Vibrationsförderer gehören zur Gruppe der Stetigförderer und werden branchenübergreifend sowohl zur Schütt- als auch zur Stückgutförderung eingesetzt. Das Förderorgan eines Vibrationsförderers versetzt ein darauf befindliches Fördergut mittels kleiner periodischer Vibrationen in eine gerichtete Bewegung. Diese Gutbewegung wird anhand der mittleren Fördergeschwindigkeit charakterisiert und stellt eine wichtige Dimensionierungsgröße dar. Gleichzeitig dient die mittlere Fördergeschwindigkeit, neben einem ruhigen Laufverhalten des Gutes, als Beurteilungskriterium der Güte eines Vibrationsförderers. Die fortschreitende Entwicklung bringt immer komplexere Geräte mit nahezu beliebigen zweidimensional ausgeformten Vibrationsbewegungen hervor, wobei diese gelegentlich auch unbeabsichtigt generiert werden. Die aus solchen Bewegungsformen resultierenden Fördergutreaktionen lassen sich mit bislang vorhandenen Berechnungsmodellen nicht beschreiben. Die vorliegende Arbeit untersucht die Einflüsse zweidimensionaler Bewegungsformen eines Förderorgans auf die daraus resultierende Gutbewegung bei Vibrationsförderern. Diesbezüglich wurde ein numerisches Berechnungsmodell entwickelt, experimentell verifiziert und mit der nach dem Stand der Technik geläufigen Berechnungsvorschrift verglichen. Das entwickelte Modell diente weiterhin als Basis theoretischer Untersuchungen, insbesondere für 2D-Bewegungsformen 1. Ordnung. Aus den Untersuchungsergebnissen konnte schließlich eine für den Anwender praktikable und erweiterte Berechnungsvorschrift abgeleitet werden. / Vibratory conveyors belong to the group of continuous conveyors and are inter-divisionally deployed for the conveyance of bulk and piece goods. The conveyor organ of a vibratory conveyor moves thereupon placed conveyed goods by means of small periodical vibrations in a directed movement. This movement of the goods is characterized via medium conveying speed and describes an important rating dimension. Next to a stable running performance of the goods, the medium conveying speed acts at the same time as an assessment criterion for the quality of a vibratory conveyor. The progressing development produces more and more complex devices with almost any two-dimensionally formed vibrating movements, which are, however, sometimes generated unintentionally. Reactions of conveying goods resulting from such movement patterns cannot be described with the so far existing analytical models. The dissertation at hand analyses the influence of two-dimensional movement patterns of a conveyor organ on the resulting movement of the goods when using vibratory conveyors. Concerning this matter, a numerical analytical model was developed, experimentally verified and, according to the calculation rule, compared to the state of the technology. The developed model provided furthermore a basis for theoretical research, here especially for 2D movement patterns of first order. Finally, a practicable and extended calculation rule could be deduced from the research results.

Nanotubular structures from a new family of misfit compounds LnS–TaS₂ with (Ln = La, Ce, Nd, Ho, Er) and LaSe–TaSe₂ (some of them not known hitherto) are reported. Stress relaxation originating from the lattice mismatch between the alternating LnS(Se) and TaS₂(Se) layers, combined with seaming of the dangling bonds in the rim, leads to the formation of a variety of nanotubular structures. Their structures are studied via scanning electron microscopy (SEM), high-resolution transmission electron microscopy (HRTEM), scanning transmission electron microscopy (STEM) and selected area electron diffraction (SAED). Tubules exhibiting a single folding vector for the LnS(Se) as well as TaS₂(Se) layers were often found. The small values of the c-axis periodicities are indicative of a strong interaction between the two constituent layers which was also supported by Raman spectroscopy and theoretical calculations.

Der vorliegende Beitrag befasst sich mit dem Verhalten von Vibrationsförderern. Speziell für Förderer, welche nach dem Gleitprinzip arbeiten, werden Zusammenhänge zwischen der Antriebslage, dem Fördergut sowie der Ausrichtung des Förderorgans beschrieben. Durch Anwendung der vorgestellten Prinzipien wird eine Berechnungsmethode für die Fördergeschwindigkeit abgeleitet und anschließend mit Versuchswerten verglichen. / This paper deals with the behavior of vibrating conveyors. Especially for conveyors, using a sliding principle of movement, relations between the drive position, the conveyed goods and the orientation of the means of transport are described. By applying the principles presented, a method for calculating the conveying velocity is derived and compared with experimental values.

