Computing presentations for subgroups of polycyclic groups and of context-free groups

Algorithms for solving uniform decision problems for algebraic structures crucially depend on the chosen finite presentations for the structures under consideration. Rewriting techniques have been used very successfully to solve uniform decision problems, when the presentations considered involve finite, noetherian, and ()-confluent rewriting systems. Whenever the class of algebraic structures considered is closed under the operation of taking finitely generated substructures, then the algorithms for solving the uniform decision problems can be applied to the substructures as well. However, since these algorithms depend on the form of the presentations, this involves the task of constructing a presentation of a certain form for a substructure given a presentation of this form for the structure itself and a finite set of generating elements for the substructure.This problem, which has received a lot of attention in algebra, is here investigated from an algorithmic point of view. The structures considered are the following two classes of groups, which have been studied extensively before: the polycyclic groups and the context-free groups.Finitely generated context-free groups can be presented by finite, monadic, and -confluent string-rewriting systems. Due to their nice algorithmic properties these systems provide a way to effectively solve many decision problems for context-free groups. Since finitely generated subgroups of context-free groups are again contextfree, they can be presented in the same way. Here we describe a process that, from a finite, monadic, and -confluent string-rewriting system presenting a context-free groupG and a finite subsetU ofG, determines a presentation of this form for the subgroup U ofG that is generated byU. For finitely presented polycyclic groups we obtain an analogous result, when we use finite confluent PCP2-presentations to describe these groups.This work was performed while this author was visiting at the Fachbereich Informatik, Universität Kaiserslautern, during his sabbatical 1991/92     

Identification of metal ion solutions using acoustic plate mode devices and pattern recognition

The temperature dependence of acoustic plate mode (APM) devices used as probes for dilute electrolytes is described. Specifically, the probe responses that consist of the frequency change and device loss were studied for dilute aqueous solutions of alkali metal ions. It is shown that by integrating the temperature dependence of the APM probe responses with pattern recognition techniques, valuable information about the solutions can be obtained that include identification and quantification. A preliminary investigation of the feasibility of identifying binary mixtures of the alkali metal ion solutions using only the temperature responses showed good results.     

Transparent, conductive graphene electrodes for dye-sensitized solar cells

Transparent, conductive, and ultrathin graphene films, as an alternative to the ubiquitously employed metal oxides window electrodes for solid-state dye-sensitized solar cells, are demonstrated. These graphene films are fabricated from exfoliated graphite oxide, followed by thermal reduction. The obtained films exhibit a high conductivity of 550 S/cm and a transparency of more than 70% over 1000-3000 nm. Furthermore, they show high chemical and thermal stabilities as well as an ultrasmooth surface with tunable wettability.     

Reconfigurable handling system

The demand for more versatile assembly and handling systems to facilitate customized production is gaining in importance, especially with regard to the constantly-increasing cost pressure, to expansion of the range of product versions and the shortening of innovation cycles. As a cost-effective approach for frequently changing assembly tasks, a novel manipulation concept has been developed by combining given robot technologies. This new handling system has a modular and adaptable layout, which consists of several mobile arms to manipulate the object in six-dimensional Cartesian space. After grasping, when the arms are attached to the object, the mechanical architecture is similar to parallel manipulators or cooperating robots. As the mounting and gripping points of the arms can easily be changed, the manipulator can be reconfigured so as to match the user’s preferences and needs. In addition to the kinematic adaption the regarding task, the hardware and new functions can be reconfigured as well. Contact elements, measurement and assembly devices as well as testing modules can easily be in integrated in the concept. A modular automatic control concept combined with a self-optimizing planning tool helps the user to find the optimal configuration and realize it in an economic way.     

Phase equilibria in the Al–Si–V system: The vanadium rich part

The V-rich part of the Al–Si–V phase diagram was determined by a combination of optical microscopy, powder X-ray diffraction (XRD), differential thermal analysis (DTA) and electron probe microanalysis (EPMA). Phase equilibria were investigated at two isothermal sections at 850 and 1300 °C. High temperature DTA was performed to identify the ternary invariant reactions yielding a ternary reaction scheme and the vertical section at 50 at.% V. As cast samples were investigated in order to gain additional information about primary crystallization fields. A liquidus surface projection was constructed for the entire ternary system by combining our experimental data with those from literature.