Dihedral Quintic Fields with a Power Basis

It is shown that there exist infinitely many dihedral quintic fields with a power basis.</p

Validation of a TELEMAC-3D model of a seamount

Water Qualit

Diagonal and Low-Rank Matrix Decompositions, Correlation Matrices, and Ellipsoid Fitting

In this paper we establish links between, and new results for, three problems that are not usually considered together. The first is a matrix decomposition problem that arises in areas such as statistical modeling and signal processing: given a matrix $X$ formed as the sum of an unknown diagonal matrix and an unknown low rank positive semidefinite matrix, decompose $X$ into these constituents. The second problem we consider is to determine the facial structure of the set of correlation matrices, a convex set also known as the elliptope. This convex body, and particularly its facial structure, plays a role in applications from combinatorial optimization to mathematical finance. The third problem is a basic geometric question: given points $v_1,v_2,...,v_n\in \R^k$ (where $n > k$) determine whether there is a centered ellipsoid passing \emph{exactly} through all of the points. We show that in a precise sense these three problems are equivalent. Furthermore we establish a simple sufficient condition on a subspace $U$ that ensures any positive semidefinite matrix $L$ with column space $U$ can be recovered from $D+L$ for any diagonal matrix $D$ using a convex optimization-based heuristic known as minimum trace factor analysis. This result leads to a new understanding of the structure of rank-deficient correlation matrices and a simple condition on a set of points that ensures there is a centered ellipsoid passing through them.Comment: 20 page

Performance Evaluation and Optimization of Math-Similarity Search

Similarity search in math is to find mathematical expressions that are similar to a user's query. We conceptualized the similarity factors between mathematical expressions, and proposed an approach to math similarity search (MSS) by defining metrics based on those similarity factors [11]. Our preliminary implementation indicated the advantage of MSS compared to non-similarity based search. In order to more effectively and efficiently search similar math expressions, MSS is further optimized. This paper focuses on performance evaluation and optimization of MSS. Our results show that the proposed optimization process significantly improved the performance of MSS with respect to both relevance ranking and recall.Comment: 15 pages, 8 figure

INTERSECTIVE POLYNOMIALS WITH GALOIS GROUP D₅

We give an infinite family of intersective polynomials with Galois group D5, the dihedral group of order 10

EXPECTATIONS OF PARENTS OF FIRST-YEAR STUDENTS REGARDING COLLEGIATE TEACHING AND CARING AT A PUBLIC UNIVERSITY

Parental involvement in higher education has greatly increased, specifically in the last 30 years. Some parents are hyper-involved in their children's lives, and educational leaders often spend almost as much time working with parents as they do students. The body of literature on parental involvement in higher education is limited. Therefore, the purpose of this study was to examine the expectations parents have for a public university's teaching and caring functions while also examining the differences, if any, of parents of first-generation college students and parents with college experience.   This quantitative study explored the expectations of parents of first-year students at a large, public university in the South. This study utilized a survey instrument developed by Young in 2006, the Parent Expectations of Collegiate Teaching and Caring (PECTAC) survey. The study was predicated on Chickering and Reisser's Theory of Psychosocial Development, and focused on vector three, moving though autonomy toward interdependence. The web-based survey was used to collect data from 1,137 parents at the beginning of the spring 2010 semester. Parents rated their expectations regarding teaching and caring in terms of importance. Expectations were analyzed in light of the dependent variables of parent gender, first time college parent experience, and parent college experience, and t tests were utilized to determine statistically significant differences. Expectations for teaching and caring were analyzed using a Pearson product moment correlation coefficient.   The findings suggest that teaching and caring are more important to mothers than fathers and more important to parents who do not have college background than parents who do. The findings also suggest that parents who view teaching as important also view caring as important and vice versa. Additionally, the following topics are important to parents: a safe and secure campus, additional support for student academic success, student access to campus resources, the availability and integration of technology, communication and contact with administrators, and individual attention for their children.  Furthermore, the study included various implications for educational leaders, including accepting parents as constituents of higher education and developing a campus-wide approach to working with parents. The study concluded with recommendations for future research.  Ed.D

Representations of integers by the form x2 + xy + y2 + z2 + zt + t2

Electronic version of an article published in International Journal of Number Theory Volume 04, Issue 05, October 2008, pp. 709-714. DOI: 10.1142/S1793042108001638. Copyright © 2008 World Scientific Publishing Company: http://www.worldscientific.com/worldscinet/ijntWe give an elementary proof of the number of representations of an integer by the quaternary quadratic form x2 + xy + y2 + z2 + zt + t2

Evolution of nature-based dredging solutions at Harwich, UK

Harwich Harbour, in the Southeast of the UK, is the location of the Port of Felixstowe and the confluence of the highly protected Stour and Orwell Estuaries. The maintenance of the approaches to the Port of Felixstowe is carried out by the Harwich Haven Authority and entails the dredging of up to 3 Mm3 of mud by trailer suction hopper dredger, almost all of which is placed offshore. Deepening of the approach channel to the Port of Felixstowe in 1998/2000 resulted in regulatory agreements for an innovative sediment recycling strategy (or mud engine) to offset the perceived effects of the deepening. This sediment recycling involves the release of a proportion of the material dredged from the maintenance areas of the Port of Felixstowe within both estuaries to enhance the sediment supply to the intertidal areas within each estuary. The present sediment recycling methodology consists of the release into the water column of around 50,000 tonnes/year of fine sediment from small trailer suction hopper dredgers, releasing on the flood tide in a number of campaigns throughout the year. Survey evidence and detailed numerical modelling shows that this strategy is effective for improving habitat, but it is still not optimal, either environmentally or on grounds of dredging efficiency, because of the current requirement for offshore disposal of most of the dredged material from the Harbour. As a result, Harwich Haven Authority intend to develop their dredging and sediment recycling strategy further. To this end they have patented and trialled an agitation dredger which removes the need for offshore disposal, greatly reduces production of CO2 and dredging costs, and takes a leap forward in providing a more nature-based dredging solution providing the recycling of sediment within the estuarine system

Disposal of hypergolic propellants. Phase 6, task 1: The cryogenic scrubber prototype

A cryogenic scrubber prototype (CSP) was evaluated as a means of removing monomethylhydrazine (MMH) vapor and dinitrogen textroxide (NTO) vapor from nitrogen or helium vent gas stream. The concept, laboratory data, design, construction and experimentation are discussed