147 research outputs found

    Mini-Workshop: Algebraic, Geometric, and Combinatorial Methods in Frame Theory

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    Frames are collections of vectors in a Hilbert space which have reconstruction properties similar to orthonormal bases and applications in areas such as signal and image processing, quantum information theory, quantization, compressed sensing, and phase retrieval. Further desirable properties of frames for robustness in these applications coincide with structures that have appeared independently in other areas of mathematics, such as special matroids, Gel’Fand-Zetlin polytopes, and combinatorial designs. Within the past few years, the desire to understand these structures has led to many new fruitful interactions between frame theory and fields in pure mathematics, such as algebraic and symplectic geometry, discrete geometry, algebraic combinatorics, combinatorial design theory, and algebraic number theory. These connections have led to the solutions of several open problems and are ripe for further exploration. The central goal of our mini-workshop was to attack open problems that were amenable to an interdisciplinary approach combining certain subfields of frame theory, geometry, and combinatorics

    Classical Algebraic Geometry

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    Progress in algebraic geometry often comes through the introduction of new tools and ideas to tackle the classical problems the development of the field. Examples include new invariants that capture some aspect of geometry in a novel way, such as the derived category, and the extension of the class of geometric objects considered to allow constructions not previously possible, such as the transition from varieties to schemes or from schemes to stacks. Many famous old problems and outstanding conjectures have been resolved in this way over the last 50 years. While the new theories are sometimes studied for their own sake, they are in the end best understood in the context of the classical questions they illuminate. The goal of the workshop was to study new developments in algebraic geometry, with a view toward their application to the classical problems

    Arithmetic results on orbits of linear groups

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    Let pp be a prime and GG a subgroup of GLd(p)GL_d(p). We define GG to be pp-exceptional if it has order divisible by pp, but all its orbits on vectors have size coprime to pp. We obtain a classification of pp-exceptional linear groups. This has consequences for a well known conjecture in representation theory, and also for a longstanding question concerning 1/2-transitive linear groups (i.e. those having all orbits on nonzero vectors of equal length), classifying those of order divisible by pp.Comment: slight revisions after referee's comment

    Automatic tolerance inspection through Reverse Engineering: a segmentation technique for plastic injection moulded parts

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    This work studies segmentations procedures to recognise features in a Reverse Engineering (RE) application that is oriented to computer-aided tolerance inspection of injection moulding die set-up, necessary to manufacture electromechanical components. It will discuss all steps of the procedures, from the initial acquisition to the final measure data management, but specific original developments will be focused on the RE post-processing method, that should solve the problem related to the automation of the surface recognition and then of the inspection process. As it will be explained in the first two Chapters, automation of the inspection process pertains, eminently, to feature recognition after the segmentation process. This work presents a voxel-based approach with the aim of reducing the computation efforts related to tessellation and curvature analysis, with or without filtering. In fact, a voxel structure approximates the shape through parallelepipeds that include small sub-set of points. In this sense, it represents a filter, since the number of voxels is less than the total number of points, but also a local approximation of the surface, if proper fitting models are applied. Through sensitivity analysis and industrial applications, limits and perspectives of the proposed algorithms are discussed and validated in terms of accuracy and save of time. Validation case-studies are taken from real applications made in ABB Sace S.p.A., that promoted this research. Plastic injection moulding of electromechanical components has a time-consuming die set-up. It is due to the necessity of providing dies with many cavities, which during the cooling phase may present different stamping conditions, thus defects that include lengths outside their dimensional tolerance, and geometrical errors. To increase the industrial efficiency, the automation of the inspection is not only due to the automatic recognition of features but also to a computer-aided inspection protocol (path planning and inspection data management). For this reason, also these steps will be faced, as the natural framework of the thesis research activity. The work structure concerns with six chapters. In Chapter 1, an introduction to the whole procedure is presented, focusing on reasons and utilities of the application of RE techniques in industrial engineering. Chapter 2 analyses acquisition issues and methods that are related to our application, describing: (a) selected hardware; (b) adopted strategy related to the cloud of point acquisition. In Chapter 3, the proposed RE post-processing is described together with a state of art about data segmentation and surface reconstruction. Chapter 4 discusses the proposed algorithms through sensitivity studies concerning thresholds and parameters utilised in segmentation phase and surface reconstruction. Chapter 5 explains briefly the inspection workflow, PDM requirements and solution, together with a preliminary assessing of measures and their reliability. These three chapters (3, 4 and 5) report final sections, called “Discussion”, in which specific considerations are given. Finally, Chapter 6 gives examples of the proposed segmentation technique in the framework of the industrial applications, through specific case studies

    Phenomenological joint modelling : theoretical aspects and implementations in MADYMO

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    Between primitive and 2-transitive : synchronization and its friends

