Symbolic computing

Stephanopoulos, G., Artificial Intelligence and Symbolic Computing in Process Engineering Design. In Foundations of Computer-Aided Process Design (J. J. Siirola, I. E. Grossmann, and G. Stephanopoulos, eds.), p. 21, Elsevier, New York, 1989. 

George Stephanopoulos, Symbolic Computing and Artificial Intelligence in Chemical Engineering A New Challenge... 

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... 

Symbolic Computer Programs Applied to Group Theory... 

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

The latter variable eliminates a finite range [42] of convergence of series both of X at 2 i e, because of a pole due to intemuclear coulombic repulsion as / 0, and of y at V2 Re, for a similar phenomenon as oo. Expressions for Fy in terms of coefficients cj in the latter series are available in a large consistent collection in Fortran coding [43] up to Cio such expressions, readily calculated, through symbolic computation with efficient procedures [44], first in terms of coefficients and thence converted to bj or Cj as required, are further converted to Fortran or C code for numerical applications. 

EXPONENTIAL BREAKDOWN SYMBOLIC COMPUTING Symmetry-conserving allosteric model, MONOD-WYMAN-CHANGEUX MODEL SYMPORT Symproportionation,... 

Thus, to completely solve the problem of symmetry reduction within the framework of the formulated algorithm above, we need to be able to perform steps 3-5 listed above. However, solving these problems for a system of partial differential equations requires enormous amount of computations moreover, these computations cannot be fully automatized with the aid of symbolic computation routines. On the other hand, it is possible to simplify drastically the computations, if one notes that for the majority of physically important realizations of the Euclid, Galileo, and Poincare groups and their extensions, the corresponding invariant solutions admit linear representation. It was this very idea that enabled us to construct broad classes of invariant solutions of a number of nonlinear spinor equations [31-33]. 

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. 

J. Cizek, F. Vinette, and E. J. Weniger, Int. ]. Quantum Chem., Quantum Chem. Symp., S25, 209 (1991). Examples on the Use of Symbolic Computation in Physics and Chemistry Applications of the Inner Projection Technique and of a New Summation Method for Divergent Series. 

George Stephanopoulos, Symbolic Computing and Artificial Intelligence in Chemical Engineering A New Challenge The Identity of Our Profession Morton M. Denn, The Identity of Our Profession... 

Adler, P.M., Thovert, J.-F. and Bekri, S. (2000) Local Geometry and Macroscopic Properties. Inteifacial Electrokinetics and Electrophoresis, 35-51, Springer-Verlag, Symbolic Computation, Tokyo... 

By applying symbolic computation of Mathematica software, a mathematical mechanization of ADM based on the principle of parameterization, was carried out to reduce the solution for approximate expressions of model equations (A.l) and (A.2). The code of parameterized ADM is listed below. 

The process of calculating the Adomian polynomials can be well mechanized by applying symbolic computation of Mathematica, based on the parameterization principle of Eq. (B.6). Then, we apply Eq. (B.7) to generate partial components of the... 

Sedoglavic, A., A probabilistic algorithm to test algebraic observability in polynomial time, J. Symbolic Computation 2002, 33 735-755. 

SYMBOL-Computer Aided Design Centre, Madingly Road, Cambridge CB10HB, England. 

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