The Lewy extension theorem asserts the holomorphic extendability of CR functions defined in a neighborhood of a point on a hypersurface in C. The edge-of-the-wedge theorem asserts the extendability of holomorphic functions defined in wedges in C with edge a maximally real submanifold. In this article we prove under suitable hypotheses the holomorphic extendability to an open set in C of CR func...

Motivated from drawing route sketches, we consider the following path schematization problem. We are given a simple embedded polygonal path P = (v1, . . . , vn) and a set C of admissible edge orientations including the coordinate axes. The problem is to redraw P schematically such that all edges are drawn as line segments that are parallel to one of the specified orientations. We also require t...

In this paper, we consider the problem of computing the minimum area triangle that circumscribes a given n-sided convex polygon touching edge-to-edge. In other words, we compute the minimum area triangle that is the intersection of 3 half-planes out of n half-planes defined by a given convex polygon. Previously, O(n logn) time algorithms were known which are based on the technique for computing...

The principal technical problem of 3D building semi-automatic acquisition from remote-sensing images was discussed by using wavelet analysis, combining digital photogrammetry and computer vision. A set of anti-symmetrical wavelet (ASWlet) functions and corresponding filters were deduced, e.g., multi-scales, symmetry, approximation compact support, good local regularity and smoothness. And it is...

spherical polyhedron S = (V, F ;E): For a 2-connected planar graph GS = (V,ES), drawn without self-intersection on a sphere (or in the plane), we record the vertices as V and the regions as faces F , and rewrite the directed edges E as ordered 4-tuples e = 〈h, i; j, k〉, where the edge from vertex h to vertex i has face j on the right and face k on the left. (The reversed edge −e = 〈i, h; k, j〉 ...

The problem of computing a minimum cost subgraph D′ = (V,A′) of a directed graph D = (V,A) so that D′ contains k edge-disjoint paths from a specified root r ∈ V to every other node in V is known to be nicely solvable since it can be formulated as a matroid intersection problem. A corresponding problem when openly disjoint paths are requested rather than edge-disjoint was solved in [12] with the...

A band is defined as the intersection of the surface of a convex polyhedron with the space between two parallel planes, as long as this space does not contain any vertices of the polyhedron. An unfolding of a given band is obtained by cutting along exactly one edge and placing all faces of the band into the plane, without causing intersections. We prove that for a specific type of band there ex...

The clique graph K(G) of a graph G is the intersection graph of all its (maximal) cliques. We explore the effect of operations like edge contraction, edge removal and others on the dynamical behaviour of a graph under the iteration of the clique operator K. As a consequence of this study, we can now prove the clique divergence of graphs for which no previously known technique would yield the re...

one of the locations of renal artery atherosclerosis is at the orifice of the renal artery, therefore thestructure of this orifice was assessed in 6 normal, adult male dogs by light microscopy (lm) andtransmission electron microscopy (tem). for the lm study, processed tissues were embedded in paraffinand sectioned serially into 6-μm thickness. sections were stained with orcein. for the tem stud...