Given a weighted graph G = (V,E) and a real number t ≥ 1, a t-spanner of G is a spanning subgraph G′ with the property that for every edge xy in G, there exists a path between x and y in G′ whose weight is no more than t times the weight of the edge xy. We review results and present open problems on different variants of the problem of constructing plane geometric t-spanners.

Wireless LANs are commonplace installations in enterprise environments. Their ease of use and deployment, however, are accompanied by a difficulty in their management and security. Proposed solutions to these problems are based on centralization; in the control plane through centralized authentication and allocation of channels and power levels, and in the data plane through time slotted medium...

A new fundamental solution of deflection for plate buckling problems is first derived through the separation of in-plane stresses into an essential part and a disturbed part and by use of the resolution theorem of differential operator. A set of new boundary element formulas for the analysis of postbuckling problems of elastic plates are presented. On the basis of these formulas, in-plane and o...

This paper is a continuation of a series of papers, dealing with contact sub-Riemannian metrics onR3. We study the special case of contact metrics that correspond to isoperimetric problems on the plane. The purpose is to understand the nature of the corresponding optimal synthesis, at least locally. It is equivalent to studying the associated sub-Riemannian spheres of small radius. It appears t...

The problem of interactions between an inclusion and multiple cracks in a thermopiezoelectric solid is considered by boundary element method (BEM) in this paper. First of all, a BEM for the crack}inclusion problem is developed by way of potential variational principle, the concept of dislocation, and Green's function. In the BE model, the continuity condition of the interface between inclusion ...

A two-dimensional body moves through a rarefied medium; the collisions of the medium particles with the body are absolutely elastic. The body performs both translational and slow rotational motion. It is required to select the body, from a given class of bodies, such that the average force of resistance of the medium to its motion is maximal. There are presented numerical and analytical results...

A family of sets in the plane is said to have a 3-transversal if there exists a set of 3 points such that each member of the family contains at least one of them. A conjecture of Grünbaum’s says that a planar family of translates of a convex compact set has a 3-transversal provided that any two of its members intersect. Recently the conjecture has been proved affirmatively (see [1]). We provide...

Semideenite feasibility problems arise in many areas of operations research. The abstract form of these problems can be described as nding a point in a nonempty bounded convex body ? in the cone of symmetric positive semideenite matrices. Assume that ? is deened by an oracle, which for any given m m symmetric positive semideenite matrix ^ Y either connrms that ^ Y 2 ? or returns a cut, i.e., a ...

The total dissipation rate for magnetohydrodynamic (MHD) flows in plane geometry with both velocity and magnetic shear is studied. For some boundary conditions it is shown that the lower bound on the dissipation rate is achieved by the equivalent of Stokes flow for MHD. Using the ‘background method’ (Doering & Constantin, Phys. Rev. Lett. 69, 1648–1651 (1992)) upper bounds for the dissipation r...