Der Beitrag stellt eine Verallgemeinerung der Ergebnisse dar, die in den Informationen/07; 1976,05 veröffentlicht wurden. Sei F_n(x) die Verteilungsfunktion der Summe X_1+X_2+...+X_n, wobei X_1, X_2, ...,X_n unabhängige und nicht notwendig identisch verteilte Zufallsgrößen mit endlichen absoluten Momenten c_m, m>2, sind, und sei Phi die standardisierte Normalverteilungsfunktion. Es werden absolute Konstanten L_m derart berechnet, dass wir Fehlerabschätzungen im unleichmäßigen zentralen Grenzwertsatz explizit angeben können. Als Spezialfall ergibt sich die ungleichmäßige Fehlerschranke von A.BIKELIS (1966) im Fall der Existenz dritter absoluter Momente. Weiterhin werden Grenzwertsätze unter Voraussetzung einseitiger Momente betrachtet. Es werden einige Literaturhinweise angegeben.:1. Grenzwertsätze für verschieden verteilte Zufallsgrößen S. 1 2. Grenzwertsätze unter Voraussetzung einseitiger Momente S. 6 3. Beweise zum Abschnitt 1 S. 7 4. Beweise zum Abschnitt 2 S. 14 Literatur S. 16 / The paper is a generalization of the results, published by the author in Informationen/07; 1976,05. Let F_n(x) be the cdf of X_1+X_2+...+X_n, where X_1, X_2, ...,X_n are non iid random variables with m-th absolute moment c_m, m>2, and Phi the cdf of the unit normal law. Explicit universal constants L_m are computed such that we have some error estimates in the nonuniform central limit theorem. A special case is the nonuniform error bound by A.BIKELIS (1966) in the case of existence of third absolute moments. Furthermore limit theorems with assumption of onesided moments are considered. Some references are given.:1. Grenzwertsätze für verschieden verteilte Zufallsgrößen S. 1 2. Grenzwertsätze unter Voraussetzung einseitiger Momente S. 6 3. Beweise zum Abschnitt 1 S. 7 4. Beweise zum Abschnitt 2 S. 14 Literatur S. 16

Es wird eine Folge unabhängiger zentrierter Zufallsgrößen betrachtet, die absolute Momente der Ordnung m, 2<m<3, besitzen mögen. Dann gelten für die normierte Verteilungsfunktion der Zufallssumme X_1+X_2+...+X_n der zentrale Grenzwertsatz und insbesondere eine ungleichmäßige Fehlerabschätzung von A.BIKELIS (1966). In der vorliegenden Note werden die analytische Struktur der in dieser Fehlerabschätzung auftretenden Konstanten L=L(m) genauer untersucht sowie dazu erzielte numerische Resultate vorgelegt. Abschließend werden einige Literaturhinweise angegeben. Der Fall m=3 wurde bereits in der Dissertation (TU Dresden 1977) des Autors untersucht. / We consider a sequence of centered and independent random variables with moments of order m, 2<m<3. Now the central limit theorem for the distribution function of the normed sum X_1+X_2+...+X_n and especially a nonuniform error estimate by A.BIKELIS (1966) hold. In this paper the analytical structure of the appearing constant L=L(m) of the error bound and numerical results are presented. Finally some references are given. The case m=3 was already studied in the thesis (Dissertation TU Dresden, 1977) by the author.

