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1
Wilder, A. J. "Algebraic tables : abstract computability and system documentation." Thesis, Swansea University, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.636599.
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This thesis builds on the work of D. Parnas and other collaborators on the Naval Research Laboratory's pilot Software Cost Reduction Scheme for the A-7E aircraft. This thesis incorporates the tabular approach pioneered by this project into an algebraic environment to benefit the writers of algebraic specifications. Using generic techniques from research from the Software Engineering Research Group at McMaster this thesis defines six classes of function tables which may be used to define algebraic operations. Four of the six classes of function tables are: simple (finite non-recursive), nested, infinite and recursive. The remaining two are constructed by combining nested infinite and nested recursive function tables. Using Effective Definition Schemes (eds) of Friedman as a model of computation, we define the semantics of the classes of infinite function tables (simple or nested). For the class of finite function tables we restrict eds to finite eds. For the class of recursive function tables we extend eds to recursive eds. For all three models of computation we compare their computability with While and Straight Line high level programs. In addition, for the recursive eds we construct both their denotional and operational semantics and prove, in detail, their equivalence. The thesis concludes by applying the defined function tables to specifying embedded-systems, or interactive deterministic systems, which are not necessarily safety-critical. The hope is that these techniques can be used to engineer software to higher standards at the design stage of a project to reduce expensive maintenance costs. To illustrate the feasibility of this aim, we describe our experiences (with the supporting company Digita International) at applying these algebraic tables to documenting a commercial software feature.
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Pietschker, Andrej. "Automated test generation from algebraic specifications." Thesis, University of Newcastle Upon Tyne, 2002. http://hdl.handle.net/10443/2015.
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This thesis is a contribution to work on the specification-based testing of computing systems. The development of computing systems is a challenging task. A great deal of research has been directed at support for analysis, design and implementation aspects, yielding a wide range of development techniques. However, the crucial area of system testing remains relatively under-explored. Because a project may spend a good part of its budget on testing, even modest improvements to the cost-effectiveness of testing represent substantial improvements in project budgets. Relatively little literature has been devoted to the entire testing process, including specification, generation, execution and validation. Most of the academic literature seems to assume a revolutionary change of the testing framework. On the contrary industry follows a more traditional approach consisting of trusted methods and based on personal experience. There is a need for testing methods that improve the effectiveness of testing but do so at reasonable cost and which do not require a revolutionary change in the development technology. The novel goal of the work described in this thesis is to "lift" traditional testing so that it takes advantage of system specifications. We provide a framework - hepTEsT- which is motivated by this goal. To that end, hepTEsT is a framework consisting of a specification language, a technology for generating tests in accordance with test strategies, a means of applying the tests to the implementations and support for validation of outcomes against the specification-based tests. We will first categorise different testing methodologies and then examine some of the past and present approaches to test data: we develop only the necessary theoretical foundations for hepSPEc and always consider the requirements of testing. The formalism hepSPEc for system description is based upon a well-defined algebraic approach. It utilises a novel approach allowing the description of finite domains in a way suitable for engineering purposes. The engineers' tasks are to provide an adequate description of the system in hepSPEC. The approach proposed in this thesis is grounded in the traditional approach to testing where test data is provided to the system under test and the outcome is compared to the expected outcome. To enhance the capabilities of the framework a general order on test inputs is proposed to be used in test strategies. Traditional testing strategies requiring an order on test inputs are introduced and their realisation in hepTEsT discussed as well as a proposal of new strategies which lend themselves to this particular approach. The manipulation of the specification yields abstract test cases which are then transformed into test cases suitable for the chosen implementation of the system. This transformation, called test reification, is necessary to bridge the "abstraction gap" between the abstract specification-derived tests and the concrete implementation on which the test must run. The transformation is necessary in order for the approach to be practical and is achieved through homomorphisms which are expressed in specially adapted grammars. This transformation is also applied to the generated test outcome and is aimed there at easing test result validation. The utility of the hepTEsT approach is illustrated by means of a simple example, a larger case study and one carried out within the aviation industry.
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Weickert, J. "Navier-Stokes equations as a differential-algebraic system." Universitätsbibliothek Chemnitz, 1998. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-199800942.
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Nonsteady Navier-Stokes equations represent a differential-algebraic system of strangeness index one after any spatial discretization. Since such systems are hard to treat in their original form, most approaches use some kind of index reduction. Processing this index reduction it is important to take care of the manifolds contained in the differential-algebraic equation (DAE). We investigate for several discretization schemes for the Navier-Stokes equations how the consideration of the manifolds is taken into account and propose a variant of solving these equations along the lines of the theoretically best index reduction. Applying this technique, the error of the time discretisation depends only on the method applied for solving the DAE.
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El, Nabrawy Iman Mohamed Omar. "Algebraic issues in linear multi-dimensional system theory." Thesis, Loughborough University, 2006. https://dspace.lboro.ac.uk/2134/36004.
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1-D Multivariable system theory has been developed richly over the past fifty years using various approaches. The classical approach includes the matrix fraction description (MFD), the state-space approach etc., while the behavioural approach is relatively new. Nowadays, however there is an enormous need to develop this theory for systems where information depends on more than one independent variable i.e. the n-D system theory (n ≥ 2), due to the vast number of applications for these kind of systems. By contrast to the 1-D system theory, the n-D system theory is less developed and its main aspects are not yet complete, where generalising the results from 1-D to n-D has proved to be not straight forward nor smooth. This could be attributed to the n-D polynomial matrices which are the basic elements used in the analysis of n-D systems. n-D polynomial matrices are more difficult to manipulate when compared to the 1-D polynomial matrices used in the analysis of 1-D systems, because the ring of n-D polynomials to which their elements belong does not possess many of the favourable properties which the ring of 1-D polynomials possesses. The work proposed in this thesis considers the Rosenbrock system matrix and the matrix fraction description approaches to the study of n-D systems.
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Hjelmblom, Magnus. "Norm-Regulation of Agent Systems : Instrumentalizing an algebraic approach to agent system norms." Doctoral thesis, Stockholms universitet, Institutionen för data- och systemvetenskap, 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-120602.
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An architecture for norm-regulated multi-agent systems based on an algebraic approach to normative systems is instrumentalized and further developed. The core of the instrumentalization is a Prolog module, which together with a Java library can be used for creating client/server-based runtime systems. Norms are represented as conditional sentences, whose normative consequences are formulated by applying normative operators to descriptive conditions. From such general normative conditions follow normative sentences regarding specific states of affairs. These in turn result in permission or prohibition of individual actions in specific situations. Furthermore, an approach to turning runtime systems into instruments for problem-solving by using evolutionary mechanisms for evolving normative systems, is presented. The construction of norm-creating operators on conditions, which forms the basis for the representation of normative systems, is approached from two angles. (i) A logical analysis based on the Kanger-Lindahl theory of normative positions is conducted. This results in two extended sets of types of normative positions, and based on an algebraic version of one of these extended systems, a set of operators for creating agent-specific norms is constructed. (ii) An alternative analysis, which takes as its starting point a systematic exploration of types of state transitions, yields a set of norm-creating operators based on prohibition of transition types. It is furthermore argued that in the context of a class of transition systems, in which transitions are deterministic and associated with a single agent performing an act, operators based on (ii) specify a meaningful semantics of operators based on (i). Theoretical results together with shared code and example applications contribute to make possible theoretically sound, transparently described, and efficiently implemented norm-regulated autonomous agent systems.En arkitektur för normreglerade multiagentsystem baserad på en algebraisk representation av normativa system instrumentaliseras och vidareutvecklas. Kärnan i instrumentaliseringen utgörs av en Prolog-modul som tillsammans med ett Java-bibliotek kan användas för att skapa client/server-baserad körbar kod. Normer representeras som ordnade par av grundvillkor och följdvillkor. De senare konstrueras genom att normativa operatorer appliceras på deskriptiva villkor. Från sådana generella normativa villkor följer normativa satser om specifika sakförhållanden, vilka i sin tur ger upphov till förbud mot eller tillåtelse att utföra enskilda handlingar i olika situationer. Vidare skisseras en metod för att göra körbara multiagentsystem till verktyg för problemlösning genom att använda evolutionära mekanismer för att odla fram normativa system. Konstruktionen av normskapande operatorer på villkor, vilka ligger till grund för representationen av normativa system, betraktas ur två olika synvinklar. (i) En logisk analys, baserad på Kanger-Lindahls teori om normativa positioner. Denna resulterar i två utökade uppsättningar av typer av normativa positioner och utgående från en algebraisk version av ett av dessa utökade system konstrueras sedan en uppsättning operatorer för att skapa agentspecifika normer. (ii) En alternativ analys, som tar sin utgångspunkt i en systematisk undersökning av olika typer av tillståndsövergångar. Denna ger upphov till en uppsättning av normskapande operatorer som är baserade på förbud mot olika typer av övergångar. Argument presenteras vidare för att inom ramen för en klass av övergångssystem, där övergångar är deterministiska och associerade med en agent som utför en handling, så specificerar operatorer baserade på (ii) en meningsfull semantik för operatorer baserade på (i). Teoretiska resultat tillsammans med tillgängliggjord programkod och exempel på tillämpningar bidrar till att underlätta skapandet av teoretiskt sunda, transparent beskrivna och effektivt implementerade normreglerade system av autonoma agenter.
