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Academic literature on the topic 'Stability theory[Forking theory]'

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Published: 4 June 2021

Last updated: 1 February 2022

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Journal articles on the topic "Stability theory[Forking theory]"

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Kim, Byunghan. "Simplicity, and stability in there." Journal of Symbolic Logic 66, no. 2 (June 2001): 822–36. http://dx.doi.org/10.2307/2695047.

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AbstractFirstly, in this paper, we prove that the equivalence of simplicity and the symmetry of forking. Secondly, we attempt to recover definability part of stability theory to simplicity theory. In particular, using elimination of hyperimaginaries we prove that for any supersimple T. canonical base of an amalgamation class is the union of names of ψ-definitions of , ψ ranging over stationary L-formulas in . Also, we prove that the same is true with stable formulas for an 1-based theory having elimination of hyperimaginaries. For such a theory, the stable forking property holds, too.

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Ng, Siu-Ah. "A generalization of forking." Journal of Symbolic Logic 56, no. 3 (September 1991): 813–22. http://dx.doi.org/10.2178/jsl/1183743730.

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Given a subset A of a fixed saturated model , we let denote the algebra of definable subsets of the domain of M of with parameters from A. Then a complete type p over A can be regarded as a measure on , assigning the value 1 to members of p and 0 to nonmembers. In [5] and [6], Keisler developed a theory of forking concerning probability measures. Therefore it generalizes the ordinary theory. On a different track, we can view the complement of the type p, or the collection of null sets of any measure on , as ideals on . Moreover, ideals and the pseudometric of a measure form examples of the so-called FN topology. Roughly speaking, an FN topology is one that topologizes the ring structure of a Boolean algebra. Associated with this topology is a special basis, called an FN basis. For , it is natural to identify such a basis with a collection of partial types approximating a certain type.In this paper, we extend the theory of forking and deal with FN bases (hence ideals in particular). By proving a few results here, we hope to indicate that this extension could become as fruitful as Keisler's theory and hence provide an alternative. Our approach here is more algebraic and less analytic. Unlike [5], methods from nonstandard analysis are not used.There are two fundamental reasons why the classical theory should be generalized. One is to extend our investigation to unstable theories. (There are no stability assumptions on the theory in the present work.) The other is to study different and more flexible ways of collecting formulas, such as FN basis.After fixing our notation in §1, we first deal with ideals in §2. We study certain nice extensions. Specifically, we prove the existence of flat nonforking ideals. We then provide a normalization theorem for ideals.

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ARGOTY, CAMILO. "FORKING AND STABILITY IN THE REPRESENTATIONS OF A C*-ALGEBRA." Journal of Symbolic Logic 80, no. 3 (July 22, 2015): 785–96. http://dx.doi.org/10.1017/jsl.2015.23.

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AbstractWe show that the theory of a nondegenerate representation of a C*-algebra ${\cal A}$ over a Hilbert space H is superstable. Also, we characterize forking, orthogonality and domination of types.

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Hart, Bradd, Byunghan Kim, and Anand Pillay. "Coordinatisation and canonical bases in simple theories." Journal of Symbolic Logic 65, no. 1 (March 2000): 293–309. http://dx.doi.org/10.2307/2586538.

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In this paper we discuss several generalization of theorems from stability theory to simple theories. Cherlin and Hrushovski, in [2] develop a substitute for canonical bases in finite rank, ω-categorical supersimple theories. Motivated by methods there, we prove the existence of canonical bases (in a suitable sense) for types in any simple theory. This is done in Section 2. In general these canonical bases will (as far as we know) exist only as “hyperimaginaries”, namely objects of the form a/E where a is a possibly infinite tuple and E a type-definable equivalence relation. (In the supersimple, ω-categorical case, these reduce to ordinary imaginaries.) So in Section 1 we develop the general theory of hyperimaginaries and show how first order model theory (including the theory of forking) generalises to hyperimaginaries. We go on, in Section 3 to show the existence and ubiquity of regular types in supersimple theories, ω-categorical simple structures and modularity is discussed in Section 4. It is also shown here how the general machinery of simplicity simplifies some of the general theory of smoothly approximable (or Lie-coordinatizable) structures from [2].Throughout this paper we will work in a large, saturated model M of a complete theory T. All types, sets and sequences will have size smaller than the size of M. We will assume that the reader is familiar with the basics of forking in simple theories as laid out in [4] and [6]. For basic stability-theoretic results concerning regular types, orthogonality etc., see [1] or [9].

