This is a short survey of known results about elimination of quantifiers over natural numbers, and some implications of these results on the power of computer algebra systems.

Stability is one of the important properties of time-stepping numerical schemes that are used to approximate partial differential equations. Stability can be analyzed using Von Neumann stability analysis which is a Fourier method. The analysis results in the Von Neumann stability condition which...

The aim of this paper is to present how the dynamic evaluation method can be used to deal with the real closure of an ordered field. Two kinds of questions, or tests, may be asked in an ordered field: equality tests (a = b?) and sign tests (a b?). Equality tests are handled through splittings,...

Engineering design is a process of generating a design solution satisfying customers’ various requirements. As the design proceeds, more and more parameters are introduced to define the design solution. As more design parameters come into design consideration, designers face increasing...