Blue, Meredith

We construct a formal model that reconciles non-formal risk-based Austrian business cycle theory with models of political business cycles. In our model, the incumbent political party induces the central bank to enact an expansionary monetary policy. This policy lowers the real interest rate, which leads to an increase in investments. As more individuals invest, assets inflate, leading to a boom-bust cycle; voter utility increases because asset values are higher. An increase in voter utility leads to an increased likelihood that the incumbent political party will be reelected. In an attempt to avoid a violent bust in assets, the central bank may implement a contractionary monetary policy to raise the real interest rate in increments. If the financial system becomes illiquid before the policy is implemented, then a speculative bubble burst occurs. The cycle regenerates a year before the next election when an accommodative monetary policy is implemented once again.

A common problem surrounding piezoelectric transducers is matching the highimpedance
active piezoelectric element with a low-impedance load, typically water
or skin. This is a common problem with medical devices [Ali00]. Matching layers
are added in an attempt to gradually decrease the impedance of the active piezoelectric
element down to the impedance of water. If the impedance is not gradually
decreased, acoustic waves are reflected at the boundaries that are proportional to
the impedance mismatch of the two materials. A dual-matching layer transducer is
analyzed, and we attempt to optimize the impedances and thicknesses of the two
matching layers using statistical design of experiments.

As Bertrand Russel once said, “The true spirit of delight, the exaltation, the sense of being more than man, which is the touchstone of the highest excellence, is to be found in mathematics as surely as poetry” (Russel 60). Poetry and mathematics are recognizably linked through aesthetics and counting at the most fundamental level, but these basic connections can be further extended to formal constraints in poetry. The link between mathematics and poetry, as well as formal poetic constraint based on mathematical structures and principles is inherently organic. The sestina and the sonnet are traditional poetic forms that contain intrinsic mathematical structures. The Fib, the S+7 algorithm, and computer-generated poetry are modern forms which have been explicitly based on mathematical structures.

The purpose of this thesis is to take a knitting pattern and to flip or rotate it, creating a new pattern. In order to accomplish this, knitting patterns are converted into matrices and then matrix properties, such as the matrix transpose and matrix multiplication, are used to transform the pattern. This project finds a particular order of matrix properties that can be applied to create rotations and flips of the original pattern. The transformed matrix can then be converted back into a knitting pattern. A program in JAVA that allows a user to input a knitting pattern and produce a rotated or flipped pattern is created using these matrix properties.

Dust particles in plasma can arrange themselves into a vertical con guration
when placed inside a glass box. What really occurs in the glass box is still unknown
and is di cult to nd out by direct methods of measurement. In this thesis, the
dust chains are investigated through probe oscillations and a Matlab simulation
that uses a parallel plate capacitor to model an electric eld. Parameters of the
plasma and dispersion relations for the transverse oscillation are extracted from
the chain's motion. For both longitudinal and transverse oscillatory motion, the
simulation is used to nd the charge on all the dust in the chains and to simulate
the chain's motion. The plasma parameter values are expected within experimental
error. The dispersion relations show that more than one wave motion
propagates through the chain. The charge found is much higher than expected,
and so the simulated motion may not be very accurate.

Epithelial morphogenesis is driven by the formation, growth, and bending of thin sheets of cells with distinct interior (apical) and exterior (basal) sides. In this study we attempted to improve on past particle-based cell models to form a model of morphogenesis based on a two-particle polarized cell structure. We began by modeling a stable cyst-like structure. We then tested and calibrated the viscoelastic properties of our model by compressing the cell structure between two plates, which is comparable to real world data collected by Forgacs et al. (1998). We also simulated the growth of a hollow sphere into a tube-like structure using directed cell growth and a theoretical version of a basal lamina. With minimal refinement, this model should generalize to 3D.