A complex hyperbolic triangle group is a group generated by three complex reflections fixing complex slices (complex geodesics) in complex hyperbolic space. Our purpose in this paper is to improve the result in [3] and to discuss discreteness of complex hyperbolic triangle groups of type (n, n,∞; k).

background: complete atrioventricular block (av block) is a serious complication of slow pathway ablation therapy in the treatment of atrioventricular nodal re-entrant tachycardia (avnrt).   the present study was aimed at determining whether the electroanatomical pace mapping of koch’s triangle could significantly improve the safety, efficiency, and efficacy of selective slow pathway ablation i...

Complex hyperbolic triangle groups are representations of a hyperbolic (p, q, r) reflection triangle group to the group of holomorphic isometries of complex hyperbolic space H C , where the generators fix complex lines. In this paper, we obtain all the discrete and faithful complex hyperbolic (3, 3, n) triangle groups. Our result solves a conjecture of Schwartz [16] in the case when p = q = 3.

We take a fresh look at voting theory, in particular at the notion of manipulation, by employing the geometry of the Saari triangle. This yields a geometric proof of the Gibbard/Satterthwaite theorem, and new insight into what it means to manipulate the vote. Next, we propose two possible strengthenings of the notion of manipulability (or weakenings of the notion of non-manipulability), and ana...

A generalized triangle group is a group that can be presented in the form G = 〈 x, y | x = y = w(x, y) = 1 〉 where p, q, r ≥ 2 and w(x, y) is an element of the free product 〈 x, y | x = y = 1 〉 involving both x and y. Rosenberger has conjectured that every generalized triangle group G satisfies the Tits alternative. It is known that the conjecture holds except possibly when the triple (p, q, r)...

(a) The medians intersect in a point interior to the triangle, called the centroid, which divides each of the medians in the ratio 2 : 1. (b) The medians form a new triangle, called the median triangle. (c) The area of the median triangle is 3/4 of the area of the given triangle in which the medians were constructed. (d) The median triangle of the median triangle is similar to the given triangl...

In this paper, the orders induced by the residual implications obtained from uninorms are investigated. A necessary and sufficient condition is presented so that the ordinal sum of fuzzy implications satisfies the law of importation with a t-norm $T$. Some relationships between the orders induced by an ordinal sum implication and its summands are determined. The algebraic structures obtained fr...

A new algorithm for mesh simplification with triangle constriction is presented in this paper. Constricting error defined by a combination of square volume error variation with constraint (SVEC), shape factor and normal constraint factor of triangle. Gauss curvature factor of each constricted triangle is used to distinguish strong feature triangle or nonstrong feature triangle. The triangle whi...