In this article we will show that there are infinitely many symmetric, integral 3 × 3 matrices, with zeros on the diagonal, whose eigenvalues are all integral. We will do this by proving that the rational points on a certain non-Kummer, singular K3 surface are dense. We will also compute the entire Néron-Severi group of this surface and find all low degree curves on it.

Background—Tissue factor pathway inhibitor (TFPI), a key regulator of tissue factor–induced coagulation, contains 3 tandem Kunitz-type inhibitory domains. Kunitz-1 binds and inhibits factor VIIa in the factor VIIa/tissue factor complex, and Kunitz-2 binds and inhibits factor Xa. The role of the Kunitz-3 domain of TFPI, however, has remained an enigma. Methods and Results—To determine the struct...

A (P3-free, K3-free)-colouring of a graph G = (V, E) is a partition of V = A ∪ B such that G[A] is P3-free and G[B] is K3-free. This problem is known to be NP-complete even when restricted to planar graphs and perfect graphs. In this paper, we provide a finite list of 17 forbidden induced subgraphs for cographs with a (P3-free, K3-free)colouring. This yields a linear time recognition algorithm.

By a K3-surface with nine cusps I mean a surface with nine isolated double points A 2 , but otherwise smooth, such that its minimal desingularisation is a K3-surface. It is shown, that such a surface admits a cyclic triple cover branched precisely over the cusps. This parallels the theorem of Nikulin, that a K3-surface with 16 nodes is a Kummer quotient of a complex torus.

Using the dynamics of self rational maps of elliptic K3 surfaces together with deformation theory, we prove that the union of rational curves is dense on a very general K3 surface and that the union of elliptic curves is dense in the 1st jet space of a very general K3 surface, both in the strong topology. The techniques developed here also lend themselves to applications to Abel-Jacobi images, ...

introduction: to compare the cleaning effectiveness of k3 and race niti rotary systems with k-flexo file instruments during the preparation of curved canals in extracted human teeth. materials and methods: a total of 50 root canals of mandibular and maxillary molars with curvatures ranging between 25º and 35 º were divided in three groups of 15 each and 5 as negative control groups. canals were...

Explicit Riemannian metrics with Euclidean signature and anti-self dual curvature that do not admit any Killing vectors are presented. The metric and the Riemann curvature scalars are homogenous functions of degree zero in a single real potential and its derivatives. The solution for the potential is a sum of exponential functions which suggests that for the choice of a suitable domain of coord...

It was the aim of this study to investigate the incidence of file breakage and distortion when the ProTaper, K3 Endo, and ProFile systems were used to instrument canals in the severely curved roots of extracted molars. Forty-five roots of extracted mandibular and maxillary molars with curvatures between 40 and 75 degrees were chosen for this study. The canals in group 1 were instrumented with t...