The aim of this paper is to compute the rational character tables of the dicyclic group $T_{4n}$, the groups of order $pq$ and $pqr$. Some general properties of rational character tables are also considered into account.The aim of this paper is to compute the rational character tables of the dicyclic group $T_{4n}$, the groups of order $pq$ and $pqr$. Some general properties of rational charact...

We find explicit models for the PSL2(C)and SL2(C)-character varieties of the fundamental groups of complements in S of an infinite family of two-bridge knots that contains the twist knots. We compute the genus of the components of these character varieties, and deduce upper bounds on the degree of the associated trace fields. We also show that these knot complements are fibered if and only if t...

1. We have shown that the type of renal lesion produced by compounds of arsenic varies widely: while some arsenicals produce changes in which vascular injury predominates, others produce an equally dominant tubular injury. 2. In either of these groups the character and degree of the vascular or tubular injury produced by different compounds shows further variation, such that the lesions of diff...

Given the large number and complexity of Chinese characters, pattern matching based on structural decomposition and analysis is believed to be necessary and essential to off-line character recognition. This paper proposes a new model of stroke extraction for Chinese characters. One problem for stroke extraction is how to extract primary strokes. Another major problem is to solve the segmentatio...

Let W be a crystallographic Weyl group, and let TW be the complex toric variety attached to the fan of cones corresponding to the reflecting hyperplanes of W , and its weight lattice. The real locus TW (R) is a smooth, connected, compact manifold with a W -action. We give a formula for the Euler characteristic of TW (R) as a generalised character of W . In type An−1 for n odd, one obtains a gen...

Given an abelian Galois extension K/F of number fields, a quaternion algebra A over F that is ramified at all infinite primes, and a character χ of the Galois group of K over F , we consider the twist of the zeta function of A by the character χ. We show that such twisted zeta functions provide a factorization of the zeta function of A(K) = A ⊗F K. Also, the quotient of the zeta function for A(...

Let G be a finite group and χ an irreducible character of G. A simple method for constructing a representation affording χ can be used whenever G has a subgroup H such that χH has a linear constituent with multiplicity 1. In this paper we show that (with a few exceptions) if G is a simple group or a covering group of a simple group and χ is an irreducible character of G of degree between 32 and...

In 1968, in a remark as wise as it is learned, Professor George Clark wrote of The Battle of Maldon that “what the poet does not create does not exist even if history inspires his poem.” Readers of the poem have been mulling this over for forty years. The historical information the poem affords us has been subject, in some degree, to alteration by imagination, to the formulae of verse, and to t...

Let k be a nite eld of characteristic p and cardinality q, a nontrivial C -valued additive character of k, and a nontrivial C -valued multiplicative character of k . We extend to a function on all of k by de ning (0) := 0: Recall that, given an integer n, a number 2 C is said to be pure of weight n (relative to q) if it and all its Aut(C =Q)-conjugates have absolute value p q. Such an is necess...

The phenomenon of connected communities shows that the Internet can be a powerful tool in promoting cohesiveness between community players. Since a community's capability to initiate development projects depends to a significant degree on the quality of the relational framework in which the players operate, we maintain that it is possible to go beyond the instrumental character of Internet appl...