Precision, definition

SmA phases, and SmA and SmC phases, meet tlie line of discontinuous transitions between tire N and SmC phase. The latter transition is first order due to fluctuations of SmC order, which are continuously degenerate, being concentrated on two rings in reciprocal space ratlier tlian two points in tire case of tire N-SmA transition [18,19 and 20], Because tire NAC point corresponds to the meeting of lines of continuous and discontinuous transitions it is an example of a Lifshitz point (a precise definition of tliis critical point is provided in [18,19 and 20]). The NAC point and associated transitions between tire tliree phases are described by tire Chen-Lubensky model [97], which is able to account for tire topology of tire experimental phase diagram. In tire vicinity of tire NAC point, universal behaviour is predicted and observed experimentally [20]. 

After these preliminaries we are now ready for a mathematically precise definition of an almost invariant set. Let p M he any probability measure. Wc say that the set B is 5-almost invariant with respect to p if... 

Derived plant and animal products make better use or upgrade the nutritional quaHty of already existing materials or products. Synthetic and manufactured products arose from knowledge of the functional properties of food ingredients and of human and animal nutrition that involved more precise definition of nutrient requirements for growth, reproduction, lactation, and body maintenance in both humans and domestic Hvestock. Pood products have been developed to meet human needs under abnormal environments, eg, military rations for arctic, tropical, or desert environments, and special products for astronauts ia space flights. 

The term lime also has a broad coimotation and frequently is used in referring to limestone. According to precise definition, lime can only be a burned form quicklime, hydrated lime, or hydraiflic lime. These products are oxides or hydroxides of calcium and magnesium, except hydraiflic types in which the CaO and MgO are chemically combined with impurities. The oxide is converted to a hydroxide by slaking, an exothermic reaction in which the water combines chemically with the lime. These reversible reactions for both high calcium and dolomitic types are Quicklime... 

A plasticizer is a substance the addition of which to another material makes that material softer and more flexible. This broad definition encompasses the use of water to plasticize clay for the production of pottery, and oils to plasticize pitch for caulking boats. A more precise definition of plasticizers is that they are materials which, when added to a polymer, cause an increase in the flexibiUty and workabiUty, brought about by a decrease in the glass-transition temperature, T, of the polymer. The most widely plasticized polymer is poly(vinyl chloride) (PVC) due to its excellent plasticizer compatibility characteristics, and the development of plasticizers closely follows the development of this commodity polymer. However, plasticizers have also been used and remain in use with other polymer types. 

The definition of heavy oil is usually based on API gravity or viscosity, but the definition is quite arbitrary. Although there have been attempts to rationalize the definition based on viscosity, API gravity, and density (2,3), such definitions, based on physical properties, are inadequate, and a more precise definition would involve some reference to the recovery method. 

The basis of all bulk conveyor engineering is the precise definition and accurate classification of materials according to individual characteristics under a specific combination of handling conditions (1). Since the late 1960s there has been an extraordinary growth in research into the fundamental properties and behavior of particulate soHds. However, as of this writing, it is not possible to predict the handling behavior of a bulk soHds material relevant to conditions in a specific conveyor, merely on the basis of the discrete particle properties. 

In order to establish consensus on the scope of the endocrine disrupter issue, to facilitate the identification of active chemicals and, ultimately, to underpin any future regulatory control, it is essential to agree a precise definition of an endocrine disrupter (ED). Such a definition was proposed at a major European Workshop on EDs. ... 

Remember from Chapter 2, the NPSHa formula is NPSHa = Ha + Hs - Hvp - Hf - Hi. If you want to raise the NPSHa, it will be necessary to increase the elements (Ha, Hs) that add energy to the fluid, or decrease the elements (Hvp, Hf, Hi) that rob e- rgy from the fluid. Also remember that the NPSHr reading, printed on a pumn c -ve, currently represents a point where the pump is already suffering a 2. ss in function due to cavitation. Some people in the industry are calling for a more precise definition of NPSHr, and higher safety margins on NPSHa. 

There is a wide range of conversion levels. The term maximum conversion type has no precise definition but is often used to describe a level of conversion, where there is no net fuel oil manufactured. A fuel products refinery with specialities may manufacture lubricating oils, asphalts, greases, solvents, waxes and chemical feed stocks in addition to the primary fuel products. The number and diversity of products will naturally vary from one refinery to another. Refineries produce chemical feed stocks for sale to the chemical affiliates and do not have responsibility for the manufacture of chemical products directly. Both operations may be carried out at the same physical location but the corporate product responsibilities are usually separate. 

To use the volume effectively, the reader should first review the Glossary of Terms section immediately preceding the first chemical entry. This section contains precise definitions used for certain parameters where data have been obtained for each chemical. A review of these terms will help the reader interpret certain information. In addition, a list of abbreviations used throughout the volume is also provided in the front section of the handbook. 

Usually, a precise definition of the input parameters in absolute terms is very difficult. Nevertheless, in many cases this does not cause crucial problems because relative results may be sufficient to compare different design options. The influence on the results of uncertainties in input should be evaluated whenever possible by using sensitivity analysis techniques. 

Note, since different types of machine have different sigma values, always take care in checking the precise definition of S. 

There has been considerable discussion about the extent of hydration of the proton and the hydroxide ion in aqueous solution. There is little doubt that this is variable (as for many other ions) and the hydration number derived depends both on the precise definition adopted for this quantity and on the experimental method used to determine it. H30" has definitely been detected by vibration spectroscopy, and by O nmr spectroscopy on a solution of HF/SbFs/Ha O in SO2 a quartet was observed at —15° which collapsed to a singlet on proton decoupling, 7( 0- H) 106 Hz. In crystalline hydrates there are a growing number of well-characterized hydrates of the series H3O+, H5O2+, H7O3+, H9O4+ and H13O6+, i.e. [H(0H2) ]+ n = 1-4, Thus... 

