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We consider a gradient interface model on the lattice with interaction potential which is a non-convex perturbation of a convex potential. Using a technique which decouples the neighboring vertices sites into even and odd vertices, we show for a class of non-convex potentials: the uniqueness of ergodic component for ∇φ-Gibbs measures, the decay of covariances, the scaling limit and the strict c...

the aim of this paper is to prove some inequalities for p-valent meromorphic functions in thepunctured unit disk δ* and find important corollaries.

In this paper, we define the notions of fuzzy congruence relations and fuzzy convex subalgebras on a commutative residuated lattice and we obtain some related results. In particular, we will show that there exists a one to one correspondence between the set of all fuzzy congruence relations and the set of all fuzzy convex subalgebras on a commutative residuated lattice. Then we study fuzzy...

In this paper, we propose a new method for fuzzy numbers. In this method, we assume that Ai= (ai1, ai2, ai3, ai4) is to be a fuzzy number. So, the convex combination of ai1 and ai2 and also the convex combination of ai3 and ai4 are obtained separately. Then, Mic and Mis that are to be the convex combinations and the standard deviation respectively we acquire them from these components. Finally,...

Let K ⊂ R be a smooth convex set and let Pλ be a Poisson point process on R of intensity λ. The convex hull of Pλ ∩ K is a random convex polytope Kλ. As λ → ∞, we show that the variance of the number of k-dimensional faces of Kλ, when properly scaled, converges to a scalar multiple of the affine surface area of K. Similar asymptotics hold for the variance of the number of k-dimensional faces fo...

A progressive lens produces a smooth increase in positive foca_or addition_ power from distance to near without any lines of demarcation. In order to provide this gradual change in power, the curvature of a convex progressive lens surface must become increasingly steeper toward the bottom of the lens (Figure 1). The addition power of a convex progressive lens surface is simply the result of the...