Let F ⊆ R denote the field of numbers which are constructible by means of ruler and compass. We prove that: (1) if x, y ∈ R (n > 1) and |x − y| is an algebraic number then there exists a finite set Sxy ⊆ R containing x and y such that each map from Sxy to R n preserving all unit distances preserves the distance between x and y; if x, y ∈ F then we can choose Sxy ⊆ F, (2) only algebraic distance...

Proof. If the edge (r, s) from the root to the sink is included in the spanning tree, then each of the principal branches of Tn may be assigned an oriented spanning tree independently, so there are t n−1 such spanning trees. On the other hand, if (r, s) is not included in the spanning tree, there is a directed path r → x1 → . . . → xn−1 → s in the spanning tree from the root to the sink. In thi...

Our goal is to give our robot the perceptual abilities it needs to actively resolve ambiguity in its environment, when the passive vision algorithms it uses fail. A key example of this is figure/ground separation [2]. By equipping our robot with a camera with a narrow, controllable depth of field, the robot can bring a questionable edge into focus and blur out distracting background. By giving ...

The classical Tower of Hanoi puzzle, invented by the French mathematician Édourd Lucas in 1883, consists of 3 wooden pegs and n disks with pairwise different diameters. The n disks are initially stacked on a single peg in order of decreasing size, from the largest at the bottom to the smallest at the top. (See Figure 1.) The goal is to move the tower of disks to another peg, moving one topmost ...

The only connected minimal surfaces foliated by circles and lines are domains on one of the following surfaces: the helicoid, the catenoid, the plane, and the examples of Riemann ([Ri] p329-33, [En] p403-6, [Ni] p85-6). All these surfaces are complete and embedded. Topologically they are planar domains: the helicoid is simply-connected, the catenoid is an annulus (conformally a twice-punctured ...

Video-oculography (VOG) is a non-intrusive method used to estimate gaze. The method is based on a remote camera(s) that provides images of the eyes that are processed by a computer to estimate the point at which the subject is gazing in the area of interest. Normally, infrared (IR) light-emitting diodes (LEDs) are used in the system, as this light is not visible to humans. The objective of the ...

1, Differential equations in one space dimension. The simplest hyperbolic differential equation is given by (1.1) du/dt = cdu/dx, where c is a constant, Its general solution is u(x, t) — F(x + ci), i.e., it is constant along the "characteristic lines" x + ct = const (see Figure 1). Therefore, if we u(l,t) = g(t) u(0,t)*g(t want to determine the solution of (1.1) in the region 0 ^ x ^ 1, t ja 0,...

Beyond the factory floor, there is an even larger opportunity to improve performance. The true world-class competitors have discovered this opportunity and have extended the principles that worked on the factory floor to the upstream processes that feed production, "white collar" factories. They have reorganized their white collar factories, moving away from junctional organization toward proce...

Let B be a 3-dimensional handlebody of genus g. Let M be the group of the isotopy classes of orientation preserving homeomorphisms of B. We construct a 2-dimensional simplicial complex X, connected and simply-connected, on which M acts by simplicial transformations and has only a finite number of orbits. From this action we derive an explicit finite presentation ofM. We consider a 3-dimensional...

In this paper, we use the term academic text to refer to any free text composed in an academic setting, covering the whole spectrum from first year students’ reviews of available scientific texts up to a scientist’s struggling, but still fragile text concerning his or her new discoveries. These academic texts can be processed by various information technologies. We can now outline the landscape...