An application area of vertex enumeration problem (VEP) is the usage within objective space based linear/convex vector optimization algorithms whose aim to generate (an approximation of) Pareto frontier. In such algorithms, VEP, which defined in space, solved each iteration and it has a special structure. Namely, recession cone polyhedron be generated ordering cone. We consider give detailed de...

We discuss the ordering of a spin-1 condensate when quenched from its paramagnetic phase to its ferromagnetic phase by reducing the magnetic field. We first elucidate the nature of the equilibrium quantum phase transition. Quenching rapidly through this transition reveals XY ordering either at a specific wave vector, or the "light-cone" correlations familiar from relativistic theories, dependin...

This paper considers metrics valued in abelian `-groups and their induced topologies. In addition to a metric into an `-group, one needs a filter in the positive cone to determine which balls are neighborhoods of their center. As a key special case, we discuss a topology on a lattice ordered abelian group from the metric dG and the filter of positives consisting of the weak units of G; in the c...

Cytoplasmic second messengers, Ca2+ and cAMP, regulate nerve growth cone turning responses induced by many guidance cues, but the causal relationship between these signaling pathways has been unclear. We here report that, for growth cone turning induced by a gradient of myelin-associated glycoprotein (MAG), cAMP acts by modulating MAG-induced Ca2+ signaling. Growth cone repulsion induced by MAG...