‎For a set of non-negative integers~$L$‎, ‎the $L$-intersection number of a graph is the smallest number~$l$ for which there is an assignment of subsets $A_v subseteq {1,dots‎, ‎l}$ to vertices $v$‎, ‎such that every two vertices $u,v$ are adjacent if and only if $|A_u cap A_v|in L$‎. ‎The bipartite $L$-intersection number is defined similarly when the conditions are considered only for the ver...

By pure analogy with a usual three-dimensional origami, we can fold a regular octahedral material along flat faces in 4-space. The octahedron comprises four congruent tetrahedra. We will show a procedure to fold a tetrahedron along bisectors of the dihedral angles. This procedure demonstrates that each two of four surfaces of the given tetrahedron coincide with each other and that the point of ...

Nontrivial periodic solutions of Lagrange Equations are investigated. Sublinear and superlinear nonlinearity are included. Convexity assumptions are significiently relaxed. The method used is the duality developed by the authors.

The internal mechanism used for a dependence test constrains its accuracy and determines its speed. The internal mechanism used for our Access Region Test (ART) is fundamentally different from that used in any other dependence test, and therefore its constraints and characteristics are likewise different. In this paper, we briefly describe our novel descriptor for representing memory accesses, ...

We consider the problem of identifying one of a set of polygonal models in the plane using point probes and nger probes. In particular, we give strategies for using a minimum number of nger probes to determine a nite number of possible locations of an unknown interior point p in one of the models. A nger probe takes as input an interior point p of a polygon P and a direction , and it outputs th...

Two-lattice polyhedra are a special class of lattice polyhedra that include network 4ow polyhedra, fractional matching polyhedra, matroid intersection polyhedra, the intersection of two polymatroids, etc. In this paper we show that the maximum sum of components of a vector in a 2-lattice polyhedron is equal to the minimum capacity of a cover for the polyhedron. For special classes of 2-lattice ...

The paper presents a new robust method for finding points of intersection of line segments in the plane. In this method the subdivision of the plane based on the Delaunay triangulation plays the main role. First, the Delaunay triangulation spanning the end points of line segments is constructed. Next, for line segments that are not realized by Delaunay edges, midpoints are inserted recursively ...

In CAD/CAM modeling, objects are represented using the Boundary Representation (ANSI Brep) model. Detection of possible intersection between objects can be based on the objects’ boundaries (i.e., triangulated surfaces), and computed using triangle-triangle intersection. Usually only a cross intersection algorithm is needed; however, it is beneficial to have a single robust and fast intersection...