The problem of counting lattice points on a hyperboloid of two sheets is Gauss’ circle problem in hyperbolic geometry. The problem of counting lattice points on a hyperboloid of one sheet does not have the same geometric interpretation, and in general, the solution(s) to Gauss’ circle problem gives a lower bound, but not an upper bound. In this paper, we describe an exception. Given an ample he...

Now imagine the elliptical cross section replaced by any curve lying on the surface of a right circular cylinder. What happens to this curve when the cylinder is unwrapped? Consider also the inverse problem, which you can experiment with by yourself: Start with a plane curve (line, circle, parabola, sine curve, etc.) drawn with a felt pen on a rectangular sheet of transparent plastic, and roll ...

The ray Inspection technology is applied for the characteristics of the tube to tube sheet welded joints, and a linear diode arrays is used as the receiving device. The system drives the digital stepper motor control card by using VC++, and the output is subdivided to drive the rotating devices to accurately rotate a week. The linear diode arrays is fixed on the rotating devices so it can accom...

the hermeneutic circle articulated by different hermeneuticans in various versions is one of the basic problems in modern hermeneutics. romanic hermeneutics introduced the circle as a methodological principle, but in philosophical hermeneutics the circle has ontological dimensions and regards as a process of understanding. heidegger believes that hermeneutic circle reflects dasein’s existential...

The single molecule detection associated with DNA sequencing has motivated intensive efforts to identify single DNA bases. However, little research has been reported utilizing single-layer hexagonal boron nitride (hBN) for DNA sequencing. Here we employ molecular dynamics simulations to explore pathways for single-strand DNA (ssDNA) sequencing by nanopore on the hBN sheet. We first investigate ...

oung people who are involved in sports report higher levels of voting, volunteering and engagement in their community than those who do not participate, according to a new CIRCLE Fact Sheet. The Fact Sheet, “Participation in Sports and Civic Engagement” by Mark Hugo Lopez and Kimberlee Moore, offers a detailed look at the role sports play in the civic development of 18-25-year-olds. The data sh...

Folding a sheet of paper along a curve can lead to structures seen in decorative art and utilitarian packing boxes. Here we present a theory for the simplest such structure: an annular circular strip that is folded along a central circular curve to form a three-dimensional buckled structure driven by geometrical frustration. We quantify this shape in terms of the radius of the circle, the dihed...