Relevant bibliographies by topics / Algebraic stack

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Algebraic stack'

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Published: 14 March 2023

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Journal articles on the topic "Algebraic stack"

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Halpern-Leistner, Daniel, and Anatoly Preygel. "Mapping stacks and categorical notions of properness." Compositio Mathematica 159, no. 3 (March 2023): 530–89. http://dx.doi.org/10.1112/s0010437x22007667.

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One fundamental consequence of a scheme $X$ being proper is that the functor classifying maps from $X$ to any other suitably nice scheme or algebraic stack is representable by an algebraic stack. This result has been generalized by replacing $X$ with a proper algebraic stack. We show, however, that it also holds when $X$ is replaced by many examples of algebraic stacks which are not proper, including many global quotient stacks. This leads us to revisit the definition of properness for stacks. We introduce the notion of a formally proper morphism of stacks and study its properties. We develop methods for establishing formal properness in a large class of examples. Along the way, we prove strong $h$ -descent results which hold in the setting of derived algebraic geometry but not in classical algebraic geometry. Our main applications are algebraicity results for mapping stacks and the stack of coherent sheaves on a flat and formally proper stack.
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Shentu, Junchao, and Dong Wang. "Notes on algebraic log stack." International Journal of Mathematics 27, no. 10 (September 2016): 1650081. http://dx.doi.org/10.1142/s0129167x16500816.

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Let [Formula: see text] be a stack over the category of fine log schemes. If [Formula: see text] has a representable fppf covering, then, it has enough compatible minimal objects. As a consequence, we prove the equivalence between two notions of log moduli stacks which appear in literatures. Also, we obtain several fundamental results of algebraic log stacks.
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Hall, Jack, and David Rydh. "Perfect complexes on algebraic stacks." Compositio Mathematica 153, no. 11 (August 17, 2017): 2318–67. http://dx.doi.org/10.1112/s0010437x17007394.

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We develop a theory of unbounded derived categories of quasi-coherent sheaves on algebraic stacks. In particular, we show that these categories are compactly generated by perfect complexes for stacks that either have finite stabilizers or are local quotient stacks. We also extend Toën and Antieau–Gepner’s results on derived Azumaya algebras and compact generation of sheaves on linear categories from derived schemes to derived Deligne–Mumford stacks. These are all consequences of our main theorem: compact generation of a presheaf of triangulated categories on an algebraic stack is local for the quasi-finite flat topology.
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Shentu, Junchao, and Dong Wang. "Erratum: "Notes on algebraic log stack"." International Journal of Mathematics 28, no. 10 (September 2017): 1792002. http://dx.doi.org/10.1142/s0129167x17920021.

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Koppensteiner, Clemens. "Hochschild Cohomology of Torus Equivariant D-modules." International Mathematics Research Notices 2020, no. 19 (August 29, 2018): 6391–420. http://dx.doi.org/10.1093/imrn/rny206.

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Abstract We discuss the Hochschild cohomology of the category of D-modules associated to an algebraic stack. In particular we describe the Hochschild cohomology of the category of torus-equivariant D-modules as the cohomology of a D-module on the loop space of the quotient stack. Finally, we give an approach for understanding the Hochschild cohomology of D-modules on general stacks via a relative compactification of the diagonal. This work is motivated by a desire to understand the support theory (in the sense of [6]) of D-modules on stacks.
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Alper, Jarod, Maksym Fedorchuk, and David Ishii Smyth. "Second flip in the Hassett–Keel program: existence of good moduli spaces." Compositio Mathematica 153, no. 8 (May 15, 2017): 1584–609. http://dx.doi.org/10.1112/s0010437x16008289.

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We prove a general criterion for an algebraic stack to admit a good moduli space. This result may be considered as a generalization of the Keel–Mori theorem, which guarantees the existence of a coarse moduli space for a separated Deligne–Mumford stack. We apply this result to prove that the moduli stacks $\overline{{\mathcal{M}}}_{g,n}(\unicode[STIX]{x1D6FC})$ parameterizing $\unicode[STIX]{x1D6FC}$-stable curves introduced in [J. Alper et al., Second flip in the Hassett–Keel program: a local description, Compositio Math. 153 (2017), 1547–1583] admit good moduli spaces.
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Martino, Ivan. "Introduction to the Ekedahl Invariants." MATHEMATICA SCANDINAVICA 120, no. 2 (May 27, 2017): 211. http://dx.doi.org/10.7146/math.scand.a-25693.