Wliile there is not a single, precise definition of market transformation in professional practice, the following definition captures the essential elements ... 

A more precise definition of corrosion is provided by ISO in ISO 8044 (see Reference 120). Attack of metal surfaces by the mechanical action of solid materials is properly described as erosion and is not discussed here. 

If, in the same way, we use (72) to define for the other processes the characteristic units J, L, and Y, similar remarks can be made with regard to J and J, with regard to L and L, and likewise with regard to Y and Y. By equation (72) a precise definition has been given to the characteristic unit of any process and we must hope that in the future the study of ionic solutions will eventually provide a complete interpretation of these quantities. At the present time we are very far from this goal. At any rate the total unitary quantity for each process must be isolated and evaluated before it can be interpreted. In the remaining chapters of this book we shall have occasion to mention only the quantities D, L, Y, J, and U, defined in accordance with (72) and (73). If, however, anyone should wish to give a precise definition to a quantity that includes less than the whole of the unitary term, the symbols in bold-faced type remain available for this purpose. 

The deviations of Class I, here called absorption and enhancement effects, are known in the literature also as matrix effects, as self-absorption, and as interelement effects. The authors consider the most important objection to each of the last three names to be as. follows. To matrix effect the element sought (ncrt included in the matrix) contributes to the absorption effect for the sample in the same kind of way as any element (free or combined) in the matrix. To self-absorption the name makes no provision for enhancement effects. To interelement effects it fails to recognize that an absorption effect occurs even when only one element is present (Equation 7-4). The term matrix is useful but requires precise definition. What is the matrix when an internal standard is added, or when a powdered sample is dissolved ... 

The term particle and particle size are so highly ambiguous as to require precise definition. As used in this article particles will.be limited by size to those distinct entities which have physically detectable boundaries in any direction within the limits of 0.05 and 10 microns (1 micron, p -0.001mm). This size range covers those particles which can be directly measured without magnification down to those which exhibit colloidal behavior... 

Chemists debated the concepts of acid and base for many years before precise definitions emerged. Among the first useful definitions was the one proposed by the Swedish chemist Svante Arrhenius in about 1884 ... 

Where e is the excess acid in mol/L and ionic concentrations are expressed as mol/L. While this more precise definition may apply in some strictly chemical responses such as soil erosion, Biydges and Summers 19) have considered the more complete reactions including biological ionic utilizations and have defined an "acidifying potential" of precipitation as ... 

The response time (relaxation time, adjustment time) of a reservoir is a time scale that characterizes the adjustment to equilibrium after a sudden change in the system. A precise definition is not easy to give except in special circumstances like in the following example. 

The aldehyde oxidoreductase from Desulfovibrio gigas shows 52% sequence identity with xanthine oxidase (199, 212) and is, so far, the single representative of the xanthine oxidase family. The 3D structure of MOP was analyzed at 1.8 A resolution in several states oxidized, reduced, desulfo and sulfo forms, and alcohol-bound (200), which has allowed more precise definition of the metal coordination site and contributed to the understanding of its role in catalysis. The overall structure, composed of a single polypeptide of 907 amino acid residues, is organized into four domains two N-terminus smaller domains, which bind the two types of [2Fe-2S] centers and two much larger domains, which harbor the molybdopterin cofactor, deeply buried in the molecule (Fig. 10). The pterin cofactor is present as a cytosine dinucleotide (MCD) and is 15 A away from the molecular surface,... 

The term stress, when used in biology, has general connotations rather than a precise definition (Osmond et al., 1987). It is therefore most useful to apply the term stress in its more general sense as an overpowering pressure of some adverse force or influence (Shorter Oxford English Dictionary, 3rd edn, 1983) that tends to inhibit normal systems from... 

We have described two highly Instrumented, data-logged and versatile pilot reactors which Integrate Into a rigorous scale-up regime. This Is necessitated by our highly complex products and the precise definition the computer-controlled full-scale plant can exploit. 

The precise definition of residence times for various stages of reactions by introducing reactants in a spatially confined manner in micro flow devices allows new ways... 

In Science, every concept, question, conclusion, experimental result, method, theory or relationship is always open to reexamination. Molecules do exist Nevertheless, there are serious questions about precise definition. Some of these questions lie at the foundations of modem physics, and some involve states of aggregation or extreme conditions such as intense radiation fields or the region of the continuum. There are some molecular properties that are definable only within limits, for example, the geometrical stmcture of non-rigid molecules, properties consistent with the uncertainty principle, or those limited by the negleet of quantum-field, relativistic or other effects. And there are properties which depend specifically on a state of aggregation, such as superconductivity, ferroelectric (and anti), ferromagnetic (and anti), superfluidity, excitons. polarons, etc. Thus, any molecular definition may need to be extended in a more complex situation. 

Baldyga and Bourne (1984) gave a more precise definition, according to which... 

The last rule needed to generate electron configurations for all the atoms in the periodic table came from a German scientist named Friedrich Hund. Hund s rule can be expressed in several ways. The most precise definition is that atoms in a higher total spin state are more stable than those in a lower spin state. Thus, the sixth electron in carbon-12 must have the same spin as the fifth one. The Pauli exclusion principle then requires that it fill an empty p orbital. 

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