Change with the Progression

Linear programming mathematical models were often introduced to find early, optimized solutions, typically considering only the shipment of finished goods to specific customer locations. Operations 

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Once thermal reactions begin, the coal undergoes structural changes through spontaneous bimolecular reactions between coal constituents or solvent species (75) or through catalytic reactions accelerated by added catalysts or the inherent mineral components (76). Hence, the reactivity changes with the progress of these reactions. 

This mathematical model describing the inhomogeneous pyrolysis reactions by a set of apparent kinetic data (which are changing with the progress of the pyrolysis) should be understood as a first attempt to set up a mechanism to predict pyrolysis. The target of the application of this model would be to evaluate the influence of temperature programs on baking behavior. 

Moreover, the e.e. of the sulfoxide products changes with the progress of the reaction indicating that the PAMO was able to catalyze the kinetic resolution of the sulfoxide to the sulfone. The enantiomeric ratio measured with methyl phenethyl sulfoxide was 110. Previous studies carried out with CHMO revealed... 

Because of the release of acetic acid during the polycondensation reaction, the content of carbon, hydrogen, and oxygen elements in the system continuously changes with the progress of polymerization. Mathematically, one can easily develop the following relationship to express carbon element content, Cg, vs. the extent of reaction, P, as... 

Sketch a diagram that shows how the energy changes with the progress of an endothermic reaction. Label the curve "Reactants," "Products, and "Activated complex. On the same diagram, sketch a second curve to show the change caused by a catalyst. 

In the same example, the total amount of the compound was 1.4 kg. On the assumption that the average density of elastomers and other additives is 0.98 g/cm and that of carbon black is 1.88 g/cm [29], the density of the compound is calculated to be 1.17 g/cm. The total volume (V ) was then 1,200 cm. Even under 0.24 MPa of ram pressure, the actual volume of the compound changes with the progress of mixing. However, the compacted volume may be taken as a reference equal to 1,200 cm. The powdered rubber compound is macroscopically uniform in composition. Therefore, the composition of the material in and the rest of the volume are the same. Because the material in is compacted, it may be compared to the total compacted volume of the compound, i.e., = 0.146V-J.. If all the rubber particles... 

Because in this mixer, the two rotors take different positions with respect to each other for each turn [18] and come back to repeat the same relative position only every eleventh turn, the pressure profile is different for each turn. The pressure profile also depends upon the material properties and is, therefore, expected to change with the progress of mixing. 

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