Multiple sclerosis epidemiological trends in Italy highlight the environmental risk factors

Italy is definitely a high-risk country for multiple sclerosis (MS). Over the last 50 years, several epidemiological studies, including longitudinal surveys, have disclosed that MS incidence and prevalence in Italy mainland and Islands (Sardinia and Sicily) have progressively increased, picturing a semi-parabolic curve. Based on the comprehensive scrutiny of 58 papers, we conclude that the latitude risk gradient does not fit to the Italian map of MS. The genetic heterogeneity of the Italian ethnicities, that likely forms the basis of MS predisposition, does not account for the dramatic increase of MS incidence and prevalence observed in Italy over the last half century that, rather, seems better explained by the effect of environmental factors.

An Efficient Method for Forming Parabolic Curves and Surfaces

A new method for the formation of parabolic curves and surfaces is proposed. It does not impose restrictions on the relative positions in space of the sequence of reference points relative to each other, meaning it compares favorably with other prototypes. The disadvantages of the Overhauser and Brever–Anderson methods are noted. The method allows one to effectively form and edit curves and surfaces when changing the coordinates of any given point. This positive effect is achieved due to the appropriate choice of local coordinate systems for the mathematical description of each parabola, which together define a composite interpolation curve or surface. The paper provides a detailed mathematical description of the method of parabolic interpolation of curves and surfaces based on the use of matrix calculations. Analytical descriptions of a composite parabolic curve and its first and second derivatives are given, and continuity analysis of these factors is carried out. For the matrix of points of the defining polyhedron, expressions are presented that describe the corresponding surfaces, as well as the unit normal at any point. The comparative table of the required number of pseudo-codes for calculating the coordinates of one point for constructing a parabolic curve for the three methods is given.

Characteristic directions of two-dimensional biholomorphisms

We prove that for each characteristic direction $[v]$ of a tangent to the identity diffeomorphism of order $k+1$ in $(\mathbb{C}^{2},0)$ there exist either an analytic curve of fixed points tangent to $[v]$ or $k$ parabolic manifolds where all the orbits are tangent to $[v]$, and that at least one of these parabolic manifolds is or contains a parabolic curve.

Features of curing polyester binder due to the different duration of exposure to ultraviolet radiation

Samples of polyester binder RO-4761 were irradiated using an ultraviolet device. The investigations established that the microhardness of the polymer along its cross section, from the surface to core of the sample, varies according to a parabolic law. With increasing time of UV exposure the sample, its microhardness increases. When the binder is fully cured, the parabolic curve transforms into a straight line. A new term is proposed that characterizes the change in microhardness in the volume of the cured polymer: “Volume anisotropy coefficient”.

Quadratic points of surfaces in projective 3-space

Quadratic points of a surface in the projective 3-space are the points which can be exceptionally well approximated by a quadric. They are also singularities of a 3-web in the elliptic part and of a line field in the hyperbolic part of the surface. We show that generically the index of the 3-web at a quadratic point is ±1/3, while the index of the line field is ±1. Moreover, for an elliptic quadratic point whose cubic form is semi-homogeneous, we can use Loewner’s conjecture to show that the index is at most 1. From the above local results, we can conclude some global results: A generic compact elliptic surface has at least 6 quadratic points, a compact elliptic surface with semi-homogeneous cubic forms has at least 2 quadratic points and the number of quadratic points in a hyperbolic disc is odd. By studying the behavior of the cubic form in a neighborhood of the parabolic curve, we also obtain a relation between the indices of the quadratic points of a generic surface with non-empty elliptic and hyperbolic regions.

Parabolic curves of diffeomorphisms asymptotic to formal invariant curves

We prove that ifFis a tangent to the identity diffeomorphism at0\in\mathbb{C}^{2}and Γ is a formal invariant curve ofFwhich is not contained in the set of fixed points then there exists a parabolic curve (attracting or repelling) ofFasymptotic to Γ.

Estimated Placental Volume and Gestational Age

Objective The objective of this study was to validate estimated placental volume (EPV) across a range of gestational ages (GAs). Study Design Three hundred sixty-six patients from 2009 to 2011 received ultrasound scans between 11 + 0 and 38 + 6 weeks GA to assess EPV. An EPV versus GA best fit curve was generated and compared with published normative curves of EPV versus GA in a different population. A subanalysis was performed to explore the relationship between EPV and birth weight (BW). Results Analysis of EPV versus GA revealed a parabolic curve with the following best fit equation: EPV = (0.372 GA − 0.00364 GA2)3. EPV was weakly correlated with BW, and patients with an EPV in the bottom 50th percentile had 2.42 times the odds of having a newborn with a BW in the bottom 50th percentile (95% confidence interval: 1.27–4.68). Microscopic evaluation of two placentas corresponding to the smallest EPV outliers revealed significant placental pathology. Conclusion Placental volume increases throughout gestation and follows a predictable parabolic curve, in agreement with the existing literature. Further validation is required, but EPV may have the potential for clinical utility as a screening tool in a variety of settings.

Generation of a double-crowned involute helical gear with twist-free tooth flanks by a CNC hobbing machine with three synchronous axes

In the conventional hobbing process, a double-crowned involute helical gear is generated by the hob cutter with parabolic-curve tooth profiles for the cross-profile crowning and varied the center distance between the hob and work gear for the longitudinal crowning. Therefore, to cut a double-crowned helical gear not only requires at least four synchronous axes and hob cutter regrinding (which increases production costs) but also induces twisted tooth flanks on the generated work gear. In this paper, I propose a hobbing method by applying a modified work gear rotation angle that enables double-crowning of involute helical gear's tooth flanks using a standard hob cutter and a computer numerical control (CNC) hobbing machine with only three synchronous axes. The proposed method has also verified by using two computer simulation examples to compare the meshing-conditions, contact ellipses, and transmission errors of the double-crowned gear pairs with that produced by applying the conventional hobbing method. Computer simulation results reveal the advantages of the proposed novel hobbing method.