Following a pretest, 8 participants who were unfamiliar with algebraic and trigonometric functions received a brief presentation on the rectangular coordinate system. Next, they participated in a computer-interactive matching-to-sample procedure that trained formula-to-formula and formula-to-graph relations. Then, they were exposed to 40 novel formula-to-graph tests and 10 novel graph-to-formul...

AbstractGeometric transformations are fundamental aspects of all computer graphics rendering and are found throughout the computer graphics pipeline. In earlier work we presented mathematical treatment of this topic. The different concepts were combined into a general mathematical procedure based on the concept of vector spaces in linear algebra. While we established the mathematical aspects of...

The concept of model transformations is of increasing importance in different areas of Computer Science, but up to now, there is a lack of common understanding concerning the mathematical and practical point of view. In this paper, we discuss some of the different aspects. Especially interesting is the new proposal of the POPL’07 keynote speaker Don Batory claiming that model transformations sh...

Conformal transformations of a Euclidean (complex) plane have some kind of completeness (sufficiency) for the solution of many mathematical and physical-mathematical problems formulated on this plane. There is no such completeness in the case of Euclidean, pseudo-Euclidean and polynumber spaces of dimension greater than two. In the present paper we show that using the concepts of analogical geo...

Transformations of object-oriented models based on a rigorous underlying semantics represent a means of obtaining the beneets of formal methods without the need for users to reason directly in mathematical formalisms. In this paper we present a set of diagrammatic transformations on UML models which represent reenement or abstraction steps. We show how the correctness of these transformations c...

he development of algorithms needed for the analytic solution of state space design equations using a computer algebra system (MapleV) is presented in this article. These calculations involve mati ix manipulations, eigenvalue-eigenvector determinations, Laplace and Inverse Laplace transformations, Z and Inverse Z transformations, which are complex, tedious, and error prone, even for simple exam...

We study the “Lie Algebra” of the group of Gauge Transformations of Space-time. We obtain topological invariants arising from this Lie Algebra. Our methods give us fresh mathematical points of view on Lorentz Transformations, orientation conventions, the Doppler shift, Pauli matrices, Electro-Magnetic Duality Rotation, Poynting vectors, and the Energy Momentum Tensor T .

Einstein had to learn the mathematics of Lorentz transformations in order to complete his covariant formulation of Maxwell’s equations. The mathematics of Lorentz transformations, called the Lorentz group, continues playing its important role in optical sciences. It is the basic mathematical language for coherent and squeezed states. It is noted that the six-parameter Lorentz group can be repre...