A More Appropriate Definition

However, defining the limit function as the limit of the polygons is problematic, and it can be avoided, merely by defining it instead as the limit of a sequence of Ck functions. The question then is what sequence of what functions . 

This is very simple. We can define it as the limit of a sequence of any well-behaved curve27 defined by the vertices of the polygons as control points. For example, we could define it as the limit of 

Every curve in the sequence would be Coo, but the limit would have divergent derivatives at the places where the analysis in previous chapters predicted it. This behaviour is not regarded as in any way abnormal. For example, tan 1(nx) is C everywhere for all finite n, but the limit as n — oo has a discontinuity at x = 0 where the first derivative diverges. 

However, there is a better choice. If we believe the limit function to be Ck, then we choose as our sequence of functions the B-splines of degree k +1. This is actually the assumption which has been made implicitly in the use of difference schemes above. If, for example, a scheme has a convergent second difference scheme, then we can think of this second difference scheme as having a polygon, so that the second derivative varies linearly. If the second derivatives vary linearly in each span, then the first derivatives vary quadrat-ically and the actual values cubically, and so, because the support is finite, the implicit approximant is a sequence of cubic B-splines28. 

This definition is also justified by the view taken of the cascade algorithm at the end of section 12.1. 

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Extensive monitoring of the chemistry of precipitation is now available fi-om networks in both North America and Europe. Representative values of the major soluble species that account for most of the measured conductance of the samples at three United States sites are shown in (Table I) (77). It will be noted that the acidity, which is measured directly as pH, is due primarily to the presence of nitrate and sulphate ions that are not balanced by associated cations. While direct pH measurements are a valid measure of precipitation acidity, Reuss (18) has proposed that a balance of the principle ionic species, as in Equation 1 would provide a more appropriate definition of the acidity in relation to possible ecosystem responses. 

Since his early pioneering work on the rhizosphere (a term Hiltner used to describe specifically the interaction between bacteria and legume roots), our knowledge of the subject has greatly increased, and today perhaps a more appropriate definition of the rhizosphere is the field of action or influence of a root (1). The rhizosphere is generally considered to be a narrow zone of soil subject to the influence of living roots, where root exudates stimulate or inhibit microbial populations and their activities. The rhizoplane or root surface also provides a... 

For cases where it is possible to readily recover unused reactant A from the product mixture for recycle to the reactor inlet, the use of the definition of yield employed in Illustrations 9.2 and 9.3 is not appropriate. In this situation, a more appropriate definition is... 

A more appropriate definition of membrane bioreactors confines them to devices in which biochemical conversion actually occurs. For example, an enzyme may be immobilized in the membrane by physical sorption or covalent... 

Comment. A more appropriate definition for an adiabatic system will be provided in Section 1.7. 

A more appropriate definition of SOC for global change requirements might be that SOC represents all dead carbon from the land surface down (i.e., from the top of the conventional litter horizon) with no dimension greater than 2 mm, including such carbon present in the litter and O-horizons. All material greater than 2 mm is thus considered litter, a size that is commonly used in soil science and a distinction that is easily made and readily quantifiable. The present distinction between litter and the O-horizon is ambiguous in that in reality a continuum exists between carbon in litter, O-horizon, and mineral soil. The present distinction also cannot account for the presence of subsurface litter derived from recently dead roots, the turnover dynamics of which may be more similar to surface litter than the mineral soil. 

In this definition, the term slurry is used to denote the phase consisting of the liquid and the solid, and thus the term bubble-free sluny would be a more appropriate term to be used for this phase. 

Thus, a more appropriate question to ask is Is it possible to measure the absolute potential of the hydrogen reaction, /H+(abs) Actually it is possible. Remembering the definition of a standard hydrogen electrode potential (see Section 6.3.4), this was defined as the potential obtained when a metal comes in contact with a solution containing H+ under thermodynamically reversible conditions at unit activity, and H2 at 1 atm, at 298 K. As to the identity of the metal base, it can in principle be any metal at which it is possible to observe the reaction H2 H+ + e taking place at equilibrium. In practice, the metals used as substrates can only be noble metals because most other metals enter into equilibria with their own species in solution. Usually platinum is the metal chosen. 

Standard, generally accepted notation has been used throughout this text. This list contains the important symbols, their definition, and, when appropriate, the page of first occurrence (where a more detailed definition is given). Symbols used only once, or within only a single section are not listed. In a few cases it has been necessary to use the same symbol twice. These occunences are rare and widely separated, so it is hoi ed no confusion will result. 

A later paper [47] gives the appropriate equation for the case of a spherical, radially directing source of sodium vapour where a complete description of transport processes depends only upon the radial coordinate and where a more exact definition of streaming effects is possible. No further studies of this type have appeared. It is of particular interest that the values appear to be in good agreement with values obtained by the life period technique. 

This term denotes distribution of a compound into/onto a sod or sediment without considering a specific mechanism. Soils are so complex that in some situations several mechanisms could be active and in an experimental context, on occasion, one could simply be observing inclusion in some pore in the sod structure distinct from any of the processes discussed. Thus sorption is a more inclusive and less definitive term and would be a more appropriate designator for the distribution of chemicals between soil and water. 

The most commonly used term to describe appropriate biological requirements of a biomaterial or biomaterials used in a medical device is biocomparibifity. A simplistic definition of biocompatibility is that a material does not aeate any adverse tissue reactions. A more helpful definition of biocompatibility is the ability of a material to perform with an appropriate host response in a specific application. This definition is helpful in that it links material properties or characteristics with... 

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