Recently, we have introduced two graph-decomposition theorems based on a new graph product, motivated by applications in the context of synchronising periodic real-time processes. This vertexremoving synchronised product (VRSP) is based on modifications of the well-known Cartesian product and is closely related to the synchronised product due to Wohrle and Thomas. Here, we ¨ show how we can relax the requirements of these two graph-decomposition theorems.
DOCUMENT
Recently, we have introduced and modified two graph-decomposition theorems based on a new graph product, motivated by applications in the context of synchronising periodic real-time processes. This vertex-removing synchronised product (VRSP), is based on modifications of the well-known Cartesian product and is closely related to the synchronised product due to Wohrle and Thomas. Here, we recall the definition of the VRSP and the two modified graph-decompositions and introduce three new graph-decomposition theorems. The first new theorem decomposes a graph with respect to the semicomplete bipartite subgraphs of the graph. For the second new theorem, we introduce a matrix graph, which is used to decompose a graph in a manner similar to the decomposition of graphs using the Cartesian product. In the third new theorem, we combine these two types of decomposition. Ultimately, the goal of these graph-decomposition theorems is to come to a prime-graph decomposition.
MULTIFILE
Recently, we have introduced two graph-decomposition theorems based on a new graph product, motivated by applications in the context of synchronising periodic real-time processes. This vertex-removing synchronised product (VRSP) is based on modifications of the well-known Cartesian product and is closely related to the synchronised product due to Wöhrle and Thomas. Here, we recall the definition of the VRSP and the two graph-decomposition theorems, we relax the requirements of these two graph-decomposition theorems and prove these two (relaxed) graph-decomposition theorems.
DOCUMENT
Many lithographically created optical components, such as photonic crystals, require the creation of periodically repeated structures [1]. The optical properties depend critically on the consistency of the shape and periodicity of the repeated structure. At the same time, the structure and its period may be similar to, or substantially below that of the optical diffraction limit, making inspection with optical microscopy difficult. Inspection tools must be able to scan an entire wafer (300 mm diameter), and identify wafers that fail to meet specifications rapidly. However, high resolution, and high throughput are often difficult to achieve simultaneously, and a compromise must be made. TeraNova is developing an optical inspection tool that can rapidly image features on wafers. Their product relies on (a) knowledge of what the features should be, and (b) a detailed and accurate model of light diffraction from the wafer surface. This combination allows deviations from features to be identified by modifying the model of the surface features until the calculated diffraction pattern matches the observed pattern. This form of microscopy—known as Fourier microscopy—has the potential to be very rapid and highly accurate. However, the solver, which calculates the wafer features from the diffraction pattern, must be very rapid and precise. To achieve this, a hardware solver will be implemented. The hardware solver must be combined with mechatronic tracking of the absolute wafer position, requiring the automatic identification of fiduciary markers. Finally, the problem of computer obsolescence in instrumentation (resulting in security weaknesses) will also be addressed by combining the digital hardware and software into a system-on-a-chip (SoC) to provide a powerful, yet secure operating environment for the microscope software.
Door producten en diensten inclusief te ontwerpen kunnen ontwerpers een belangrijke bijdrage leveren aan een inclusievere samenleving, waarin iedereen op eigen wijze kan participeren. In AID gaan negen mkb-ontwerpbureaus Afdeling Buitengewone Zaken (A/BZ), theRevolution, Design Innovation Group, Greenberry, Ideate, Keen Public, Muzus, Netrex Internet Solutions (Leer Zelf Online) en Vrienden van verandering) die rijke maar uiteenlopende ervaring hebben met inclusief ontwerpen op zoek naar antwoorden op de vraag hoe hun vermogen voor inclusief ontwerpen kan worden versterkt. Ze doen dit middels actie-onderzoek in hun eigen beroepspraktijk en door hun ervaringen te delen met onderzoekers, docenten en co-ontwerpers in een ‘learning community’.
Dit project richt zich op de ontwikkeling van de biotechnologische en chemische procesvoering om op basis van mycelium een alternatief voor leer te produceren. In vergelijking met leer is het voordeel van mycelium dat geen runderen nodig zijn, de productie kan plaatsvinden onder industriële condities en met gebruik van reststromen, de CO2 uitstoot alsook hoeveelheid afval verlaagd wordt, en het gebruik van toxische stoffen zoals chroom wordt vervangen door biobased alternatieven. In het project zullen de procescondities worden bepaald die leiden tot de vorming van optimaal mycelium. Daartoe zullen twee verschillende schimmels worden gekweekt in bioreactoren bij de Hogeschool Arnhem Nijmegen (HAN), waarbij specifiek de effecten van de procescondities (temperatuur, pH, shear, beluchting) en de samenstelling van het kweekmedium op groei van het mycelium en materiaal eigenschappen zullen worden onderzocht. De meest optimale condities zullen vervolgens worden opgeschaald. Op het op deze wijze verkregen materiaal zal Mylium BV een aantal nabehandelingsstappen uitvoeren om de sterkte, elasticiteit, en duurzaamheid van het product te vergroten. Daartoe worden biobased plasticizers, cross-linkers en/of flexibility agents gebruikt. Het resulterende eindproduct zal middels specifiek fysieke testen vergeleken worden met leer alsook worden voorgelegd aan mogelijke klanten. Indien beide resultaten positief zijn kan het betreffende proces na het project verder worden opgeschaald voor toepassing naar de markt.
Lectoraat, onderdeel van HAS green academy
