The weighted $${\mathcal {T}}$$ -free 2-matching problem is the following problem: given an undirected graph G, a weight function on its edge set, and set of triangles in find maximum containing no triangle . When all this known as triangle-free problem, which long-standing open problem. A main contribution paper to give first polynomial-time algorithm for under assumption that edge-disjoint tr...

The geodesic and induced path transit functions are the two well-studied interval functions in graphs. Two important transit functions related to the geodesic and induced path functions are the triangle path transit functions which consist of all vertices on all u, v-shortest (induced) paths or all vertices adjacent to two adjacent vertices on all u, v-shortest (induced) paths, for any two vert...

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)...

We study the proximal point algorithm with Bregman type distance to minimize the problem , , . ) ( min S x to s x f ∈ where S is an open convex subset of a complete simply connected Riemannian manifold M of non positive sectional curvature and f is a convex function in this manifold. Introducing a strong assumption on the geodesic triangle on this manifold we obtain the convergence of the seque...

We present a new tensor-based morphometric framework that quantifies cortical shape variations using the local area element. The local area element is obtained from the Riemannian metric tensors, which are, in turn, obtained from the smooth functional parametrization of a triangle mesh. For the smooth parametrization, we have developed a novel weighted spherical harmonic (SPHARM) representation...

In this paper, we present a method to synthesize high-quality virtual viewpoint image targeting the detailed texture objects. About 30 images are taken from multiple uncalibrated cameras around the object, and the Visual Hull model is reconstructed with Shape from Silhouette method. To deform 3D surface model that is converted from Visual Hull Model using the information such as image texture a...

Methods of linear algebra are applied to triangle geometry. The vertex triangle of distinct circumcevian triangles is proved to be perspective to the reference triangle ABC, and similar results hold for three other classes of vertex triangles. Homogeneous coordinates of the perspectors define four mappings Mi on pairs of points (U, X). Many triangles homothetic to ABC are examined, and properti...

as one can check using induction on l. The usual absolute value function |x| satisfies these conditions with the ordinary triangle inequality (4). If N(x) = 0 when x = 0 and N(x) = 1 when x 6= 0, then N(x) satisfies these conditions with the ultrametric version of the triangle inequality. For each prime number p, the p-adic absolute value of a rational number x is denoted |x|p and defined by |x...