Let $C$ be a hyperelliptic curve defined over $\mathbb{Q}$, whose Weierstrass points are extensions of $\mathbb{Q}$ degree at most three, and least one them is rational. Generalizing result R. Soleng (in the case elliptic curves), we prove that any line bundle $0$ on which not torsion can specialised into ideal classes imaginary quadratic fields order made arbitrarily large. This gives positive...

We present a calculation of the net baryon number density as function imaginary chemical potential, obtained with highly improved staggered quarks at temporal lattice extent ${N}_{\ensuremath{\tau}}=4$, 6. construct various rational approximations data and discuss how poles in complex plane can be determined from them. compare our results singularities potential to theoretically expected positi...

Nathaniel Dean asks the following: Is it possible to find four nonconcyclic points on the parabola y = x2 such that each of the six distances between pairs of points is rational? We demonstrate that there is a correspondence between all rational points satisfying this condition and orbits under a particular group action of rational points on a fiber product of (three copies of) an elliptic surf...

Nathaniel Dean asks the following: Is it possible to find four nonconcyclic points on the parabola y = x2 such that each of the six distances between pairs of points is rational? We demonstrate that there is a correspondence between all rational points satisfying this condition and orbits under a particular group action of rational points on a fiber product of (three copies of) an elliptic surf...

We propose Imaginary Devices, a set of freehand gestures that mimic the use of physical input devices. Imaginary Devices allow users to choose the input modality best suited for the task at hand, such as a steering wheel for a driving game or a joystick for a flight simulator. Exploiting the skills that users have acquired using physical input devices, they can instantly begin interacting with ...

Leaders today seem to be suffering from what might be called a failure of the imagination. We seem to be continually finding ourselves in situations where the leaders say something like “no one could have imagined that this would happen.” For example: Who could imagined that Hurricane Katrina would breach the levies in New Orleans; who could have imagined that an insurgency would arise from the...

Self-deception is a special kind of motivational dominance in belief-formation. We develop criteria which set paradigmatic self-deception apart from related phenomena of auto-manipulation such as pretense and motivational bias. In self-deception rational subjects defend or develop beliefs of high subjective importance in response to strong counter-evidence. Self-deceivers make or keep these bel...

In two experiments, participants were asked to rate the riskiness of three imaginary diseases after reading a short description of each, varying in controllability and severity, two of the most important determinants of risk perception. Cognitive load was also manipulated in Experiment 1, to check whether any of the two factors can be moderated by System 2 processes. The main effects of control...