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d’Elbée, Christian. "Expansions and Neostability in Model Theory." Bulletin of Symbolic Logic 27, no. 2 (June 2021): 216–17. http://dx.doi.org/10.1017/bsl.2021.26.

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AbstractThis thesis is concerned with the expansions of algebraic structures and their fit in Shelah’s classification landscape.The first part deals with the expansion of a theory by a random predicate for a substructure model of a reduct of the theory. Let T be a theory in a language $\mathcal {L}$ . Let $T_0$ be a reduct of T. Let $\mathcal {L}_S = \mathcal {L}\cup \{S\}$ , for S a new unary predicate symbol, and $T_S$ be the $\mathcal {L}_S$ -theory that axiomatises the following structures: $(\mathscr {M},\mathscr {M}_0)$ consist of a model $\mathscr {M}$ of T and S is a predicate for a model $\mathscr {M}_0$ of $T_0$ which is a substructure of $\mathscr {M}$ . We present a setting for the existence of a model-companion $TS$ of $T_S$ . As a consequence, we obtain the existence of the model-companion of the following theories, for $p>0$ a prime number: • $\mathrm {ACF}_p$ , $\mathrm {SCF}_{e,p}$ , $\mathrm {Psf}_p$ , $\mathrm {ACFA}_p$ , $\mathrm {ACVF}_{p,p}$ in appropriate languages expanded by arbitrarily many predicates for additive subgroups;• $\mathrm {ACF}_p$ , $\mathrm {ACF}_0$ in the language of rings expanded by a single predicate for a multiplicative subgroup;• $\mathrm {PAC}_p$ -fields, in an appropriate language expanded by arbitrarily many predicates for additive subgroups.From an independence relation in T, we define independence relations in $TS$ and identify which properties of are transferred to those new independence relations in $TS$ , and under which conditions. This allows us to exhibit hypotheses under which the expansion from T to $TS$ preserves $\mathrm {NSOP}_{1}$ , simplicity, or stability. In particular, under some technical hypothesis on T, we may draw the following picture (the left column implies the right column): Configuration $T_0\subseteq T$ Generic expansion $TS$ $T_0 = T$ Preserves stability $T_0\subseteq T$ Preserves $\mathrm {NSOP}_{1}$ $T_0 = \emptyset $ Preserves simplicityIn particular, this construction produces new examples of $\mathrm {NSOP}_{1}$ not simple theories, and we study in depth a particular example: the expansion of an algebraically closed field of positive characteristic by a generic additive subgroup. We give a full description of imaginaries, forking, and Kim-forking in this example.The second part studies expansions of the group of integers by p-adic valuations. We prove quantifier elimination in a natural language and compute the dp-rank of these expansions: it equals the number of independent p-adic valuations considered. Thus, the expansion of the integers by one p-adic valuation is a new dp-minimal expansion of the group of integers. Finally, we prove that the latter expansion does not admit intermediate structures: any definable set in the expansion is either definable in the group structure or is able to “reconstruct” the valuation using only the group operation.Abstract prepared by Christian d’Elbée.E-mail: delbee@math.univ-lyon1.frURL: https://choum.net/~chris/page_perso

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Ben-Yaacov, Itay, Ivan Tomašić, and Frank O. Wagner. "The Group Configuration in Simple Theories and its Applications." Bulletin of Symbolic Logic 8, no. 2 (June 2002): 283–98. http://dx.doi.org/10.2178/bsl/1182353874.

