The most recent results from the B-factories on the time-dependent CP asymmetries measured in B -decays mediated by b → cc̄s quark-transitions are reviewed. The Standard Model interpretation of the results in terms of the parameter sin 2β leads to a four-fold ambiguity on the unitarity triangle β which can be reduced to a two-fold ambiguity by measuring the sign of the parameter cos 2β. The resu...

The goal of this paper is to give a conjectural census of complex hyperbolic sporadic triangle groups. We prove that only finitely many of these sporadic groups are lattices. We also give a conjectural list of all lattices among sporadic groups, and for each group in the list we give a conjectural group presentation, as well as a list of cusps and generators for their stabilisers. We describe s...

A latin bitrade (T , T⊗) is a pair of partial latin squares that define the difference between two arbitrary latin squares L ⊇ T and L⊗ ⊇ T⊗ of the same order. A 3-homogeneous bitrade (T , T⊗) has three entries in each row, three entries in each column, and each symbol appears three times in T . Cavenagh [2] showed that any 3-homogeneous bitrade may be partitioned into three transversals. In th...

We study the number of connected spanning subgraphs fd,b(n) on the generalized Sierpinski gasket SGd,b(n) at stage n with dimension d equal to two, three and four for b = 2, and layer b equal to three and four for d = 2. The upper and lower bounds for the asymptotic growth constant, defined as zSGd,b = limv→∞ ln fd,b(n)/v where v is the number of vertices, on SG2,b(n) with b = 2, 3, 4 are deriv...

In an Apollonian circle packing, the curvatures a, b, c, d of any four mutually tangent circles satisfy Descartes’ equation, 2(a + b + c + d) = (a+ b+ c+ d). For an equilateral triangle and a point P , if a, b, c, d denote the squares of the lengths of the sides of the triangle and the distances from P to the vertices of the triangle, then a, b, c, d, satisfy 3(a+ b+ c+d) = (a+ b+ c+d). Define ...

We present a new method for simulating volume conserving deformable bodies using an impulse-based approach. In order to simulate a deformable body a tetrahedral model is generated from an arbitrary triangle mesh. All resulting tetrahedrons are assigned to volume constraints which ensure the conservation of the total volume. For the simulation of such a constraint impulses are computed and appli...

We present a novel algorithm to compute multi-scale curvature fields on triangle meshes. Our algorithm is based on finding robust mean curvatures using the ball neighborhood, where the radius of a ball corresponds to the scale of the features. The essential problem is to find a good radius for each ball to obtain a reliable curvature estimation. We propose an algorithm that finds suitable radii...

In [3] have been constructed very high order residual distribution schemes for scalar problems. They were using triangle unstructured meshes. However, the construction was quite involved and was not very flexible. Here, following [1], we develop a systematic way of constructing very high order non oscillatory schemes for such meshes. Applications to scalar and systems problems are given.

We show that the natural action of the absolute Galois group on the ideals defining principal congruence subgroups of certain nonarithmetic Fuchsian triangle groups is compatible with its action on the algebraic curves that these congruence groups uniformize.

in this paper we revisit the classical approach of the didactic triangle designed for the classical learning situation (face to face) and adapt it to the situation of an adaptive learning system, we discuss also the different components involved in this didactic triangle and how they interact and influence the learning process in an adaptive learning system.