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In 2009, T. Ekedahl introduced certain cohomological invariants for finite groups. In this work we present these invariants and we give an equivalent definition that does not involve the notion of algebraic stacks. Moreover we show certain properties for the class of the classifying stack of a finite group in the Kontsevich value ring.
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NITSURE, NITIN. "SCHEMATIC HARDER–NARASIMHAN STRATIFICATION." International Journal of Mathematics 22, no. 10 (October 2011): 1365–73. http://dx.doi.org/10.1142/s0129167x11007264.

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For any flat family of pure-dimensional coherent sheaves on a family of projective schemes, the Harder–Narasimhan type (in the sense of Gieseker semistability) of its restriction to each fiber is known to vary semicontinuously on the parameter scheme of the family. This defines a stratification of the parameter scheme by locally closed subsets, known as the Harder–Narasimhan stratification. In this paper, we show how to endow each Harder–Narasimhan stratum with the structure of a locally closed subscheme of the parameter scheme, which enjoys the universal property that under any base change the pullback family admits a relative Harder–Narasimhan filtration with a given Harder–Narasimhan type if and only if the base change factors through the schematic stratum corresponding to that Harder–Narasimhan type. The above schematic stratification induces a stacky stratification on the algebraic stack of pure-dimensional coherent sheaves. We deduce that coherent sheaves of a fixed Harder–Narasimhan type form an algebraic stack in the sense of Artin.
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Annala, Toni, and Ryomei Iwasa. "Cohomology of the moduli stack of algebraic vector bundles." Advances in Mathematics 409 (November 2022): 108638. http://dx.doi.org/10.1016/j.aim.2022.108638.

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Sakellaridis, Yiannis. "The Schwartz space of a smooth semi-algebraic stack." Selecta Mathematica 22, no. 4 (October 2016): 2401–90. http://dx.doi.org/10.1007/s00029-016-0285-3.

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Dissertations / Theses on the topic "Algebraic stack"

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Bergh, Daniel. "Destackification and Motivic Classes of Stacks." Doctoral thesis, Stockholms universitet, Matematiska institutionen, 2014. http://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-107526.

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This thesis consists of three articles treating topics in the theory of algebraic stacks. The first two papers deal with motivic invariants. In the first, we show that the class of the classifying stack BPGLn is the inverse of the class of PGLn in the Grothendieck ring of stacks for n ≤ 3. This shows that the multiplicativity relation holds for the universal torsors, although it is known not to hold for torsors ingeneral for the groups PGL2 and PGL3. In the second paper, we introduce an exponential function which can be viewed as a generalisation of Kapranov's motivic zeta function. We use this to derive a binomial theorem for a power operation defined on the Grothendieck ring of varieties. As an application, we give an explicit expression for the motivic class of a universal quasi-split torus, which generalises a result by Rökaeus. The last paper treats destackification. We give an algorithm for removing stackiness from smooth, tame stacks with abelian stabilisers by repeatedly applying stacky blow-ups. As applications, we indicate how the result can be used for destackifying general Deligne–Mumford stacks in characteristic zero, and to obtain a weak factorisation theorem for such stacks.

At the time of the doctoral defense, the following papers were unpublished and had a status as follows: Paper 1: Manuscript. Paper 2: Manuscript. Paper 3: Manuscript.

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Maggiolo, Stefano. "On the automorphism group of certain algebraic varieties." Doctoral thesis, SISSA, 2012. http://hdl.handle.net/20.500.11767/4690.

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We study the automorphism groups of two families of varieties. The first is the family of stable curves of low genus. To every such curve, we can associate a combinatorial object, a stable graph, which encode many properties of the curve. Combining the automorphisms of the graph with the known results on the automorphisms of smooth curves, we obtain precise descriptions of the automorphism groups for stable curves with low genera. The second is the family of numerical Godeaux surfaces. We compute in details the automorphism groups of numerical Godeaux surfaces with certain invariants; that is, corresponding to points in some specific connected components of the moduli space; we also give some estimates on the order of the automorphism groups of the other numerical Godeaux surfaces and some characterization on their structures.
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Poma, Flavia. "Gromov-Witten theory of tame Deligne-Mumford stacks in mixed characteristic." Doctoral thesis, SISSA, 2012. http://hdl.handle.net/20.500.11767/4718.

