An Elementary Proof of Dodgson's Condensation Method for Calculating Determinants

In 1866, Charles Ludwidge Dodgson published a paper concerning a method for evaluating determinants called the condensation method. His paper documented a new method to calculate determinants that was based on Jacobi's Theorem. The condensation method is presented and proven here, and is demonstrated by a series of examples. The condensation method can be applied to a number of situations, including calculating eigenvalues, solving a system of linear equations, and even determining the different energy levels of a molecular system. The method is much more efficient than cofactor expansions, particularly for large matrices; for a 5 x 5 matrix, the condensation method requires about half as many calculations. Zeros appearing in the interior of a matrix can cause problems, but a way around the issue can usually be found. Overall, Dodgson's condensation method is an interesting and simple way to find determinants. This paper presents an elementary proof of Dodgson's method.Comment: 7 pages, no figure

Effects of Marsh Fragmentation and Patch Area On Fish and Nekton Assemblages in Mississippi

Fragmentation divides continuous habitat into smaller patches. Fragmentation can also produce smaller populations of species, because fragmentation can split a population into smaller groups. Both terrestrial and aquatic ecosystems suffer from fragmentation. There are a variety of fishes that live along marsh, each depending upon the marsh for protection, food, and sometimes even competition. Species richness of fishes can be altered due to marsh fragmentation. I predict islands with a larger patch index should have a higher species richness of fishes. For this study, fish assemblages at 20 islands of marsh were sampled in the months of June and July of 2016 with two 5m pulls of a 9.1 × 1.2 m bag seine. A total of 3305 fishes, representing 34 species, and 190 Farfantepenaeus aztecus and 18 Litopenaeus setiferus were collected across all samples. A drone was used to take aerial images of the smaller islands of marsh and Google Earth was used for the larger islands to determine the patch size and fragmentation index of each island. I found a positive relationship between species richness and patch area. I also found that there was not a significant effect of fragmentation index on the species richness

Exceptional Points in Atomic Spectra

We report the existence of exceptional points for the hydrogen atom in crossed magnetic and electric fields in numerical calculations. The resonances of the system are investigated and it is shown how exceptional points can be found by exploiting characteristic properties of the degeneracies, which are branch point singularities. A possibility for the observation of exceptional points in an experiment with atoms is proposed.Comment: 4 pages, 4 figures, 1 table, to be published in Physical Review Letter

Cost Comparison of Short Span Bridge Structures

This report attempts to give the county engineer a guide for estimating the cost of several types of bridge structures for a particular situation

Reduced healthcare utilisation following successful HCV treatment in HIV co-infected patients with mild liver disease

New direct-acting antivirals (DAA) for hepatitis C virus (HCV) infection have achieved high cure rates in many patient groups previously considered difficult-to-treat, including those HIV/HCV co-infected. The high price of these medications is likely to limit access to treatment, at least in the short term. Early treatment priority is likely to be given to those with advanced disease, but a more detailed understanding of the potential benefits in treating those with mild disease is needed. We hypothesized that successful HCV treatment within a co-infected population with mild liver disease would lead to a reduction in the use and costs of healthcare services in the 5 years following treatment completion. We performed a retrospective cohort study of HIV/HCV-co-infected patients without evidence of fibrosis/cirrhosis who received a course of HCV therapy between 2004 and 2013. Detailed analysis of healthcare utilization up to 5 years following treatment for each patient using clinical and electronic records was used to estimate healthcare costs. Sixty-three patients were investigated, of whom 48 of 63 (76.2%) achieved sustained virological response 12 weeks following completion of therapy (SVR12). Individuals achieving SVR12 incurred lower health utilization costs (£5000 per-patient) compared to (£10 775 per-patient) non-SVR patients in the 5 years after treatment. Healthcare utilization rates and costs in the immediate 5 years following treatment were significantly higher in co-infected patients with mild disease that failed to achieve SVR12. These data suggest additional value to achieving cure beyond the prevention of complications of disease

Work-Life Expectations of Christian Millennials

As more and more Millennials reject a religious label, we are curious as to whether those who have faith are somehow different, not only in their spiritual lives but in their work lives as well. This study analyzes the supposedly declining work ethic of Millennials and aims to determine if Christian Millennials differ from their peers. We found a significant difference in the work values and work ethic scores between Christians and non-Christians. These results seem to support the idea that religion has a noticeable influence on individual work ethic

A Minimal Periods Algorithm with Applications

Kosaraju in ``Computation of squares in a string'' briefly described a linear-time algorithm for computing the minimal squares starting at each position in a word. Using the same construction of suffix trees, we generalize his result and describe in detail how to compute in O(k|w|)-time the minimal k-th power, with period of length larger than s, starting at each position in a word w for arbitrary exponent $k\geq2$ and integer $s\geq0$. We provide the complete proof of correctness of the algorithm, which is somehow not completely clear in Kosaraju's original paper. The algorithm can be used as a sub-routine to detect certain types of pseudo-patterns in words, which is our original intention to study the generalization.Comment: 14 page

Sound propagation over uneven ground and irregular topography

The development of theoretical, computational, and experimental techniques for predicting the effects of irregular topography on long range sound propagation in the atmosphere is discussed. Irregular topography here is understood to imply a ground surface that (1) is not idealizable as being perfectly flat or (2) that is not idealizable as having a constant specific acoustic impedance. The study focuses on circumstances where the propagation is similar to what might be expected for noise from low-altitude air vehicles flying over suburban or rural terrain, such that rays from the source arrive at angles close to grazing incidence