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    The second author was supported by the Fundação para a Ciência e Tecnologia (Portuguese Foundation for Science and Technology) through the project CEMAT-CIÊNCIAS UID/Multi/ 04621/2013An automaton (consisting of a finite set of states with given transitions) is said to be synchronizing if there is a word in the transitions which sends all states of the automaton to a single state. Research on this topic has been driven by the Černý conjecture, one of the oldest and most famous problems in automata theory, according to which a synchronizing n-state automaton has a reset word of length at most (n − 1)2 . The transitions of an automaton generate a transformation monoid on the set of states, and so an automaton can be regarded as a transformation monoid with a prescribed set of generators. In this setting, an automaton is synchronizing if the transitions generate a constant map. A permutation group G on a set Ω is said to synchronize a map f if the monoid (G, f) generated by G and f is synchronizing in the above sense; we say G is synchronizing if it synchronizes every non-permutation. The classes of synchronizing groups and friends form an hierarchy of natural and elegant classes of groups lying strictly between the classes of primitive and 2-homogeneous groups. These classes have been floating around for some years and it is now time to provide a unified reference on them. The study of all these classes has been prompted by the Černý conjecture, but it is of independent interest since it involves a rich mix of group theory, combinatorics, graph endomorphisms, semigroup theory, finite geometry, and representation theory, and has interesting computational aspects as well. So as to make the paper self-contained, we have provided background material on these topics. Our purpose here is to present recent work on synchronizing groups and related topics. In addition to the results that show the connections between the various areas of mathematics mentioned above, we include a new result on the Černý conjecture (a strengthening of a theorem of Rystsov), some challenges to finite geometers (which classical polar spaces can be partitioned into ovoids?), some thoughts about infinite analogues, and a long list of open problems to stimulate further work.PostprintPeer reviewe

    Design and Dynamic Analysis of a Novel Subsea Shuttle Tanker

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    PhD thesis in Offshore technologyUnderwater pipelines, tanker ships, and liquefied gas carriers have traditionally been employed to transport hydrocarbons between offshore oil and gas facilities and onshore locations. However, both methods come with limitations. Underwater pipelines are costly to install and maintain, while the operation of tanker ships and liquefied gas carriers is heavily dependent on weather conditions, rendering them impractical in severe sea states. As an alternative, a pioneering subsea shuttle tanker (SST) system was proposed as an alternative for offshore transportation. The SST was designed to function at a constant speed and depth beneath the ocean surface, specifically designed for transporting liquid carbon dioxide from existing onshore/offshore sites where carbon dioxide is captured or temporarily stored, to subsea wells for reservoir injection. Nonetheless, the potential applications of the SST extend to being a versatile freight carrier, capable of transporting diverse cargoes such as subsea tools, hydrocarbons, chemicals, and even electricity. This PhD project unfolds in two phases: design and dynamic analysis. In the design phase, a baseline design for the SST was formulated based on existing literature. This comprehensive design encompasses critical aspects of SST design and operation, including structural design, hydrostatic stability computations, resistance and propulsion estimations, operational scenarios, and offloading methodologies. Challenges inherent to CO2 SST transportation were scrutinised, involving thermodynamic properties, purity considerations, and hydrate formation of CO2 during various vessel-transportation states. These aspects were explored in relation to cargo sizing, material selection, and energy consumption. The second phase revolves around dynamic analysis, centred on the derived baseline SST. A manoeuvring model for the SST was constructed as a foundation. Hydrodynamic derivatives were calculated using semi-empirical formulas. Subsequently, the SST’s capability to maintain position during the offloading process was evaluated. A linear quadratic regulator was employed to address the SST’s stationkeeping challenge in stochastic currents, ensuring the vessel remains stationary during offloading. The model was further extended to explore the station-keeping under extreme current conditions, utilising probabilistic methods to predict maximum and minimum depth excursions. These predictions offer valuable insights for cost-effective SST design and operational decision-making. The study then delved into the SST’s recoverability under undesired malfunctions through the establishment of a safety operating envelope (SOE). This envelope considered potential submersible malfunctions, such as partial flooding, jam-to-rise, and jam-to-dive incidents. By identifying feasible speed and depth ranges from an operational safety perspective, the SOE contributes to a reduction in the designed collapse depth, leading to cost savings in materials and enhanced payload capacity. Furthermore, computational fluid dynamics (CFD) analysis was conducted to predict pressure, skin friction, drag, and lift forces affecting the SST. This included scenarios of the SST’s near-wall voyage and hovering. Collectively, the original contributions of this thesis encompass the conceptual design, application of control systems and dynamic analysis of the SST. These contributions pave the way for future exploration in the development of commercial submarine concepts and diverse ocean space utlisation strategies
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