Symbolic capability

The above steps show one way to use Mathematica to obtain various properties of reactants (sum of species), but it is much more efficient to use the symbolic capabilities of Mathematica to derive the function of pH and ionic strength that yields the desired property. The following program (14) derives the function for the standard transformed Gibbs energy of formation of a reactant as a function of pH and ionic strength at 298.15 K. 

This book presents Maple solutions to a wide range of problems relevant to chemical engineers and others. Many of these solutions use Maple s symbolic capability to help bridge the gap between analytical and numerical solutions. The readers are strongly encouraged to refer to the references included in the book for a better understanding of the physics involved, and for the mathematical analysis. 

In the previous sections, we discussed how to use MATLAB to solve eng eering problems with numerical values. In this section, we briefly explain the symbolic capabilities of MATLAB. In symbolic mathematics, as the name implies, the problem and the solution are presented using symbols, such as x instead of numerical values. We will demonstrate MATLAB s symbolic capabilities using Examples 15.7 and 15.8. 

Mathematica has packages available for calling MATLAB from within Mathematica and vice versa. MATLAB also has toolboxes that incorporate some of the symbolic capabilities of MAPLE, as pointed out in the hterature [10]. 

The measured stiffnesses for two- and three-layered special cross-ply laminates are shown with symbols in Figure 4-28, and the theoretical results are shown with solid lines. In all cases, the load was kept so low that no strain exceeded SOOp. Thus, the behavior was linear and elastic. The agreement between theory and experiment is quite good. Both the qualitative and the quantitative aspects of the theory are verified. Thus, the capability to predict cross-ply laminate stiffnesses exists and is quite accurate. 

Guthrie and Guthrie and Jencks have proposed an alternative mechanistic symbolism that is capable of more detailed description than the Ingold system, although at the expense of greater complexity. This system may be useful for the computer representation of reaction mechanisms. 

Different test results are available to the designer wanting friction and wear data as well as the usual mechanical short and long term data, corrosion resistance, readings, and so on. The data presented include the load and velocity capabilities of a bearing material as expressed by the product of the unit load P based on the projected bearing area and linear shaft velocity V. The symbol PV denotes the important property of the pressure-velocity relationship. 

The beginning of the industrial age saw a substantial increase in demand for basic materials and chemicals, and the chemical industry was established to satisfy these demands for high production volumes. The tall and impressive silhouettes of modern chemical plants dominate industrial estates, visible from afar as symbols for the vast capabilities and capacities of today s chemical industry. Without this industry and its equipment of enormous proportions, our economic wealth would be quite inconceivable. 

Dielectric constant (DE) values are reported as permittivity with the symbol e or K The polymer cylindrical donuts were used for the measurement of DE on a Hewlett-Packard 8510 automated network analyzer. The analyzer is capable of measuring 401 data points over a frequency band of 500 MHz to 18.5GHz. Typically Sll and S21 values, which correspond to reflection and transmission, respectively, are measured and then these values are used to calculate the permittivity and permeability. 

The processors in a physical model can be modeled as objects, their states modeled as attributes, their capabilities modeled as attributes, and communication links shown as explicit objects. It is useful to make visual distinctions between categories using stereotypes or a distinguished notation such as the one UML provides or, you can use traditional network diagram symbols for the different hardware objects. Base operating systems can be shown as part of this hardware architecture (see Figure 12.1). 

The user can generate FORTRAN expressions that allow numeric computers to run faster and more efficiently. This saves CPU cycles and makes computing more economical. The user can generate FORTRAN expressions from MACSYMA expressions. The FORTRAN capability is an extremely important feature combining symbolic and numeric capabilities. The trend is clear, and in a few years we will have powerful, inexpensive desktop or notebook computers that merge the symbolic, numeric and graphic capabilities in a scientific workstation. 

The user can explore extremely complex problems that cannot be solved in any other manner. This capability is often thought of as the major use of Computer Algebra systems. However, one should not lose sight of the fact that MACSYMA is often used as an advanced calculator to perform everyday symbolic and numeric problems. It also complements conventional tools such as reference tables or numeric processors. 

If we succeed with these objectives, the final goal is to apply the same methods with minor modification to generate all reasonable conformers of a compound, i.e., to develop a symbolic conformational search capability. 

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