In order to elucidate the general Stokes flow characteristics present for slender bodies of finite centre-line curvature the singularity method for Stokesflow has been employed to construct solutions to the flow past a slender torus. The symmetry of the geometry and absence of ends has made a highly accurate analysis possible. The no-slip boundary condition on the body surface is satisfied up t...

One of the main problems in all-optical packet-switched networks is the lack of optical buffers, and one feasible technology for the constructions of optical buffers is to use optical crossbar Switches and fiber Delay Lines (SDL). In this two-part paper, we consider SDL constructions of optical queues with a limited number of recirculations through the optical switches and the fiber delay lines...

Let K be any finite abelian extension of Q, k any subfield of K and r any integer. We complete the proof of the equivariant Tamagawa Number Conjecture for the pair (h(Spec(K))(r),Z[Gal(K/k)]). 2000 Mathematics Subject Classification: Primary 11G40; Secondary 11R65 19A31 19B28

We present some examples of mathematically natural nonrecursive sets of integers and relations on integers by combining results from Part 1, from recursion theory, and from the negative solution to Hilbert’s 10th Problem.

For quadratic fields whose discriminant has few prime divisors, there are explicit formulas for the 4-rank of K2OE . For quadratic fields whose discriminant has arbitarily many prime divisors, the formulas are less explicit. In this paper we will study fields of the form Q[ √ p1 · · · pk], where the primes pi are all congruent to 1 mod 8. We will prove a theorem conjectured by Conner and Hurrel...

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For a real number x, we let ⌊x⌉ be the closest integer to x. In this paper, we look at the arithmetic properties of the integers ⌊θ⌉ when n ≥ 0, where θ > 1 is a fixed algebraic number.

This work continues the generalized stability theory (GST) analysis of baroclinic shear flow in the primitive equations (PE), focusing on the regime in which the mean baroclinic shear and the stratification are of the same order. The Eady model basic state is used and solutions obtained using the PE are compared to quasigeostrophic (QG) solutions. Similar optimal growth is obtained in the PE an...

We show that the number α = (1 + √ 3 + 2 √ 5)/2 with minimal polynomial x4 − 2x3 + x − 1 is the only Pisot number whose four distinct conjugates α1, α2, α3, α4 satisfy the additive relation α1+α2 = α3+α4. This implies that there exists no two non-real conjugates of a Pisot number with the same imaginary part and also that at most two conjugates of a Pisot number can have the same real part. On ...

1 Topics in Number Theory 2 1.1 Subgroups of the Integers . . . . . . . . . . . . . . . . . . . . 2 1.2 Greatest Common Divisors . . . . . . . . . . . . . . . . . . . . 2 1.3 The Euclidean Algorithm . . . . . . . . . . . . . . . . . . . . . 3 1.4 Prime Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.5 The Fundamental Theorem of Arithmetic . . . . . . . . . . . . 5 1.6 The Infini...