Relevant bibliographies by topics / Bounded Symmetric domain

Contents

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

Academic literature on the topic 'Bounded Symmetric domain'

Author: Grafiati
Published: 6 September 2023

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Journal articles on the topic "Bounded Symmetric domain"

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ROOS, Guy. "Bergman–Hartogs domains and their automorphisms." Tambov University Reports. Series: Natural and Technical Sciences, no. 127 (2019): 316–23. http://dx.doi.org/10.20310/2686-9667-2019-24-127-316-323.

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For Cartan–Hartogs domains and also for Bergman–Hartogs domains, the determination of their automorphism groups is given for the cases when the base is any bounded symmetric domain and a general bounded homogeneous domain respectively.
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BERSHTEIN, OLGA. "REGULAR FUNCTIONS ON THE SHILOV BOUNDARY." Journal of Algebra and Its Applications 04, no. 06 (December 2005): 613–29. http://dx.doi.org/10.1142/s0219498805001447.

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In this paper a *-algebra of regular functions on the Shilov boundary S(𝔻) of bounded symmetric domain 𝔻 is constructed. The algebras of regular functions on S(𝔻) are described in terms of generators and relations for two particular series of bounded symmetric domains. Also, the degenerate principal series of quantum Harish–Chandra modules related to S(𝔻) = Un is investigated.
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Ramachandran, C., R. Ambrose Prabhu, and Srikandan Sivasubramanian. "Starlike and convex functions with respect to symmetric conjugate points involving conical domain." Mathematica Slovaca 68, no. 1 (February 23, 2018): 89–102. http://dx.doi.org/10.1515/ms-2017-0083.

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AbstractEnough attentions to domains related to conical sections has not been done so far although it deserves more. Making use of the conical domain the authors have defined a new class of starlike and Convex Functions with respect to symmetric points involving the conical domain. Growth and distortion estimates are studied with convolution using domains bounded by conic regions. Certain coefficient estimates are obtained for domains bounded by conical region. Finally interesting application of the results are also highlighted for the function Ωk,βdefined by Noor.
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Di Scala, Antonio J., Andrea Loi, and Guy Roos. "The Bisymplectomorphism Group of a Bounded Symmetric Domain." Transformation Groups 13, no. 2 (June 2008): 283–304. http://dx.doi.org/10.1007/s00031-008-9015-z.

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Mackey and Mellon. "The Bergmann-Shilov boundary of a Bounded Symmetric Domain." Mathematical Proceedings of the Royal Irish Academy 121A, no. 2 (2021): 33. http://dx.doi.org/10.3318/pria.2021.121.03.

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Mackey, M., and P. Mellon. "The Bergmann-Shilov boundary of a Bounded Symmetric Domain." Mathematical Proceedings of the Royal Irish Academy 121, no. 2 (2021): 33–49. http://dx.doi.org/10.1353/mpr.2021.0002.

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Choi, Ki-Seong. "NOTES ON CARLESON TYPE MEASURES ON BOUNDED SYMMETRIC DOMAIN." Communications of the Korean Mathematical Society 22, no. 1 (January 31, 2007): 65–74. http://dx.doi.org/10.4134/ckms.2007.22.1.065.

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PAN, LISHUANG, AN WANG, and LIYOU ZHANG. "ON THE KÄHLER–EINSTEIN METRIC OF BERGMAN–HARTOGS DOMAINS." Nagoya Mathematical Journal 221, no. 1 (March 2016): 184–206. http://dx.doi.org/10.1017/nmj.2016.4.

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We study the complete Kähler–Einstein metric of certain Hartogs domains ${\rm\Omega}_{s}$ over bounded homogeneous domains in $\mathbb{C}^{n}$. The generating function of the Kähler–Einstein metric satisfies a complex Monge–Ampère equation with Dirichlet boundary condition. We reduce the Monge–Ampère equation to an ordinary differential equation and solve it explicitly when we take the parameter $s$ for some critical value. This generalizes previous results when the base is either the Euclidean unit ball or a bounded symmetric domain.
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Neidhardt, H., and V. A. Zagrebnov. "Does Each Symmetric Operator Have a Stability Domain?" Reviews in Mathematical Physics 10, no. 06 (August 1998): 829–50. http://dx.doi.org/10.1142/s0129055x98000276.