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AbstractIn recent work, the authors have established the group configuration theorem for simple theories, as well as some of its main applications from geometric stability theory, such as the binding group theorem, or, in the ω-categorical case, the characterization of the forking geometry of a finitely based non-trivial locally modular regular type as projective geometry over a finite field and the equivalence of pseudolinearity and local modularity.The proof necessitated an extension of the model-theoretic framework to include almost hyperimaginaries, and the study of polygroups.

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García, Darío, Dugald Macpherson, and Charles Steinhorn. "Pseudofinite structures and simplicity." Journal of Mathematical Logic 15, no. 01 (June 2015): 1550002. http://dx.doi.org/10.1142/s0219061315500026.

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We explore a notion of pseudofinite dimension, introduced by Hrushovski and Wagner, on an infinite ultraproduct of finite structures. Certain conditions on pseudofinite dimension are identified that guarantee simplicity or supersimplicity of the underlying theory, and that a drop in pseudofinite dimension is equivalent to forking. Under a suitable assumption, a measure-theoretic condition is shown to be equivalent to local stability. Many examples are explored, including vector spaces over finite fields viewed as 2-sorted finite structures, and homocyclic groups. Connections are made to products of sets in finite groups, in particular to word maps, and a generalization of Tao's Algebraic Regularity Lemma is noted.

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Tsuboi, Akito. "On the number of independent partitions." Journal of Symbolic Logic 50, no. 3 (September 1985): 809–14. http://dx.doi.org/10.2307/2274333.

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In [3], Shelah defined the cardinals κn(T) and , for each theory T and n < ω. κn(T) is the least cardinal κ without a sequence (pi)i<κ of complete n-types such that pi is a forking extension of pj for all i < j < κ. It is essential in computing the stability spectrum of a stable theory. On the other hand is called the number of independent partitions of T. (See Definition 1.2 below.) Unfortunately this invariant has not been investigated deeply. In the author's opinion, this unfortunate situation of is partially due to the fact that its definition is complicated in expression. In this paper, we shall give equivalents of which can be easily handled.In §1 we shall state the definitions of κn(T) and . Some basic properties of forking will be stated in this section. We shall also show that if = ∞ then T has the independence property.In §2 we shall give some conditions on κ, n, and T which are equivalent to the statement . (See Theorem 2.1 below.) We shall show that does not depend on n. We introduce the cardinal ı(T), which is essential in computing the number of types over a set which is independent over some set, and show that ı(T) is closely related to . (See Theorems 2.5 and 2.6 below.) The author expects the reader will discover the importance of via these theorems.Some of our results are motivated by exercises and questions in [3, Chapter III, §7]. The author wishes to express his heartfelt thanks to the referee for a number of helpful suggestions.

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Iovino, José. "On the maximality of logics with approximations." Journal of Symbolic Logic 66, no. 4 (December 2001): 1909–18. http://dx.doi.org/10.2307/2694984.

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In this paper we analyze some aspects of the question of using methods from model theory to study structures of functional analysis.By a well known result of P. Lindström, one cannot extend the expressive power of first order logic and yet preserve its most outstanding model theoretic characteristics (e.g., compactness and the Löwenheim-Skolem theorem). However, one may consider extending the scope of first order in a different sense, specifically, by expanding the class of structures that are regarded as models (e.g., including Banach algebras or other structures of functional analysis), and ask whether the resulting extensions of first order model theory preserve some of its desirable characteristics.A formal framework for the study of structures based on Banach spaces from the perspective of model theory was first introduced by C. W. Henson in [8] and [6]. Notions of syntax and semantics for these structures were defined, and it was shown that using them one obtains a model theoretic apparatus that satisfies many of the fundamental properties of first order model theory. For instance, one has compactness, Löwenheim-Skolem, and omitting types theorems. Further aspects of the theory, namely, the fundamentals of stability and forking, were first introduced in [10] and [9].The classes of mathematical structures formally encompassed by this framework are normed linear spaces, possibly expanded with additional structure, e.g., operations, real-valued relations, and constants. This notion subsumes wide classes of structures from functional analysis. However, the restriction that the universe of a structure be a normed space is not necessary. (This restriction has a historical, rather than technical origin; specifically, the development of the theory was originally motivated by questions in Banach space geometry.) Analogous techniques can be applied if the universe is a metric space. Now, when the underlying metric topology is discrete, the resulting model theory coincides with first order model theory, so this logic extends first order in the sense described above. Furthermore, without any cost in the mathematical complexity, one can also work in multi-sorted contexts, so, for instance, one sort could be an operator algebra while another is. say, a metric space.

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Zhang, Xue Peng. "Stability Bearing Capacity of Concrete Filled Thin-Walled Circular Steel Tubular Column under Axial Compression." Advanced Materials Research 690-693 (May 2013): 720–23. http://dx.doi.org/10.4028/www.scientific.net/amr.690-693.720.

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The bearing capacity formula of concrete filled thin-walled steel tubular (CFTST) short column was established based on limit equilibrium method, and the reasonable value fork1in Richart Strength Model was regression introduced adapted with concrete stress-strain relations. According to the elasticity modulus theory, the calculation formulas of stability bearing capacity of CFTST slender column were deduced, reasonable considering the interactions between steel tube and concrete. And the calculation process is relatively simple which avoiding complicated iterations used in the conventional calculation method. Finally, the comparative evaluation on calculation formula was done based on 79 groups of test results of concrete filled steel tubular column at home and abroad. Results of calculation formula agree well with the test results in safe range.

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Dissertations / Theses on the topic "Stability theory[Forking theory]"

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Wagner, Frank O. "Stable groups and generic types." Thesis, University of Oxford, 1990. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.258015.

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Pourmahdian, M. "Model theory of simple theories." Thesis, University of Oxford, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.325836.

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Craft, Colin N. "On Morley's Categoricity Theorem with an Eye Toward Forking." Miami University / OhioLINK, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=miami1323475348.

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Potier, Joris. "A few things about hyperimaginaries and stable forking." Doctoral thesis, Universitat de Barcelona, 2015. http://hdl.handle.net/10803/394029.

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The core of this PhD dissertation is basically twofold : On one hand, I get some new results on the relationship between compact groups and bounded hyperimaginaries, extending a little bit the classical results of Lascar and Pillay in Hyperimaginaries And Automorphism Groups. On the other hand, I prove some new results around the so called "stable forking" property, more specifically that a simple theory T has stable forking if Teq has. Quite surprisingly, the proof is not so straigtforward.
En este texto se trata, por una parte, de la relación entre grupos compactos e hiper-imaginarios acotados, y por otra parte se prueba que una teoría T tiene la propiedad de bifurcación estable si i solo si Teq la tiene.

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Farina, John Dominic. "Stability properties in ring theory." Connect to a 24 p. preview or request complete full text in PDF format. Access restricted to UC campuses, 2006. http://wwwlib.umi.com/cr/ucsd/fullcit?p3237384.

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Thesis (Ph. D.)--University of California, San Diego, 2006.
Title from first page of PDF file (viewed December 8, 2006). Available via ProQuest Digital Dissertations. Vita. Includes bibliographical references (p. 86-90).

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Tsaparas, Panayiotis. "Stability in adversarial queueing theory." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1997. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp04/mq28768.pdf.

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Haykazyan, Levon. "Aspects of nonelementary stability theory." Thesis, University of Oxford, 2016. https://ora.ox.ac.uk/objects/uuid:940cd0bf-e4bb-4074-a521-d3c139d16743.

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This thesis aims to contribute to neostability and in particular to the stability theory of nonelementary classes. The central themes of the thesis are quasiminimality and excellence. We explore both classical and geometric aspects of stability theory for such classes. In particular our methods aim to utilise the topology on the space of types in these settings. Chapter 1 is introductory and sets the necessary background on nonelementary classes. In Chapter 2 we use infinitary methods to study quasiminimal excellent classes. We give a simplified proof of the Categoricity Theorem. In Chapter 3 we study quasiminimality from the first order perspective. We look for conditions on a first order theory that allow us to build quasiminimal models with various additional properties. In Chapter 4 we look at excellent groups. We aim to generalise various results from (geometric) stability theory to this nonelementary setting.

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Palacín, Cruz Daniel. "Forking in simple theories and CM-triviality." Doctoral thesis, Universitat de Barcelona, 2012. http://hdl.handle.net/10803/84023.

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Aquesta tesi té tres objectius. En primer lloc, estudiem generalitzacions de la jerarquia no ample relatives a una família de tipus parcials. Aquestes jerarquies en permeten classificar la complexitat del “forking” respecte a una família de tipus parcials. Si considerem la família de tipus algebraics, aquestes generalitzacions corresponen a la jerarquia ordinària, on el primer i el segon nivell corresponen a one-basedness i a CM-trivialitat, respectivament. Fixada la família de tipus regulars “no one-based”, el primer nivell d'una d'aquestes possibles jerarquies no ample ens diu que el tipus de la base canònica sobre una realització és analitzable en la família. Demostrem que tota teoria simple amb suficients tipus regulars pertany al primer nivell de la jerarquia dèbil relativa a la família de tipus regulars no one-based. Aquest resultat generalitza una versió dèbil de la “Canonical Base Property” estudiada per Chatzidakis i Pillay. En segon lloc, discutim problemes d'eliminació de hiperimaginaris assumint que la teoria és CM-trivial, en tal cas la independència del “forking” té un bon comportament. Més concretament, demostrem que tota teoria simple CM-trivial elimina els hiperimaginaris si elimina els hiperimaginaris finitaris. En particular, tota teoria petita simple CM-trivial elimina els hiperimaginaris. Cal remarcar que totes les teories omega-categòriques simples que es coneixen són CM-trivials; en particular, aquelles teories obtingudes mitjançant una construcció de Hrushovski. Finalment, tractem problemes de classificació en les teories simples. Estudiem la classe de les teories simples baixes; classe que inclou les teories estables i les teories supersimples de D-rang finit. Demostrem que les teories simples amb pes finit acotat també pertanyen a aquesta classe. A més, provem que tota teoria omega-categòrica simple CM-trivial és baixa. Aquest darrer fet resol parcialment una pregunta formulada per Casanovas i Wagner.
The development of first-order stable theories required two crucial abstract notions: forking independence, and the related notion of canonical base. Forking independence generalizes the linear independence in vector spaces and the algebraic independence in algebraically closed fields. On the other hand, the concept of canonical base generalizes the field of definition of an algebraic variety. The general theory of independence adapted to simple theories, a class of first-order theories which includes all stable theories and other interesting examples such as algebraically closed fields with an automorphism and the random graph. Nevertheless, in order to obtain canonical bases for simple theories, the model-theoretic development of hyperimaginaries --equivalence classes of arbitrary tuple modulo a type-definable (without parameters) equivalence relation-- was required. In the present thesis we deal with topics around the geometry of forking in simple theories. Our first goal is to study generalizations of the non ample hierarchy which will code the complexity of forking with respect to a family of partial types. We introduce two hierarchies: the non (weak) ample hierarchy with respect to a fixed family of partial types. If we work with respect to the family of bounded types, these generalizations correspond to the ordinary non ample hierarchy. Recall that in the ordinary non ample hierarchy the first and the second level correspond to one-basedness and CM-triviality, respectively. The first level of the non weak ample hierarchy with respect to some fixed family of partial types states that the type of the canonical base over a realization is analysable in the family. Considering the family of regular non one-based types, the first level of the non weak ample hierarchy corresponds to the weak version of the Canonical Base Property studied by Chatzidakis and Pillay. We generalize Chatzidakis' result showing that in any simple theory with enough regular types, the canonical base of a type over a realization is analysable in the family of regular non one-based types. We hope that this result can be useful for the applications; for instance, the Canonical Base Property plays an essential role in the proof of Mordell-Lang for function fields in characteristic zero and Manin-Mumford due to Hrushovski. Our second aim is to use combinatorial properties of forking independence to solve elimination of hyperimaginaries problems. For this we assume the theory to be simple and CM-trivial. This implies that the forking independence is well-behaved. Our goal is to prove that any simple CM-trivial theory which eliminates finitary hyperimaginaries --hyperimaginaries which are definable over a finite tuple-- eliminates all hyperimaginaries. Using a result due to Kim, small simple CM-trivial theories eliminate hyperimaginaries. It is worth mentioning that all currently known omega-categorical simple theories are CM-trivial, even those obtained by an ab initio Hrushovski construction. To conclude, we study a classification problem inside simple theories. We study the class of simple low theories, which includes all stable theories and supersimple theories of finite D-rank. In addition, we prove that it also includes the class of simple theories of bounded finite weight. Moreover, we partially solve a question posed by Casanovas and Wagner: Are all omega-categorical simple theories low? We solve affirmatively this question under the assumption of CM-triviality. In fact, our proof exemplifies that the geometry of forking independence in a possible counterexample cannot come from finite sets.

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De, Bruyne Peter J. J. "Aspects of solar coronal stability theory." Thesis, University of St Andrews, 1991. http://hdl.handle.net/10023/14071.

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Solar coronal stability theory is a powerful tool for understanding the complex behaviour of the Sun's atmosphere. It enables one to discover the driving forces behind some intriguing phenomena and to gauge the soundness of theoretical models for observed structures. In this thesis, the linear stability analysis of line-tied symmetric magnetohydrostatic equilibria is studied within the framework of ideal MHD, aimed at its application to the solar corona. Firstly, a tractable stability procedure based on a variational method is devised. It provides a necessary condition for stability to disturbances localised about a particular flux surface, and a sufficient condition for stability to all accessible perturbations that vanish at the photosphere. The tests require the minimisation of a line integral along the magnetic field lines. For 1-D equilibria, this can be performed analytically, and simple stability criteria are obtained. The necessary condition then serves as an extended Suydam criterion, incorporating the stabilising effect of line-tying. For 2-D equilibria, the minimisation requires the integration of a system of ordinary differential equations along the field lines. This stability technique is applied to arcade, loop, and prominence models, yielding tight bounds on the equilibrium parameters. Secondly, global modes in 1-D coronal loops are investigated using a normal mode method, in order to clarify their link with localised interchange modes. For nearly force-free fields it is shown that instability to localised modes implies the existence of a fast growing global kink mode driven in the neighbourhood of the radius predicted by the local analysis. This confers a new significance on the study of localised interchange modes and the associated extended Suydam criterion.

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Cerri, Andrea <1978&gt. "Stability and computation in multidimensional size theory." Doctoral thesis, Alma Mater Studiorum - Università di Bologna, 2007. http://amsdottorato.unibo.it/562/.

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Books on the topic "Stability theory[Forking theory]"

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V, Hahn, ed. Stability theory. New York: Prentice Hall, 1993.

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Leipholz, Horst. Stability Theory. Wiesbaden: Vieweg+Teubner Verlag, 1987. http://dx.doi.org/10.1007/978-3-663-10648-7.

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Jeltsch, Rolf, and Mohamed Mansour, eds. Stability Theory. Basel: Birkhäuser Basel, 1996. http://dx.doi.org/10.1007/978-3-0348-9208-7.

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Pillay, Anand. Geometric stability theory. Oxford: Clarendon Press, 1996.

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Buechler, Steven. Essential stability theory. Berlin: Springer, 1996.

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Buechler, Steven. Essential Stability Theory. Berlin, Heidelberg: Springer Berlin Heidelberg, 1996. http://dx.doi.org/10.1007/978-3-642-80177-8.