At the time of the doctoral defense, the following papers were unpublished and had a status as follows: Paper 4: Submitted. Paper 5: Forthcoming.
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Moyer, Nathan Thomas. "A knapsack-type cryptographic system using algebraic number rings." Pullman, Wash. : Washington State University, 2010. http://www.dissertations.wsu.edu/Dissertations/Spring2010/n_moyer_032610.pdf.
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Almaghrawi, Ahmed Almaamoun. "The application of an algebraic constraint system in electromagnetics." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1999. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape8/PQDD_0021/MQ55016.pdf.
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Almaghrawi, Ahmed Almaamoun. "The application of an algebraic constraint system in electormagnetics /." Thesis, McGill University, 1999. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=29852.
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Constraint propagation by means of an Algebraic Constraint System (ACS) can be used to assist the designer to explore a design space. Network transformation has been used for two purposes: first to find implicit constraints that can then be used to avoid the Missing Propagation Path problem (MPP). These new constraints can allow local propagation to succeed. Secondly, network transformation has been used to help verify the algebraic integrity of the model.ACS has the ability to solve a set of equations. Also, it is able to answer user queries and reveal the reasoning process used in obtaining a solution. With respect to inconsistencies, the system is able to verify the data provided by the user. In the case of inconsistencies, the user is notified as to the appropriate course of action to be taken.
The system has the ability to permit the user to investigate other design possibilities and find alternate design paths. Also, the system allows a default design strategy that can be imposed by an expert and invoked by a novice designer. The purpose is to provide assistance and guidelines to a novice designer, thereby allowing him to reach the desired solution.
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Scott, B. G. O. "A methodology for formal system development using process algebraic techniques." Thesis, University of Oxford, 1994. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.294356.
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Hays, Christopher Thomas. "An algebraic axiom environment for software testing (axenvironment)." Diss., The University of Arizona, 1993. http://hdl.handle.net/10150/186399.
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This dissertation describes the design and implementation of an algebraic axiom support environment for software testing. Since absolute software correctness is undecidable, "approximate" correctness is as good as software engineering can hope to do. The approximately correct behavior of a software system with respect to a specification can only be demonstrated incrementally, beginning with the modules of a system and finishing with the external interface. Software module specification in the form of algebraic axioms provides a base from which we can be complete and concise in developing and testing the behavior of modules. Algebraic axioms can also be useful for a variety of software issues such as reusability, completeness and consistency of a requirements specification, and the definition of abstract and hierarchical data types. The primary focus of this dissertation is that algebraic axioms can provide a complete and consistent means to record a specification with which to test a software system's behavior at the module level. A major aim of this research has been to specify and develop sufficient support software to demonstrate the viability of this approach in actual software development, making design for testability a development parameter. This research focuses on the following issues: (1) The relationship between algebraic axioms and other formal methods for specifying software behavior. (2) Extensions needed to make the algebraic axiom method encompass testing. (3) What software support is necessary to make algebraic specifications, with our extensions, useful for real-world software development. Results indicate that using the formal method of algebraic specifications can have a positive impact on software development when adequate and realistic support software is introduced into the process. The approach results in additional initial labor for a software system, but is shown to be economical in terms of testing completeness, maintenance, and potential reuse.
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Saldanha, Carlos M. "An algebraic constraint system for computer-aided design in magnetics /." Thesis, McGill University, 1988. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=64003.
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Eghosa, Edeghagba Elijah. "Ω-Algebraic Structures." Phd thesis, Univerzitet u Novom Sadu, Prirodno-matematički fakultet u Novom Sadu, 2017. https://www.cris.uns.ac.rs/record.jsf?recordId=104206&source=NDLTD&language=en.
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The research work carried out in this thesis is aimed at fuzzifying algebraic and relational structures in the framework of Ω-sets, where Ω is a complete lattice.Therefore we attempt to synthesis universal algebra and fuzzy set theory. Our investigations of Ω-algebraic structures are based on Ω-valued equality, satisability of identities and cut techniques. We introduce Ω-algebras, Ω-valued congruences, corresponding quotient Ω-valued-algebras and Ω-valued homomorphisms and we investigate connections among these notions. We prove that there is an Ω-valued homomorphism from an Ω-algebra to the corresponding quotient Ω-algebra. The kernelof an Ω-valued homomorphism is an Ω-valued congruence. When dealing with cut structures, we prove that an Ω-valued homomorphism determines classical homomorphisms among the corresponding quotient structures over cut subalgebras. In addition, an Ω-valued congruence determines a closure system of classical congruences on cut subalgebras. In addition, identities are preserved under Ω-valued homomorphisms. Therefore in the framework of Ω-sets we were able to introduce Ω-attice both as an ordered and algebraic structures. By this Ω-poset is defined as an Ω-set equipped with Ω-valued order which is antisymmetric with respect to the corresponding Ω-valued equality. Thus defining the notion of pseudo-infimum and pseudo-supremum we obtained the definition of Ω-lattice as an ordered structure. It is also defined that the an Ω-lattice as an algebra is a bi-groupoid equipped with an Ω-valued equality fulfilling some particular lattice Ω-theoretical formulas. Thus using axiom of choice we proved that the two approaches are equivalent. Then we also introduced the notion of complete Ω-lattice based on Ω-lattice. It was defined as a generalization of the classical complete lattice.We proved results that characterizes Ω-structures and many other interesting results.Also the connection between Ω-algebra and the notion of weak congruences is presented.We conclude with what we feel are most interesting areas for future work.Tema ovog rada je fazifikovanje algebarskih i relacijskih struktura u okviru omega- skupova, gdeje Ω kompletna mreza. U radu se bavimo sintezom oblasti univerzalne algebre i teorije rasplinutih (fazi) skupova. Naša istraživanja omega-algebarskih struktura bazirana su na omega-vrednosnoj jednakosti,zadovoljivosti identiteta i tehnici rada sa nivoima. U radu uvodimo omega-algebre,omega-vrednosne kongruencije, odgovarajuće omega-strukture, i omega-vrednosne homomorfizme i istražujemo veze izmedju ovih pojmova. Dokazujemo da postoji Ω -vrednosni homomorfizam iz Ω -algebre na odgovarajuću količničku Ω -algebru. Jezgro Ω -vrednosnog homomorfizma je Ω- vrednosna kongruencija. U vezi sa nivoima struktura, dokazujemo da Ω -vrednosni homomorfizam odredjuje klasične homomorfizme na odgovarajućim količničkim strukturama preko nivoa podalgebri. Osim toga, Ω-vrednosna kongruencija odredjuje sistem zatvaranja klasične kongruencije na nivo podalgebrama. Dalje, identiteti su očuvani u Ω- vrednosnim homomorfnim slikama.U nastavku smo u okviru Ω-skupova uveli Ω-mreže kao uredjene skupove i kao algebre i dokazali ekvivalenciju ovih pojmova. Ω-poset je definisan kao Ω -relacija koja je antisimetrična i tranzitivna u odnosu na odgovarajuću Ω-vrednosnu jednakost. Definisani su pojmovi pseudo-infimuma i pseudo-supremuma i tako smo dobili definiciju Ω-mreže kao uredjene strukture. Takodje je definisana Ω-mreža kao algebra, u ovim kontekstu nosač te strukture je bi-grupoid koji je saglasan sa Ω-vrednosnom jednakošću i ispunjava neke mrežno-teorijske formule. Koristeći aksiom izbora dokazali smo da su dva pristupa ekvivalentna. Dalje smo uveli i pojam potpune Ω-mreže kao uopštenje klasične potpune mreže. Dokazali smo još neke rezultate koji karakterišu Ω-strukture.Data je i veza izmedju Ω-algebre i pojma slabih kongruencija.Na kraju je dat prikaz pravaca daljih istrazivanja.