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We show that any symmetric operator H has a dense maximal b-stability domain [Formula: see text] (i.e. [Formula: see text], b∈R1) if and only if H is unbounded from above. This abstract result allows an application to singular perturbed Schrödinger operators which are not semi-bounded from below, i.e., to the so-called "fall to the center problem". It turns out that in this case the regularization problem is always ill-posed which implies that there is no unique "right Hamiltonian" for corresponding perturbed system. We give an example of singular perturbed Schrödinger operator for which stability domains are described explicitly.
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Wu, Hio Tong, Ieng Tak Leong, and Tao Qian. "Adaptive rational approximation in Bergman space on bounded symmetric domain." Journal of Mathematical Analysis and Applications 506, no. 1 (February 2022): 125591. http://dx.doi.org/10.1016/j.jmaa.2021.125591.

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Dissertations / Theses on the topic "Bounded Symmetric domain"

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Schilling, René L., and Toshihiro Uemura. "On the Structure of the Domain of a Symmetric Jump-type Dirichlet Form." Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2014. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-145198.

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We characterize the structure of the domain of a pure jump-type Dirichlet form which is given by a Beurling–Deny formula. In particular, we obtain su cient conditions in terms of the jumping kernel guaranteeing that the test functions are a core for the Dirichlet form and that the form is a Silverstein extension. As an application we show that for recurrent Dirichlet forms the extended Dirichlet space can be interpreted in a natural way as a homogeneous Dirichlet space. For reflected Dirichlet spaces this leads to a simple purely analytic proof that the active reflected Dirichlet space (in the sense of Chen, Fukushima and Kuwae) coincides with the extended active reflected Dirichlet space
Dieser Beitrag ist mit Zustimmung des Rechteinhabers aufgrund einer (DFG-geförderten) Allianz- bzw. Nationallizenz frei zugänglich
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Schilling, René L., and Toshihiro Uemura. "On the Structure of the Domain of a Symmetric Jump-type Dirichlet Form." EMS Publishing House, 2012. https://tud.qucosa.de/id/qucosa%3A28135.

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We characterize the structure of the domain of a pure jump-type Dirichlet form which is given by a Beurling–Deny formula. In particular, we obtain su cient conditions in terms of the jumping kernel guaranteeing that the test functions are a core for the Dirichlet form and that the form is a Silverstein extension. As an application we show that for recurrent Dirichlet forms the extended Dirichlet space can be interpreted in a natural way as a homogeneous Dirichlet space. For reflected Dirichlet spaces this leads to a simple purely analytic proof that the active reflected Dirichlet space (in the sense of Chen, Fukushima and Kuwae) coincides with the extended active reflected Dirichlet space.
Dieser Beitrag ist mit Zustimmung des Rechteinhabers aufgrund einer (DFG-geförderten) Allianz- bzw. Nationallizenz frei zugänglich.
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涂振漢 and Zhenhan Tu. "Rigidity of proper holomorphic mappings between bounded symmetric domains." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2000. http://hub.hku.hk/bib/B42575643.

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Tu, Zhenhan. "Rigidity of proper holomorphic mappings between bounded symmetric domains." Click to view the E-thesis via HKUTO, 2000. http://sunzi.lib.hku.hk/hkuto/record/B42575643.

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Mckenzie, Daniel. "On uniformization of compact Kähler manifolds with negative first chern class by bounded symmetric domains." Master's thesis, University of Cape Town, 2014. http://hdl.handle.net/11427/9609.

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Includes bibliographical references.
We consider two complementary problems: given a compact Kähler manifold with negative first Chern Class, when is its universal cover a Bounded Symmetric Domain? And if it is, which Bounded Symmetric Domain is it? Existing literature is discussed, with particular attention given to two recent papers of Catanese and Di Scala ([CDS12] and [CDS]) which answer both questions first for Bounded Symmetric Domains of Tube Type, and then for all Bounded Symmetric Domains without Ball Factors. Using work of Yau and others on ball quotients we extend the main result of [CDS] to all bounded Symmetric Domains, including those with ball factors, thus answering the two questions posed in full generality.
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Cadorel, Benoît. "Hyperbolicité complexe et quotients de domaines symétriques bornés." Thesis, Aix-Marseille, 2018. http://www.theses.fr/2018AIXM0198.

