Problems, sharing

The two problems considered in the derivation of the methodology are formally given below. In essence the problems share many of the same characteristics, but the objectives are slightly different. 

The second problem shares some characteristics of the first problem and is stated as follows. 

The mathematical formulation that addresses the above two problems share the same constraints, the only difference is in the solution procedure and the objective functions. 

Although both the microporous (crystallite) and the macroporous (pellet) problem share instructive sim-... 

Both problems share the common property that P(p) is of measure zero for p < Pc, with the critical threshold value pc as a function of the type of lattice considered. Few exact formulas exist for P(p) or even pc. There are, however, a number of empirical rules. For instance, for the bond percolation problem,... 

Do you have a new solution to an operations, maintenance or design problem Share it with other engineers by sending it in to Plant Notebook. 

Fig. 28.1. In a genetic switch, the total state of the system depends on two variables whether the DNA site is occupied or not and the number of copies of the transcription factor. In the left panel, the logarithm of the steady state probability for the occupancy state and protein number is plotted. This probability acts like an effective potential. In the right panel, the effective potential for a charge transfer or two site polaron is plotted as a function of the enviromnent polarization for the two electronic states. The governing time-dependent eqnations for the two problems share many similarities...

Several related problems have been previously considered in the literature. In addition to the afore mentioned statistical approaches for structural change detection in data sets and their application for linear system identification [7], the joint problem of model structure determination and parameter estimation was addressed by [8-10]. A related approach was used by [11-13] in the context of data reconciliation. Additional aspects of model selection in chemical engineering are covered in [14]. Although the present problem shares common features with the all of the previous applications, it also presents unique characteristics that require a specific formulation. 

An important problem shared by all the current approaches is the difficulty in determining a unique, well-defined binding model that includes conformationally flexible ligands this is usually a very underdetermined problem. 

A PROBLEM SHARED, DISTRIBUTED DATA AS YET UNSHARED, AND KNOWLEDGE FROM IT... 

The first question one must ask is Why would anyone want to share a knowledge base A knowledge base is a collection of information which offers the potential to solve specific problems. Sharing this knowledge base would solve that problem for other... 

It has also become more difficult to generate sales for a given dollar of plant expenditure, as seen from Figure 4. This is a problem shared with other industries. From 1963 to 1966 sales per dollar of new plant expenditures declined from 19 to 13. It is too early to tell whether the upswing in 1967 is temporary. 

Some other kinds of models have shown parameters that seem to follow useful correlation relationships. Among these are the virial coefficient model of Bums (2), the interaction coefficient model of Helgeson, Kirkham, and Flowers (4), and the hydration theory model of Stokes and Robinson (1). The problem shared by all three of these models is that they employ individual ion size parameters in the Debye-Hiickel submodel. This led to restricted applicability to solutions of pure aqueous electrolytes, or thermodynamic inconsistencies in applications to electrolyte mixtures. Wolery and Jackson (in prep.) discuss empirical modification of the Debye-Huckel model to allow ion-size mixing without introducing thermodynamic inconsistencies. It appears worthwhile to examine what might be gained by modifying these other models. This paper looks at the hydration tlieory approach. 

A problem shared by the crossed-wire anode detector with resistor chain, the resistive-anode detector and the wedge-and-strip detector is that ratios of the pulse amplitudes have to be calculated. However, it is difficult to calculate ratios with high speed, no matter whether analog or digital calculation is being used (see Sect. 3.5, page 39). 

All algorithms based on Newton s method and predisposed to solve large-scale problems share the following common features ... 

The locally stable equilibrium states of the surface Coulomb problem share many of the characteristics of planar magnetic dipole configura-... 

A common problem shared by many industrial processes is the inability to measure key process variables noninva-sively and in real time, especially the compositions of process streams and product properties. The development of improved sensors, based on new techniques of analytical chemistry and modern electronic devices using fiber optics and semiconductors, has been an active area (cf. Appendix A). As an alternative, the use of easily measured secondary variables to infer values of unmeasured process variables is now receiving great interest the term soft sensors is often used to denote this approach. Chemometrics is a term related to soft sensors that describes how data from process analyzers (e.g., spectra) can be analyzed and modeled for use in process monitoring and control (Brown, 1998). 

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