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We define Gromov-Witten classes and invariants of smooth proper tame Deligne-Mumford stacks of finite presentation over a Dedekind domain. We prove that they are deformation invariants and verify the fundamental axioms. For a smooth proper tame Deligne-Mumford stack over a Dedekind domain, we prove that the invariants of fibers in different characteristics are the same. We show that genus zero Gromov-Witten invariants define a potential which satisfies the WDVV equation and we deduce from this a reconstruction theorem for genus zero Gromov-Witten invariants in arbitrary characteristic.
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Ronagh, Pooya. "The inertia operator and Hall algebra of algebraic stacks." Thesis, University of British Columbia, 2016. http://hdl.handle.net/2429/58120.

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We view the inertia construction of algebraic stacks as an operator on the Grothendieck groups of various categories of algebraic stacks. We are interested in showing that the inertia operator is (locally finite and) diagonalizable over for instance the field of rational functions of the motivic class of the affine line q = [A¹]. This is proved for the Grothendieck group of Deligne-Mumford stacks and the category of quasi-split Artin stacks. Motivated by the quasi-splitness condition we then develop a theory of linear algebraic stacks and algebroids, and define a space of stack functions over a linear algebraic stack. We prove diagonalization of the semisimple inertia for the space of stack functions. A different family of operators is then defined that are closely related to the semisimple inertia. These operators are diagonalizable on the Grothendieck ring itself (i.e. without inverting polynomials in q) and their corresponding eigenvalue decompositions are used to define a graded structure on the Grothendieck ring. We then define the structure of a Hall algebra on the space of stack functions. The commutative and non-commutative products of the Hall algebra respect the graded structure defined above. Moreover, the two multiplications coincide on the associated graded algebra. This result provides a geometric way of defining a Lie subalgebra of virtually indecomposables. Finally, for any algebroid, an ε-element is defined and shown to be contained in the space of virtually indecomposables. This is a new approach to the theory of generalized Donaldson-Thomas invariants.
Science, Faculty of
Mathematics, Department of
Graduate
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Schadeck, Laurent. "On the K-theory of tame Artim stacks." Doctoral thesis, Scuola Normale Superiore, 2019. http://hdl.handle.net/11384/85745.

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This thesis pertains to the algebraic K-theory of tame Artin stacks. Building on earlier work of Vezzosi and Vistoli in equivariant K-theory, which we translate in stacky language, we give a description of the algebraic K-groups of tame quotient stacks. Using a strategy of Vistoli, we recover Grothendieck-Riemann-Roch-like formulae for tame quotient stacks that refine Toën’s Grothendieck-Riemann-Roch formula for Deligne-Mumford stacks (as it was realized that the latter pertains to quotient stacks since it relies on the resolution property). Our formulae differ from Toën’s in that, instead of using the standard inertia stack, we use the cyclotomic inertia stack introduced by Abramovich, Graber and Vistoli in the early 2000s. Our results involve the rational part of the K'-theory of the object considered. We establish a few conjectures, the main one (Conjecture 6.3) pertaining to the covariance of our Lefschetz-Riemann-Roch map for proper morphisms of tame stacks (not necessarily representable). Other future works might be dedicated to the study of torsion in K'-groups as well as more general Artin stacks.
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Hall, Jack, and David Rydh. "Perfect complexes on algebraic stacks." CAMBRIDGE UNIV PRESS, 2017. http://hdl.handle.net/10150/626173.

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We develop a theory of unbounded derived categories of quasi-coherent sheaves on algebraic stacks. In particular, we show that these categories are compactly generated by perfect complexes for stacks that either have finite stabilizers or are local quotient stacks. We also extend Toën and Antieau–Gepner’s results on derived Azumaya algebras and compact generation of sheaves on linear categories from derived schemes to derived Deligne–Mumford stacks. These are all consequences of our main theorem: compact generation of a presheaf of triangulated categories on an algebraic stack is local for the quasi-finite flat topology.
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Cliff, Emily Rose. "Universal D-modules, and factorisation structures on Hilbert schemes of points." Thesis, University of Oxford, 2015. https://ora.ox.ac.uk/objects/uuid:9edee0a0-f30a-4a54-baf5-c833222303ca.