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Ce travail de thèse porte sur l’étude de l’hyperbolicité complexe de compactifications de quotients de domaines symétriques bornés, et plus spécifiquement, de quotients de la boule. On souhaite ainsi comprendre la géométrie des courbes entières que ces compactifications contiennent, ainsi que le type de leurs sous-variétés. On prouve d'abord un critère métrique de positivité du fibré co-tangent d’une variété complexe, reposant notamment sur les travaux de J.-P. Demailly et de S. Boucksom. Ce critère peut s’appliquer à une large classe de variétés, dépassant le cadre précédent ; avec Y. Brunebarbe, on s'est ainsi intéressé aux variétés supportant une variation de structures de Hodge complexes. Dans le cas d’un quotient de la boule, ce critère permet de montrer qu’un revêtement ramifié d’une compactification toroïdale lisse, étale sur l’intérieur, et ramifiant à des ordres supérieurs à 7 sur le bord, ne contient que des variétés de type général en dehors de son bord. Dans ce cadre, ceci fournit une version effective d’un théorème de Y. Brunebarbe. On étudie par ailleurs d’autres situations que ces compactifications lisses : avec E.Rousseau et B. Taji, on donne des critères d'hyperbolicité complexe de ces compactifications lorsque les quotients sont singuliers. On présente aussi une version effective d’un théorème de J.-P. Demailly, concernant le caractère big des différentielles de jets sur la compactification donnée. Enfin, on montre que les méthodes métriques présentées précédemment s’étendent au cas de tous les domaines symétriques bornés ; elles fournissent alors des résultats effectifs d'hyperbolicité algébrique et transcendante pour d’autres domaines que la boule
This work deals with the study of complex hyperbolicity of compactifications of quotients of bounded symmetric domains, and more specifically, of quotients of the ball. We are interested in the geometry of the entire curves such a compactification contains, as well as to the type of its subvarietes. We first prove a metric criterion for the positivity of the cotangent bundle of a complex manifold, based in particular on the work of J.-P. Demailly and of S. Boucksom. This criterion can be applied to a large class of manifolds, going beyond the previous frame; with Y. Brunebarbe, we apply in particular these methods to the case of manifolds supporting a complex variation of Hodge structures.In the case of a ball quotient, the criterion shows that on a ramified cover of a toroidal compactification, étale on the inside part, and ramifying at orders higher than 7 on the boundary, there is no subvariety which is not of general type, and not included in the boundary. In this setting, this gives an effective version of a theorem of Y. Brunebarbe. We also study other situations than these smooth compactifications : with E. Rousseau and B. Taji, we give metric criterions for the complex hyperbolicity of these compactifications, if the quotients are singular. In the case of the ball, we present also an effective version of a theorem of J.-P. Demailly, concerning the bigness of the Green-Griffiths jet differentials on the given compactification. Finally, we show that the previous metric methods can be applied to the case of all bounded symmetric domains ; they give effective hyperbolicity results, algebraic and transcendental, for other bounded symmetric domains than the ball
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MOSSA, ROBERTO. "Balanced metrics on complex vector bundles and the diastatic exponential of a symmetric space." Doctoral thesis, Università degli Studi di Cagliari, 2011. http://hdl.handle.net/11584/266274.

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This thesis deals with two different subjects: balanced metrics on complex vector bundles and the diastatic exponential of a symmetric space. Correspondingly we have two main results. In the first one we prove that if a holomorphic vector bundle E over a compact Kähler manifold (M,ω) admits a ω-balanced metric then this metric is unique. In the second one, after defining the diastatic exponential of a real analytic Kähler manifold, we prove that for every point p of an Hermitian symmetric space of noncompact type there exists a globally defined diastatic exponential centered in p which is a diffeomorphism and it is uniquely determined by its restriction to polydisks.
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Saldaña, de Fuentes Alberto [Verfasser], Tobias [Akademischer Betreuer] Weth, and Nils [Akademischer Betreuer] Ackermann. "Partial symmetries of solutions to nonlinear elliptic and parabolic problems in bounded radial domains / Alberto Saldaña De Fuentes. Gutachter: Tobias Weth ; Nils Ackermann. Betreuer: Tobias Weth." Frankfurt am Main : Univ.-Bibliothek Frankfurt am Main, 2014. http://d-nb.info/1053704186/34.

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Pramanick, Paramita. "Trace Estimate For The Determinant Operator And K- Homogeneous Operators." Thesis, 2020. https://etd.iisc.ac.in/handle/2005/4872.

