Integration of parts

An example of integration of part of the downstream processing in the actual bioreactor is two-liquid-phase biocatalysis (see above), in which the organic-solvent phase is used as extractant for the product. The liquid-impelled loop reactor (Fig. 7.3) is specifically designed for this purpose. It is based on the well-known air-lift principle, but instead of air, a water-immiscible, heavier or lighter organic solvent is injected. 

Conflicting evidence has been obtained as a result of experiments with CO2. One set of data indicates formation of the pyrrolidine ring via at least one symmetrical intermediate whereas the other is consistent with a route involving only unsymmetrical intermediates. " Some doubt about the integrity of part of the degradation procedure used for determining the activity at C-5 has been resolved without affecting the tracer results. ... 

High reaction rates could thus be maintained, and more concentrated feeds were allowed for fermentation [58,59]. The integration of part of the downstream processing in the bioreactor, allowing for ISPR-decreased product recovery costs [58], thus increased the competitiveness of the biochemical process. 

The automotive industry uses CT scanners to evaluate the integrity of parts, such as rims and tires, without destroying them. 

Weld or knit lines are perhaps the most common and difficult injection molding defect to eliminate. They occur when melt flow fronts collide in a mold cavity. Material characteristics can affect the knitting of the melt fracture. A poor knit line can cause only cosmetic blemishes or it can significantly weaken the structural integrity of part strength. 

By contrast. Fig. 13.46 shows an endothermic reactor integrated below the pinch. The reactor imports Qreact from part of the process that needs to reject heat. Thus integration of the reactor serves to reduce the cold utility consumption by Qreact- There is an overall reduction in hot utility because, without integration, the process and reactor would require (Qumin + Qreact) from the utility. 

Assessing the effectiveness and reliability of Acoustic Emission (AE) in continuous, on-line monitoring of the structural integrity of critical thermal power plant components, such as steam headers and steamline sections, is the main objective of the work reported in this paper. This is part of the work carried within the BRITE - EURAM 6056 "SIMON" Project from 10.1993 to 9.1997 with the support of the EU Commission. The "SIMON" Project Consortium included CISE [I, coordinator], MITSUI BABCOCK ENERGY [UK] HERIOT WATT University [UK], PROET / EDP[P]andENEL[I],... 

Integration by parts (Green s theorem) of the second order term in Equation (2.90) gives the weak form of the problem as... 

In practice, in order to maintain the symmetry of elemental coefficient matrices, some of the first order derivatives in the discretized equations may also be integrated by parts. 

The area under a parabolic arc concave upward is bh, where b is the base of the figure and h is its height. The area of a parabolic arc concave downward is jh/t. The areas of parts of the figure diagrammed for Simpson s rule integration are shown in Fig. 1-3. The area A under the parabolic arc in Fig. 1-3 is given by the sum of four terms ... 

Let us assume that kij = 0 on L. This enables us to integrate by parts in the second and the third terms of (2.231) and to obtain the inequality... 

In fact, we can integrate by parts on the right-hand side of (4.127), which gives... 

The formula (4.127) can be written in the form which does not contain the function 9. To show this we choose a ball B, (r) of radius r with the boundary T(r) such that 9 = 1 on Bx, r). In this case the integration by parts in (4.127) yields... 

We have obtained the Griffith formula (4.159). It is not difficult to show that the right-hand side of (4.159) does not depend on 9. To prove this, consider the difference between right-hand sides of (4.159) corresponding to any two functions 9i, 02- Let 9 = 9i — 92- We integrate by parts, which implies that the difference A between the right-hand sides of (4.159) evaluated for is equal to... 

We do not show the dependence of v,a,, f on t in (5.87). The integration by parts in the third term of the left-hand side of (5.87) can be done. Recall that satisfies the equation (5.68). As a result the following inequality is obtained ... 

Integrate by parts in the fifth and sixth terms of the left-hand side of (5.152) taking into account the boundary conditions (5.149)-(5.151) and the Green formula like (5.138) for the domain fic- The penalty term is nonnegative and satisfy the equation (5.144). Hence the uniform in the s,5 estimate follows. 

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