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Rashed, Shawki al [Verfasser], and Gerhard [Akademischer Betreuer] Pfister. "Numerical Algorithms in Algebraic Geometry with Implementation in Computer Algebra System SINGULAR / Shawki Al-Rashed. Betreuer: Gerhard Pfister." Kaiserslautern : Universitätsbibliothek Kaiserslautern, 2011. http://d-nb.info/1017757763/34.
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Sato, Kazuhiro. "An Algebraic Analysis Approach to Trajectory Tracking Control." 京都大学 (Kyoto University), 2014. http://hdl.handle.net/2433/188865.
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Syrmos, Vassilis L. "Feedback design techniques in linear system theory : geometric and algebraic approaches." Diss., Georgia Institute of Technology, 1991. http://hdl.handle.net/1853/13348.
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Song, Xuefeng. "Dynamic modeling issues for power system applications." Texas A&M University, 2003. http://hdl.handle.net/1969.1/1591.
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Power system dynamics are commonly modeled by parameter dependent nonlinear differential-algebraic equations (DAE) x p y x f ) and 0 = p y x g ) . Due to
(,, (,, the algebraic constraints, we cannot directly perform integration based on the DAE. Traditionally, we use implicit function theorem to solve for fast variables y to get a reduced model in terms of slow dynamics locally around x or we compute y numerically at each x . However, it is well known that solving nonlinear algebraic equations analytically is quite difficult and numerical solution methods also face many uncertainties since nonlinear algebraic equations may have many solutions, especially around bifurcation points. In this thesis, we apply the singular perturbation method to model power system dynamics in a singularly perturbed ODE (ordinary-differential equation) form, which makes it easier to observe time responses and trace bifurcations without reduction process. The requirements of introducing the fast dynamics are investigated and the complexities in the procedures are explored. Finally, we propose PTE (Perturb and Taylors expansion) technique to carry out our goal to convert a DAE to an explicit state space form of ODE. A simplified unreduced Jacobian matrix is also introduced. A dynamic voltage stability case shows that the proposed method works well without complicating the applications.
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Lin, Chuan-kai. "Practical Type Inference for the GADT Type System." PDXScholar, 2010. https://pdxscholar.library.pdx.edu/open_access_etds/367.
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Generalized algebraic data types (GADTs) are a type system extension to algebraic data types that allows the type of an algebraic data value to vary with its shape. The GADT type system allows programmers to express detailed program properties as types (for example, that a function should return a list of the same length as its input), and a general-purpose type checker will automatically check those properties at compile time. Type inference for the GADT type system and the properties of the type system are both currently areas of active research. In this dissertation, I attack both problems simultaneously by exploiting the symbiosis between type system research and type inference research. Deficiencies of GADT type inference algorithms motivate research on specific aspects of the type system, and discoveries about the type system bring in new insights that lead to improved GADT type inference algorithms. The technical contributions of this dissertation are therefore twofold: in addition to new GADT type system properties (such as the prevalence of pointwise type information flow in GADT patterns, a generalized notion of existential types, and the effects of enforcing the GADT branch reachability requirement), I will also present a new GADT type inference algorithm that is significantly more powerful than existing algorithms. These contributions should help programmers use the GADT type system more effectively, and they should also enable language implementers to provide better support for the GADT type system.
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Gabrielson, Donald D. "Battle group stationing algebraic modeling system : an anti-air warfare tactical decision aid methodology /." Thesis, Monterey, Calif. : Springfield, Va. : Naval Postgraduate School ; Available from National Technical Information Service, 1995. http://handle.dtic.mil/100.2/ADA296246.
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Barrachina, Sergio, Peter Benner, and Enrique S. Quintana-Ortí. "Solving Large-Scale Generalized Algebraic Bernoulli Equations via the Matrix Sign Function." Universitätsbibliothek Chemnitz, 2006. http://nbn-resolving.de/urn:nbn:de:swb:ch1-200601684.
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We investigate the solution of large-scale generalized algebraic Bernoulli equations as those arising in control and systems theory in the context of stabilization of linear dynamical systems, coprime factorization of rational matrix-valued functions, and model reduction. The algorithms we propose, based on a generalization of the Newton iteration for the matrix sign function, are easy to parallelize, yielding an efficient numerical tool to solve large-scale problems. Both the accuracy and the parallel performance of our implementations on a cluster of Intel Xeon processors are reported.
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Miscione, Steven. "Loop algebras and algebraic geometry." Thesis, McGill University, 2008. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=116115.
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This thesis primarily discusses the results of two papers, [Hu] and [HaHu]. The first is an overview of algebraic-geometric techniques for integrable systems in which the AKS theorem is proven. Under certain conditions, this theorem asserts the commutatvity and (potential) non-triviality of the Hamiltonian flow of Ad*-invariant functions once they're restricted to subalgebras. This theorem is applied to the case of coadjoint orbits on loop algebras, identifying the flow with a spectral curve and a line bundle via the Lax equation. These results play an important role in the discussion of [HaHu], wherein we consider three levels of spaces, each possessing a linear family of Poisson spaces. It is shown that there exist Poisson mappings between these levels. We consider the two cases where the underlying Riemann surface is an elliptic curve, as well as its degeneration to a Riemann sphere with two points identified (the trigonometric case). Background in necessary areas is provided.
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Groechenig, Michael. "Autoduality of the Hitchin system and the geometric Langlands programme." Thesis, University of Oxford, 2013. http://ora.ox.ac.uk/objects/uuid:f0a08e96-2f25-4df1-9e56-99931e411f73.
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This thesis is concerned with the study of the geometry and derived categories associated to the moduli problems of local systems and Higgs bundles in positive characteristic. As a cornerstone of our investigation, we establish a local system analogue of the BNR correspondence for Higgs bundles. This result (Proposition 4.3.1) relates flat connections to certain modules of an Azumaya algebra on the family of spectral curves. We prove properness over the semistable locus of the Hitchin map for local systems introduced by Laszlo–Pauly (Theorem 4.4.1). Moreover, we show that with respect to this Hitchin map, the moduli stack of local systems is étale locally equivalent to the moduli stack of Higgs bundles (Theorem 4.6.3) (with or without stability conditions). Subsequently, we study two-dimensional examples of moduli spaces of parabolic Higgs bundles and local systems (Theorem 5.2.1), given by equivariant Hilbert schemes of cotangent bundles of elliptic curves. Furthermore, the Hilbert schemes of points of these surfaces are equivalent to moduli spaces of parabolic Higgs bundles, respectively local systems (Theorem 5.3.1). The proof for local systems in positive characteristic relies on the properness results for the Hitchin fibration established earlier. The Autoduality Conjecture of Donagi–Pantev follows from Bridgeland–King–Reid’s McKay equivalence in these examples. The last chapter of this thesis is concerned with the con- struction of derived equivalences, resembling a Geometric Langlands Correspondence in positive characteristic, generalizing work of Bezrukavnikov–Braverman. Away from finitely many primes, we show that over the locus of integral spectral curves, the derived category of coherent sheaves on the stack of local systems is equivalent to a derived category of coherent D-modules on the stack of vector bundles. We conclude by establishing the Hecke eigenproperty of Arinkin’s autoduality and thereby of the Geometric Langlands equivalence in positive characteristic.
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PUERTO, AUBEL ADRIAN. "Algebraic Structures for the Analysis of Distributability of Elementary Systems and their Processes." Doctoral thesis, Università degli Studi di Milano-Bicocca, 2019. http://hdl.handle.net/10281/241253.
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In questa tesi studio in che modi si possono distribuire i sistemi e i
processi che quei sistemi eseguono. La nozione centrale per raggiungere
l'obiettivo è che, quando un sistema è distribuito, una sua osservazione
"da lontano" richiede uno scambio d'informazioni con le diverse parti
del sistema. Questo approccio si caratterizza per il fatto che la
"sincronizzazione" (o "handshaking") è il modo fondamentale di interazione.
I formalismi impiegati sono presi dalla teoria delle reti di Petri.
I sistemi elementari e i sistemi di condizioni ed eventi in quella teoria
costituiscono le specificazioni di sistemi. Le reti causali e gli insiemi
parzialmente ordinati permettono di modellare processi. In questi modelli,
lo stato dell'arte offre una nozione di sottoprocesso, cui si può
associare una struttura che porta l'informazione su come distribuire il
processo. Formalmente, questa struttura è un reticolo ortomodulare.
Nella tesi mostro che gli elementi minimali non banali di quel reticolo
(sottoprocessi minimali) possono essere ordinati in modo da formare
un'astrazione del processo dato. La natura di questa nozione di
sottoprocesso consente di mostrare che l'astrazione rappresenta le
componenti del processo, cioè le parti che possono operare indipendentemente.
