Fundamental meaning

Although the first impulse for emission reduction is often to add a control device, this may not be the environmentally best or least cosdy approach. Process examination may reveal changes or alternatives that can eliminate or reduce pollutants, decrease the gas quantity to be treated, or render pollutants mote amenable to collection. Following are principles to consider for controlling pollutants without the addition of specific treatment devices, ie, the fundamental means of reducing or eliminating pollutant emissions to the atmosphere (30) ... 

Volume median mass median) D,m- This has no fundamental meaning but is easy to determine since it is at the midpoint of a cumulative-volume plot. 

Although we include adsorption here following the chapter on mass transfer, we should be clear that it is a very specific process in its fullest fundamental meaning. Adsorption is the process by which molecules in the fluid phase in contact with a solid move to the solid surface and interact with it. Once at the solid surface these molecules may be reversible or irreversible adsorbed, that is, they may come back off the surface to the fluid phase with their full molecular integrity intact, or they may be so strongly bound that the rate of removal is for all purposes close enough to zero to be considered zero. 

Electrostatic precipitation is one of the fundamental means of separating solid or liquid particles from gas streams. This technique has been utilized in numerous applications, including industrial gas-cleaning systems, air cleaning in general ventilation systems, and household room air cleaners. 

Many linear eorrelation equations have been deseribed between pairs of empirieal parameters, espeeially the solvatochromie parameters. - - Aside from their fundamental meaning that linearly eorrelated seales are responding similarly to... 

The traditional derivation of the Fokker-Planck equation (1.5) or (VIII. 1.1) is based on Kolmogorov s mathematical proof, which assumes infinitely many infinitely small jumps. In nature, however, all jumps are of some finite size. Consequently W is never a differential operator, but always of the type (V.1.1). Usually it also has a suitable expansion parameter and has the canonical form (X.2.3). If it then happens that (1.1) holds, the expansion leads to the nonlinear Fokker-Planck equation (1.5) as the lowest approximation. There is no justification for attributing a more fundamental meaning to Fokker-Planck and Langevin equations than in this approximate sense. 

The fundamental meaning of temperature may be described in terms of the zeroth law of thermodynamics. This states that when two bodies are each in thermal equilibrium with a third body they are then in thermal equilibrium with each other, i.e. 

Of course, Eq. (3) is valid for any particle. The question is Why is the speed of the photon there One may conjecture with DiMarzio [26] that there is a more fundamental meaning for c. In this context, Munera [27] explored the possibility of deriving the main predictions of STR from Newton s theory plus a postulate of mass-energy equivalence E = mK2. The value of the unknown constant K was obtained from the acceleration of electrons [28]. The numerical value is c within the limits of accuracy of the (large) experimental error. 

The enthalpy H is defined as H-U + PV and is a property of state derived from the fundamental property 11. If heat is stored reversibly and isobari-cally in a system, it is stored as an increase in the system s ff-value. H has been defined for our convenience it has no fundamental meaning other than that, under certain conditions, its change is related to the heat absorbed by the system. It can be shown that the specific heat at constant volume and pressure, cv and cp, respectively, can be expressed as... 

The optimization of rate coefficients of such complex models from experimental results poses the following fundamental questions. How many parameters can be estimated Which parameters can be estimated and how will this optimization be carried out Will the estimated parameters have a fundamental meaning ... 

After a reaction model has been constructed, numerical values must be assigned to the model parameters. In the case of non-fundamental models, including empirical, pseudo-kinetic and molecular reaction models they can only be estimated by fitting the model to experimental data since the parameters have no fundamental meaning. In the case... 

The band picture of metals developed by physicists accounts very well for conduction and other electric and magnetic properties. The valence bond description of the bonds in metals related to the concepts of chemistry explains much better than the former theory such properties as lattice energies and bond distances. Today, however, the V.B. picture does not lend itself well to a priori quantitative calculations of these properties and it seems doubtful to what extent a bond in solid lithium with a bond order of o. 11 (with respect to the bond order one in a gas molecule) has any fundamental meaning. There is no doubt, however, that in less typical metals and compounds Pauling s theory is valuable as a counterpart to the band picture, just as the V.B. and the M.O. methods are both of great importance for the description of the constitution of organic molecules. 

