In this paper, we consider the metric packing problem for the commodity graph of disjoint two triangles K3+K3, which is dual to the multiflow feasibility problem for the commodity graph K3 +K3. We prove a strengthening of Karzanov’s conjecture concerning quarter-integral packings by certain bipartite metrics.

Examples 1. A K3 surface of degree two is a double cover of P, ramified in a smooth sextic. K3 surfaces of degree four are smooth quartics in P. A K3 surface of degree six is a smooth complete intersection of a quadric and a cubic in P. And, finally, K3 surfaces of degree eight are smooth complete intersections of three quadrics in P. The Picard group of a K3 surface is isomorphic to Zn where n...

The vitamin K analog menadione (K3), capable of both redox cycling and arylating nucleophilic substrates by Michael addition, has been extensively studied as a model stress-inducing quinone in both cell culture and animal model systems. Exposure of keratin 8 (k-8) expressing human breast cancer cells (MCF7, T47D, SKBr3) to K3 (50-100 microM) induced rapid, sustained, and site-specific k-8 serin...

Kaposi's sarcoma (KS) is a highly disseminated angiogenic tumor of endothelial cells linked to infection by Kaposi's sarcoma-associated herpesvirus (KSHV). KSHV encodes more than two dozens of miRNAs but their roles in KSHV-induced tumor dissemination and metastasis remain unknown. Here, we found that ectopic expression of miR-K12-3 (miR-K3) promoted endothelial cell migration and invasion. Bio...

We study presentations of Cox rings of K3 surfaces of Picard number two. In particular we consider the Cox rings of classical examples of K3 surfaces, such as quartic surfaces containing a line and doubly elliptic K3 surfaces.

A K3 surface X is a compact complex surface with KX ∼ 0 and H (X,OX) = 0. An Enriques surface is a compact complex surface with H(Y,OY ) = H (Y,OY ) = 0 and 2KY ∼ 0. The universal covering of an Enriques surface is a K3 surface. Conversely every quotient of a K3 surface by a free involution is an Enriques surface. Here a free involution is an automorphism of order 2 without any fixed points. Th...

The purpose of this study was to evaluate the effect of heat treatment on the transformation temperatures of K3, K3XF and MTwo endodontic files. DSC was used to investigate the domains of transformation temperatures and how the transformation temperatures vary along the file. The files were analysed as received and subjected to heat treatment. X-ray diffraction analysis was also used to investi...

We have finalized the old (1979) results from [11] about enumeration of connected components of moduli or real polarized K3 surfaces. As an application, using recent results of [13] (see also math.AG/0312396), we completely classify real polarized K3 surfaces which are deformations of real hyper-elliptically polarized K3 surfaces. This could be important in some questions, because real hyper-el...

We consider complex K3 surfaces with a non-symplectic group acting trivially on the algebraic cycles. Vorontsov and Kondō classified those K3 surfaces with transcendental lattice of minimal rank. The purpose of this note is to study the Galois representations associated to these K3 surfaces. The rank of the transcendental lattices is even and varies from 2 to 20, excluding 8 and 14. We show tha...

We show that certain classes of K3 fibered Calabi-Yau manifolds derive from orbifolds of global products of K3 surfaces and particular types of curves. This observation explains why the gauge groups of the heterotic duals are determined by the structure of a single K3 surface and provides the dual heterotic picture of conifold transitions between K3 fibrations. Abstracting our construction from...