An explicit expression for the ε-factor εK((V,N),ψ,dμ) of a representation (V,N) of the Weil-Deligne group WDK of a local field K is given in terms of the nonabelian local class field theory of K.

Many attempts have been made to trace the path by which carcinogens are metabolized, with the hope that this may shed some light on the mecha nism of carcinogenesis. Current literature still con tains conflicting evidence on the question of whether the hydrocarbon itself, perhaps in a pro tein complex, or a metabolite is the active carcino genic agent. The work of Peacock et al. (7) sug gests t...

Let C be a smooth irreducible projective curve defined over a finite field Fq of q elements of characteristic p > 3 andK = Fq(C) its function field and φE : E → C the minimal regular model of E/K. For each P ∈ C denote EP = φ −1 E (P ). The elliptic curve E/K has good reduction at P ∈ C if and only if EP is an elliptic curve defined over the residue field κP of P . This field is a finite extens...

In this survey article, we first review the Chern-Weil theory of characteristic classes of vector bundles over smooth manifolds. Then some well-known characteristic classes appearing in many places in geometry and topology as well as some interesting results on them related to elliptic genera which involve some of my joint work in [HZ1, 2], are briefly introduced. 1. Chern-Weil theory for chara...

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In this short review article we sketch some developments which should ultimately lead to the analogy of the Chern-Weil homomorphism for principle bundles in the realm of non commutative differential geometry. Principal bundles there should have Hopf algebras as structure ‘cogroups’. Since the usual machinery of Lie algebras, connection forms, etc., just is not available in this setting, we base...

In his work on Diophantine equations of the form y2=ax4+bx3+cx2+dx+e, Fermat introduced the notion of primitive solutions. In this expository note we intend to interpret this notion more geometrically, and explain what it means in terms of the arithmetic of elliptic curves. The specific equation y2 =x4 + 4x3 + 102 +20x+ 1 was used extensively by Fermat as an example. We illustrate the nowadays ...

We address the issue of altruism when standard-of-living aspirations are transmitted from one generation to the other. In that case, the in uence of altruistic parents is not limited to the bequest they could leave; indeed, they direct the evolution of children's aspirations toward raising their utility by refraining their own consumption standard. We show that, even if there is no bequest, alt...

Citation: Daniels CA, Baumgarten S, Yum LK, Michell CT, Bayer T, Arif C, Roder C, Weil E and Voolstra CR (2015) Metatranscriptome analysis of the reef-building coral Orbicella faveolata indicates holobiont response to coral disease. Front. Mar. Sci. 2:62. doi: 10.3389/fmars.2015.00062 Metatranscriptome analysis of the reef-building coral Orbicella faveolata indicates holobiont response to coral...

WEIL'S DISEASE, since its original clinical description by Adolf Weil of Heidelberg in 1886, has been diagnosed clinically in many parts of the world. Inade and Ido in 1914 discovered the pathogenic agent by inoculating the blood from a patient during the first week of the disease into a guinea-pig and found that the organism responsible was a spirochaete. Noguchi, who also studied the organism...