Let F0 = Q(√ −d) be an imaginary quadratic field with 3 ∤ d and let K0 = Q(√ 3d). Let ε0 be the fundamental unit of K0 and let λ be the Iwasawa λ-invariant for the cyclotomic Z3-extension of F0. The theory of 3-adic L-functions gives conditions for λ ≥ 2 in terms of ǫ0 and the class numbers of F0 and K0. We construct units of K1, the first level of the Z3-extension of K0, that potentially occur...

This article concerns an extension of the topological derivative concept for 2D potential problems involving penetrable inclusions, whereby a cost function J is expanded in powers of the characteristic size ε of a small inclusion. The O(ε) approximation of J is established for a small inclusion of given location, shape and conductivity embedded in a 2-D region of arbitrary shape and conductivit...

This article concerns an extension of the topological derivative concept for 3D inverse acoustic scattering problems, whereby the featured cost function J is expanded in powers of the characteristic size ε of a sound-hard scatterer about ε = 0. The O(ε) approximation of J is established for a small scatterer of arbitrary shape of given location embedded in an arbitrary acoustic domain, and gene...

The firstand second-order optimum achievable exponents in the simple hypothesis testing problem are investigated. The optimum achievable exponent for type II error probability, under the constraint that the type I error probability is allowed asymptotically up to ε, is called the ε-optimum exponent. In this paper, we first give the second-order ε-optimum exponent in the case where the null hypo...

We develop a resummed thermodynamic perturbation theory for bond cooperativity in associating fluids by extension of Wertheim's multi-density formalism. We specifically consider the case of an associating hard sphere with two association sites and both pairwise and triplet contributions to the energy, such that the first bond in an associated cluster receives an energy -ε((1)) and each subseque...

The commonly used linear k-ε turbulence model is shown to be incapable of accurate prediction of turbulent flows, where non-isotropy is dominant. Two examples of non-isotropic flows, which have a wide range of applications in marine waters, are saline water flow and the stratified flows due to temperature gradients. These relate to stratification and consequently, variation of density through...

Let q be odd and squarefree, and let χq be the quadratic Dirichlet character of conductor q. Let uj be a Hecke-Maass cusp form on Γ0(q) with spectral parameter tj . By an extension of work of Conrey and Iwaniec, we show L(uj ×χq, 1/2) ≪ε (q(1 + |tj |))1/3+ε, uniformly in both q and tj . A similar bound holds for twists of a holomorphic Hecke cusp form of large weight k. Furthermore, we show tha...

We present an extension of System F with call-by-name exceptions. The type system is enriched with two syntactic constructs: a union type A ? ∪{ε} for programs of type A whose execution may raise the exception ε at top level, and a corruption type A{ε} for programs that may raise the exception ε in any evaluation context (not necessarily at top level). We present the syntax and reduction rules ...

An analytical and numerical study is presented of transmission of radiation through a multi-mode waveguide containing a randommedium with a complex dielectric constant ε = ε′ + iε′′. Depending on the sign of ε′′, the medium is absorbing or amplifying. The transmitted intensity decays exponentially ∝ exp(−L/ξ) as the waveguide length L → ∞, regardless of the sign of ε′′. The localization length ...

Let M be a number field. Let W be a set of non-archimedean primes of M . Let OM,W = {x ∈ M | ordpx ≥ 0∀p 6∈ W}. The author continues her investigation of Diophantine definability and decidability in rings OM,W where W is infinite. In this paper she improves her previous density estimates and extends the results to the totally complex extensions of degree 2 of the totally real fields. In particu...