Solving the Selesnick-Burrus Filter Design Equations Using Computational Algebra and Algebraic Geometry

In a recent paper, I. Selesnick and C.S. Burrus developed a design method for maximally flat FIR low-pass digital filters with reduced group delay. Their approach leads to a system of polynomial equations depending on three integer design parameters $K,L,M$. In certain cases (their ``Region I''), Selesnick and Burrus were able to derive solutions using only linear algebra; for the remaining cases ("Region II''), they proposed using Gr\"obner bases. This paper introduces a different method, based on multipolynomial resultants, for analyzing and solving the Selesnick-Burrus design equations. The results of calculations are presented, and some patterns concerning the number of solutions as a function of the design parameters are proved.Comment: 34 pages, 2 .eps figure

Toric surface codes and Minkowski sums

Toric codes are evaluation codes obtained from an integral convex polytope $P \subset \R^n$ and finite field \F_q. They are, in a sense, a natural extension of Reed-Solomon codes, and have been studied recently by J. Hansen and D. Joyner. In this paper, we obtain upper and lower bounds on the minimum distance of a toric code constructed from a polygon $P \subset \R^2$ by examining Minkowski sum decompositions of subpolygons of $P$. Our results give a simple and unifying explanation of bounds of Hansen and empirical results of Joyner; they also apply to previously unknown cases.Comment: 15 pages, 7 figures; This version contains some minor editorial revisions -- to appear SIAM Journal on Discrete Mathematic

Structural studies of a fucogalactoxyloglucan from pinus radiata primary cell walls : a thesis presented in partial fulfilment of the requirements for the degree of Master of Science in Biochemistry at Massey University

1. The changes in carbohydrate composition of elongating Pinus radiata primary cell walls were investigated. In the hemicellulose B extracts, a large increase in the percentage of non-starch, non-cellulosic, glucose was found to occur on cessation of cell-wall elongation. 2. By fractionation of the hemicellulose B extracts, with a variety of methods involving precipitation from an aqueous solution, a xyloglucan was purified. This xyloglucan was the major hemicellulose of the Pinus radiata hypocotyl cell wall. 3. Characterisation studies on the xyloglucan involved: quantitative analysis of the monosaccharides derived by nitric acid/urea hydrolysis; identification of the partial hydrolysis products derived by trifluoroacetic acid hydrolysis; quantitation of the sugar linkages using methylation by the Hakomori method; and analysis of the anomeric configuration of component sugars using chromium trioxide oxidation. 4. From the results a tentative structure has been suggested for the xyloglucan, consisting of a backbone of B-D-gluco-pyranose residues linked together by 1-4 glycosidic bonds, and with sidechains of single xylose residues linked through C-6 of the glucose units. Galacto and fuco-1,2- galacto sidechains are attached to some of the xylose residues, probably through the C-2 of the xylose

A Review of Work Based Learning in Higher Education

The idea of work based learning in higher education might sound like a contradiction in terms. Work based learning is surely in the the workplace. The senses in which it might also, under certain conditions, be in higher education are explored in this review. There are increasing arrangements whereby people can obtain academic recognition for learning which has taken place outside of educational institutions. In addition to traditional forms of professional education and sandwich courses, one can add a host of relationships between employers and higher education institutions which involve quite fundamental questioning of the roles and responsibilities of each in the continuing education and training of adults. Such developments can be related to broader themes concerning the organisation of knowledge in society, the changing nature of work and career, the learning society and the implications they hold for individual workers, their employers and educational providers. The Department for Education and Employment sponsored the study to produce a substantial literature review of progress and issues raised in the field of work based learning in higher education. The first part of the book provides a contextual and conceptual backdrop against which more practical aspects of work based learning are then considered in part two. The final part considers strategic issues of implementation for higher education institutions, employers and individuals, before turning to more wide ranging issues of policy

Graduate competences and relationships with the labour market: the UK case

The paper compares the early employment experiences of graduates from the shorter UK bachelors degree with those from the somewhat longer masters programmes to be found in continental Europe. The UK graduates appear to be less prepared for entry to employment and to find their degrees to be less appropriate to that employment. However, many of the differences between UK and other European graduates in the labour market have largely disappeared five years after graduation. And there are many similarities in the perceptions of graduates from different countries about the competences required by employers. The paper sets these differences and similarities within the context of the different higher education and labour market traditions of the UK and the rest of Europe and raises questions about the consequences of greater labour mobility across Europe and the Bologna harmonisation of qualification structures

Cayley-Bacharach and evaluation codes on complete intersections

In recent work, J. Hansen uses cohomological methods to find a lower bound for the minimum distance of an evaluation code determined by a reduced complete intersection in the projective plane. In this paper, we generalize Hansen's results from P^2 to P^m; we also show that the hypotheses in Hansen's work may be weakened. The proof is succinct and follows by combining the Cayley-Bacharach theorem and bounds on evaluation codes obtained from reduced zero-schemes.Comment: 10 pages. v2: minor expository change