The hyperbola $xy = N$

On the mapping xy→(xy)n in an associative ring

We consider the following condition (*) on an associative ring R : (*). There exists a function f from R into R such that f is a group homomorphism of (R,+), f is injective on R2, and f(xy) = (xy)n(x,y) for some positive integer n(x,y) > 1. Commutativity and structure are established for Artinian rings R satisfying (*), and a counterexample is given for nonArtinian rings. The results generalize...

On a subclass of n-convex functions associated with some hyperbola

In this paper we define a subclass of n-convex functions associated with some hyperbola and we obtain some properties regarding this class.

The critical hyperbola for a Hamiltonian elliptic system with weights

In this paper we look for existence results for nontrivial solutions to the system, ⎧ ⎪⎪⎨ ⎪⎪⎩ − u = v p |x |α in , − v = u q |x |β in , with Dirichlet boundary conditions, u = v = 0 on ∂ and α, β < N . We find the existence of a critical hyperbola in the (p, q) plane (depending on α, β and N ) below which there exists nontrivial solutions. For the proof we use a variational argument (a linking ...

Xy and Xy-ising Models

We consider the 2D J 1 −J 2 classical XY model on a square lattice. In the frustrated phase corresponding to J 2 > J 1 /2, an Ising order parameter emerges by an " order due to disorder " effect. This leads to a discrete symmetry plus the O(2) global one. We formulate the problem in a Coulomb gas language and show by a renormalization group analysis that only two phases are still possible: a lo...

Hyperbola of external debt: A Lesson from the Asian Crisis