Distillation is the leading thermal separation technology that is carried out in many industrial tray columns worldwide. Although distillation columns are expensive in terms of cost and energy, they will remain in service due to unavailability of any equivalent industrially-viable alternative. However, rising energy costs and urgent needs to reduce greenhouse gas emissions demand improvements in the energy efficiency of separation processes, globally. This can be achieved by tuning the dynamics of the evolving two-phase dispersion on column trays via design modification and revamping. Thus, it becomes necessary to understand how the two phases evolve over the tray and how they link to tray efficiency for given tray designs, systems and operating conditions. Only then, the cost and energy reduction can be achieved by strategically iterating the tray design and revamps with respect to the resulting tray efficiency. To pursue this strategy, accurate prediction of the separation efficiency based on flow and mixing patterns on the trays is an important prerequisite. In this thesis, the mathematical models relying on flow and mixing patterns for predicting the tray efficiencies were reviewed. These models were developed based on the analyses of two-phase flow, crossflow hydraulics and mass transfer over the trays. Several limitations in the existing models were identified that could lead to inaccurate tray efficiency predictions. First, the conventional models do not account for any variation in the local two-phase flow in their formulation. These models rather consider a homogeneous flow scenario based on flow monitoring at the tray boundaries only, which indicates a black box efficiency estimation. Second, the existing models do not consider any vapor flow maldistribution, which can be detrimental to the tray efficiency. In response to these limitations, a new model based on refinement of the conventional residence time distribution (RTD) model (referred to as the ‘Refined RRTD model’) was proposed. The new model involves geometric partitioning of the tray into compartments along the flow path length, which permits computing the tray efficiency through quantification of the efficiency of the individual compartments. The proposed model ensures that the fluid dynamics of each compartment contribute towards the overall tray efficiency, which specifically targets the black box prediction of the tray efficiency by the conventional models. The tray discretization further aids in analyzing the impact of vapor flow maldistribution on the tray efficiency. In the initial assessment, the new model capabilities were demonstrated in appropriate case studies after theoretical validation of the model for the limiting cases of the two-phase flows. For the experimental validation of the new model, a full hydrodynamic and mass transfer description of the two-phase dispersion specific to the tray operation is indispensable. Because of the inherently complex dispersion characteristics, significant advancements in the imaging and efficiency modeling methods were required. In this thesis, a DN800 column simulator equipped with two sieve trays (each with 13.55% fractional free area) was used with air and tap water as the working fluids. Deionized water was used as a tracer. The gas loadings in the column in terms of F-factor were 1.77 Pa0.5 and 2.05 Pa0.5, whereas the weir loadings were 2.15 m3m-1h-1, 4.30 m3m-1h-1 and 6.45 m3m-1h-1. An advanced multiplex flow profiler comprising 776 dual-tip conductivity probes for simultaneous conductivity measurements was introduced for hydrodynamic characterization. The spatial resolution of the profiler based on the inter-probe distance was 21 mm × 24 mm, whereas the temporal resolution was 5000 Hz. The design characteristics of the new profiler, electronic scheme, measurement principle, reference framework, and data processing schemes are explained in detail. By analyzing the two-phase dispersion data gathered by the profiler at multiple elevations above the tray, the effective froth height distributions were obtained for the first time based on a newly proposed approach. Uniform froth heights were seen over the majority of the tray deck, whereas both minimum and maximum froth heights were detected immediately after the tray inlet. Based on threshold-based calculation (accompanied by γ-ray CT scans), 3D time-averaged liquid holdup distributions were visualized for the first time, too. Homogeneous liquid holdup distributions were observed at multiple elevations above the deck with the highest holdups occurring near the average effective froth heights. The detailed flow and mixing patterns of the liquid in the two-phase dispersion were retrieved via tracer monitoring. With respect to tray centerline, axisymmetric liquid flow and mixing patterns were detected with parabolic velocity distributions near the tray inlet. The liquid velocities over the remaining tray deck were nearly uniform for the prescribed loadings. Eventually, the RRTD model was applied by discretizing the tray geometrically, and accordingly employing the available hydrodynamic data. The conventional models often applied in the literature were also evaluated with the new model. For evaluating the model predictions, a new system add-on for the existing air-water column facility was proposed for direct efficiency measurements. The air-led stripping of isobutyl acetate from the aqueous solution is a safe and viable approach that overcomes numerous limitations posed by the existing chemical systems. Based on liquid sampling at different tray locations, the liquid concentration distributions were obtained at each operating condition via UV spectroscopy. The tray and point efficiencies as well as stripping factors were calculated from those distributions. Because of the low liquid diffusivity and high liquid backmixing, low efficiencies were observed at the given loadings. The model predictions were consistent with the experimental counterparts (even for the extrapolated values of the involved parameters), because of the uniform liquid flow and mixing in the compartments. For the given predictions, those corresponding to the new RRTD model were the most accurate. Additional hydrodynamic and efficiency data are needed for more conclusive evidence regarding the promise of the RRTD model.