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This thesis concerns the study of chiral algebras over schemes of arbitrary dimension n. In Chapter I, we construct a chiral algebra over each smooth variety X of dimension n. We do this via the Hilbert scheme of points of X, which we use to build a factorisation space over X. Linearising this space produces a factorisation algebra over X, and hence, by Koszul duality, the desired chiral algebra. We begin the chapter with an overview of the theory of factorisation and chiral algebras, before introducing our main constructions. We compute the chiral homology of our factorisation algebra, and show that the D-modules underlying the corresponding chiral algebras form a universal D-module of dimension n. In Chapter II, we discuss the theory of universal D-modules and OO- modules more generally. We show that universal modules are equivalent to sheaves on certain stacks of étale germs of n-dimensional varieties. Furthermore, we identify these stacks with the classifying stacks of groups of automorphisms of the n-dimensional disc, and hence obtain an equivalence between the categories of universal modules and the representation categories of these groups. We also define categories of convergent universal modules and study them from the perspectives of the stacks of étale germs and the representation theory of the automorphism groups.
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Nichols-Barrer, Joshua Paul. "On quasi-categories as a foundation for higher algebraic stacks." Thesis, Massachusetts Institute of Technology, 2007. http://hdl.handle.net/1721.1/39088.

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Thesis (Ph. D. )--Massachusetts Institute of Technology, Dept. of Mathematics, 2007.
Includes bibliographical references (p. 139-140).
We develop the basic theory of quasi-categories (a.k.a. weak Kan complexes or ([infinity], 1)- categories as in [BV73], [Joy], [Lur06]) from first principles, i.e. without reference to model categories or other ideas from algebraic topology. Starting from the definition of a quasi-category as a simplicial set satisfying the inner horn-filling condition, we define and prove various properties of quasi-categories which are direct generalizations of categorical analogues. In particular, we look at functor quasi-categories, Hom-spaces, isomorphisms, equivalences between quasi-categories, and limits. In doing so, we employ exclusively combinatorial methods, as well as adapting an idea of Makkai's ("very subjective morphisms," what turn out in this case to be simply trivial Kan fibrations) to get a handle on various notions of equivalence. We then begin to discuss a new approach to the theory of left (or right) fibrations, wherein the quasi-category of all left fibrations over a given base S is described simply as the large simplicial set whose n-simplices consist of all left fibrations over S x [delta]n.
(cont.) We conjecture that this large simplicial set is a quasi-category, and moreover that the case S = * gives an equivalent quasi-category to the commonly-held quasi-category of spaces; we offer some steps towards proving this. Finally, assuming the conjecture true, we apply it to give simple descriptions of limits in this quasi-category, as well as a straightforward construction of a Yoneda functor for quasi-categories which we then prove is fully faithful.
by Joshua Paul Nicholas-Barrer.
Ph.D.
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Wallbridge, James. "Higher Tannaka duality." Toulouse 3, 2011. http://thesesups.ups-tlse.fr/1440/.

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Dans cette thèse, nous prouvons un théorème de dualité de Tannaka pour les (infini, 1)-catégories. La dualité classique de Tannaka est une dualité entre certains groupes et catégories monoïdales munies d'une structure particulière. La dualité de Tannaka supérieure renvoie, elle, à une dualité entre certains champs en groupes dérivés et certaines (infini, 1)-catégories monoïdales munies d'une structure particulière. Cette dualité supérieure est définie sur les anneaux dérivés et englobe la théorie de dualité classique. Nous comparons la dualité de Tannaka supérieure à la théorie de dualité de Tannaka classique et portons une attention particulière à la dualité de Tannaka sur les corps. Dans ce dernier cas, cette théorie a une relation étroite avec la théorie des types d'homotopie schématique de Toën. Nous décrivons également trois applications de la théorie : les complexes parfaits, les motifs et leur analogue non-commutatif dû à Kontsevich
In this thesis we prove a Tannaka duality theorem for (infini, 1)-categories. Classical Tannaka duality is a duality between certain groups and certain monoidal categories endowed with particular structure. Higher Tannaka duality refers to a duality between certain derived group stacks and certain monoidal (infini, 1)-categories endowed with particular structure. This higher duality theorem is defined over derived rings and subsumes the classical statement. We compare the higher Tannaka duality to the classical theory and pay particular attention to higher Tannaka duality over fields. In the later case this theory has a close relationship with the theory of schematic homotopy types of Toën. We also describe three applications of our theory : perfect complexes and that of both motives and its non-commutative ana­logue due to Kontsevich
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Sitte, Tobias [Verfasser], Niko [Akademischer Betreuer] Naumann, and Tarrío Leovigildo [Akademischer Betreuer] Alonso. "Local cohomology sheaves on algebraic stacks / Tobias Sitte. Betreuer: Niko Naumann ; Leovigildo Alonso Tarrío." Regensburg : Universitätsbibliothek Regensburg, 2014. http://d-nb.info/1054802912/34.

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Books on the topic "Algebraic stack"

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1966-, Vezzosi Gabriele, ed. Homotopical algebraic geometry II: Geometric stacks and applications. Providence, R.I: American Mathematical Society, 2008.

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Algebraic spaces and stacks. Providence, Rhode Island: American Mathematical Society, 2016.

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Breen, Lawrence. On the classification of 2-gerbes and 2-stacks. Paris: Société mathématique de France, 1994.

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Algebraic numbers and algebraic functions. London: Chapman & Hall, 1991.

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France, Société mathématique de, and Centre national de la recherche scientifique (France), eds. String topology for stacks. Paris: Société mathématique de France, 2012.

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Crystalline cohomology of algebraic stacks and Hyodo-Kato cohomology. Paris: Société Mathématique de France, 2007.

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Donaldson type invariants for algebraic surfaces: Transition of moduli stacks. Berlin: Springer, 2009.

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Mathematik, Max-Planck-Institut für, ed. Deformation spaces: Perspectives on algebro-geometric moduli. Wiesbaden: Vieweg+Teubner, 2010.

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Pantev, Tony. Stacks and catetories in geometry, topology, and algebra: CATS4 Conference Higher Categorical Structures and Their Interactions with Algebraic Geometry, Algebraic Topology and Algebra, July 2-7, 2012, CIRM, Luminy, France. Providence, Rhode Island: American Mathematical Society, 2015.

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Topological modular forms. Providence, Rhode Island: American Mathematical Society, 2014.

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Book chapters on the topic "Algebraic stack"

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Tarrío, Leovigildo Alonso. "Homological Algebra on an Adams Algebraic Stack." In Trends in Mathematics, 1–5. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-45441-2_1.

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McConnell, B., and J. V. Tucker. "Infinite Synchronous Concurrent Algorithms The Algebraic Specification and Verification of a Hardware Stack." In Logic and Algebra of Specification, 321–75. Berlin, Heidelberg: Springer Berlin Heidelberg, 1993. http://dx.doi.org/10.1007/978-3-642-58041-3_9.

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Moerdijk, Ieke, and Bertrand Toën. "Algebraic stacks." In Simplicial Methods for Operads and Algebraic Geometry, 143–58. Basel: Springer Basel, 2010. http://dx.doi.org/10.1007/978-3-0348-0052-5_11.

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Chiari, Michele. "Temporal Logic and Model Checking for Operator Precedence Languages: Theory and Applications." In Special Topics in Information Technology, 67–78. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-15374-7_6.

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AbstractTemporal logic is an established tool for writing requirement specifications for computer systems, thanks to its balance between expressive power and efficiency of verification algorithms. Linear Temporal Logic (LTL), one of the most commonly used, allows for naturally expressing safety and liveness requirements on a linear timeline, but incurs into some limitations when utilized to express requirements of procedural programs. In fact, such programs exhibit a typically context-free behavior, which LTL formulas cannot represent. Precedence Oriented Temporal Logic (POTL), a temporal logic based on Operator Precedence Languages (OPLs), a subclass of Deterministic Context-Free Languages. With POTL, we can express requirements involving Hoare-style pre/post-conditions, stack inspection, and others, also in the presence of exception-like constructs. We prove that POTL is as expressive as First-Order Logic (FOL) on its algebraic structure, and devise and implement an explicit-state satisfiability and model-checking algorithm for it, obtaining some promising experimental results.
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Grigoriev, Dima, Edward A. Hirsch, and Dmitrii V. Pasechnik. "Complexity of Semi-algebraic Proofs." In STACS 2002, 419–30. Berlin, Heidelberg: Springer Berlin Heidelberg, 2002. http://dx.doi.org/10.1007/3-540-45841-7_34.

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Clerbout, Mireille, and Yves Roos. "Semi-commutations and algebraic languages." In STACS 90, 82–94. Berlin, Heidelberg: Springer Berlin Heidelberg, 1990. http://dx.doi.org/10.1007/3-540-52282-4_34.

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Mateescu, Alexandru. "Shuffle of ω-words: Algebraic aspects." In STACS 98, 150–60. Berlin, Heidelberg: Springer Berlin Heidelberg, 1998. http://dx.doi.org/10.1007/bfb0028557.

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Frandsen, Gudmund Skovbjerg, Johan P. Hansen, and Peter Bro Miltersen. "Lower Bounds for Dynamic Algebraic Problems." In STACS 99, 362–72. Berlin, Heidelberg: Springer Berlin Heidelberg, 1999. http://dx.doi.org/10.1007/3-540-49116-3_34.

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Koiran, Pascal. "Circuits versus Trees in Algebraic Complexity." In STACS 2000, 35–52. Berlin, Heidelberg: Springer Berlin Heidelberg, 2000. http://dx.doi.org/10.1007/3-540-46541-3_3.

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Boudol, Cérard, Cérard Roucairol, and Robert de Simone. "Petri nets and algebraic calculi of processes." In STACS 85, 59–70. Berlin, Heidelberg: Springer Berlin Heidelberg, 1985. http://dx.doi.org/10.1007/bfb0023995.

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Conference papers on the topic "Algebraic stack"

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O’Rourke, Judith, Murat Arcak, and Manikandan Ramani. "Estimating Air Flow Rates in a Fuel Cell System Using Electrochemical Impedance." In ASME 2008 Dynamic Systems and Control Conference. ASMEDC, 2008. http://dx.doi.org/10.1115/dscc2008-2172.

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This paper proposes the use of electrochemical impedance spectroscopy (EIS) to estimate the cathode flow rate in a fuel cell system. Through experimental testing of an eight-cell, hydrogen-fueled polymer electrolyte stack, it shows that the ac impedance measurements are highly sensitive to the air flow rates at varying current densities. The ac impedance magnitude at 0.1Hz allows the distinction of air flow rates (stoichiometry of 1.5–3.0) at current densities as low as 0.1A/cm2. Using experimental data and regression analysis, a simple algebraic equation that estimates the air flow rate using impedance measurements at a frequency of 0.1Hz is developed. The derivation of this equation is based on the operating cell voltage equation that accounts for all the irreversibilities.
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Bermúdez Montaña, Marisol, Orgaz E, Renato Lemus, and Marisol Rodríguez Arcos. "AN ALGEBRAIC DVR APPROACH TO DESCRIBE THE STARK EFFECT." In 2020 International Symposium on Molecular Spectroscopy. Urbana, Illinois: University of Illinois at Urbana-Champaign, 2020. http://dx.doi.org/10.15278/isms.2020.tk08.

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de Roeck, Y.-H. "Pre-Stack Depth Migration and Sparse Linear Algebra." In 62nd EAGE Conference & Exhibition. European Association of Geoscientists & Engineers, 2000. http://dx.doi.org/10.3997/2214-4609-pdb.28.b54.

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Nelson, Donald D., and Elaine Cohen. "Algebraic Surface Derivatives for Rendering Virtual Contact Force." In ASME 2000 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2000. http://dx.doi.org/10.1115/imece2000-2426.

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Abstract Previous augmented reality displays have rendered crisp virtual walls and virtual objects with finger-surface reactions through haptics feedback devices. The widely used stiffness (or impedance) methods penalize a user’s intrusion into a virtual surface with a force response dependent on the amount of penetration along the contact normal at the virtual proxy location. We present an alternative approach for computing the surface impact response that projects Lagrange multipliers associated with a unilateral surface constraint onto a multivariate surface constraint Jacobian for the case where the two objects (finger and model) do not stick together. Advantages of our method are that the surface Jacobian is already being computed from an exact NURBS-NURBS collision update algorithm previously developed by the authors, and that the force response is accurate to numerical precision; no polygonal or numerical approximations are employed.
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Andersen, Brian, Mogens Blanke, and Jan Helbo. "Two-Mode Resonator and Contact Model for Standing Wave Piezomotor." In ASME 2001 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2001. http://dx.doi.org/10.1115/detc2001/vib-21484.

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Abstract The paper presents a model for a standing wave piezoelectric motor with a two bending mode resonator. The resonator is modelled using Hamilton’s principle and the Rayleigh-Ritz method. The contact is modelled using the Lagrange Multiplier method under the assumption of slip and it is shown how to solve the set of differential-algebraic equations. Detailed simulations show resonance frequencies as function of the piezoelement’s position, tip trajectories and contact forces. The paper demonstrates that contact stiffness and stick should be included in such a model to obtain physically realistic results and a method to include stick is suggested.
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6

Surana, K. S., and H. Vijayendra Nayak. "Computations of the Numerical Solutions of Higher Class of Navier-Stokes Equations: 2D Newtonian Fluid Flow." In ASME 2001 Engineering Technology Conference on Energy. American Society of Mechanical Engineers, 2001. http://dx.doi.org/10.1115/etce2001-17143.

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Abstract This paper presents formulations, computations, investigations and consequences of the various aspects of the numerical solutions of classes C00 and C11 of the two dimensional Navier-Stokes equations in primitive variables u, v, p, τxx, τxy and τyy for incompressible, isothermal and laminar Newtonian fluid flows using p-version Least Squares Finite Element Formulations (LSFEF). The stick-slip problem is used as a model problem in all investigations since this model problem is typical of many other flow situations like contraction, expansion etc. The major thrust of the work presented is to attempt to resolve the local behavior of the solutions in the immediate vicinity of the stick-slip point. The investigations reveal the following: a) The manner in which the stresses are non-dimensionalized in the governing differential equations (GDEs) influences the performance of the iterative procedure of solving non-linear algebraic equations and thus, computational efficiency. b) Solutions of the class C00 are always the wrong class of solutions and thus are always spurious. c) In the flow domains, containing sharp gradients of dependent variables, conservation of mass is difficult to achieve specially at lower p-levels. d) C11 solutions of the Navier-Stokes equations are in conformity with the continuity considerations in the GDEs. e) An augmented form of the Navier-Stokes equations is proposed that always ensures conservation of mass regardless of mesh, p-levels and the nature of the solution gradients. This approach yields the most desired class of C11 solutions. f) It is mathematically established and numerically demonstrated using stick-slip problem that τij are in fact zero at the stick-slip point and the peak values of τxx and τyy must occur, and in fact do, past the stick-slip point in the free field and that peak values of τxy must occur before the stick-slip point on the no-slip boundary. Thus, there is no singularity of τij in the stick-slip problem at the stick-slip point. A significant finding is that imposition of symmetry boundary condition (necessary based on physics) at the stick-slip point even in C11 interpolations is not possible without deteriorating τij behavior in the vicinity of the stick-slip point. However, with the boundary condition, the peak of τxy does occur before the stick-slip point, while the locations of τxx and τyy remain past the stick-slip point in the free field. h) A significant feature of our research work is that we utilize straightforward p-version LSFEF with C00 and C11 type interpolation without linearizing GDEs and that SUPG, SUPG/DC, SUPG/DC/LS operators are neither needed nor used. All numerical studies are conducted and presented using three different meshes (progressively refined and graded) for two different velocities (0.01 and 100 m/s).
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7

Rodriguez, Adrian, and Alan Bowling. "Analytic Solution for Planar Indeterminate Multiple Point Impact Problems With Coulomb Friction." In ASME 2014 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/detc2014-35390.

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This work analyzes the effects of the stick-slip transition of planar rigid body systems undergoing simultaneous, multiple point impact with Coulomb friction. A discrete, algebraic approach is used in conjunction with an event-driven scheme which detects impact events. The system equations of motion for the examples considered are indeterminate with respect to the impact forces. Constraints consistent with rigid body assumptions are implemented to overcome the indeterminacy. The post-impact velocities of a system are determined by exploiting the work-energy relationship of a collision and using an energetic coefficient of restitution to model energy dissipation. These developments lead to a unique and energetically consistent solution to the post-impact velocities. A frictionless rocking block example is analyzed as a benchmark case and compared to experimental results to demonstrate the accuracy of the proposed method. Simulation results are also presented for a planar ball example with friction.
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8

Mankala, Kalyan K., and Sunil K. Agrawal. "Dynamic Modeling and Simulation of Impact in Tether Net/Gripper Systems." In ASME 2003 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2003. http://dx.doi.org/10.1115/detc2003/vib-48505.

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The objective of this paper is to study the dynamic modeling and simulation of a tether-net/gripper system during an impact, while it is being deployed or retrieved by a winch on a satellite orbiting around earth. We stick to Tether-Net system but the analysis is applicable to Tether-Gripper systems too. We assume that the net is deployed from the satellite in orbit and the motion is restricted to the orbital plane. This net captures a second satellite and tows it. The motion of a tether-net system can be broken down into the following phases: (i) Phase 1: Net is shot out from the satellite with the tether completely slack, (ii) Phase 2: Net comes to a location where the tether is taut while the drum on the orbiter is locked, (iii) Phase 3: Drum is unlocked and the net moves with the tether, (iv) Phase 4: Net captures a body. The continua (tether) is modeled using mode functions and coordinates. The theory of impulse and momentum can be used to model Phases 1, 2, and 4 of motion of the tether-net system. The dynamics of the motion of the system in phase 3 is characterized by differential and algebraic equations (DAEs). Matlab ODE solvers were used to solve these DAEs.
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Chen, J. J., and C. H. Menq. "Prediction of Periodic Response of Blades Having 3D Nonlinear Shroud Constraints." In ASME 1999 International Gas Turbine and Aeroengine Congress and Exhibition. American Society of Mechanical Engineers, 1999. http://dx.doi.org/10.1115/99-gt-289.

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In this paper, a 3D shroud contact model is employed to predict the periodic response of blades having 3D nonlinear shroud constraint. When subjected to periodic excitation, the resulting relative motion at the shroud contact is assumed to be periodic in three-dimensional space. Based on the 3D shroud contact model, analytical criteria are used to determine the transitions between stick, slip, and separation of the contact interface and are used to simulate hysteresis loops of the induced constrained force, when experiencing periodic relative motion. The constrained force can be considered as a feedback force that influences the response of the shrouded blade. By using the Multi-Harmonic Balance Method along with Fast Fourier Transform, the constrained force can be approximated by a series of harmonic functions so as to predict the periodic response of a shrouded blade. This approach results in a set of nonlinear algebraic equations, which can be solved iteratively to yield the periodic response of blades having 3D nonlinear shroud constraint. In order to validate the proposed approach, the predicted results are compared with those of the direct time integration method. The resonant frequency shift, the damping effect, and the jump phenomenon due to nonlinear shroud constraint are examined. The implications of the developed solution procedure to the design of shroud contact are also discussed.
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10

Ouakad, Hassen M., and Mohammad I. Younis. "Modeling and Simulations of Collapse Instabilities of Microbeams Due to Capillary Forces." In ASME 2008 International Mechanical Engineering Congress and Exposition. ASMEDC, 2008. http://dx.doi.org/10.1115/imece2008-67502.

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We present modeling and analysis for the static behavior and collapse instabilities of doubly-clamped and cantilever microbeams subjected to capillary forces. These forces can be as a result of a volume of liquid trapped underneath the microbeam during the rinsing and drying process in fabrication. The model considers the microbeam as a continuous medium, the capillary force as a nonlinear function of displacement, and accounts for the mid-plane stretching nonlinearity. The capillary force is assumed to be distributed over a specific length underneath the microbeam. The Galerkin procedure is used to derive a reduced-order model consisting of a set of nonlinear algebraic and differential equations that describe the microbeams static and dynamic behaviors. We study the collapse instability, which brings the microbeam from its unstuck configuration to touch the substrate and gets stuck in the so-called pinned configuration. We calculate the pull-in length that distinguishes the free from the pinned configurations as a function of the beam thickness and gap width for both microbeams. Comparisons are made with analytical results reported in the literature based on the Ritz method for linear and nonlinear beam models. The instability problem, which brings the microbeam from a pinned to adhered configuration is also investigated. For this case, we use a shooting technique to solve the boundary-value problem governing the deflection of the microbeams. The critical microbeam length for this second instability is also calculated.
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