Functional definitions

Functional Definitions Heat-transfer equipment can be designated by type (e.g., fixed tube sheet, outside packed head, etc.) or by... 

The yield of a gas-solid heterogeneous reaction depends not on the total time that molecules spend in the reactor but on the time that they spend on the catalyst surface. The contact time distribution provides a standardized measure of times spent in the absorbed state. A functional definition is provided by the following equation applicable to a first-order, heterogeneous reaction in an isothermal reactor ... 

According to this extension of the cost function definition, the following two conditions are always satisfied ... 

Contrasting this with the Dirac 5-function definition, viz.,... 

This is a central quantity in chemistry [14], which was introduced by Pauling as the power of an atom in a molecule to attract electrons to itself and was quantified originally by thermochemical data [15]. The density functional definition of this quantity can be viewed as a generalization of the Mulliken definition [16] and is in accordance with earlier work of Iczkowski and Margrave [17]. 

The chemical composition of petroleum also varies over a wide range. A broad functional definition of petroleum hydrocarbons is that hydrocarbons are composed primarily of many organic compounds of natural origin and low water solubility. 

We do not distinguish here this density functional definition of exchange energy from that of Hartree-Fock (HF). This simplification is well-justified, if the HF electron density and the exact electron density differ only slightly [40]. Similarly, the coupling-constant averaged exchange-correlation hole is the usual... 

The blind, functional definition of reward runs into the same problem in psychology that the simple marketplace model has encountered in economics people often fail to maximize any shopping list of goods, but rather behave in ways that look internally contradictory. At least seven such problems can be defined ... 

Problem 1. Many rewards seem to function simultaneously or in close succession as both rewards and punishments. For instance, a person may in the same day or at the same instant both pay for cigarettes and pay for a smoking cure. Such conflictual rewards utterly defeat the Premack strategy of functional definition. 

One important use of the stream function is for the visualization of flow fields that have been determined from the solution of Navier-Stokes equations, usually by numerical methods. Plotting stream function contours (i.e., streamlines) provides an easily interpreted visual picture of the flow field. Once the velocity and density fields are known, the stream function field can be determined by solving a stream-function-vorticity equation, which is an elliptic partial differential equation. The formulation of this equation is discussed subsequently in Section 3.13.1. Solution of this equation requires boundary values for l around the entire domain. These can be evaluated by integration of the stream-function definitions, Eqs. 3.14, around the boundaries using known velocities on the boundaries. For example, for a boundary of constant z with a specified inlet velocity u(r),... 

In two-dimensional, incompressible, steady flows, there is a relatively simple relationship between the vorticity and the stream function. Consider the axisymmetric flow as might occur in a channel, Fig. 3.12. Beginning with the axisymmetric stream function as discussed in Section 3.1.2, substitute the stream-function definition into the definition of the circumferential vorticity u>q ... 

Notice several important aspects about the transformed equations. Of course, xjr is now an independent variable, with the relationship between r and x/r coming from the stream-function definition... 

A functional definition of / V I insoluble is that some of the compound remains in the solid state when about 10-3 mol of the compound is placed in contact with one liter of water. It does not mean that none of the compound dissolves. 

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