Abstract. We consider unbounded spin systems on the one dimensional Lattice with interactions that go beyond the usual strict convexity and without uniform bound on the second derivative. We assume that the one dimensional without interactions (boundary-free) measure satisfies the Log-sobolev inequality and we determine conditions under which the Log-Sobolev Inequality can be extended to the in...

We investigate two greedy strategies for finding an approximation to the minimum of a convex function E defined on a Hilbert space H. We prove convergence rates for these algorithms under suitable conditions on the objective function E. These conditions involve the behavior of the modulus of smoothness and the modulus of uniform convexity of E.

— Goodman [8] showed that uniform subdivision of triangular Bézier nets preserves convexity. Hère, a very short proofofthis f act is given which applies even to box spline surfaces and degree élévation instead of subdivision. Secondiy, it is shown that every Bézier net of a quadratic convex Bézier triangle can be subdivided such that the net becomes convex.

A set K of nodes of a graph G is geodesically convex (respectively, monophonically convex) if K contains every node on every shortest (respectively, chordless) path joining nodes in K. We investigate the classes of graphs which are characterized by certain local convexity conditions with respect to geodesic convexity, in particular, those graphs in which balls around nodes are convex, and those...

Based on a classic paper by Ginibre [Commun. Math. Phys. 8, 26 (1968)] it is shown that, whenever Bogoliubov's approximation, that is, the replacement of a(0) and a*(0) by complex numbers in the Hamiltonian, asymptotically yields the right pressure, it also implies the asymptotic equality of |a(0)|(2)/V and a*(0)a(0)/V in symmetry breaking fields, irrespective of the existence or absence of Bos...

We show that for the Hardy class of functions H 1 with domain the ball or polydisc in CN , a certain type of uniform convexity property (the uniform Kadec-Klee-Huff property) holds with respect to the topology of pointwise convergence on the interior; which coincides with both the topology of uniform convergence on compacta and the weak ∗ topology on bounded subsets of H 1. Also, we show that i...

We investigate testing of properties of 2-dimensional figures that consist of a black object on a white background. Given a parameter ∈ (0, 1/2), a tester for a specified property has to accept with probability at least 2/3 if the input figure satisfies the property and reject with probability at least 2/3 if it does not. In general, property testers can query the color of any point in the inpu...