Projective Hjelmslev planes (PH-planes) are a generalization of projective planes in which each point-pair is joined by at least one line and, dually, each line-pair has a nontrivial intersection. Multiply joined points (and multiply intersecting lines) are called neighbor points (and neighbor lines). By hypothesis, the neighbor relations of a PH-plane A are equivalence relations which induce a...

A Halin graph is a graph H = T ∪ C , where T is a tree with no vertex of degree two, and C is a cycle connecting the end-vertices of T in the cyclic order determined by a plane embedding of T. In this paper, we define classes of generalized Halin graphs, called k-Halin graphs, and investigate their Hamiltonian properties.

This paper shows that for any plane geometric graph G with n vertices there exists a triangulation T that conforms to G i e each edge of G is the union of some edges of T where T has O n vertices with each angle of its triangles measuring no more than Additionally T can be computed in O n log n time

Consider an abstract evolution problem in a Hilbert space H u̇ = A(t)u+G(t, u) + f(t), u(0) = u0, (1) where A(t) is a linear, closed, densely defined operator in H with domain independent of t ≥ 0, G(t, u) is a nonlinear operator such that ||G(t, u)|| ≤ a(t)||u||, p = const > 1, ||f(t)|| ≤ b(t). We allow the spectrum of A(t) to be in the right half-plane Re(λ) < λ0(t), λ0(t) > 0, but assume that...

a fundamental assumption in prosthetic dentistry is that the axis-orbital plane will usually be parallel to the horizontal reference plane. most articulator systems have incorporated this concept into their designs and use orbitale as the anterior reference point for transferring the vertical position of the maxilla to the articulator. clinical observations of cantonese patients suggest that in...

We report on the magnetic and electrical properties of a ${({\mathrm{Mn}}_{3}\mathrm{Sn})}_{2}$ triangular network kagome structured high quality Ho substituted ${\mathrm{ErMn}}_{6}{\mathrm{Sn}}_{6}$ single-crystal sample by magnetotransport measurements. ${\mathrm{Er}}_{0.5}{\mathrm{Ho}}_{0.5}{\mathrm{Mn}}_{6}{\mathrm{Sn}}_{6}$ orders antiferromagnetically at N\'eel temperature ${T}_{\mathrm{N...

Θk-graphs are geometric graphs that appear in the context of graph navigation. The shortest-path metric of these graphs is known to approximate the Euclidean complete graph up to a factor depending on the cone number k and the dimension of the space. TD-Delaunay graphs, a.k.a. triangular-distance Delaunay triangulations introduced by Chew, have been shown to be plane 2-spanners of the 2D Euclid...

In many cases, a real-valued signal x(t) may be associated with a complex-valued signal a(t)e ~°(t) , the analytic signal associated with x'(t) with the characteristic properties x(t) = a(t) cos O(t) and "H(a(.)cos0(-))(t) = a(t)sin0(t). Using such obtained amplitude-frequency modulation the instantaneous frequency of x(t) at the time to may be defined to be 0'(t0), provided O'(to) >_ O. The pr...

We report magnetization (\ensuremath{\chi}, $M$), magnetic specific heat (${C}_{\mathrm{M}}$), and neutron powder diffraction results on a quasi-two-dimensional (2D) $S=2$ square lattice antiferromagnet ${\mathrm{Ba}}_{2}{\mathrm{FeSi}}_{2}{\mathrm{O}}_{7}$ consisting of ${\mathrm{FeO}}_{4}$ tetrahedrons with highly compressive tetragonal distortion (27%). Despite the quasi-2D structure, both \...