311 research outputs found
Some generalizations of the MacMahon Master Theorem
No full textAbstractWe consider a number of generalizations of the β-extended MacMahon Master Theorem for a matrix. The generalizations are based on replacing permutations on multisets formed from matrix indices by partial permutations over matrix or submatrix indices
Specializations of MacMahon symmetric functions and the polynomial algebra
No full textA MacMahon symmetric function is a formal power series in a finite number of alphabets that is invariant under the diagonal action of the symmetric group. We use a combinatorial construction of the different bases of the vector space of MacMahon symmetric functions found by the author to obtain their image under the principal specialization: the powers, rising and falling factorials. Then, we compute the connection coefficients of the different polynomial bases in a combinatorial way
Certain infinite products in terms of MacMahon type series
No full textRecently, Ono and the third author discovered that the reciprocals of the theta series and have infinitely many closed formulas in terms of MacMahon\u27s quasimodular forms and . In this article, we use the well-known infinite product identities due to Jacobi, Watson, and Hirschhorn to derive further such closed formulas for reciprocals of other interesting infinite products. Moreover, with these formulas, we approximate these reciprocals to arbitrary order simply using MacMahon\u27s functions and {\it MacMahon type} functions. For example, let be the theta function corresponding to the odd quadratic character modulo . Then for any positive integer , we have where and .16 page
Sweet Ella MacMahon
No full textA man loves an Irish womanhttps://egrove.olemiss.edu/kgbsides_uk/1045/thumbnail.jp
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Acrylamide content of vegetable chips
No full textVegetable chips—beets, sweet potatoes, carrots, and parsnips fried like potato chips and sold separately or as a mixture—are an increasingly popular snack. Little data currently exists on acrylamide levels in these products, and there is sparse information on the free amino acid composition of these four vegetables, with asparagine, a precursor of acrylamide, being of interest. Acrylamide concentrations in 35 vegetable chip samples and free amino acids in two to three samples of each of the four vegetables were measured. Of the chip samples, nearly 70% (24 samples) contained levels of acrylamide above the European Commission’s benchmark value of 750 µg/kg for potato chips. In comparison, from 2012 to 2016, approximately 10% of potato chip samples exceeded this value. The food industry has reduced the acrylamide content of potato chips by using cultivars developed specifically for chip manufacturing. Because the vegetable chip market is still significantly smaller than the potato chip market, equivalent cultivar development has not yet occurred. Hence, it is more likely for vegetable chips to be high in acrylamide than potato chips
Cautionary tale: a systematic review of understanding the police caution for adults in the criminal justice system, and an examination of increasing listenability of the caution
No full textRationale: Research has repeatedly demonstrated that people have difficulty
understanding their interrogation rights, as presented in an orally presented police
caution. There has been a limited amount of research into possible means of
improving understanding, with the application of linguistic, listenability, techniques to
caution wording proving most effective amongst students.
Methods: This thesis systematically reviewed research exploring verbal caution
comprehension amongst adults involved in the criminal justice system, to isolate
possible predictors of performance. It then assessed understanding of the Scottish
police caution amongst people with an intellectual disability and if this can be
improved using a modified (listenability) version.
Results: IQ and verbal comprehension appear to have a positive association with
understanding. However, the reviewed literature tends to use broad inclusion criteria
that may increase confounding variables and reduce opportunity to isolate further
possible predictors. People with intellectual disabilities performed poorly in
assessment of their understanding of the Scottish police caution, even when the
modified version was used. This was despite every participant claiming they had
understood.
Conclusions: The thesis questions whether the use of a verbal police caution fulfils
the intention of communicating interrogation rights as required by law. It suggests
more research into caution comprehension is required, with more specific inclusion
criteria, to help better understand variables that predict understanding. The
relationship between verbal ability and IQ suggest efforts to improve comprehension
should be directed to people who have challenges in these abilities, such as people
with intellectual disabilities. This should ensure any improvements can benefit a
greater number of people. The thesis’ empirical study suggests the method found
effective amongst students does not extend to people with intellectual disabilities
Letter from P.J. Walsh to Hagan
No full textHolograph letter from P.J. Walsh, Archbishop's House, Dublin, to Hagan, enclosing the MacMahon brief (not extant). In thanks for the dispensation for student O'Carroll. Then listing enquiries concerning the career of the late Archbishop Walsh of Dublin; surmising that material exists at the Irish College that can clear up these points. Michael Dwyer and Tom Hill will be able to give Hagan all the gossip when in Rome
More Than a Ramble: A Law Student\u27s Review of Hugh G.E. MacMahon\u27s Progress, Stability, and the Struggle for Equality: A Ramble Through the Early Years of Maine Law, 1820-1920
No full textHugh MacMahon’s work, Progress, Stability, and the Struggle for Equality: A Ramble Through the Early Years of Maine Law, 1820–1920, is a thoroughly researched, well-written narrative that provides readers with a glimpse into Maine’s past while making them contemplate legal problems that will persist far into the future. MacMahon maintains a careful balance in his writing, ensuring it is not too dulled down for legal professionals, but not too complex—with superfluous legalese—for laymen. He does a wonderful job introducing legal concepts and demonstrating how those principles were first introduced into the Pine Tree State. Through the use of legal history, the author illustrates a seemingly simpler time, in which past Maine industries, like ice harvesting and logging, flourished; demonstrates how rapidly society was changing with the Industrial Revolution, the Civil War, and the Women’s Rights Movement; and discusses how the Maine Supreme Judicial Court, sitting as the Law Court—conservative in its nature—had to delicately balance these complic
The Color Cubes Puzzle with Two and Three Colors
No full textThis chapter analyzes a puzzle related to a classic problem first posed by English mathematician Percy MacMahon. MacMahon Given a palette of six colors, a 6-color cube is one where each face is one color and all six colors appear on some face. It is a straightforward counting argument to show that there are exactly thirty distinct 6-color cubes up to rigid isometry. MacMahon introduced this set of cubes and posed a number of questions about it. The most natural one—and the motivating problem for this chapter—was whether one could take twenty-seven cubes from the set and build a 3 × 3 × 3 cube where each face was one color. The chapter first provides background and terminology, including the coloring condition and a description of a useful partial order on cubes. It then applies these tools to solve the 2-color case, the 3-color problem, and the problem for frames of all sizes.</p
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