Iterated snap rounding with bounded drift

Snap Rounding and its variant, Iterated Snap Rounding, are methods for converting arbitrary-precision arrangements of segments into a fixed-precision representation (we call them SR and ISR for short). Both methods approximate each original segment by a polygonal chain, and both may lead, for certain inputs, to rounded arrangements with undesirable properties: in SR the distance between a vertex and a non-incident edge of the rounded arrangement can be extremely small, inducing potential degeneracies. In ISR, a vertex and a non-incident edge are well separated, but the approximating chain may drift far away from the original segment it approximates. We propose a new variant, Iterated Snap Rounding with Bounded Drift, which overcomes these two shortcomings of the earlier methods. The new solution augments ISR with simple and efficient procedures that guarantee the quality of the geometric approximation of the original segments, while still maintaining the property that a vertex and a non-incident edge in the rounded arrangement are well separated. We investigate the properties of the new method and compare it with the earlier variants. We have implemented the new scheme on top of CGAL, the Computational Geometry Algorithms Library, and report on experimental results.     

The properties and geodesics related to the NUT--Taub-like spacetime

Some properties related to the NUT--Taub-like spacetime, such as the surface of infinite red-shift, horizon, singularity and the area of the NUT--Taub-like black hole are discussed. Furthermore, the geodesics in the NUT--Taub-like spacetime are obtained in some special cases. Specifically, the circular orbits for a massive particle are derived, which can reduce to the cases of the Schwarzschild spacetime and the NUT--Taub spacetime when m^*=0 and m^*\ll M, respectively.     

A Blinking Mesoporous TiO2−x Composed of Nanosized Anatase with Unusually Long-Lived Trapped Charge Carriers

A mesoporous TiO_2−x material comprised of small, crystalline, vacancy-rich anatase nanoparticles (NPs) shows unique optical, thermal, and electronic properties. It is synthesized using polymer-derived mesoporous carbon (PDMC) as a template. The PDMC pores serve as physical barriers during the condensation and pyrolysis of a titania precursor, preventing the titania NPs from growing beyond 10 nm in size. Unlike most titania nanomaterials, during pyrolysis the NPs undergo no transition from the anatase to rutile phase and they become catalytically active reduced TiO_2−x. When exposed to a slow electron beam, the NPs exhibit a charge/discharge behavior, lighting up and fading away for an average period of 15 s for an extended period of time. The NPs also show a 50 nm red-shift in their UV/Vis absorption and long-lived charge carriers (electrons and holes) at room temperature in the dark, even long after UV irradiation. The NPs as photocatalysts show a good activity for CO₂ reduction.     

Electrochemical and mechanical stability of ion-exchange membranes in alkaline solution

This paper focuses on the transport and mechanical properties of ion-exchange membranes (IEMs) in an aqueous NaOH solution. Heterogeneous IEMs based on styrene–divinylbenzene and polyethylene reinforced with polyester (PES) or polyamide (PAD) fabric were studied. The IEMs were exposed to a 5% NaOH solution for 30 and 90 days and the changes in electrochemical resistance, transport number and permselectivity were evaluated. Moreover, the structure of the IEMs was observed after exposure and their mechanical properties were evaluated. The results show that NaOH solution has the most damaging effect, especially to PES cloth and the membrane as whole, mainly due to dimensional changes. Furthermore, changes in electrochemical resistance were observed.     

Properties and structure of heterogeneous ion-exchange membranes after exposure to chemical agents

This work deals with resistance of ion-exchange membranes in selected chemical solutions. Specimens of heterogeneous membranes were analyzed after exposure to chemically aggressive agents such as nitric acid, sodium hydroxide, etc. The analyses were carried out after period up to 6 months. The chemical resistance was evaluated from the mechanical and electrochemical property changes’ point of view before and after exposure. The tested materials were not only the membranes themselves but also their individual components, i.e., ion-exchange resins from various manufacturers and polyester reinforcing fabrics. The results show that exposure to NaOH solution has the most damaging effect especially on reinforcing fabric and a membrane as whole due mainly to dimension changes. The same stands for electrochemical resistance of the membrane and permselectivity. Ion-exchange capacity remains almost the same after exposure.     

Eigenmode analysis of phased-coupled VCSEL arrays using spatial coherence measurements

We apply the modal coherence theory to evaluate the spatial mode structure of a 2×2 phase-coupled array of vertical cavity surface emitting lasers (VCSELs). The eigenmode structure is extracted for different pump currents by measuring the degree of spatial coherence of all VCSEL pairs in the array. The results reveal the impact of optical disorder and spatial hole burning on the modal discrimination. The approach is useful more generally for the evaluation of spatial mode content of other laser array.     

A Tree Version of Kőnig's Theorem

Kőnig's theorem states that the covering number and the matching number of a bipartite graph are equal. We prove a generalization, in which the point in one fixed side of the graph of each edge is replaced by a subtree of a given tree. The proof uses a recent extension of Hall's theorem to families of hypergraphs, by the first author and P. Haxell [2]. As an application we prove a special case (that of chordal graphs) of a conjecture of B. Reed. Received January 27, 2000/Revised November 2, 2000 RID=" " ID=" " The research of the first author was supported by grants from the Israel Science Foundation, the M. & M.L Bank Mathematics Research Fund and the fund for the promotion of research at the Technion.     

Explicit norm one elements for ring actions of finite abelian groups

It is known that the norm map N _G for the action of a finite groupG on a ringR is surjective if and only if for every elementary abelian subgroupU ofG the norm map N _U is surjective. Equivalently, there exists an elementx _G ∈R satisfying N _G (x _G )=1 if and only if for every elementary abelian subgroupU there exists an elementx _U ∈R such that N _U (x _U )=1. When the ringR is noncommutative, it is an open problem to find an explicit formula forx _G in terms of the elementsx _U . We solve this problem when the groupG is abelian. The main part of the proof, which was inspired by cohomological considerations, deals with the case whenG is a cyclicp-group. Supported by TMR-Grant ERB FMRX-CT97-0100 of the European Union.     

Decay of the diocotron rotation and transport in a new low-density asymmetry-dominated regime

The decay of the diocotron rotation was studied in a new regime in which trap asymmetries dominate. Decay within a few diocotron periods was observed, sometimes orders of magnitude faster than predicted by the traditional "rotational pumping" theory. The decay does not conserve angular momentum, and is strongest for small, low-density columns. The new regime appears when "magnetron-like" rotation from the end confinement fields becomes dominant, and appears to be associated with errors in these fields. Transition to decay dominated by rotational pumping was observed for larger and denser columns. The asymmetry-dominated transport was also studied, and found to depend linearly on the line density (and not the density) over nearly 4 orders of magnitude.