Il comportamento dei sistemi elementari e dei sistemi di condizioni e
eventi è modellato per mezzo di sistemi di transizioni etichettate.
Nella tesi si applica un'interpretazione delle regioni elementari come
proprietà localmente osservabili del sistema, motivata dalla sintesi di
reti elementari. Secondo questa interpretazione, le regioni elementari
offrono una specificazione adeguata dell'infrastruttura su cui si può
distribuire un sistema.
Era già noto che l'insieme delle regioni di un sistema elementare o di
condizioni ed eventi forma un insieme ortomodulare, da cui si può ricavare
un sistema di transizioni etichettate canonico, che contiene tutte le
regioni dell'insieme ortomodulare dato. Stabilire se il sistema canonico
ha più regioni di quelle specificate è un problema aperto.
Il sistema canonico è il più "grande" che si può ottenere dall'insieme
ortomodulare, nel senso che ogni altro sistema conforme alla specificazione
è un suo sottosistema. D'altra parte, non tutti i sottosistemi hanno
la stessa struttura regionale. Definisco una condizione sufficiente per
avere l'isomorfismo. Il risultato si ottiene dotando di un'opportuna
struttura l'insieme degli eventi, o delle etichette, del sistema canonico,
così da riflettere la concorrenza.
Un insieme ortomodulare si dice stabile quando è isomorfo all'insieme delle
regioni del sistema di transizioni canonico derivato. Erano già note
condizioni sotto le quali il primo insieme si immerge nel secondo.
Si congettura che tutti gli insiemi parzialmente ordinati ottenuti come
insiemi di regioni di sistemi elementari (insiemi regionali) sono stabili.
Nella tesi si dà una nuova condizione necessaria perché un insieme ortomodulare
sia regionale, e si mostra che in quel caso l'immersione è forte.
Non tutte le immersioni sono forti, ma tutti gli isomorfismi sono
immersioni forti. Dal risultato segue che l'immersione mappa regioni
minimali su regioni minimali.This work studies systems, and the processes they execute, in the way they can be distributed. To this aim, the central notion is that when a system is distributed, a remote observation requires an exchange of information from the different locations of the system. This approach is characterised by the fact that handshaking is the basic mode of interaction. The chosen formalisms are taken in the framework Petri net theory. Elemen- tary net systems, and condition/event net systems provide specifications for the systems. Causal nets and partially ordered sets allow for modelling processes. With these last formalisations, the state of the art provides a notion of subpro- cesses that can be structured so as to carry information on how a process can be distributed. This structure is formalised as an orthomodular lattice. This work shows that the minimal non trivial elements of this lattice, the minimal subprocesses, can be ordered so as to provide an abstraction of the process. The nature of this notion of subprocess permits to show that this abstraction depicts the localities of the process, parts of the process which can run independently from each other. The behaviour of elementary, and condition/event net systems, is modelled with labelled transition systems. This work adheres to an interpretation of the set of elementary regions, as the one of locally observable properties of the sys- tem, motivated by elementary net synthesis. According to this interpretation, elementary regions represent a suitable specification of the available infrastruc- ture on which to distribute a system. The state of the art shows that the set of regions of an elementary, or condition/event system, forms an orthomodular poset, and a way to retrieve a canonical labelled transition system such that all regions of the orthomodular poset are also regions of it. The question of whether this canonical transition system has more regions than the specified ones is an open problem. The canonical transition system is the largest one can obtain from an orthomodular poset, in the sense that systems complying with the specification, can be found as subsystems of it. However, not all its subsystems display the same regional structure. This work presents a sufficient condition for this to happen. This is achieved by providing a structure to the set of events, or labels, of the canonical system, which reflects concurrency. An orthomodular poset is called stable when it is isomorphic to the set of regions of its canonical transition system. The state of the art shows that when the first poset is of a given class, it embeds in the second. It is conjectured that all posets that arise as the set of elementary regions of an elementary system, regional posets, are stable. This work provides a condition necessary for an orthomodular poset to be regional, and shows that when it holds, the embedding is strong. Not every embedding is strong, but all isomorphisms are, in particular, strong embeddings. This result implies that the embedding maps minimal regions to minimal regions.
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Rebahi, Yacine. "Irrégularité des D-modules algébriques holonomes." Université Joseph Fourier (Grenoble ; 1971-2015), 1996. http://www.theses.fr/1996GRE10205.
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Ce travail est consacre a l'etude de l'irregularite des systemes differentiels algebriques holonomes. Nous demontrons que les complexes de solutions de type exponentiel, associes a ces systemes, sont a cohomologie constructible et nous calculons leur caracteristique d'euler poincare. Pour cela, et dans le cas d'un fibre de rang un, nous utilisons un passage a l'infini qui nous permet de nous ramener a des resultats connus pour des solutions formelles de croissance appropriee pour des systemes analytiques holonomes. D'autre part, si nous microlocalisons nos constructions, nous obtenons des resultats analogues dans le cas d'un fibre de rang quelconque
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Chapman, Suzannah M. "TEACHING AN ALGEBRAIC EQUATION TO HIGH SCHOOL STUDENTS WITH MODERATE TO SEVERE INTELLECTUAL DISABILITY." UKnowledge, 2016. http://uknowledge.uky.edu/edsrc_etds/25.
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The purpose of this study was to examine the effectiveness of using the system of least prompts and concrete representations to teach students with moderate and severe disabilities (MSD) to solve simple linear equations. A multiple-probe (days) across participants, single case research design was used to evaluate the effectiveness of task analytic instruction along with concrete representation on teaching students with MSD to solve algebraic equations. The results showed the system of least prompts and concrete representations were effective in teaching students with MSD to solve simple linear equations.
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Leclerc, Marc-Antoine. "Homogeneous Projective Varieties of Rank 2 Groups." Thèse, Université d'Ottawa / University of Ottawa, 2012. http://hdl.handle.net/10393/23558.
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Root systems are a fundamental concept in the theory of Lie algebra. In this thesis, we will use two different kind of graphs to represent the group generated by reflections acting on the elements of the root system. The root
systems we are interested in are those of type A2, B2 and G2. After drawing the graphs, we will study the algebraic groups corresponding to those root systems. We will use three different techniques to give a geometric description of the homogeneous spaces G/P where G is the algebraic group corresponding to the root system and P is one of its parabolic subgroup. Finally, we will make a link between the graphs and the multiplication of
basis elements in the Chow group CH(G/P).
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Haiech, Mercedes. "Étude algébrique des systèmes d'équations différentielles polynomiales d'ordre arbitraire." Thesis, Rennes 1, 2020. http://www.theses.fr/2020REN1S035.
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Dans cette thèse, plusieurs axes d'études dont le dénominateur commun est l'algèbre différentielle ont été suivis pour mettre en lumière certaines propriétés algébriques des systèmes d'équations différentielles. Dans une partie nous nous sommes interessée à la surdétermination des systèmes d'équations différentielles linéaires ordinaires et avons produit un algorithme permettant de trouver les générateurs d'un tel système.Une autre partie se penche sur la compréhension du support de solutions d'équations différentielles partielles à l'aide d'outils issus de la géométrie tropicale. Dans une troisième partie, nous nous intéressons à l'objet géométrique décrit par l'ensemble des solutions d'une équation différentielle ordinaire et mettons en relation l'existence de composantes singulières essentielles pour l'équation différentielle considérée et la décroissance de la dimension de l'espace tangent de cet objet calculé au voisinage de solutions non dégénérées. En particulier, cette étude implique de se pencher sur la complétiond'anneaux non noethériens ; cette situation et les pathologies afférentessont par ailleurs au coeur de deux autres parties de cette thèseIn this thesis, several lines of study whose common denominator is differential algebra have been followed to highlight some algebraic properties of systems of differential equations. In one part we have been interested in the overdetermination of ordinary linear differential equation systems and have produced an algorithm to find the generators of such a system.Another part deals with the understanding of the support of partial differential equation solutions using tools from tropical geometry. In a third part, we were interested in the geometrical object described by the set of solutions of an ordinary differential equation and relate the existence of singular essential components for the considered differential equation and the decrease of the dimension of the tangent space of this object calculated at the neighborhood of non-degenerated solutions. In particular, this study involves looking at completion of non-Netherian rings; this situation and the related pathologies are also at the heart of two other parts of this thesis
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Sauthoff, Georg [Verfasser]. "Bellman's GAP : a 2nd generation language and system for algebraic dynamic programming / Georg Sauthoff. Technische Fakultät - AG Praktische Informatik." Bielefeld : Universitätsbibliothek Bielefeld, Hochschulschriften, 2011. http://d-nb.info/1015210317/34.
