purpose: to report a case who had optic disc duplication, a rare congenital disorder characterized by two well-defined discs in one eye. case report: a 19 months-old child presented with unilateral epiphora in the right eye since birthday. the right eye was smaller than the left eye and mild ptosis was apparent. nasolacrimal duct probing was performed under general anesthesia. the examination r...

Edge nanoscrolls are shown to strongly influence transport properties of suspended graphene in the quantum Hall regime. The relatively long arclength of the scrolls in combination with their compact transverse size results in formation of many nonchiral transport channels in the scrolls. They short circuit the bulk current paths and inhibit the observation of the quantized two-terminal resistan...

Given a simple n-gon P in the plane, normalized to contain the unit disk, we define a map from P to the unit circle so that (1) the map extends to be 8-quasiconformal on the interior, (2) it contracts arclength on the boundary and (3) the images of all n vertices can be computed in time O(n). Thus we obtain a fast QC-approximation to the Riemann map with constant independent of the domain. Date...

Abstract In this paper we consider a spatial discretization scheme with an adaptive grid for the Nagumo PDE. particular, commonly used time dependent moving mesh method that aims to equidistribute arclength of solution under consideration. We assume discrete analogue equidistribution is strictly enforced, which allows us reduce effective dynamics scalar non-local problem infinite range interact...

In 1811, Legendre published an identity between integrals involving the constant k:= sin ⁡π12 that inspired Abel to create his brilliant theory of complex multiplication. Then k reappeared as eccentricity ellipse whose arclength Ramanujan computed explicitly in terms gamma functions with rational arguments. Finally, appeared a consequence three-body choreography along Bernoulli’s lemniscate. We...

Regions of high curvature of a material line as they evolve in a chaotic flow are considered. In such a region, the curvature as a function of arclength along the line is found to have a universal form with the peak curvature the only parameter involved. The alignment of the principal axes of the strain tensor with respect to the local tangent vector of the curve and the ratio of the two larges...

A simplified analytical form of the on-axis magnetic well and Mercier's criterion for interchange instabilities arbitrary three-dimensional field geometries is derived. For this purpose, a near-axis expansion based on direct coordinate approach used by expressing toroidal flux in terms powers radial distance to axis. first time, are then written as one-dimensional integral with respect axis arc...

Given a simple n-gon P in the plane, normalized to contain the unit disk, we define a map from P to the unit circle so that (1) the map extends to be 8-quasiconformal on the interior, (2) it contracts arclength on the boundary and (3) the images of all n vertices can be computed in time O(n). Thus we obtain a fast K-QC-approximation to the Riemann map with constant K independent of the domain. ...

Zeros of Kac polynomials spanned by monomials with i.i.d. random coefficients are asymptotically uniformly distributed near the unit circumference. We give estimates of the expected discrepancy between the zero counting measure and the normalized arclength on the unit circle. Similar results are established for polynomials with random coefficients spanned by different bases, e.g., by orthogonal...

In R2, we consider an analytic family of operators Hz , z ∈ C, whose convolution kernel is obtained by taking −z − 1 derivatives of arclength measure on the parabola (t, t2) in a homogeneous way, defined in such a way so that H−1 be the standard parabolic Hilbert transform. For a fixed z, we study the set of p for which Hz is bounded on Lp(R2) and for the critical z that captures the degree of ...