We compute the number of rhombus tilings of a hexagon with sides n, n, N , n, n, N , where two triangles on the symmetry axis touching in one vertex are removed. The case of the common vertex being the center of the hexagon solves a problem posed by Propp.

In this note, we study a chain of circles whose pairwise intersection points, taken in certain order, also lie on two circles. We give short elementary proof the following fact. There exists conic which touches each line connecting centres adjacent such chain. case six chain, means that these form Brianchon hexagon. consider all cases possible radically distinct positions original when touching...

A study of the implant to abutment connection is of paramount importance as it is the primary determinant of the strength and stability of the implant supported restoration, which in turn determines the restoration’s prosthetic stability. Traditionally, the Branemark's external hexagon has been widely used but its significant complications like abutment screw loosening, rotational misfit at imp...

In this note, we prove the uniqueness of the one-point extension S of a generalized hexagon of order 2 and prove the non-existence of such an extension S of any other finite generalized hexagon of classical order, different from the one of order 2, and of the known finite generalized octagons provided the following property holds: for any three points x, y and z of S, the graph theoretic distan...

Database queries expressing user preferences have been found to be crucial for personalized applications. Such preference queries, in particular Pareto preference queries, pose new optimization challenges for efficient evaluation. So far however, all known generic Pareto evaluation algorithms suffer from non-linear worst case runtimes. Here we present the first generic algorithm, called Hexagon...

1 Aristotelian versus Duality Square (1) Piaget (1949) inversion réciprocation corrélation Gottschalk (1953) complement contradual dual Löbner (1990) negation (NEG) subnegation (SNEG) dual (DUAL) Westerstahl (2010) outer negation inner negation dual Quantifier (domain/restrictor, predicate/nuclear scope) 2-place second-order predicates All (children , be asleep) <,,t> (3) All children a...

Two leapfrog isomers of a B(112) boron fullerene are constructed from small C(28) fullerenes (T(d) and D(2) symmetries) by the leapfrog transformation combined with omnicapping of the new hexagons. Their electronic structure is analyzed using the density functional theory at the B3LYP/SVP and BHLYP/SVP levels. Both isomers are characterized as minima on the potential energy hypersurface with a ...

The purpose of the paper is to develop a new method for obtaining explicit formulas for the error of approximation of bivariate functions by sums of univariate functions. It should be remarked that formulas of this type have been known only for functions defined on a rectangle with sides parallel to coordinate axes. Our method, based on a maximization process over closed bolts, allows the consi...