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Hanselmann, Thomas. "Approximate dynamic programming with adaptive critics and the algebraic perceptron as a fast neural network related to support vector machines." University of Western Australia. School of Electrical, Electronic and Computer Engineering, 2003. http://theses.library.uwa.edu.au/adt-WU2004.0005.
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[Truncated abstract. Please see the pdf version for the complete text. Also, formulae and special characters can only be approximated here. Please see the pdf version of this abstract for an accurate reproduction.] This thesis treats two aspects of intelligent control: The first part is about long-term optimization by approximating dynamic programming and in the second part a specific class of a fast neural network, related to support vector machines (SVMs), is considered. The first part relates to approximate dynamic programming, especially in the framework of adaptive critic designs (ACDs). Dynamic programming can be used to find an optimal decision or control policy over a long-term period. However, in practice it is difficult, and often impossible, to calculate a dynamic programming solution, due to the 'curse of dimensionality'. The adaptive critic design framework addresses this issue and tries to find a good solution by approximating the dynamic programming process for a stationary environment. In an adaptive critic design there are three modules, the plant or environment to be controlled, a critic to estimate the long-term cost and an action or controller module to produce the decision or control strategy. Even though there have been many publications on the subject over the past two decades, there are some points that have had less attention. While most of the publications address the training of the critic, one of the points that has not received systematic attention is training of the action module.¹ Normally, training starts with an arbitrary, hopefully stable, decision policy and its long-term cost is then estimated by the critic. Often the critic is a neural network that has to be trained, using a temporal difference and Bellman's principle of optimality. Once the critic network has converged, a policy improvement step is carried out by gradient descent to adjust the parameters of the controller network. Then the critic is retrained again to give the new long-term cost estimate. However, it would be preferable to focus more on extremal policies earlier in the training. Therefore, the Calculus of Variations is investigated to discard the idea of using the Euler equations to train the actor. However, an adaptive critic formulation for a continuous plant with a short-term cost as an integral cost density is made and the chain rule is applied to calculate the total derivative of the short-term cost with respect to the actor weights. This is different from the discrete systems, usually used in adaptive critics, which are used in conjunction with total ordered derivatives. This idea is then extended to second order derivatives such that Newton's method can be applied to speed up convergence. Based on this, an almost concurrent actor and critic training was proposed. The equations are developed for any non-linear system and short-term cost density function and these were tested on a linear quadratic regulator (LQR) setup. With this approach the solution to the actor and critic weights can be achieved in only a few actor-critic training cycles. Some other, more minor issues, in the adaptive critic framework are investigated, such as the influence of the discounting factor in the Bellman equation on total ordered derivatives, the target interpretation in backpropagation through time as moving and fixed targets, the relation between simultaneous recurrent networks and dynamic programming is stated and a reinterpretation of the recurrent generalized multilayer perceptron (GMLP) as a recurrent generalized finite impulse MLP (GFIR-MLP) is made. Another subject in this area that is investigated, is that of a hybrid dynamical system, characterized as a continuous plant and a set of basic feedback controllers, which are used to control the plant by finding a switching sequence to select one basic controller at a time. The special but important case is considered when the plant is linear but with some uncertainty in the state space and in the observation vector, and a quadratic cost function. This is a form of robust control, where a dynamic programming solution has to be calculated. ¹Werbos comments that most treatment of action nets or policies either assume enumerative maximization, which is good only for small problems, except for the games of Backgammon or Go [1], or, gradient-based training. The latter is prone to difficulties with local minima due to the non-convex nature of the cost-to-go function. With incremental methods, such as backpropagation through time, calculus of variations and model-predictive control, the dangers of non-convexity of the cost-to-go function with respect to the control is much less than the with respect to the critic parameters, when the sampling times are small. Therefore, getting the critic right has priority. But with larger sampling times, when the control represents a more complex plan, non-convexity becomes more serious.
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Almabruk, Bleblou Omalkhear Salem. "Some new lattice valued algebraic structures with comparative analysis of various approaches." Phd thesis, Univerzitet u Novom Sadu, Prirodno-matematički fakultet u Novom Sadu, 2017. https://www.cris.uns.ac.rs/record.jsf?recordId=105400&source=NDLTD&language=en.
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In this work a comparative analysis of several approaches to fuzzy algebraic structures and comparison of previous approaches to the recent one developed at University of Novi Sad has been done. Special attention is paid to reducts and expansions of algebraic structures in fuzzy settings. Besides mentioning all the relevant algebras and properties developed in this setting, particular new algebras and properties are developed and investigated. Some new structures, in particular Omega Boolean algebras, Omega Boolean lattices and Omega Boolean rings are developed in the framework of omega structures. Equivalences among these structures are elaborated in details. Transfers from Omega groupoids to Omega groups and back are demonstrated. Moreover, normal subgroups are introduced in a particular way. Their connections to congruences are elaborated in this settings. Subgroups, congruences and normal subgroups are investigated for Ω-groups. These are latticevalued algebraic structures, defined on crisp algebras which are not necessarily groups, and in which the classical equality is replaced by a lattice-valued one. A normal Ω-subgroup is defined as a particular class in an Ω-congruence. Our main result is that the quotient groups over cuts of a normal Ω- subgroup of an Ω-group G, are classical normal subgroups of the corresponding quotient groups over G. We also describe the minimal normal Ω-subgroup of an Ω-group, and some other constructions related to Ω-valued congruences.Further results that are obtained are theorems that connect various approaches of fuzzy algebraic structures. A special notion of a generalized lattice valued Boolean algebra is introduced. The universe of this structure is an algebra with two binary, an unary and two nullary operations (as usual), but which is not a crisp Boolean algebra in general. A main element in our approach is a fuzzy quivalence relation such that the Boolean algebras identities are approximately satisfied related to the considered fuzzy equivalence. Main properties of the new introduced notions are proved, and a connection with the notion of a structure of a generalized fuzzy lattice is provided.Ovaj rad bavi se komparativnom analizom različitih pristupa rasplinutim (fazi) algebarskim strukturama i odnosom tih struktura sa odgovarajućim klasičnim algebrama. Posebna pažnja posvećena je poredenju postojećih pristupa ovom problemu sa novim tehnikama i pojmovima nedavno razvijenim na Univerzitetu u Novom Sadu. U okviru ove analize, proučavana su i proširenja kao i redukti algebarskih struktura u kontekstu rasplinutih algebri. Brojne važne konkretne algebarske strukture istraživane su u ovom kontekstu, a neke nove uvedene su i ispitane. Bavili smo se detaljnim istrazivanjima Ω-grupa, sa stanovista kongruencija, normalnih podgrupa i veze sa klasicnim grupama. Nove strukture koje su u radu uvedene u posebnom delu, istrazene su sa aspekta svojstava i medusobne ekvivalentnosti. To su Ω-Bulove algebre, kao i odgo-varajuce mreže i Bulovi prsteni. Uspostavljena je uzajamna ekvivalentnost tih struktura analogno odnosima u klasičnoj algebri. U osnovi naše konstrukcije su mrežno vrednosne algebarske strukture denisane na klasičnim algebrama koje ne zadovoljavaju nužno identitete ispunjene na odgovarajucim klasičnim strukturama (Bulove algebre, prsteni, grupe itd.), već su to samo algebre istog tipa. Klasična jednakost zamenjena je posebnom kompatibilnom rasplinutom (mrežno-vrednosnom) relacijom ekvivalencije. Na navedeni nacin i u cilju koji je u osnovi teze (poredenja sa postojecim pristupima u ovoj naucnoj oblasti) proucavane su (vec denisane) Ω-grupe. U nasim istraživanju uvedene su odgovarajuće normalne podgrupe. Uspostavljena je i istražena njihova veza sa Ω-kongruencijama. Normalna podgrupa Ω-grupe definisana je kao posebna klasa Ω-kongruencije. Jedan od rezultata u ovom delu je da su količničke grupe definisane pomocu nivoa Ω-jednakosti klasične normalne podgrupe odgovarajućih količničkih podgrupa polazne -grupe. I u ovom slučaju osnovna struktura na kojoj je denisana Ω-grupa je grupoid, ne nužno grupa. Opisane su osobine najmanje normalne podgrupe u terminima Ω-kongruencija, a date su i neke konstrukcije Ω-kongruencija.Rezultati koji su izloženi u nastavku povezuju različite pristupe nekim mrežno- vrednosnim strukturama. Ω-Bulova algebra je uvedena na strukturi sa dve binarne, unarnom i dve nularne operacije, ali za koju se ne zahteva ispunjenost klasičnih aksioma. Identiteti za Bulove algebre važe kao mrežno-teoretske formule u odnosu na mrežno-vrednosnu jednakost. Klasicne Bulove algebre ih zadovoljavaju, ali obratno ne vazi: iz tih formula ne slede standardne aksiome za Bulove algebre. Na analogan nacin uveden je i Ω-Bulov prsten. Glavna svojstva ovih struktura su opisana. Osnovna osobina je da se klasične Bulove algebre odnosno Bulovi prsteni javljaju kao količničke strukture na nivoima Ω -jednakosti. Veza ove strukture sa Ω-Bulovom mrežom je pokazana.Kao ilustracija ovih istraživanja, u radu je navedeno više primera.