A vast number of online services is based on users contributing their personal information. Examples are manifold, including social networks, electronic commerce, sharing websites, lodging platforms, and genealogy. In all cases user privacy depends on a collective trust upon all involved intermediaries, like service providers, operators, administrators or even help desk staff. A single adversarial party in the whole chain of trust voids user privacy. Even more, the number of intermediaries is ever growing. Thus, user privacy must be preserved at every time and stage, independent of the intrinsic goals any involved party. Furthermore, next to these new services, traditional offline analytic systems are replaced by online services run in large data centers. Centralized processing of electronic medical records, genomic data or other health-related information is anticipated due to advances in medical research, better analytic results based on large amounts of medical information and lowered costs. In these scenarios privacy is of utmost concern due to the large amount of personal information contained within the centralized data. We focus on the challenge of privacy-preserving processing on genomic data, specifically comparing genomic sequences. The problem that arises is how to efficiently compare private sequences of two parties while preserving confidentiality of the compared data. It follows that the privacy of the data owner must be preserved, which means that as little information as possible must be leaked to any party participating in the comparison. Leakage can happen at several points during a comparison. The secured inputs for the comparing party might leak some information about the original input, or the output might leak information about the inputs. In the latter case, results of several comparisons can be combined to infer information about the confidential input of the party under observation. Genomic sequences serve as a use-case, but the proposed solutions are more general and can be applied to the generic field of privacy-preserving comparison of sequences. The solution should be efficient such that performing a comparison yields runtimes linear in the length of the input sequences and thus producing acceptable costs for a typical use-case. To tackle the problem of efficient, privacy-preserving sequence comparisons, we propose a framework consisting of three main parts. a) The basic protocol presents an efficient sequence comparison algorithm, which transforms a sequence into a set representation, allowing to approximate distance measures over input sequences using distance measures over sets. The sets are then represented by an efficient data structure - the Bloom filter -, which allows evaluation of certain set operations without storing the actual elements of the possibly large set. This representation yields low distortion for comparing similar sequences. Operations upon the set representation are carried out using efficient, partially homomorphic cryptographic systems for data confidentiality of the inputs. The output can be adjusted to either return the actual approximated distance or the result of an in-range check of the approximated distance. b) Building upon this efficient basic protocol we introduce the first mechanism to reduce the success of inference attacks by detecting and rejecting similar queries in a privacy-preserving way. This is achieved by generating generalized commitments for inputs. This generalization is done by treating inputs as messages received from a noise channel, upon which error-correction from coding theory is applied. This way similar inputs are defined as inputs having a hamming distance of their generalized inputs below a certain predefined threshold. We present a protocol to perform a zero-knowledge proof to assess if the generalized input is indeed a generalization of the actual input. Furthermore, we generalize a very efficient inference attack on privacy-preserving sequence comparison protocols and use it to evaluate our inference-control mechanism. c) The third part of the framework lightens the computational load of the client taking part in the comparison protocol by presenting a compression mechanism for partially homomorphic cryptographic schemes. It reduces the transmission and storage overhead induced by the semantically secure homomorphic encryption schemes, as well as encryption latency. The compression is achieved by constructing an asymmetric stream cipher such that the generated ciphertext can be converted into a ciphertext of an associated homomorphic encryption scheme without revealing any information about the plaintext. This is the first compression scheme available for partially homomorphic encryption schemes. Compression of ciphertexts of fully homomorphic encryption schemes are several orders of magnitude slower at the conversion from the transmission ciphertext to the homomorphically encrypted ciphertext. Indeed our compression scheme achieves optimal conversion performance. It further allows to generate keystreams offline and thus supports offloading to trusted devices. This way transmission-, storage- and power-efficiency is improved. We give security proofs for all relevant parts of the proposed protocols and algorithms to evaluate their security. A performance evaluation of the core components demonstrates the practicability of our proposed solutions including a theoretical analysis and practical experiments to show the accuracy as well as efficiency of approximations and probabilistic algorithms. Several variations and configurations to detect similar inputs are studied during an in-depth discussion of the inference-control mechanism. A human mitochondrial genome database is used for the practical evaluation to compare genomic sequences and detect similar inputs as described by the use-case. In summary we show that it is indeed possible to construct an efficient and privacy-preserving (genomic) sequences comparison, while being able to control the amount of information that leaves the comparison. To the best of our knowledge we also contribute to the field by proposing the first efficient privacy-preserving inference detection and control mechanism, as well as the first ciphertext compression system for partially homomorphic cryptographic systems.

Dieser Beitrag ist der Vibrationsfördertechnik zuzuordnen und befasst sich speziell mit dem Prinzip der Gleitförderung bei nichtharmonischer Beschleunigung in horizontaler Ebene. Es werden Zusammenhänge zwischen der Bewegung des Förderorgans und der Berechnung der resultierenden Fördergeschwindigkeit vorgestellt. Anhand der maximalen Fördergeschwindigkeit und der Effizienz einer Bewegungsform werden schließlich optimale Bewegungsgesetze abgeleitet. / This work is assigned to vibratory conveyor engineering and is dealing with the operation principle of sliding conveying by non-harmonical accelaration along horizontal plane surfaces. The relations between motion of the conveyor organ and calculation of the resulting conveying velocity are explained in this paper. Finally, optimal motion laws regarding a high efficiency of the motion patterns are derived from the maximum conveying velocity.