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Georgescu, Adelina. Hydrodynamic stability theory. Dordrecht: Springer Netherlands, 1985. http://dx.doi.org/10.1007/978-94-017-1814-1.

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Hydrodynamic stability theory. Dordrecht: M. Nijhoff, 1985.

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Buechler, Steven. Essential stability theory. Berlin: Springer, 1996.

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Theory of hydromagnetic stability. New York: Gordon and Breach Science Publishers, 1986.

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Book chapters on the topic "Stability theory[Forking theory]"

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Lakshmikantham, V., S. Leela, Zahia Drici, and F. A. McRae. "Stability Theory." In Atlantis Studies in Mathematics for Engineering and Science, 105–36. Paris: Atlantis Press, 2009. http://dx.doi.org/10.2991/978-94-91216-25-1_4.

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Agarwal, Ravi P., Simona Hodis, and Donal O’Regan. "Stability Theory." In 500 Examples and Problems of Applied Differential Equations, 183–220. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-26384-3_7.

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Ahmad, Shair, and Antonio Ambrosetti. "Stability theory." In UNITEXT, 233–57. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-02129-4_12.

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Polderman, Jan Willem, and Jan C. Willems. "Stability Theory." In Texts in Applied Mathematics, 241–79. New York, NY: Springer New York, 1998. http://dx.doi.org/10.1007/978-1-4757-2953-5_7.

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Betounes, David. "Stability Theory." In Differential Equations: Theory and Applications, 267–332. New York, NY: Springer New York, 2009. http://dx.doi.org/10.1007/978-1-4419-1163-6_6.

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Layek, G. C. "Stability Theory." In An Introduction to Dynamical Systems and Chaos, 129–58. New Delhi: Springer India, 2015. http://dx.doi.org/10.1007/978-81-322-2556-0_4.

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Ahmad, Shair, and Antonio Ambrosetti. "Stability theory." In UNITEXT, 251–73. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-16408-3_12.

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Hinrichsen, Diederich, and Anthony J. Pritchard. "Stability Theory." In Mathematical Systems Theory I, 193–368. Berlin, Heidelberg: Springer Berlin Heidelberg, 2005. http://dx.doi.org/10.1007/3-540-26410-8_3.

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Bhatia, Nam Parshad, and George Philip Szegö. "Stability Theory." In Stability Theory of Dynamical Systems, 56–113. Berlin, Heidelberg: Springer Berlin Heidelberg, 2002. http://dx.doi.org/10.1007/978-3-642-62006-5_6.

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Knauf, Andreas. "Stability Theory." In UNITEXT, 137–53. Berlin, Heidelberg: Springer Berlin Heidelberg, 2018. http://dx.doi.org/10.1007/978-3-662-55774-7_7.

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Conference papers on the topic "Stability theory[Forking theory]"

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Pedersen, Erik Kjær, and Masayuki Yamasaki. "Stability in controlled L–theory." In Workshop on Exotic Homology Manifolds. Mathematical Sciences Publishers, 2006. http://dx.doi.org/10.2140/gtm.2006.9.67.

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Sun, Andy. "Stability Theory of Swing Equations." In 2020 European Control Conference (ECC). IEEE, 2020. http://dx.doi.org/10.23919/ecc51009.2020.9143692.

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WANAS, M. I., and M. A. BAKRY. "A GENERAL COVARIANT STABILITY THEORY." In Proceedings of the MG11 Meeting on General Relativity. World Scientific Publishing Company, 2008. http://dx.doi.org/10.1142/9789812834300_0341.

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Chill, Ralph, and Yuri Tomilov. "Stability of operator semigroups: ideas and results." In Perspectives in Operator Theory. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2007. http://dx.doi.org/10.4064/bc75-0-6.

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Hender, T. C., I. T. Chapman, M. S. Chu, Y.-Q. Liu, Olivier Sauter, Xavier Garbet, and Elio Sindoni. "Kinetic Effects on Resistive Wall Mode Stability." In THEORY OF FUSION PLASMAS. AIP, 2008. http://dx.doi.org/10.1063/1.3033693.