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Jones, Clinton Christopher. "Determining Coefficients of Checking Polynomials for an Algebraic Method of Fault Tolerant Computations of Numerical Functions." Thesis, Georgia Institute of Technology, 2004. http://hdl.handle.net/1853/5242.
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This thesis presents a practical means for determining checking polynomials for the fault tolerant computation of numerical functions. This method is based on certain algebraic features of the numerical functions such as the transcendence degree of a field extension. Checking polynomials are given for representative simple and compound numerical functions. Some of these checking models are implemented in a simulation environment. The program developed provides the means for generating checking polynomials for a broad class of numerical functions. Considerations for designing and deploying checking models are given. This numerical technique can lower costs and conserve system resources when engineering for remote or nanoscale supercomputing environments.
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Song, Kyle Seregay. "Two-Phase Flow Measurement using Fast X-ray Line Detector System." Diss., Virginia Tech, 2019. http://hdl.handle.net/10919/103371.
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Void fraction is an essential parameter for understanding the interfacial structure, and heat and mass transfer mechanisms in various gas-liquid flow systems. It becomes critically important to accurately measure void fraction as advanced high fidelity two-phase flow models require high-quality validation data. However, void fraction measurement remains a challenging task to date due to the complexity and rapid-changing characteristic of the gas-liquid boundary flow structure. This study aims to develop an advanced void fraction measurement system based on x-ray and fast line detector technologies. The dissertation has covered the major components necessary to develop a complete measurement system. Spectral analysis of x-ray attenuation in two-phase flow has been performed, and a new void fraction model is developed based on the analysis. The newly developed pixel-to-radial conversion algorithm is capable of converting measured void fraction along with the detector array to the radial distribution in a circular pipe for a wide range of void fraction conditions. The x-ray system attains the radial distributions of key measurable factors such as void fraction and gas velocity. The data are compared with the double-sensor conductivity probe and gas flowmeter for various flow conditions. The results show reasonable agreements between the x-ray and the other measurement techniques. Finally, various 2-D tomography algorithms are implemented for the non-axisymmetric two-phase flow reconstruction. A comprehensive summary of classical absorption tomography for the two-phase flow study is provided. An in-depth sensitivity study is carried out using synthetic bubbles, aiming to investigate the effect of various uncertainty factors such as background noise, off-center shift, void profile effect, etc. The sensitivity study provides a general guideline for the performance of existing 2-D reconstruction algorithms.Doctor of Philosophy
Gas-liquid flow phenomenon exists in an extensive range of natural and engineering systems, for example, hydraulic pipelines in a nuclear reactor, heat exchanger, pump cavitation, and boilers in the gas-fired power stations. Accurate measurement of the void fraction is essential to understand the behaviors of the two-phase flow phenomenon. However, measuring void fraction distribution in two-phase flow is a difficult task due to its complex and fast-changing interfacial structure. This study developed a comprehensive suite of the non-intrusive x-ray measurement techniques, and a pixel-to-radial conversion algorithm to process the line- and time-averaged void fraction information. The newly developed algorithm, called the Area-based Onion-Peeling (ABOP) method, can convert the pixel measurement to the radial void fraction distribution, which is more useful for studying and modeling axisymmetric flows. Various flow conditions are measured and evaluated for the benchmarking of the algorithm. Finally, classical 2-D reconstruction algorithms are investigated for the void fraction measurement in non-axisymmetric flows. A comprehensive summary of the performance of these algorithms for a two-phase flow study is provided. An in-depth sensitivity study using synthetic bubbles has been performed to examine the effect of uncertainty factors and to benchmark the algorithms for the non-axisymmetric flows.
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Kipps, Mark Rew. "A modular approach to modeling an isolated power system on a finite voltage bus using a differential algebraic equation solving routine." Thesis, Monterey, Calif. : Springfield, Va. : Naval Postgraduate School ; Available from National Technical Information Service, 1994. http://handle.dtic.mil/100.2/ADA281036.
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Longhi, Maurício Borges. "Controle de sistemas quadráticos sujeitos à saturação de atuadores." reponame:Biblioteca Digital de Teses e Dissertações da UFRGS, 2014. http://hdl.handle.net/10183/107486.
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O presente trabalho aborda o problema de estabilização local de sistemas não lineares quadráticos contínuos no tempo (possivelmente instáveis em malha aberta) e sujeitos a saturação de atuadores. Além disso o trabalho apresenta um estudo de técnicas de síntese de compensadores de anti-windup para sistemas quadráticos sujeitos à saturação de atuadores. A abordagem do estudo é comparativa em relação a duas formas de representação dos sistemas quadráticos. A primeira forma de abordagem é a Representação Algébrico-Diferencial — DAR (do inglês, Differential Algebraic Representation), aplicável a toda a classe de sistemas racionais. A segunda forma, por sua vez, consiste em uma decomposição quadrática, particular para sistemas quadráticos. Em ambos os casos, utiliza-se a não linearidade de zona morta e uma condição generalizada de setor para tratar da saturação. Para ambas representações, condições baseadas em Desigualdades Matriciais Lineares — LMIs (do inglês, Linear Matrix Inequalities) dependentes dos estados são obtidas para fornecer uma lei de controle linear, com o objetivo de estabilizar o sistema em malha fechada enquanto fornece uma região maximizada de estabilidade garantida associada a uma função de Lyapunov. A partir da mesma metodologia, são propostas técnicas de síntese de compensadores de anti-windup estáticos e dinâmicos. Exemplos numéricos são apresentados para verificar a eficácia dos métodos propostos.This work addresses the problem of local stabilization of continuous-time quadratic systems (possibly open-loop unstable) and subject to actuator saturation. Furthermore, the work addresses a study of techniques for synthesis of anti-windup compensators for quadratic systems subject to actuator saturation. The study approach is comparative in the sense of considering two representations of quadratic systems. The first one is the Differential Algebraic Representation — DAR, suitable for the entire class of rational systems. The second representation consists in a quadratic decomposition, particular for quadratic systems. In both cases, it is used the deadzone nonlinearity and the generalized sector condition in order to deal with the saturation. For both representations, state-dependent Linear Matrix Inequalities — LMIs conditions are obtained to provide a control law with the aim of stabilize the closed-loop system while providing a region of guaranteed stability, associated to a Lyapunov function. Based on the same methodology, techniques are proposed for the synthesis of static and dynamic anti-windup compensators. Numerical examples are presented to verify the effectiveness of proposed methods.
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Arruda, Rafael Lucas de [UNESP]. "Teorema de Riemann-Roch e aplicações." Universidade Estadual Paulista (UNESP), 2011. http://hdl.handle.net/11449/86493.
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Made available in DSpace on 2014-06-11T19:22:18Z (GMT). No. of bitstreams: 0
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arruda_rl_me_sjrp.pdf: 624072 bytes, checksum: 23ddd00e27d1ad781e2d1cec2cb65dee (MD5)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)
O objetivo principal deste trabalho é estudar o Teorema de Riemann-Roch, um dos resultados fundamentais na teoria de curvas algébricas, e apresentar algumas de suas aplicações. Este teorema é uma importante ferramenta para a classificação das curvas algébricas, pois relaciona propriedades algébricas e topológicas. Daremos uma descrição das curvas algébricas de gênero g, 1≤ g ≤ 5, e faremos um breve estudo dos pontos de inflexão de um sistema linear sobre uma curva algébrica
The main purpose of this work is to discuss The Riemann-Roch Theorem, wich is one of the most important results of the theory algebraic curves, and to present some applications. This theorem is an important tool of the classification of algebraic curves, sinces relates algebraic and topological properties. We will describle the algebraic curves of genus g, 1≤ g ≤ 5, and also study inflection points of a linear system on an algebraic curve
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Pierce, Robyn U. "An exploration of algebraic insight and effective use of computer algebra systems /." Connect to thesis, 2001. http://eprints.unimelb.edu.au/archive/00000739.
