Volume 1 Issue 4 March 2003

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https://doi.org/10.33697/ajur.2003.001

Year One and Counting

https://doi.org/10.33697/ajur.2003.002

Author(s):

C.C. Chancey

Affiliation:

American Journal of Undergraduate Research, University of Northern Iowa, Cedar Falls, Iowa 50614-0150 USA


Filtered Intersections and Filtered Products

https://doi.org/10.33697/ajur.2003.003

Author(s):

Nicholas Roersma

Affiliation:

Mathematics and Computer Science Department, Wabash College, Crawfordsville, Indiana 47933-0352 USA

ABSTRACT:

We explore the filtered intersections and filtered products of ideals, modules, and other properties of commutative rings with zero divisors. Set theoretic properties of orderings are considered. The focus is then turned to the compliment of filters, ideals, and similar topics considered for ideal intersections.


Solar Thermal Design: Research, Design and Installation of a Solar Hot Water System for Redwood National Park

https://doi.org/10.33697/ajur.2003.004

Author(s):

Andrew Sorter, Kelly Miess, Richard Engel, and Angelique Sorensen

Affiliation:

Environmental Resources Engineering, Humboldt State University, Arcata, California 95521 USA

ABSTRACT:

This paper details the research, design and installation of the solar thermal water-heating project at the Redwood Information Center (RIC) in Orick, California, USA. The project was completed as part of the University-National Park Energy Partnership Program (UNPEPP) for the summer of 2002.


A Comparison of Two Equivalent Real Formulations for Complex-Valued Linear Systems Part 2: Results

https://doi.org/10.33697/ajur.2003.005

Author(s):

Abnita Munankarmy and Michael A. Heroux

Affiliation:

Department of Computer Science, College of Saint Benedict, 37 South College Avenue, St. Joseph, Minnesota 56374 USA

ABSTRACT:

Many iterative linear solver packages focus on real-valued systems and do not deal well with complex-valued systems, even though preconditioned iterative methods typically apply to both real and complex-valued linear systems. Instead, commonly available packages such as PETSc and Aztec tend to focus on the real-valued systems, while complex-valued systems are seen as a late addition. At the same time, by changing the complex problem into an equivalent real formulation (ERF), a real valued solver can be used. In this paper we consider two ERF’s that can be used to solve complex-valued linear systems. We investigate the spectral properties of each and show how each can be preconditioned to move eigenvalues in a cloud around the point (1,0) in the complex plane. Finally, we consider an interleaved formulation, combining each of the previously mentioned approaches, and show that the interleaved form achieves a better outcome than either separate ERF.

[This article is the second part of a sequence of reports. See the December 2002 issue for Part 1—Editor.]


Computational Modeling of Pool Games: Sensitivity of Outcomes to Initial Conditions

https://doi.org/10.33697/ajur.2003.006

Author(s):

Christian Leerberg and M.W. Roth

Affiliation:

Department of Physics, University of Northern Iowa, Cedar Falls, Iowa 50614-0150 USA

ABSTRACT:

We present a study of the sensitivity of trajectories of pool balls to initial conditions. In the first component of the study our simulations include all sixteen balls. Variables include cue ball initial velocity and position on the “table”. We find that in a certain regime of initial conditions the system seems to show self-similarity, but as the range of initial cue ball angle and initial velocity is restricted, the system exhibits an interesting evolution towards a single point in parameter space, with the ball landing in only one pocket. We also examine the effects of varying the number of balls on the table, and how their dynamics may be interpreted using various plots and maps. Finally, the trajectory of a single cue ball is examined while it moves through the table space. Starting with the cue ball placed in the middle of the right wall of the table (traditional and rectangular in shape) and fired directly downward the system exhibits a two-cycle pattern. Then as the angle of fire is increased the system exhibits a four cycle, a three cycle and finally a two cycle all separated by noisy patterns. Effects of numerical artificialities are briefly discussed.