Symbolic computational programs

Symbolic Computer Programs Applied to Group Theory... 

RENKES Symbolic Computer Programs Applied to Group Theory Table II. Terminal Display of Classes... 

For the formation of the differentials and the solution of the sets of equations, symbolic computational programs can be used in favor, such as DERIVE(r) or Mathematica . 

First, we assume that the oxidation number of a certain element is alike in all compounds. We replace the element symbol S by the generating function S = exp(5x) and the index by the exponent. The lower case letter s means the oxidation number. For example, H2O exp(2/ix) exp(ox) = exp((2/i + o)x). By differentiating with respect to x at x = 0, we obtain 2h + o. This formalism simplifies the application in symbolic computational programs. 

Computers are well suited to the manipulation of numbers, but the ES relies on symbolic computation, in which symbols stand for properties, concepts, and relationships. The degree to which an ES can manage a task may depend on the complexity of the problem. For example, computer vision is an area of great interest within AI and many programs exist that can, without human assistance, use the output from a digital camera to extract information, such as the characters on a car number plate. However, automatic analysis of more complex images, such as a sample of soil viewed through a microscope, is far... 

Definition 7 An expert system is a computer program that manipulates large amounts of symbolic knowledge using qualitative techniques, to solve problems that can otherwise be solved only by expert human problem solvers. Expert systems capture the human problem solvers expertise in the form of domain-specific knowledge and domain-independent problem-solving strategies. 

Definition 2 Knowledge-based systems are computer programs that encode symbolic knowledge about domains and tasks, and solve problems by manipulating this knowledge using qualitative techniques. 

Jiri Cizek s research program centers on the quantum theory of molecular electronic structure and related developments in quantum chemical methodology, coupled-cluster approaches to many-electron correlation problems,105 large-order perturbation theory,106 dynamical groups and exactly solvable models, lower bounds, and the use of symbolic computation language in physics and in chemistry. 

There are approximately 40 three loop diagrams to be computed for this reason the choice of the appropriate strategy is of significant importance. Any approach has to rely heavily on the use of symbolic manipulation computer programs. Our principal tool in this calculation is the so called integration-by-parts technique [9], which is common in perturbative calculations in high energy physics. 

A number of standard computer programs easily handle problems of this type such as spreadsheet packages, Matlab, Mathcad, Polymath, and so on as well as symbolic manipulators such as Mathematica, Maple, Derive, etc. Most statistic packages and equation solvers will also solve linear equations and have a simple user interface. 

Descriptions of symbolic mathematics programs and some of their applications can be found, for example, in W. H. Cropper, Mathematica Computer Programs for Physical Chemistry, Springer-Verlag, New York (1998) and in J. F. Ogilvie, Mathematics for Chemistry with Symbolic Computation, an electronic text containing Maple worksheets, available at http //www.maplesoft.com. 

The computer program (TGPL78) is written to extract the copper, tin, and lead values for individual objects from a data file, to normalize the values, and to plot them on a modified teletype terminal. Details of the program can be seen in the Appendixes I-V. Various plotting parameters, such as the computation and plotting of centroids, partitioning of symbols, normalization procedure, and labeling of individual points can be adjusted by the operator. 

In Mathematica reactants need to named with words starting with lower case letters because words starting with capital letters refer to operations. Also the names of reactants need to be as short as convenient and cannot involve spaces, subscripts, superscripts, hyphens, dots or other symbols that are Mathematica operations. Therefore, ATP is referred to as atp both in the text and in computer programs. Most of these abbreviated names will be recognized immediately, but a glossary of names is provided in the Appendix. 

Symbols used in the computer program are in parentheses. Minimum fluidizing rate by Leva s formula ... 

Figure 10. Distribution of zinc content (left panel) and arsenic content (right panel) in coals from the Illinois basin. Data sources are given in the text. The size of the symbol is proportional to the abundance of the element. The breakpoints for the element distributions were chosen using the default natural breaks algorithm in the computer program Arcview . Faults are shown as light lines. Note the concentration of zinc and arsenic associated with the intense faulting in the southern Illinois Basin, and the localization of zinc and arsenic in the northwestern portion of the basin.

Figure 15. Arsenic concentrations in coals of the Black Warrior basin, Alabama. Shaded areas show the extent of coalfields of Alabama. The proportionally sized symbols. show the content of arsenic in coal samples analyzed by the USGS. Some symbols that plot inside each other are from the same core or coal face. The break points for the symbol groups were calculated using the natural breaks algorithm in the computer program Arcview . Dashed lines are contours of vitrinite reflectance data from coals. We are presently evaluating whether the tack of correspondence of high arsenic content with high vitrinite reflectance values is an artifact due to low sample density or reflects an actual trend in the data.

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