This paper is Part 2 of a four-part series of our research on the development of a general framework for error analysis in measurement-based geographic information systems (MBGIS). In this paper, we discuss the problem of point-in-polygon analysis under randomness, i.e., with random measurement error (ME). It is well known that overlay is one of the most important operations in GIS, and point-i...

We present a unified approach for consistent remeshing of arbitrary non-manifold triangle meshes with additional user-defined feature lines, which together form a feature skeleton. Our method is based on local operations only and produces meshes of high regularity and triangle quality while preserving the geometry as well as topology of the feature skeleton and the input mesh. ACM Computing Cla...

Stature of the triangle): On the wisdom of the triangle and geometry and some rules on qualities and algebra. Jerusalem Such a really remarkable discovery. I wanted your opinion on it. You know the formula m over naught equals infinity, m being any positive number? [m/0 = ∞]. Well, why not reduce the equation to a simpler form by multiplying both sides by naught? In which case you have m equals...

A generalized triangle group is a group that can be presented in the form G = x, y | x p = y q = w(x, y) r = 1 where p, q, r ≥ 2 and w(x, y) is a cyclically reduced word of length at least 2 in the free product Z p * Z q = x, y | x p = y q = 1. Rosenberger has conjectured that every generalized triangle group G satisfies the Tits alternative. It is known that the conjecture holds except possibl...

In this paper we calculate the Ehrhart’s polynomial associated with a 2-dimensional regular polytope (i.e. equilateral triangles) in Z. The polynomial takes a relatively simple form in terms of the coordinates of the vertices of the triangle. We give some equivalent formula in terms of a parametrization of these objects which allows one to construct equilateral triangles with given properties. ...

A Kanizsa triangle is usually generated by placing three circular tokens, with deleted wedges, at the apexes of an equilateral triangle. If the token angles do not each subtend 60 degrees, a Kanizsa triangle may still be evident, but with illusory contours that appear to be curvilinear. We investigated whether this curved-contour distortion in shape can be nulled by radial background image moti...

The title compound, [Fe(3)(C(8)H(8)N(2)O)S(2)(CO)(8)], was prepared by the direct reaction of Fe(3)(CO)(12) and 5-meth-oxy-1H-benzoimidazole-2-thiol in tetra-hydro-furan. Desulfurization took place readily to form a sulfide carbonyl cluster. The mol-ecule contains a triangle consisting of three Fe atoms capped by two S atoms above and below. There are two Fe-Fe bonds [2.6322 (5) and 2.5582 (5) ...

Lumbar hernia is a rare form of abdominal hernia, which has been recognized later along the early development of the modern surgery. it has been, on many occasions, the object of heavy debate regarding its anatomical background and as well its etiology. The authors reports the historical aspects of this rare pathology, focusing on the earliest descriptions of hernia arising in lumbar regions, o...

Validity of the triangle inequality and minimality, both axioms for twowaydissimilarities, ensures that a two-waydissimilarity is nonnegative and symmetric. Three-way generalizations of the triangle inequality andminimality from the literature are reviewed and it is investigated what forms of symmetry and nonnegativity are implied by the three-way axioms. A special form of three-way symmetry th...

Let G and H be connected graphs and let G ∗ H be the strong product of G by H. We show that every retract R of G ∗ H is of the form R = G′ ∗ H ′, where G′ is a subgraph of G and H ′ one of H. For triangle–free graphs G and H both G′ and H ′ are retracts of G and H, respectively. Furthermore, a product of finitely many finite, triangle–free graphs is retract–rigid if and only if all factors are ...