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KUSAKARI, Keiichirou, Masahiko SAKAI, and Toshiki SAKABE. "Primitive Inductive Theorems Bridge Implicit Induction Methods and Inductive Theorems in Higher-Order Rewriting." IEICE, 2005. http://hdl.handle.net/2237/9580.
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Kondo, Naoya, Kimihiro Umemura, Liren Zhou, and Hideyuki Azegami. "Shape optimization for a link mechanism." Springer, 2013. http://hdl.handle.net/2237/21125.
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Sydney, Ali. "The evaluation of software defined networking for communication and control of cyber physical systems." Diss., Kansas State University, 2013. http://hdl.handle.net/2097/15577.
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Doctor of PhilosophyDepartment of Electrical and Computer Engineering
Don Gruenbacher
Caterina Scoglio
Cyber physical systems emerge when physical systems are integrated with communication networks. In particular, communication networks facilitate dissemination of data among components of physical systems to meet key requirements, such as efficiency and reliability, in achieving an objective. In this dissertation, we consider one of the most important cyber physical systems: the smart grid. The North American Electric Reliability Corporation (NERC) envisions a smart grid that aggressively explores advance communication network solutions to facilitate real-time monitoring and dynamic control of the bulk electric power system. At the distribution level, the smart grid integrates renewable generation and energy storage mechanisms to improve reliability of the grid. Furthermore, dynamic pricing and demand management provide customers an avenue to interact with the power system to determine electricity usage that satisfies their lifestyle. At the transmission level, efficient communication and a highly automated architecture provide visibility in the power system; hence, faults are mitigated faster than they can propagate. However, higher levels of reliability and efficiency rely on the supporting physical communication infrastructure and the network technologies employed. Conventionally, the topology of the communication network tends to be identical to that of the power network. In this dissertation, however, we employ a Demand Response (DR) application to illustrate that a topology that may be ideal for the power network may not necessarily be ideal for the communication network. To develop this illustration, we realize that communication network issues, such as congestion, are addressed by protocols, middle-ware, and software mechanisms. Additionally, a network whose physical topology is designed to avoid congestion realizes an even higher level of performance. For this reason, characterizing the communication infrastructure of smart grids provides mechanisms to improve performance while minimizing cost. Most recently, algebraic connectivity has been used in the ongoing research effort characterizing the robustness of networks to failures and attacks. Therefore, we first derive analytical methods for increasing algebraic connectivity and validate these methods numerically. Secondly, we investigate impact on the topology and traffic characteristics as algebraic connectivity is increased. Finally, we construct a DR application to demonstrate how concepts from graph theory can dramatically improve the performance of a communication network. With a hybrid simulation of both power and communication network, we illustrate that a topology which may be ideal for the power network may not necessarily be ideal for the communication network. To date, utility companies are embracing network technologies such as Multiprotocol Label Switching (MPLS) because of the available support for legacy devices, traffic engineering, and virtual private networks (VPNs) which are essential to the functioning of the smart grid. Furthermore, this particular network technology meets the requirement of non-routability as stipulated by NERC, but these benefits are costly for the infrastructure that supports the full MPLS specification. More importantly, with MPLS routing and other switching technologies, innovation is restricted to the features provided by the equipment. In particular, no practical method exists for utility consultants or researchers to test new ideas, such as alternatives to IP or MPLS, on a realistic scale in order to obtain the experience and confidence necessary for real-world deployments. As a result, novel ideas remain untested. On the contrary, OpenFlow, which has gained support from network providers such as Microsoft and Google and equipment vendors such as NEC and Cisco, provides the programmability and flexibility necessary to enable innovation in next-generation communication architectures for the smart grid. This level of flexibility allows OpenFlow to provide all features of MPLS and allows OpenFlow devices to co-exist with existing MPLS devices. Therefore, in this dissertation we explore a low-cost OpenFlow Software Defined Networking solution and compare its performance to that of MPLS. In summary, we develop methods for designing robust networks and evaluate software defined networking for communication and control in cyber physical systems where the smart grid is the system under consideration.
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Kochinke, Sebastian. "Special Linear Systems on Curves and Algorithmic Applications." Doctoral thesis, Universitätsbibliothek Leipzig, 2017. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-219598.
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Seit W. Diffie und M. Hellman im Jahr 1976 ihren Ansatz für einen sicheren kryptographischen Schlüsselaustausch vorgestellten, ist der sogenannte Diskrete Logarithmus zu einem zentrales Thema der Kryptoanalyse geworden. Dieser stellt eine Erweiterung des bekannten Logarithmus auf beliebige endliche Gruppen dar.
In der vorliegenden Dissertation werden zwei von C. Diem eingeführte Algorithmen untersucht, mit deren Hilfe der diskrete Logarithmus in der Picardgruppe glatter, nichthyperelliptischer Kurven vom Geschlecht g > 3 bzw. g > 4 über endlichen Körpern berechnet werden kann. Beide Ansätze basieren auf der sogenannten Indexkalkül-Methode und benutzen zur Erzeugung der dafür benötigten Relationen spezielle Linearsysteme, welche durch Schneiden von ebenen Modellen der Kurve mit Geraden erzeugt werden.
Um Aussagen zur Laufzeit der Algorithmen tätigen zu können, werden verschiedene Sätze über die Geometrie von Kurven bewiesen. Als zentrale Aussage wird zum einem gezeigt, dass ebene Modelle niedrigen Grades effizient berechnet werden können. Zum anderen wird bewiesen, dass sich bei genügend großem Grundkörper die Anzahl der vollständig über dem Grundkörper zerfallenden Geraden wie heuristisch erwartet verhällt. Für beide Aussagen werden dabei Familien von Kurven betrachtet und diese gelten daher uniform für alle glatten, nichthyperelliptischen Kurven eines festen Geschlechts.
Die genannten Resultate führen schlussendlich zu dem Beweis einer erwarteten Laufzeit von O(q^(2-2/(g-1))) für den ersten der beiden Algorithmen, wobei q die Anzahl der Elemente im Grundkörper darstellt. Der zweite Algoritmus verbessert dies auf eine heuristische Laufzeit in O(q^(2-2/(g-2))), imdem er Divisoren von höherem Spezialiätsgrad erzeugt. Es wird bewiesen, dass dieser Ansatz für einen uniform gegen 1 konvergierenden Anteil an glatten, nichthyperelliptischen Kurven eines festen Geschlechts über Grundkörpern großer Charakteristik eine große Anzahl an Relationen erzeugt. Wiederum werden zum Beweis der zugrundeliegenden geometrischen Aussagen Familien von Kurven betrachtet, um so die Uniformität zu gewährleisten.
Beide Algorithmen wurden zudem implementiert. Zum Abschluss der Arbeit werden die Ergebnisse der entsprechenden Experimente vorgestellt und eingeordnet.
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Höfner, Peter. "Algebraic calculi for hybrid systems." Norderstedt Books on Demand, 2009. http://d-nb.info/1000477002/34.
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Grundling, Hendrik. "Algebraic structure of degenerate systems /." Title page, table of contents and summary only, 1986. http://web4.library.adelaide.edu.au/theses/09PH/09phg888.pdf.
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Hadj, Said Yanis. "Prise en compte de la complexité de modélisation dans la gestion énergétique des bâtiments." Thesis, Université Grenoble Alpes (ComUE), 2016. http://www.theses.fr/2016GREAT121/document.