Determination of the number of active centers is one of the fundamental means to investigate the kinetics and mechanism of catalytic reactions. Its importance is enhanced in the case of Ziegler-Natta (Z-N) catalysis because the diversity of reactions involved makes understanding of the processes very difficult. 

The Diels-Alder reaction is one of the most fundamental means of preparing cyclic compounds. Since discovery of the accelerating effect of Lewis acids on the Diels-Alder reaction of a,)3-unsaturated carbonyl compounds [341-344], its broad and fine application under mild reaction conditions has been amplified. Equations (140) [341] and (141) [345], respectively, illustrate typical dramatic effects from an early reaction and from one reported more recently. Lewis acid-promoted Diels-Alder reactions have been reviewed [7,8,346-353]. In addition to the acceleration of the reaction, other important feature is its alteration of chemo-, regio-, and diastereoselectivity this will be discussed below. The titanium compounds used in Diels-Alder reaction are titanium halides (TiX4), alkoxides (Ti(OR)4), or their mixed salts (TiX (OR)4 n = 1-3). A cyclopentadienyl complex such as Cp2Ti(OTf)2 is also documented as a very effective promoter of a Diels-Alder reaction [354], In addition to these titanium salts, a few compounds such as those in Eq. (142) [355] have recently been reported to effect the Diels-Alder reaction. The third, [(/-PrO)2Ti(bpy)(OTf)(i-PrOH)] (OTf), was estimated to be a more active catalyst than Cp2Ti(OTf)2. 

At the time of this writing, however, it still remains unclear whether schemas will overtake DTDs as the fundamental means of modeling XML documents. 

Pytkowicz and his co-workers (4,5,6) have avoided these diflBculties in a manner that has proved highly suitable in evaluating dissociation equilibria in seawater. Apparent equilibrium constants are defined in terms of the operational pH value, which may be regarded as an apparent conventional hydrogen activity. Although the fundamental meaning of these two quantities is unclear in seawater, their combination yields correctly the desired ratio of acid to conjugate base, the correct solubility, etc. (7). 

AAarket research in the field of chemicals consists of obtaining facts and figures, then correlating them to arrive at answers necessary to the conduct of business. Methods of obtaining the basic data as well as the identification of sources are fundamental means to the end. Execution embraces whatever is necessary in order to answer all or some of the following questions who, what, when, where, why, how, and how much The remainder is common sense. 

The measurement of temperature is one of the fundamental means of assessing the properties of a system, going back to the simple method of putting one s hand on or in a system such as a pool of water. It is useful to consider this apparently trivial example in more detail as many of the principles of thermal analysis may be understood in this way. In reality, what is being performed is a comparison of the hotness of the water to that of the body (or more specifically that of the skin). This leads to two of the underpinning concepts of thermal analysis. The first is that we make measurements of thermal... 

Directional spectral quantities. These describe the directional and wavelength distribution of the radiative energy in a detailed manner. They are of fundamental meaning, but are very difficult to determine experimentally or theoretically. This is why we frequently employ radiation quantities that only include one effect, either the dependence on the wavelength or the direction. 

Conformational transitions and the corresponding stimuli response of macromolecules provide fundamental means for the molecular assembly and function of biological systems.1 7 Establishing a likewise control factor in the field of synthetic macromolecules is recognized as a major challenge in nanotechnology. 

Closing the k-e model by turbulence modeling we relate the unknown Reynolds stress tensor and the turbulent transport terms to the fundamental mean flow variables, or the scaled variables in turbulent boundary layers, introducing additional approximations. 

Two additional conmiciits apply at tliis point. First, there is a conceptual difference between the probabilistic element in quantum and classic statistical physics. For instance, in quantum mechanics, the outcome of a measurement of properties even of a single particle can be known in principle only w ith a certain probability. In classic mechanics, on the other hand, a probabilistic element is usually introduced for many-particle systems where we would in principle bo able to specify the state of the system with absolute certainty however, in practice, this is not possible because we are dealing wdth too many degrees of freedom. Recourse to a probabilistic description within the framework of classic mechanics must therefore be regarded a matter of mere convenience. The reader should appreciate this less fundamental meaning of probabilistic concepts in classic as opposed to quantiun mechanics. 

Biphasic catalysis, not anchoring on solid supports, was recognized as providing the fundamental means for combining all the advantages of homogeneous... 

We emphasize here that in this theorem the number four has a fundamental meaning. Many of molecular properties are of the modulo four as will be shown later. 

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