If C is a smooth curve over an algebraically closed field k of characteristic exponent p, then the structure of the maximal prime-top quotient of thé etale fundamental group is known by analytic methods. In this paper, we discuss the properties of the fundamental group that can be deduced by purely algebraic techniques. We describe a general reduction from an arbitrary curve to the projective l...

Article history: Received 24 June 2008 Revised 29 January 2009 Available online 27 February 2009 Communicated by H. Stichtenoth This note contains general remarks concerning finite fields over which a so-called maximal, hyperelliptic curve of genus 3 exists. Moreover, the geometry of some specific hyperelliptic curves of genus 3 arising as quotients of Fermat curves, is studied. In particular, ...

The complete classification of hexapods — also known as Stewart Gough platforms — of mobility one is still open. To tackle this problem, we can associate to each hexapod of mobility one an algebraic curve, called the configuration curve. In this paper we establish an upper bound for the degree of this curve, assuming the hexapod is general enough. Moreover, we provide a construction of hexapods...

The theoretical basis for analyzing the effects of an allosteric modulator on the response to an agonist is described. The effects of an allosteric modulator on the concentration-response curve to an agonist can be attributed to changes in the observed dissociation constant and intrinsic efficacy of the agonist-receptor complex. Each of these two changes can be represented by a coefficient or f...

BACKGROUND Accurate functional diagnosis of coronary stenosis is vital for decision making in coronary revascularization. With recent advances in computational fluid dynamics (CFD), fractional flow reserve (FFR) can be derived non-invasively from coronary computed tomography angiography images (FFRCT) for functional measurement of stenosis. However, the accuracy of FFRCT is limited due to the a...

In this paper, which is a sequel of [BKLV], we study the convex-geometric properties cone pseudoeffective $n$-cycles in symmetric product $C_d$ smooth curve $C$. We introduce and Abel-Jacobi faces, related to contractibility morphism classical Brill-Noether varieties. investigate when faces are non-trivial, prove that for $d$ sufficiently large (with respect genus $C$) they form maximal chain p...

The equation goes back to F. Klein who derived it as a model for the modular curve X(7) [9]. In characteristic zero, the curve is the unique curve of genus three, up to isomorphism, with the maximal number of 168 automorphisms. Various aspects of the curve are described in the recent papers [8], [14], [6], in [7], and in other contributions to [10]. For further and older references dealing with...

We explore maximal unitarity for nonplanar two-loop integrals with up to four massive external legs. In this framework, the amplitude is reduced to a basis of master integrals whose coefficients are extracted from maximal cuts. The hepta-cut of the nonplanar double box defines a nodal algebraic curve associated with a multiply pinched genus-3 Riemann surface. All possible configurations of exte...

We provide a representation of the maximal difference between a standard Brownian bridge and its concave majorant on the unit interval, from which we deduce expressions for the distribution and density functions and moments of this difference. This maximal difference has an application in nonparametric statistics where it arises in testing monotonicity of a density or regression curve.