Commutative Schur Rings Over Symmetric Groups II: The Case n=6

We determine the commutative Schur rings over $S_6$ that contain the sum of all the transpositions in $S_6$. There are eight such types (up to conjugacy), of which four have the set of all the transpositions as a principal set of the Schur ring

Effective lower bounds for L(1,χ) via Eisenstein series

We give effective lower bounds for L(1,χ) via Eisenstein series on Γ0(q)∖ℍ. The proof uses the Maass–Selberg relation for truncated Eisenstein series and sieve theory in the form of the Brun–Titchmarsh inequality. The method follows closely the work of Sarnak in using Eisenstein series to find effective lower bounds for ζ(1+it)

Test vectors for non‐Archimedean Godement–Jacquet zeta integrals

Given an induced representation of Langlands type ( π , V π ) of GL n ( F ) with F non‐Archimedean, we show that there exist explicit choices of matrix coefficient β and Schwartz–Bruhat function Φ for which the Godement–Jacquet zeta integral Z ( s , β , Φ ) attains the L ‐function L ( s , π )

Mapping biodiversity value worldwide: combining higher-taxon richness from different groups

Maps of large-scale biodiversity are urgently needed to guide conservation, and yet complete enumeration of organisms is impractical at present. One indirect approach is to measure richness at higher taxonomic ranks, such as families. The difficulty is how to combine information from different groups on numbers of higher taxa, when these taxa may in effect have been defined in different ways, particularly for more distantly related major groups. In this paper, the regional family richness of terrestrial and freshwater seed plants, amphibians, reptiles and mammals is mapped worldwide by combining: (i) absolute family richness; (ii) proportional family richness; and (iii) proportional family richness weighted for the total species richness in each major group. The assumptions of the three methods and their effects on the results are discussed, although for these data the broad pattern is surprisingly robust with respect to the method of combination. Scores from each of the methods of combining families are used to rank the top five richness hotspots and complementary areas, and hotspots of endemism are mapped by unweighted combination of range-size rarity scores

Lower Respiratory Tract Infection: An Unrecognised Risk Factor for High Altitude Pulmonary Oedema?

The case of a 25-year-old expedition doctor who developed high altitude pulmonary oedema (HAPE) while climbing in the Swiss Alps is presented, with reference to the literature. The patient’s symptoms of HAPE were typical. Less typical was the fact that the doctor had previously been to similar altitudes uneventfully. The only differentiator is that on this expedition he developed a mild lower respiratory tract infection (LRTI) 2 days prior to travel. There has been limited, conflicting evidence regarding LRTI as a risk factor for HAPE and high quality research has not focused on this area. LRTI is not commonly recognised as being a risk in high altitude environments, which may be resulting in lethal consequences. This report aims to inform, provide a clinical question for future high altitude research expeditions, and encourage consideration by expedition and high altitude doctors

Braid groups, infinite Lie algebras of Cartan type and rings of invariants

AbstractIn this paper we show that each element α of the pure braid group Pn or the pure symmetric automorphism group H(n) of the free group Fn of rank n can be represented as α=exp(D)=id+D+(D2/2!)+(D3/3!)+⋯, where D=D(α) is an element of an infinite-dimensional Lie algebra h(n). Each such D is a derivation of the power series ring C[[a1,…,ar]], r=n2−n, which fixes the volume form a1∧⋯∧ar and so h(n) is a subalgebra of Sn2−n, the special Lie algebra of Cartan type. There is a corresponding action of these groups on C[[a1,…,ar]] and C[a1,…,ar]. We use the representation α=exp(D) to prove results about the ring of invariants for this action of the pure braid group. The Lie algebra h(n) is a subalgebra of a graded Lie algebra h(n); we also calculate the Poincaré series of the Lie algebra l(n) and of certain of its subalgebras, and show that these Poincaré series are rational

Cogrowth of groups and a matrix of redheffer

AbstractWe describe a relationship between the cogrowth function (and other similarly defined functions) of a presentation of a torsion-free group and the Riemann hypothesis. This relationship is determined using a certain matrix of Redheffer

Discourses Of Prejudice In The professions: The Case Of Sign Languages

There is no evidence that learning a natural human language is cognitively harmful to children. To the contrary, multilingualism has been argued to be beneficial to all. Nevertheless, many professionals advise the parents of deaf children that their children should not learn a sign language during their early years, despite strong evidence across many research disciplines that sign languages are natural human languages. Their recommendations are based on a combination of misperceptions about (1) the difficulty of learning a sign language, (2) the effects of bilingualism, and particularly bimodalism, (3) the bona fide status of languages that lack a written form, (4) the effects of a sign language on acquiring literacy, (5) the ability of technologies to address the needs of deaf children and (6) the effects that use of a sign language will have on family cohesion. We expose these misperceptions as based in prejudice and urge institutions involved in educating professionals concerned with the healthcare, raising and educating of deaf children to include appropriate information about first language acquisition and the importance of a sign language for deaf children. We further urge such professionals to advise the parents of deaf children properly, which means to strongly advise the introduction of a sign language as soon as hearing loss is detected