g., thickened, dusty, binary), or a note for historical context. For example, "White Star" was a gas blend that was employed by the British in World War I consisting of 50% phosgene and 50% chlorine. The entry appears as ... 

The establishment of a formula for the a functions essentially involves solving the order-disorder problem in a suitable notation. Mayer s method is similar to that discussed by Domb and Hiley201 following earlier work of Rushbrooke and Scoins78 and Fournet20 . We shall not discuss it in detail, but it may help to clarify the difference between the expansions of Section IV and that above by considering the evaluation of (cf. Eq. (78))... 

This is a rather casual notation and we need to clarify what is meant. p+Ap is a new parameter vector with only the i-th parameter p shifted by the small amount Apu In Main NG2, m, Ap is calculated as lxlO 4 p . The factor lxlCk4 is somewhat arbitrary and experimentation is usually the best way of... 

If a specific A-B bond is denoted as A—By, the bond length is written b Ai, By). Abbreviated notations, such as bi, may be used if this meaning is clarified by a diagram. 

Fig. 3.3.1 Pathways of essential fatty acid formation from the dietary (poly)unsaturated fatty acids. The total set of elongases and desaturases has not been completely clarified. The notation (n-3) and (n-6) are alternatives for ( -3) and (co-6), respectively...

Since the publication of some prolegomena to the rational analysis of systems of chemical reaction [1] other cognate work has come to light and some earlier statements have been made more precise and comprehensive. I would like first to advert to an earlier work previously overlooked and to mention some recent publications that partially fill some of the undeveloped areas noticed before. Secondly, I wish to extend the theorem on the uniqueness of equilibrium to a more general case and to establish the conditions for the consistency of the kinetic and equilibrium expressions ( 2, 3). Thirdly, the conception of a reaction mechanism is to be reformulated in a more general way and the metrical connection between the kinetics of the mechanism and those of the ostensible reactions clarified. The notation of the earlier paper ([1], hereinafter referred to as P) will be followed and augmented where necessary. In particular the reader is reminded that the range of each affix is carefully specified and the summation convention of tensor analysis is employed. 

All the system response curves in frequency and time domains were calculated numerically from equations that are much too involved to reproduce in detail here. Transfer functions in Laplace transform notation are easily defined for the potentiostat and cell of Figure 7.1. Appropriate combinations of these functions then yield system transfer functions that may be cast into time- or frequency-dependent equations by inverse Laplace transformation or by using complex number manipulation techniques. These methods have become rather common in electrochemical literature and are not described here. The interested reader will find several citations in the bibliography to be helpful in clarifying details. 

Some confusion exists in the proper utilization of the expression band or absorption band. The following statement, taken directly from Mulliken s report on notation (6), should help clarify matters ... 

From the difference in electronegativity between O (3.5) and Ti (1.32), it is inferred that the Ti—O bond has a marked ionic character, but the designation of these ions as Ti4+ and O2 seems exaggerated the notation Tilv will therefore be used, except in the case of reduction/oxidation reactions where Ti4+ and Ti3 + better clarify the transformation taking place. 

The principles of nomenclature for copolymers are based on their structure and are given in Table 1.2, where A and B represent the names of repeating units. For example, a statistical copolymer of ethylene and propylene would be called poly(ethylene-stat-propylene), and a triblock copolymer of styrene (A) sand isoprene (B) would be called polystyrene-Z)/oeA -polyisoprene- /ocA -polystyrene. In some cases it is necessary to introduce square brackets in the nomenclature to clarify the notation. Let us see an example An alternating copolymer of styrene and maleic anhydride would be called poly[styrene-a/ (maleic anhydride)]. 

Three distinct types of information are presented (1) descriptions of chemicals, raw materials, processes, and equipment (2) expanded definitions of chemical entities, phenomena, and terminology and (3) descriptions or identifications of a wide range of trademarked products used in the chemical industries. Supplementing these are listings of accepted chemical abbreviations used in the literature, short biographies of chemists of historic importance, and winners of the Nobel prize in chemistry. Also included are descriptions or notations of the nature and location of many U.S. technical societies and trade associations. In special cases editorial notes have been supplied where it was felt necessary to clarify or amplify a definition or description. A few entries written by specialists are acknowledged by use of the author s name. 

First, however, let us introduce a notation which may look a little perverse at first sight but which helps to clarify the problem. It is to number the stages from the last to the first as shown in Fig. 7.25. Thus the feed to reactor n is from reactor n + 1... 

The notation in this section tends to be more complex than we have encountered in previous chapters. A worked example using the data from Section 10.5.1 may clarify the description. In a randomized, double-blind, 12-week study, the test treatment was compared with placebo. The primary endpoint of the study was the proportion of participants who attained an SBP goal < 140 mmHg. Of 146 participants assigned to placebo, 34 attained an SBP < 140 mmHg at week 12. Of 154 assigned to test treatment, 82 attained the goal. 

The first question that we may ask is the form of the relationship between D/Dt and the ordinary partial time derivative 3/31. The so-called sky-diver problem illustrated in Fig. 2-4 provides a simple physical example that may serve to clarify the nature of this relationship without the need for notational complexity. A sky diver leaps from an airplane at high altitude and begins to record the temperature T of the atmosphere at regular intervals of time as he falls toward the Earth. We denote his velocity as —Uc/iveri-, where izis a unit vector in the vertical direction, and the time derivative of the temperature he records as D T/Dt. Here, D /Dt represents the time rate of change (of 7) measured in a reference frame that moves with the velocity of the diver. Evidently there is a close relationship between this derivative and the convected derivative that was introduced in the preceding paragraph. Let us now suppose, for simplicity, that the temperature of the atmosphere varies with the distance above the Earth s surface but is independent of time at any fixed point, say, z = z. In this case, the partial time derivative 3 T/dt is identically equal to zero. Nevertheless, in the frame of reference of the sky diver, D T/Dt is not zero. Instead,... 

This is the usual thermodynamic averaging, which amounts to averaging over initial states aa and summing over final states a a . To clarify the notation, we shall write explicitly the first term in Eq. (49) ... 

As a complement to this section on crystallography, some remarks on the old notations are given. In the nineteenth-century treatises, the crystallographic notations are varied and difficult to understand. However C. Friedel (1893) recorded all notations used from Haiy onward. For all the simple forms, he compared five different modes (Levy, Weiss, Naumann, Dana, Miller) which could be reduced substantially to two different schemes. Some crystallographers assigned a symbol to a simple form (e.g., p is cube in Levy, O is octahedron in Naumann), whereas others referred to the intercepts of the faces on axes and assigned some numbers to each face in comparison with a reference face, with direct (Weiss) or inverse (Miller) proportionality. The following table, which reports the various symbols for some simple forms of the cubic system, clarifies these differences. 

We introduce the discrete notation in order to clarify the ensuing discussion. What we want to demonstrate is how the time-correlation function varies with time. In Fig. 2.2.1 we present the noise signal A(t). Note that many of the terms in the sum Eq. (2.2.3) are negative. For example, in Fig. 2.2.1 AjAj+n is negative. Consequently, this sum will involve some cancellation between positive and negative terms. Now consider the case . The sum contributing to this is J AjAj = J Aj2. Since... 

Einstein and Mayer (Bibl. 1931, 3) always use these general coordinate systems. In their work the mapping (21) plays a sinificant role that we hope to clarify in the following. Einstein and Mayer used the notation li instead... 

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