Browsing by Subject "Complex"
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Item A college approach to fractals in middle school(2005-08) Duke, Billy J.; Dwyer, Jerry F.; Wilhelm, Jennifer A.The algebra and geometry of complex numbers were presented to eighth and ninth grade mathematics classes. The purpose of the presentations was to determine if this college level mathematics would have an influence on the algebra and geometry skills of the K-12 students. Pre and post surveys were employed. Results showed an increase in both student mathematics skills and student interest in the ninth grade class. In the eighth grade class there was not a significant improvement. It may be conjectured that ninth grade students benefit from this kind of intervention, but that the average eighth grade student does not have the mathematical skills required to handle the college level material.Item An introductory study of the complex variable(Texas Tech University, 1937-08) West, Veda IonaNot availableItem Item Maximizing the generalized Fekete-Szego functional over a class of hyperbolically convex functions(2006-08) Martin, David R.; Barnard, Roger W.; Williams, G. Brock; Monico, Christopher J.; Pearce, Kent; Solynin, Alexander Y.In this paper, we are attempting to find an extremal for the "generalized" Fekete-Szego functional over the class of hyperbolically convex functions. In trying to find the extremal, the Julia variational formula will be used to reduce the problem to mappings having no more than two proper sides. We will then find a range of t-values for which the one-sided mapping is extremal over all those mappings having non-zero second coefficient.Item Space-variant incoherent optical processing using color(Texas Tech University, 1981-05) Tavenner, David StanleyIncoherent optical processing techniques offer superior noise immunity, among other benefits, over coherent optical processing techniques. However, the complex amplitude linearity exhibited by coherent optical systems that provides a natural means for performing operations on complex functions, is lacking with incoherent optical systems. Bipolar values, as well as complex values, must be synthesized in incoherent optical systems. Bipolar values can be represented with unipolar quantities by adding biases to the bipolar values, exponentiating them, taking their logarithms, or separating the positive and negative parts into two components. Complex values can be represented with the polar, rectangular, and ternary basis forms of complex numbers. These representations are applied to add and multiply, and to evaluate the 1-D and 2-D superposition integrals with complex functions in additive, subtractive, and hybrid additive- subtractive incoherent optical processing systems. Data obtained from laboratory models of those systems demonstrate the additive and multiplicative properties of the systems. Electronic post-processing schemes are suggested to decode the unipolar outputs. Electronic post-processing schemes decode the unipolar outputs.Item Visualizing complex solutions of polynomials(2012-08) Perez, Alicia Monique; Odell, E. (Edward); Daniels, MarkThis report discusses two methods of visualizing complex solutions of polynomials: modulus surfaces and vector fields. Both provide valuable information about the location of complex solutions and their multiplicity. A sketch of a proof of The Fundamental Theorem of Algebra utilizing modulus surfaces and complex analysis is also included.