Using elimination to describe Maxwell curves

Cartesian ovals are curves in the plane that have been studied for hundreds of years. A Cartesian oval is the set of points whose distances from two fixed points called foci satisfy the property that a linear combination of these distances is a fixed constant. These ovals are a special case of what we call Maxwell curves. A Maxwell curve is the set of points with the property that a specific weighted sum of the distances to n foci is constant. We shall describe these curves geometrically. We will then examine Maxwell curves with two foci and a special case with three foci by deriving a system of equations that describe each of them. Since their solution spaces have too many dimensions, we will eliminate all but two variables from these systems in order to study the curves in xy-space. We will show how to do this first by hand. Then, after some background from algebraic geometry, we will discuss two other methods of eliminating variables, Groebner bases and resultants. Finally we will find the same elimination polynomials with these two methods and study them

Policy Impact in Criminal Justice: Intended and Unintended Consequences

This dissertation contains three chapters dealing with criminal justice policy. First, through time series analysis, it is found that there is no deterrent effect to the juvenile death penalty. Next, the idea of symbolic bureaucratic representation is explored using police stop data. The final chapter looks for any positive economic impact prison privatization has upon local economies

Simulating Interactions Between Coronal Mass Ejections

Coronal mass ejections (CMEs) launch large amounts of plasma and magnetic fields into the interplanetary medium. Under the right initial conditions, this ejecta can reach Earth and cause issues with electronic devices. As such, we would like to have an accurate model that depicts how these CMEs propagate as they leave the sun. By using fluid dynamics and one-minute resolution in-situ solar wind data, we sought to simulate CME plasma propagation with analytical and numerical models. Because the interstellar medium contains other material and other events happen on the sun simultaneously, CMEs can interact with each other and other ejecta, which can cause them to change, so in order to have an accurate simulation we considered these interactions in our model. For our model, we made the assumption that the plasma was an ideal fluid, was super-alfvenic, and we employed an injection radius of 10 R⦿

Nursing case management : a new perspective to caring for patients with hip fracture

Nursing Case Management has motivated nurses to examine the effects of care provided to patients, and to devise means of improving this care. The success of this nursing care delivery model is well documented among a variety of acute and chronically ill patients. Utilizing nonparametric ANOVA for comparison of two means, this study investigates the outcome of the implementation of a nursingcase management model on an orthopedic unit of a local hospital. A convenience sample (N=149) of hip-fracture patients for two separate eight months charting periods were used. The first period was pre-case management and the second period was after the implementation of nursing managed care on the unit. Results suggested that nursing case management was effective in reducing the total length of hospital stay and post-operative days significantly

Synchronization from Second Order Network Connectivity Statistics

We investigate how network structure can influence the tendency for a neuronal network to synchronize, or its synchronizability, independent of the dynamical model for each neuron. The synchrony analysis takes advantage of the framework of second order networks, which defines four second order connectivity statistics based on the relative frequency of two-connection network motifs. The analysis identifies two of these statistics, convergent connections, and chain connections, as highly influencing the synchrony. Simulations verify that synchrony decreases with the frequency of convergent connections and increases with the frequency of chain connections. These trends persist with simulations of multiple models for the neuron dynamics and for different types of networks. Surprisingly, divergent connections, which determine the fraction of shared inputs, do not strongly influence the synchrony. The critical role of chains, rather than divergent connections, in influencing synchrony can be explained by their increasing the effective coupling strength. The decrease of synchrony with convergent connections is primarily due to the resulting heterogeneity in firing rates