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Let $\boldsymbol T=(T_1, \ldots , T_d)$ be a $d$- tuple of commuting operators on a Hilbert space $\mathcal H$. Assume that $\boldsymbol T$ is hyponormal, that is, $\big [\!\!\big [ \boldsymbol T^*, \boldsymbol T \big ]\!\! \big ]:=\big (\!\!\big ( \big [ T_j^*,T_i] \big )\!\!\big )$ acting on the $d$ - fold direct sum of the Hilbert space $\mathcal H$ is non-negative definite. The commutator $[T_j^*,T_i]$, $1\leq i,j \leq d$, of a finitely ctyclic and hyponormal $d$ - tuple is not necessarily compact and therefore the question of finding trace inequalities for such a $d$- tuple does not arise. A generalization of the Berger-Shaw theorem for a commuting tuple $\boldsymbol T$ of hyponormal operators was obtained by Douglas and Yan decades ago. We discuss several examples of this generalization in an attempt to understand if the crucial hypothesis in their theorem requiring the Krull dimension of the Hilbert module over the polynomial ring defined by the map $p\to p(\boldsymbol T)$, $p\in \mathbb C[\boldsymbol z]$, is optimal or not. Indeed, we find examples $\boldsymbol T$ to show that there is a large class of operators for which $\text{trace}\,[T_j^*,T_i]$, $1\leq j,i \leq d$, is finite but the $d$ - tuple is not finitely polynomially cyclic, which is one of the hypotheses of the Douglas-Yan theorem. We also introduce the weaker notion of ``projectively hyponormal operators" and show that the Douglas-Yan thorem remains valid even under this weaker hypothesis. We introduce the determinant operator $\text{dEt}\,(\big[\!\! \big [\boldsymbol{T}^*, \boldsymbol{T}\big ]\!\! \big ]\big) $, which coincides with the generalized commutator introduced by Helton and Howe earlier. We identify a class $BS_{m, \vartheta}(\Omega)$ consisting of commuting $d$- tuples of hyponormal operators $\boldsymbol T$, $\sigma(\boldsymbol T) = \overbar{\Omega}$, satisfying a growth condition for which the dEt is a non-negative definite operator. We then obtain the trace estimate given in the Theorem below. \begin{thmAbs} Let $\boldsymbol{T}=(T_1,\ldots, T_d)$ be a commuting tuple of operators on a Hilbert space $\mathcal{H}$ such that $\boldsymbol{T}$ is in the class $BS_{m, \vartheta}(\Omega)$. Then the determinant operator $\text{dEt}\,\big(\big[\!\! \big [\boldsymbol{T}^*, \boldsymbol{T}\big ]\!\! \big ]\big)$ is in trace-class and \[\text{trace}\,\big (\text{dEt}\,\big(\big[\!\! \big [\boldsymbol{T}^*, \boldsymbol{T}\big ]\!\!\big]\big)\big )\leq m\, \vartheta \,d!\prod_{i=1}^{d}\|T_i\|^2.\] \end{thmAbs} In the case of a commuting $d$ - tuple $\boldsymbol T$ of operators, where $\sigma(\boldsymbol T)$ is of the form $\overbar{\Omega}_1 \times \cdots \times \overbar{\Omega}_d$, we obtain a slightly different but a related estimate for the trace of $\text{dEt}\,\big(\big[\!\! \big [\boldsymbol{T}^*, \boldsymbol{T}\big ]\!\!\big]\big)\big )$. Explicit computation of $\text{dEt}\,\big(\big[\!\! \big [\boldsymbol{T}^*, \boldsymbol{T}\big ]\!\!\big ]\big)$ in several examples and based on some numerical evidence, we make the following conjecture refining the estimate from the Theorem: \begin{conjAbs} Let $\boldsymbol{T}=(T_1,\ldots, T_d)$ be a commuting tuple of operators on a Hilbert space $\mathcal{H}$ such that $\boldsymbol{T}$ is in the class $BS_{m, \vartheta}(\Omega)$. Then the determinant operator $\text{dEt}\,\big(\big[\!\!\big [\boldsymbol{T}^*, \boldsymbol{T}\big ]\!\! \big ]\big)$ is in trace-class, and \[\text{\rm trace}\,\big (\text{dEt}\,\big(\big[\!\! \big [\boldsymbol{T}^*, \boldsymbol{T}\big ]\!\!\big ]\big) \big )\leq \frac{m d!}{\pi^d} \nu(\overline{\Omega}), \] where $\nu$ is the Lebesgue measure. \end{conjAbs} Let $\Omega$ be an irreducible classical bounded symmetric domain of rank $r$ in $\mathbb C^d.$ Let $\mathbb K$ be the maximal compact subgroup of the identity component $G$ of the biholomorphic automorphism group of the domain $\Omega$. The group $\mathbb K$ consisting of linear transformations acts naturally on any $d$-tuple $\boldsymbol T$ of commuting bounded linear operators by the rule: \[k\cdot\boldsymbol{T}:=\big(k_1(T_1, \ldots, T_d), \ldots, k_d(T_1, \ldots, T_d)\big),\,\,k\in \mathbb K, \] where $k_1(\boldsymbol z), \ldots, k_d(\boldsymbol z)$ are linear polynomials. If the orbit of this action modulo unitary equivalence is a singleton, then we say that $\boldsymbol T$ is $\mathbb{K}$-homogeneous. We realize a certain class of $\mathbb{K}$-homogeneous $d$-tuples $\boldsymbol{T}$ as a $d$ -tuple of multiplication by the coordinate functions $z_1,\ldots ,z_d$ on a reproducing kernel Hilbert space $\mathcal H_K$. (The Hilbert space $\mathcal H_K$ consisting of holomorphic functions defined on $\Omega$ and $K$ is the reproducing kernel.) Using this model we obtain a criterion for (i) boundedness, (ii) membership in the Cowen-Douglas class, (iii) unitary equivalence and similarity of these $d$-tuples. In particular, we show that the adjoint of the $d$-tuple of multiplication by the coordinate functions on the weighted Bergman spaces are in the Cowen-Douglas class $B_1(\Omega)$. For an irreducible bounded symmetric domain $\Omega$ of rank $2$, an explicit description of the operator $\sum_{i=1}^d T_i^*T_i$ is given. Based on this formula, a conjecture giving the form of this operator in any rank $r \geq 1$ was made. This conjecture was recently verified by H. Upmeier.
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Yang, Chi-Ru, and 楊其儒. "Multiple solutions and its stability in a bounded symmetry domain." Thesis, 2004. http://ndltd.ncl.edu.tw/handle/15295097185650383645.