Schneckenradgetriebe sind aufgrund ihrer Verzahnungsgeometrie prädestiniert für Getriebeanwendungen mit diskontinuierlichem und schwingungsbehaftetem Betrieb. Bei hohen Momenten und geringen Drehzahlen stellt dabei die Zahnfußtragfähigkeit die primäre Auslegungsgrenze dar. Das Ziel der vorliegenden Arbeit lag in der Erhöhung der Genauigkeit der Berechnungsmethoden für die Zahnfußtragfähigkeit von Schneckenrädern, auch zur Steigerung des Volumennutzwertes dieser Getriebe. Hierzu wurden alle die Tragfähigkeit des Zahnfußes beeinflussenden Parameter durch eine Vielzahl von Experimenten und FE Simulationen untersucht. Dies schließt eine genaue Analyse der Geometrie von Schneckengetrieben, deren Fertigung und Einbausituation, die verwendeten Werkstoffe und deren Beanspruchung mit ein. Auf dieser Basis gelang neben der Entwicklung eines vergleichsspannungsbasierten analytischen Berechnungsverfahrens die Erstellung eines örtlichen Berechnungskonzeptes nach dem Kerbspannungskonzept. Hiermit konnte die Einschätzung der Zahnfußtragfähigkeit bei der Neuentwicklung und die Optimierung von Getrieben verbessert werden. / Worm gears are well suited for gearbox applications in environments with discontinuous conditions and mechanical vibrations. In the case of high torque and low speed, the tooth root strength is the primary design limit. The aim of the present paper is to improve the accuracy of the calculation methods for the tooth root strength of worm wheels. To reach this, all parameters which affects the strength of the tooth root were examined. This includes the geometry, the manufacturing, the materials and the stresses of worm wheels. Through this investigation, the development of a new analytical calculation method based on the equivalent stress concept could be done. Furthermore, a local calculation method based on the notch stress concept was developed. Thus, the forecast of the tooth root strength of worm wheels for redevelopment and optimization could be improved.

Draft and proof of an algorithm computing incremental changes within a labeled layouted concept lattice upon insertion or removal of an attribute column in the underlying formal context. Furthermore some implementational details and mathematical background knowledge are presented.:1 Introduction 1.1 Acknowledgements 1.2 Supporting University: TU Dresden, Institute for Algebra 1.3 Supporting Corporation: SAP AG, Research Center Dresden 1.4 Research Project: CUBIST 1.5 Task Description und Structure of the Diploma Thesis I Mathematical Details 2 Fundamentals of Formal Concept Analysis 2.1 Concepts and Concept Lattice 2.2 Visualizations of Concept Lattices 2.2.1 Transitive Closure and Transitive Reduction 2.2.2 Neighborhood Relation 2.2.3 Line Diagram 2.2.4 Concept Diagram 2.2.5 Vertical Hybridization 2.2.6 Omitting the top and bottom concept node 2.2.7 Actions on Concept Diagrams 2.2.8 Metrics on Concept Diagrams 2.2.9 Heatmaps for Concept Diagrams 2.2.10 Biplots of Concept Diagrams 2.2.11 Seeds Selection 2.3 Apposition of Contexts 3 Incremental Updates for Concept Diagrams 3.1 Insertion & Removal of a single Attribute Column 3.1.1 Updating the Concepts 3.1.2 Structural Remarks 3.1.3 Updating the Order 3.1.4 Updating the Neighborhood 3.1.5 Updating the Concept Labels 3.1.6 Updating the Reducibility 3.1.7 Updating the Arrows 3.1.8 Updating the Seed Vectors 3.1.9 Complete IFOX Algorithm 3.1.10 An Example: Stepwise Construction of FCD(3) 3.2 Setting & Deleting a single cross 4 Iterative Exploration of Concept Lattices 4.1 Iceberg Lattices 4.2 Alpha Iceberg Lattices 4.3 Partly selections 4.3.1 Example with EMAGE data 4.4 Overview