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Du fait de son impact énergétique, la gestion énergétique dans le bâtiment est devenu un enjeu majeur ses dernières années, qu'il s'agisse d'encourager la sobriété énergétique ou de s'adapter aux besoins des réseaux énergétiques. Différents travaux de recherche ont conduit à des gestionnaires énergétiques souvent dotés de capacités d'anticipation. Les premiers résultats, bien qu'encourageants, n'envisagent pas la complexité tant du fait nombre d'éléments que de la diversité des applications de gestion énergétique.Cette thèse propose d'apporter des éléments de solution à la problématique de complexité. Les travaux ont démarré par l'analyse du gestionnaire énergétique GHomeTech et son adaptation au prototype de bâtiment complexe CANOPEA. Les problématiques de composition sont explorées. Une solution favorisant la réutilisabilité d'éléments de modèles, l'agrégation et la transformation vers des modèles d'optimisation de type programmation linéaire en nombres entiers (PLNE), est proposée. L'outil résultant a été validé sur le projet CANOPEA.La gestion énergétique ne se limite pas à l'optimisation PLNE. Différentes natures d'applications permettent d'offrir d'autres services : l'estimation paramétrique de modèles pour simplifier la configuration des gestionnaires énergétiques, la simulation pour la validation et la prédiction fonction de scénarios définis par exemple. Cette autre dimension de la complexité est abordée dans un second volet du manuscrit. Des solutions de réécriture automatique de modèles sont proposées grâce à des manipulations symboliques permettant différents types de transformation. Plusieurs exemples de génération automatique de modèles applicatifs sont présentésEnergy management for building has become a major issue this last decade because of its energy impact. Building energy management reduces energy wastes and enable a better matching between energy needs and grid capabilities. Different types of energy management systems are proposed in scientific literature, most of them with anticipation capacities.The first results do not really consider the complexity issue coming from the number of modeling elements and also coming from the diversity of energy management applications.This thesis proposes elements of solution to the complexity problem. The work started by analyzing the energy management system 'GHomeTech' and its adaptation to the complex building prototype CANOPEA. The issue of composition from elementary models is explored. A solution is proposed; it enables the reusability of elementary models. Aggregation and transformation into mixed integer linear programming optimization models is presented. The resulting tool has been validated on the CANOPEA project.Energy management is not limited to MILP optimization. Different types of applications are also used to provide other services: parametric estimation models to simplify the configuration of energy management systems, simulation for validation and prediction depending on pre-defined scenarios for example. This other dimension of complexity is discussed in a second part of the manuscript. Solutions for automatic rewriting of models are detailed. It relies on symbolic manipulations in different types of processing. Several examples of applications illustrating the automatic generation of models are presented
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Molgado, Alberto. "Refined algebraic quantisation : finite dimensional systems." Thesis, University of Nottingham, 2005. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.423639.
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Scheufele, Wolfgang. "Algebraic query optimization in Database Systems /." [S.l. : s.n.], 1999. http://www.bsz-bw.de/cgi-bin/xvms.cgi?SWB8299303.
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Junqueira, Luiz Antonio Custódio Manganelli. "Estudo de suavizadores para o método Multigrid algébrico baseado em wavelet." Universidade de São Paulo, 2008. http://www.teses.usp.br/teses/disponiveis/3/3143/tde-18082008-141740/.
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Este trabalho consiste na análise do comportamento do método WAMG (Wavelet-Based Algebraic Multigrid), método numérico de resolução de sistemas de equações lineares desenvolvido no LMAG-Laboratório de Eletromagnetismo Aplicado, com relação a diversos suavizadores. O fato dos vetores que compõem os operadores matriciais Pronlongamento e Restrição do método WAMG serem ortonormais viabiliza uma série de análises teóricas e de dados experimentais, permitindo visualizar características não permitidas nos outros métodos Multigrid (MG), englobando o Multigrid Geométrico (GMG) e o Multigrid Algébrico (AMG). O método WAMG V-Cycle com Filtro Haar é testado em uma variedade de sistemas de equações lineares variando o suavizador, o coeficiente de relaxação nos suavizadores Damped Jacobi e Sobre Relaxação Sucessiva (SOR), e a configuração de pré e pós-suavização. Entre os suavizadores testados, estão os métodos iterativos estacionários Damped Jacobi, SOR, Esparsa Aproximada a Inversa tipo Diagonal (SPAI-0) e métodos propostos com a característica de suavização para-otimizada. A título de comparação, métodos iterativos não estacionários são testados também como suavizadores como Gradientes Conjugados, Gradientes Bi-Conjugados e ICCG. Os resultados dos testes são apresentados e comentados.This work is comprised of WAMG (Wavelet-Based Algebraic Multigrid) method behavioral analysis based on variety of smoothers, numerical method based on linear equation systems resolution developed at LMAG (Applied Electromagnetism Laboratory). Based on the fact that the vectors represented by WAMG Prolongation and Restriction matrix operators are orthonormals allows the use of a variety of theoretical and practical analysis, and therefore gain visibility of characteristics not feasible through others Multigrid (MG) methods, such as Geometric Multigrid (GMG) and Algebraic Multigrid (AMG). WAMG V-Cycle method with Haar Filter is tested under a variety of linear equation systems, by varying smoothers, relaxation coefficient at Damped Jacobi and Successive Over Relaxation (SOR) smoothers, and pre and post smoothers configurations. The tested smoothers are stationary iterative methods such as Damped Jacobi, SOR, Diagonal type-Sparse Approximate Inverse (SPAI-0) and suggested ones with optimized smoothing characteristic. For comparison purposes, the Conjugate Gradients, Bi-Conjugate Gradient and ICCG non-stationary iterative methods are also tested as smoothers. The testing results are formally presented and commented.
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Sehnalová, Pavla. "Konvergence řešení soustav algebraických rovnic." Master's thesis, Vysoké učení technické v Brně. Fakulta informačních technologií, 2007. http://www.nusl.cz/ntk/nusl-236797.
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The work describes techniques for solving systems of linear and differential equations. It explains the definition of conversion from system of linear to system of differential equations. The method of the elementary transmission and the transform algorithm are presented. Both of methods are demonstrated on simply examples and properties of conversion are shown. The work compares fast and accurate solutions of methods and algorithm. For computing examples and solving experiments following programs were used: TKSL and TKSL/C. The program TKSL/C was enriched with the graphic user interface which makes the conversion of systems and computing results easier.
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Höfner, Peter [Verfasser]. "Algebraic calculi for hybrid systems / Peter Höfner." Norderstedt : Books on Demand, 2009. http://d-nb.info/1000477002/34.
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Matooane, ʾMantśika Amelia. "Parallel systems in symbolic and algebraic computation." Thesis, University of Cambridge, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.621402.
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Kammar, Ohad. "Algebraic theory of type-and-effect systems." Thesis, University of Edinburgh, 2014. http://hdl.handle.net/1842/8910.
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We present a general semantic account of Gifford-style type-and-effect systems. These type systems provide lightweight static analyses annotating program phrases with the sets of possible computational effects they may cause, such as memory access and modification, exception raising, and non-deterministic choice. The analyses are used, for example, to justify the program transformations typically used in optimising compilers, such as code reordering and inlining. Despite their existence for over two decades, there is no prior comprehensive theory of type-and-effect systems accounting for their syntax and semantics, and justifying their use in effect-dependent program transformation. We achieve this generality by recourse to the theory of algebraic effects, a development of Moggi’s monadic theory of computational effects that emphasises the operations causing the effects at hand and their equational theory. The key observation is that annotation effects can be identified with the effect operations. Our first main contribution is the uniform construction of semantic models for typeand- effect analysis by a process we call conservative restriction. Our construction requires an algebraic model of the unannotated programming language and a relevant notion of predicate. It then generates a model for Gifford-style type-and-effect analysis. This uniform construction subsumes existing ad-hoc models for type-and-effect systems, and is applicable in all cases in which the semantics can be given via enriched Lawvere theories. Our second main contribution is a demonstration that our theory accounts for the various aspects of Gifford-style effect systems. We begin with a version of Levy’s Callby- push-value that includes algebraic effects. We add effect annotations, and design a general type-and-effect system for such call-by-push-value variants. The annotated language can be thought of as an intermediate representation used for program optimisation. We relate the unannotated semantics to the conservative restriction semantics, and establish the soundness of program transformations based on this effect analysis. We develop and classify a range of validated transformations, generalising many existing ones and adding some new ones. We also give modularly-checkable sufficient conditions for the validity of these optimisations. In the final part of this thesis, we demonstrate our theory by analysing a simple example language involving global state with multiple regions, exceptions, and nondeterminism. We give decision procedures for the applicability of the various effect-dependent transformations, and establish their soundness and completeness.
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Rabehaja, Mananjanahary Tahiry. "Algebraic verification of probabilistic and concurrent systems." Thesis, University of Sheffield, 2014. http://etheses.whiterose.ac.uk/7456/.
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This thesis provides an algebraic modelling and verification of probabilistic concurrent systems in the style of Kleene algebra. Without concurrency, it is shown that the equational theory of continuous probabilistic Kleene algebra is complete with respect to an automata model under standard simulation equivalence. This yields a minimisation-based decision procedure for the algebra. Without probability, an event structure model of Hoare et al.'s concurrent Kleene algebra is constructed. These two algebras are then ``merged" to provide probabilistic concurrent Kleene algebra which is used to discover and prove development rules for probabilistic concurrent systems (e.g. rely/guarantee calculus). Soundness of the new algebra is ensured by models based on probabilistic automata (interleaving) and probabilistic bundle event structures (true concurrency) quotiented with the respective simulation equivalences. Lastly, event structures with implicit probabilities are constructed to provide a state based model for the soundness of the probabilistic rely/guarantee rules.