background: malocclusion, as a worldwide issue, can cause a lot of problems for patients. panoramic (pr) and lateral cephalometric (lcr) radiographs are both usually indicated for orthodontic treatments. the aim of this study was to analyze vertical and sagittal parameters of both jaws on prs and to compare them on lcrs. materials and methods: in this cross sectional study, 61 samples from all ...

let r be a right gf-closed ring with finite left and right gorenstein global dimension. we prove that if i is an ideal of r such that r/i is a semi-simple ring, then the gorensntein flat dimensnion of r/i as a right r-module and the gorensntein injective dimensnnion of r/i as a left r-module are identical. in particular, we show that for a simple module s over a commutative gorensntein ring r, ...

Given a minimal surface S equipped with a generically finite map to an Abelian variety and C ⊂ S a rational or an elliptic curve, we show that the canonical degree of C is bounded by four times the self-intersection of the canonical divisor of S. As a corollary, we obtain the finiteness of rational and elliptic curves with an optimal uniform bound on their canonical degrees on any surface of ge...

We study the null controllability of the parabolic equation associated with the Grushin-type operator A = ∂ x+|x|∂ y , (γ > 0), in the rectangle Ω = (−1, 1) × (0, 1), under an additive control supported in an open subset ω of Ω. We prove that the equation is null controllable in any positive time for γ < 1 and that there is no time for which it is null controllable for γ > 1. In the transition ...

We show that the Calabi-Yau dimension of the stable module category of a selfinjective algebra of finite representation type is determined by the action of the Nakayama and suspension functors on objects. Our arguments are based on recent results of C. Amiot, and hence apply more generally to triangulated categories having only finitely many indecomposable objects. Throughout, k is an algebraic...

Let Y be an algebraic manifold of dimension 3 with H(Y,ΩjY ) = 0 for all j ≥ 0, i > 0 and h0(Y,OY ) > 1. Let X be a smooth completion of Y such that the boundary X − Y is the support of an effective divisor D on X with simple normal crossings. We prove that the D-dimension of X cannot be 2, i.e., either any two nonconstant regular functions are algebraically dependent or there are three algebra...

OBJECTIVE To examine the prospective association of retinal vascular fractal dimension with diabetic retinopathy risk in young people with type 1 diabetes. RESEARCH DESIGN AND METHODS This was a hospital-based prospective study of 590 patients aged 12-20 years with type 1 diabetes free of retinopathy at baseline. All patients had seven-field retinal photographs taken of both eyes. Incident re...

Given a division ring K containing the field k in its center and two finite subsets A and B of K∗, we give some analogues of Plünnecke and Kneser Theorems for the dimension of the k-linear span of the Minkowski product AB in terms of the dimensions of the k-linear spans of A and B. We also explain how they imply the corresponding more classical theorems for abelian groups. These Plünnecke type ...

In this paper, the dynamical behavior of different optimal iterative schemes for solving nonlinear equations with increasing order, is studied. The tendency of the complexity of the Julia set is analyzed and referred to the fractal dimension. In fact, this fractal dimension can be shown to be a powerful tool to compare iterative schemes that estimate the solution of a nonlinear equation. Based ...