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Krikidis, Ioannis, J. Nicholas Laneman, John Thompson, and Steve McLaughlin. "Stability analysis for cognitive radio with cooperative enhancements." In 2009 IEEE Information Theory Workshop on Networking and Information Theory (ITW). IEEE, 2009. http://dx.doi.org/10.1109/itwnit.2009.5158588.

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Stearns, S. D. "Non-foster circuits and stability theory." In 2011 IEEE Antennas and Propagation Society International Symposium and USNC/URSI National Radio Science Meeting. IEEE, 2011. http://dx.doi.org/10.1109/aps.2011.5996883.

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KUZMINA, LYUDMILA K. "STABILITY THEORY METHODS IN MODELLING PROBLEMS." In Proceedings of the MS'10 International Conference. WORLD SCIENTIFIC, 2010. http://dx.doi.org/10.1142/9789814324441_0091.

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Nainn-Ping Ke. "Singularity theory and stability robustness analysis." In UKACC International Conference on Control (CONTROL '98). IEE, 1998. http://dx.doi.org/10.1049/cp:19980301.

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Glick, Robert. "Acoustic Stability Theory, L-Star Stability, and Heterogeneous Propellant." In 43rd AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit. Reston, Virigina: American Institute of Aeronautics and Astronautics, 2007. http://dx.doi.org/10.2514/6.2007-5860.

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Reports on the topic "Stability theory[Forking theory]"

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Ellis, J., A. E. Faraggi, and D. V. Nanopoulos. M-theory model-building and proton stability. Office of Scientific and Technical Information (OSTI), September 1997. http://dx.doi.org/10.2172/541933.

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Stiglitz, Joseph. The Theory of Credit and Macro-economic Stability. Cambridge, MA: National Bureau of Economic Research, November 2016. http://dx.doi.org/10.3386/w22837.

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Ding, Dong, Mingfei Liu, Samson Lai, Kevin Blinn, and Meilin Liu. Theory, Investigation and Stability of Cathode Electrocatalytic Activity. Office of Scientific and Technical Information (OSTI), September 2012. http://dx.doi.org/10.2172/1084035.

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Oster, Emily. Unobservable Selection and Coefficient Stability: Theory and Validation. Cambridge, MA: National Bureau of Economic Research, May 2013. http://dx.doi.org/10.3386/w19054.

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Heifets, Sam. Advanced Nonlinear Theory: Long-Term Stability at the SSC. Office of Scientific and Technical Information (OSTI), July 1987. http://dx.doi.org/10.2172/954110.

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Clarida, Richard, Jordi Gali, and Mark Gertler. Monetary Policy Rules and Macroeconomic Stability: Evidence and Some Theory. Cambridge, MA: National Bureau of Economic Research, March 1998. http://dx.doi.org/10.3386/w6442.

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Teel, Andrew R., and Joao P. Hespanha. A Robust Stability and Control Theory for Hybrid Dynamical Systems. Fort Belvoir, VA: Defense Technical Information Center, September 2006. http://dx.doi.org/10.21236/ada470821.

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Scheinker, Alexander. Introduction to Control Theory. Part 3. State Space, Stability, and Lyapunov Functions. Office of Scientific and Technical Information (OSTI), September 2015. http://dx.doi.org/10.2172/1214625.

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Tomsovic, Steven. Ray Theory Applied to Stability, Fluctuations, and Time-reversal in Deep Water Acoustics. Fort Belvoir, VA: Defense Technical Information Center, September 2003. http://dx.doi.org/10.21236/ada628568.

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Goldberg, Moshe, and Marvin Marcus. Stability Analysis of Finite Difference Approximations to Hyperbolic Systems, and Problems in Applied and Computational Matrix Theory. Fort Belvoir, VA: Defense Technical Information Center, July 1988. http://dx.doi.org/10.21236/ada200755.

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