on Pruning & Interaction Techniques II Implementation Details 5 Requirement Analysis 5.1 Introduction 5.2 User-Level Requirements for Graphs 5.2.1 Select 5.2.2 Explore 5.2.3 Reconfigure 5.2.4 Encode 5.2.5 Abstract/Elaborate 5.2.6 Filter 5.2.7 Connect 5.2.8 Animate 5.3 Low-Level Requirements for Graphs 5.3.1 Panel 5.3.2 Node and Edge 5.3.3 Interface 5.3.4 Algorithm 5.4 Mapping of Low-Level Requirements to User-Level Requirements 5.5 Specific Visualization Requirements for Lattices 5.5.1 Lattice Zoom/Recursive Lattices/Partly Nested Lattices 5.5.2 Planarity 5.5.3 Labels 5.5.4 Selection of Ideals, Filters and Intervalls 5.5.5 Restricted Moving of Elements 5.5.6 Layout Algorithms 5.5.7 Additional Feature: Three Dimensions and Rotation 5.5.8 Additional Feature: Nesting 6 FCAFOX Framework for Formal Concept Analysis in JAVA 6.1 Architecture A Appendix A.1 Synonym Lexicon A.2 Galois Connections & Galois Lattices A.3 Fault Tolerance Extensions to Formal Concept Analysis / Entwurf und Beweis eines Algorithmus zur Berechnung inkrementeller Änderungen in einem beschrifteten dargestellten Begriffsverband beim Einfügen oder Entfernen einer Merkmalsspalte im zugrundeliegenden formalen Kontext. Weiterhin sind einige Details zur Implementation sowie zum mathematischen Hintergrundwissen dargestellt.:1 Introduction 1.1 Acknowledgements 1.2 Supporting University: TU Dresden, Institute for Algebra 1.3 Supporting Corporation: SAP AG, Research Center Dresden 1.4 Research Project: CUBIST 1.5 Task Description und Structure of the Diploma Thesis I Mathematical Details 2 Fundamentals of Formal Concept Analysis 2.1 Concepts and Concept Lattice 2.2 Visualizations of Concept Lattices 2.2.1 Transitive Closure and Transitive Reduction 2.2.2 Neighborhood Relation 2.2.3 Line Diagram 2.2.4 Concept Diagram 2.2.5 Vertical Hybridization 2.2.6 Omitting the top and bottom concept node 2.2.7 Actions on Concept Diagrams 2.2.8 Metrics on Concept Diagrams 2.2.9 Heatmaps for Concept Diagrams 2.2.10 Biplots of Concept Diagrams 2.2.11 Seeds Selection 2.3 Apposition of Contexts 3 Incremental Updates for Concept Diagrams 3.1 Insertion & Removal of a single Attribute Column 3.1.1 Updating the Concepts 3.1.2 Structural Remarks 3.1.3 Updating the Order 3.1.4 Updating the Neighborhood 3.1.5 Updating the Concept Labels 3.1.6 Updating the Reducibility 3.1.7 Updating the Arrows 3.1.8 Updating the Seed Vectors 3.1.9 Complete IFOX Algorithm 3.1.10 An Example: Stepwise Construction of FCD(3) 3.2 Setting & Deleting a single cross 4 Iterative Exploration of Concept Lattices 4.1 Iceberg Lattices 4.2 Alpha Iceberg Lattices 4.3 Partly selections 4.3.1 Example with EMAGE data 4.4 Overview on Pruning & Interaction Techniques II Implementation Details 5 Requirement Analysis 5.1 Introduction 5.2 User-Level Requirements for Graphs 5.2.1 Select 5.2.2 Explore 5.2.3 Reconfigure 5.2.4 Encode 5.2.5 Abstract/Elaborate 5.2.6 Filter 5.2.7 Connect 5.2.8 Animate 5.3 Low-Level Requirements for Graphs 5.3.1 Panel 5.3.2 Node and Edge 5.3.3 Interface 5.3.4 Algorithm 5.4 Mapping of Low-Level Requirements to User-Level Requirements 5.5 Specific Visualization Requirements for Lattices 5.5.1 Lattice Zoom/Recursive Lattices/Partly Nested Lattices 5.5.2 Planarity 5.5.3 Labels 5.5.4 Selection of Ideals, Filters and Intervalls 5.5.5 Restricted Moving of Elements 5.5.6 Layout Algorithms 5.5.7 Additional Feature: Three Dimensions and Rotation 5.5.8 Additional Feature: Nesting 6 FCAFOX Framework for Formal Concept Analysis in JAVA 6.1 Architecture A Appendix A.1 Synonym Lexicon A.2 Galois Connections & Galois Lattices A.3 Fault Tolerance Extensions to Formal Concept Analysis