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碩士
國立清華大學
數學系
92
In this article, we prove that there are three positive solutions of a semilinear elliptic equation in a bounded symmetric domain Dt for large t > 0 in which one is axially symmetric and the other two are nonaxially symmetric. Moreover, we prove that these three solutions are unstable.
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Books on the topic "Bounded Symmetric domain"

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Quantum bounded symmetric domains. Providence, R.I: American Mathematical Society, 2010.

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Christensen, Jens Gerlach. Trends in harmonic analysis and its applications: AMS special session on harmonic analysis and its applications : March 29-30, 2014, University of Maryland, Baltimore County, Baltimore, MD. Providence, Rhode Island: American Mathematical Society, 2015.

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Jordan Triple Systems in Complex and Functional Analysis. American Mathematical Society, 2020.

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Book chapters on the topic "Bounded Symmetric domain"

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Friedman, Yaakov, and Tzvi Scarr. "The classical bounded symmetric domains." In Physical Applications of Homogeneous Balls, 153–93. Boston, MA: Birkhäuser Boston, 2005. http://dx.doi.org/10.1007/978-0-8176-8208-8_4.

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Koranyi, A. "Holomorphic and Harmonic Functions on Bounded Symmetric Domains." In Geometry of Homogeneous Bounded Domains, 125–97. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-11060-3_4.

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Chu, Cho-Ho. "Jordan Structures in Bounded Symmetric Domains." In Springer INdAM Series, 43–61. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-73126-1_4.

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Zhu, Kehe. "Harmonic Analysis on Bounded Symmetric Domains." In Harmonic Analysis in China, 287–307. Dordrecht: Springer Netherlands, 1995. http://dx.doi.org/10.1007/978-94-011-0141-7_17.

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Honda, Tatsuhiro. "Bloch Mappings on Bounded Symmetric Domains." In Trends in Mathematics, 49–70. Singapore: Springer Singapore, 2017. http://dx.doi.org/10.1007/978-981-10-4337-6_3.

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Kim, Sung-Yeon. "Proper Holomorphic Maps Between Bounded Symmetric Domains." In Complex Analysis and Geometry, 207–19. Tokyo: Springer Japan, 2015. http://dx.doi.org/10.1007/978-4-431-55744-9_15.

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Seo, Aeryeong. "Proper Holomorphic Maps Between Bounded Symmetric Domains." In Complex Analysis and Geometry, 319–26. Tokyo: Springer Japan, 2015. http://dx.doi.org/10.1007/978-4-431-55744-9_24.

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Shimura, Goro. "On canonical models of arithmetic quotients of bounded symmetric domains." In Collected Papers, 299–377. New York, NY: Springer New York, 2002. http://dx.doi.org/10.1007/978-1-4612-2076-3_8.

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Shimura, Goro. "On canonical models of arithmetic quotients of bounded symmetric domains: II." In Collected Papers, 378–99. New York, NY: Springer New York, 2002. http://dx.doi.org/10.1007/978-1-4612-2076-3_9.

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Kaup, Wilhelm. "Hermitian Jordan Triple Systems and the Automorphisms of Bounded Symmetric Domains." In Non-Associative Algebra and Its Applications, 204–14. