Relevant bibliographies by topics / Algebraic system

Academic literature on the topic 'Algebraic system'

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Published: 6 July 2023

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Journal articles on the topic "Algebraic system"

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Kravtsov, H. O., S. M. Hrechko, V. V. Nikitchenko, and A. M. Prymushko. "Cognitive Algebraic System." Èlektronnoe modelirovanie 44, no. 3 (June 10, 2022): 14–30. http://dx.doi.org/10.15407/emodel.44.03.014.

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Omarov, A. I. "Orthogonally complete algebraic system." Algebra and Logic 30, no. 2 (March 1991): 134–39. http://dx.doi.org/10.1007/bf01978833.

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Fu, Jun, Jinzhao Wu, and Hongyan Tan. "A Deductive Approach towards Reasoning about Algebraic Transition Systems." Mathematical Problems in Engineering 2015 (2015): 1–12. http://dx.doi.org/10.1155/2015/607013.

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Algebraic transition systems are extended from labeled transition systems by allowing transitions labeled by algebraic equations for modeling more complex systems in detail. We present a deductive approach for specifying and verifying algebraic transition systems. We modify the standard dynamic logic by introducing algebraic equations into modalities. Algebraic transition systems are embedded in modalities of logic formulas which specify properties of algebraic transition systems. The semantics of modalities and formulas is defined with solutions of algebraic equations. A proof system for this logic is constructed to verify properties of algebraic transition systems. The proof system combines with inference rules decision procedures on the theory of polynomial ideals to reduce a proof-search problem to an algebraic computation problem. The proof system proves to be sound but inherently incomplete. Finally, a typical example illustrates that reasoning about algebraic transition systems with our approach is feasible.
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Holcombe, M. "Algebraic Techniques of System Specification." Irish Mathematical Society Bulletin 0021 (1988): 13–28. http://dx.doi.org/10.33232/bims.0021.13.28.

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Cadzow, J., and O. Solomon. "Algebraic approach to system identification." IEEE Transactions on Acoustics, Speech, and Signal Processing 34, no. 3 (June 1986): 462–69. http://dx.doi.org/10.1109/tassp.1986.1164849.

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Jang, Youngho. "Algebraic Weyl system and application." Annales mathématiques Blaise Pascal 4, no. 2 (1997): 27–40. http://dx.doi.org/10.5802/ambp.95.

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HINDMAN, NEIL. "The Topological-Algebraic System(?N, +, ?)." Annals of the New York Academy of Sciences 704, no. 1 Papers on Gen (December 1993): 155–63. http://dx.doi.org/10.1111/j.1749-6632.1993.tb52519.x.

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Letichevskii, A. A., and V. G. Marinchenko. "Objects in algebraic programming system." Cybernetics and Systems Analysis 33, no. 2 (March 1997): 283–99. http://dx.doi.org/10.1007/bf02665902.

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Phusanga, D., and J. Koppitz. "Some varieties of algebraic systems of type ((n),(m))." Asian-European Journal of Mathematics 12, no. 01 (February 2019): 1950005. http://dx.doi.org/10.1142/s1793557119500050.

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In the present paper, we classify varieties of algebraic systems of the type [Formula: see text], for natural numbers [Formula: see text] and [Formula: see text], which are closed under particular derived algebraic systems. If we replace in an algebraic system the [Formula: see text]-ary operation by an [Formula: see text]-ary term operation and the [Formula: see text]-ary relation by the [Formula: see text]-ary relation generated by an [Formula: see text]-ary formula, we obtain a new algebraic system of the same type, which we call derived algebraic system. We shall restrict the replacement to so-called “linear” terms and atomic “linear” formulas, respectively.
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ŚWIRSZCZ, GRZEGORZ. "AN ALGORITHM FOR FINDING INVARIANT ALGEBRAIC CURVES OF A GIVEN DEGREE FOR POLYNOMIAL PLANAR VECTOR FIELDS." International Journal of Bifurcation and Chaos 15, no. 03 (March 2005): 1033–44. http://dx.doi.org/10.1142/s0218127405012442.

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Given a system of two autonomous ordinary differential equations whose right-hand sides are polynomials, it is very hard to tell if any nonsingular trajectories of the system are contained in algebraic curves. We present an effective method of deciding whether a given system has an invariant algebraic curve of a given degree. The method also allows the construction of examples of polynomial systems with invariant algebraic curves of a given degree. We present the first known example of a degree 6 algebraic saddle-loop for polynomial system of degree 2, which has been found using the described method. We also present some new examples of invariant algebraic curves of degrees 4 and 5 with an interesting geometry.
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Dissertations / Theses on the topic "Algebraic system"

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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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Books on the topic "Algebraic system"

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Bidoit, Michel, Hans-Jörg Kreowski, Pierre Lescanne, Fernando Orejas, and Donald Sannella, eds. Algebraic system specification and development. Berlin/Heidelberg: Springer-Verlag, 1991. http://dx.doi.org/10.1007/bfb0018512.

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Bogdan, Marinescu, ed. Linear time-varying systems: Algebraic-analytic approach. Berlin: Springer-Verlag, 2011.

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Moore, Derek. An expert system for linear algebraic equations. [S.l: The author], 1985.

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Astesiano, Egidio. Algebraic Foundations of Systems Specification. Berlin, Heidelberg: Springer Berlin Heidelberg, 1999.

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Ilchmann, Achim. Surveys in Differential-Algebraic Equations I. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013.

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Chen, Chi-Tsong. Control system design: Conventional, algebraic, and optimal methods. Stony Brook, NY: Pond Woods Press, 1987.

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1946-, Trivedi Kishor Shridharbhai, and Institute for Computer Applications in Science and Engineering., eds. Boolean algebraic methods for phased-mission system analysis. Hampton, Va: Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 1997.

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1946-, Trivedi Kishor Shridharbhai, and Langley Research Center, eds. Phased-mission system analysis using Boolean algebraic methods. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1993.

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1946-, Trivedi Kishor Shridharbhai, and Langley Research Center, eds. Phased-mission system analysis using Boolean algebraic methods. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1993.

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1946-, Trivedi Kishor Shridharbhai, and Langley Research Center, eds. Phased-mission system analysis using Boolean algebraic methods. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1993.

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Book chapters on the topic "Algebraic system"

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Schmid, Todd, Tobias Kappé, and Alexandra Silva. "A Complete Inference System for Skip-free Guarded Kleene Algebra with Tests." In Programming Languages and Systems, 309–36. Cham: Springer Nature Switzerland, 2023. http://dx.doi.org/10.1007/978-3-031-30044-8_12.

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AbstractGuarded Kleene Algebra with Tests (GKAT) is a fragment of Kleene Algebra with Tests (KAT) that was recently introduced to reason efficiently about imperative programs. In contrast to KAT, GKAT does not have an algebraic axiomatization, but relies on an analogue of Salomaa’s axiomatization of Kleene Algebra. In this paper, we present an algebraic axiomatization and prove two completeness results for a large fragment of GKAT consisting of skip-free programs.
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Forney, G. D. "Algebraic Structure of Convolutional Codes, and Algebraic System Theory." In Mathematical System Theory, 527–57. Berlin, Heidelberg: Springer Berlin Heidelberg, 1991. http://dx.doi.org/10.1007/978-3-662-08546-2_31.

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Baras, J. S. "Algebraic System Theory, Computer Algebra and Controller Synthesis." In Mathematical System Theory, 355–70. Berlin, Heidelberg: Springer Berlin Heidelberg, 1991. http://dx.doi.org/10.1007/978-3-662-08546-2_20.

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Rubin, Karl. "Kolyvagin’s System of Gauss Sums." In Arithmetic Algebraic Geometry, 309–24. Boston, MA: Birkhäuser Boston, 1991. http://dx.doi.org/10.1007/978-1-4612-0457-2_14.

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Fuhrmann, P. A. "Algebraic Methods in System Theory." In Mathematical System Theory, 233–65. Berlin, Heidelberg: Springer Berlin Heidelberg, 1991. http://dx.doi.org/10.1007/978-3-662-08546-2_13.

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Ferrareso Lona, Liliane Maria. "Solving an Algebraic Equations System." In A Step by Step Approach to the Modeling of Chemical Engineering Processes, 89–111. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-66047-9_5.

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Bussieck, Michael R., and Alex Meeraus. "General Algebraic Modeling System (GAMS)." In Applied Optimization, 137–57. Boston, MA: Springer US, 2004. http://dx.doi.org/10.1007/978-1-4613-0215-5_8.

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Basu, Saugata, Richard Pollack, and Marie-Francoise Roy. "Polynomial System Solving." In Algorithms in Real Algebraic Geometry, 365–419. Berlin, Heidelberg: Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/978-3-662-05355-3_12.

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Cerone, Antonio, Alex J. Cowie, and George J. Milne. "The circal system." In Algebraic Methodology and Software Technology, 563–64. Berlin, Heidelberg: Springer Berlin Heidelberg, 1997. http://dx.doi.org/10.1007/bfb0000498.

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Sahraoui, Houari A. "The METAGEN system." In Algebraic Methodology and Software Technology, 590–91. Berlin, Heidelberg: Springer Berlin Heidelberg, 1995. http://dx.doi.org/10.1007/3-540-60043-4_84.

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Conference papers on the topic "Algebraic system"

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Wang, Qing-Wen, and K. P. Shum. "The Solvability of a System of Matrix Equations over an Arbitrary Division Ring." In The International Conference on Algebra 2010 - Advances in Algebraic Structures. WORLD SCIENTIFIC, 2011. http://dx.doi.org/10.1142/9789814366311_0052.

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French, Tim, John McCabe-Dansted, and Mark Reynolds. "An Algebraic System of Temporal Structures." In 2013 20th International Symposium on Temporal Representation and Reasoning (TIME). IEEE, 2013. http://dx.doi.org/10.1109/time.2013.18.

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Letichevsky, A. A., and J. V. Kapitonova. "Algebraic programming in the APS system." In the international symposium. New York, New York, USA: ACM Press, 1990. http://dx.doi.org/10.1145/96877.96896.

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Abdali, S. Kamal, Guy W. Cherry, and Neil Soffer. "A Smalltalk system for algebraic manipulation." In Conference proceedings. New York, New York, USA: ACM Press, 1986. http://dx.doi.org/10.1145/28697.28724.

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wu, Dan, and Bin Wang. "Influence of Load Models on Equilibria, Stability and Algebraic Manifolds of Power System Differential-Algebraic System." In 2019 57th Annual Allerton Conference on Communication, Control, and Computing (Allerton). IEEE, 2019. http://dx.doi.org/10.1109/allerton.2019.8919649.

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Ghosh, Bijoy. "Algebraic geometric methods in simultaneous system design." In 1985 24th IEEE Conference on Decision and Control. IEEE, 1985. http://dx.doi.org/10.1109/cdc.1985.268660.

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Nett, Carl. "Algebraic aspects of linear control system stability." In 1985 24th IEEE Conference on Decision and Control. IEEE, 1985. http://dx.doi.org/10.1109/cdc.1985.268848.

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SCHWARZ, FRITZ. "ALLTYPES: AN ALGEBRAIC LANGUAGE AND TYPE SYSTEM." In Proceedings of the First International Congress of Mathematical Software. WORLD SCIENTIFIC, 2002. http://dx.doi.org/10.1142/9789812777171_0051.

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Moallem, M. "Attenuation of disturbances for an algebraic system." In Proceedings of American Control Conference. IEEE, 2001. http://dx.doi.org/10.1109/acc.2001.945927.

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Hojjat, H., M. R. Mousavi, and M. Sirjani. "Process algebraic verification of SystemC codes." In 2008 8th International Conference on Application of Concurrency to System Design. IEEE, 2008. http://dx.doi.org/10.1109/acsd.2008.4574597.

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Reports on the topic "Algebraic system"

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Bates, Daniel J., Daniel A. Brake, Wenrui Hao, Jonathan D. Hauenstein, Andrew J. Sommese, and Charles W. Wampler. Real Numerical Algebraic Geometry: Finding All Real Solutions of a Polynomial System. Fort Belvoir, VA: Defense Technical Information Center, February 2014. http://dx.doi.org/10.21236/ada597283.

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McWilliams, J. Algebraic coarsening methods for linear and nonlinear PDE and systems. Office of Scientific and Technical Information (OSTI), November 2000. http://dx.doi.org/10.2172/15013125.

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Brannick, J. Final Report: Subcontract B623868 Algebraic Multigrid solvers for coupled PDE systems. Office of Scientific and Technical Information (OSTI), October 2017. http://dx.doi.org/10.2172/1406429.

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Abhyankar, Shrirang, Mihai Anitescu, Emil Constantinescu, and Hong Zhang. Efficient Adjoint Computation of Hybrid Systems of Differential Algebraic Equations with Applications in Power Systems. Office of Scientific and Technical Information (OSTI), March 2016. http://dx.doi.org/10.2172/1245175.

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Lou, Xi-Cheng, Alan S. Willsky, and George C. Verghese. An Algebraic Approach to Time Scale Analysis of Singularly Perturbed Linear Systems,. Fort Belvoir, VA: Defense Technical Information Center, September 1986. http://dx.doi.org/10.21236/ada186040.

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Petzold, L. R., and J. B. Rosen. Sensitivity analysis and model reduction of nonlinear differential-algebraic systems. Final progress report. Office of Scientific and Technical Information (OSTI), December 1997. http://dx.doi.org/10.2172/354988.

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Fateman, Richard J., and Carl G. Ponder. Speed and Data Structures in Computer Algebra Systems. Fort Belvoir, VA: Defense Technical Information Center, August 1987. http://dx.doi.org/10.21236/ada197131.

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Anderson, Mitchell J., and Robert Mathews. Algebraic and Topological Structure of QOS (End to End) Within Large Scale Distributed Information Systems. Fort Belvoir, VA: Defense Technical Information Center, January 1999. http://dx.doi.org/10.21236/ada359965.

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Chang, P. A Differential Algebraic Integration Algorithm for Symplectic Mappings in Systems with Three-Dimensional Magnetic Field. Office of Scientific and Technical Information (OSTI), September 2004. http://dx.doi.org/10.2172/833057.

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10

Brannick, J. Final Report on Subcontract B601287: Auxiliary Space Preconditioners and Algebraic Multilevel Solvers for Systems of PDEs. Office of Scientific and Technical Information (OSTI), June 2013. http://dx.doi.org/10.2172/1088445.

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