We construct unramified central simple algebras representing 2-torsion classes in the Brauer group of a hyperelliptic curve, and show that every 2-torsion class can be constructed this way when the curve has a rational Weierstrass point or when the base field is C1. In general, we show that a large (but in general proper) subgroup of the 2torsion classes are given by the construction. Examples ...

We provide an integral formula for the free energy of the two-matrix model with polynomial potentials of arbitrary degree (or formal power series). This is known to coincide with the τ function of the dispersionless two–dimensional Toda hierarchy. The formula generalizes the case studied by Kostov, Krichever, Mineev-Weinstein, Wiegmann, Zabrodin and separately Takhtajan in the case of conformal...

Abstract In this paper we give a complete description of the integral Chow ring stack $\mathscr{H}_{g,1}$ 1-pointed hyperelliptic curves, lifting relations and generators from $\mathscr{H}_g$. We also geometric interpretation for generators.

We first recall results on the boundary of the so-called admissible set for state and input constrained nonlinear systems, namely that the boundary is made up of two parts: one included in the state constraints and its complement called the barrier, made of integral curves that satisfy a minimum-like principle. Then we define the notions of barrier stopping points by intersection and by self-in...

The mobility of entrepreneurs, which is an integral part of human life, can occur in all aspects of occupation and location. Finding out the general trends of mobility in entrepreneurship can be used in the effective motivational activities. As Sylhet is a remittance and raw materials rich but industrially backward area, the mobility of entrepreneurship in both aspects in this area is to be ana...

Quantum transport properties of pure and functioned infinite lead-connection region-lead systembased on the zigzag graphene nanoribbon (2-zGNR) have been investigated. In this work the effectof the doping functionalization on the quantum transport of the 2-zGNR has been computationallystudied. Also, the effect of the imposed gate voltages (-3.0, 0.0 and +3.0 V) and bias voltages 0.0 to2.0 V hav...

The GKZ system for the Hesse pencil of elliptic curves has more solutions than the period integrals. In this work we give different realizations and interpretations of the extra solution, in terms of oscillating integral, Eichler integral, chain integral on the elliptic curve, limit of a period of a certain compact Calabi–Yau threefold geometry, etc. We also highlight the role played by the orb...

We propose a simple generalization of Shephard’s interpolation to piecewise smooth, convex closed curves that yields a family of boundary interpolants with linear precision. Two instances of this family reduce to previously known interpolants: one based on a generalization of Wachspress coordinates to smooth curves and the other an integral version of mean value coordinates for smooth curves. A...

We prove some new degeneracy results for integral points and entire curves on surfaces; in particular, we provide the first examples, to our knowledge, of a simply connected smooth variety whose sets of integral points are never Zariski-dense (and no entire curve has Zariski-dense image). Some of our results are connected with divisibility problems, i.e. the problem of describing the integral p...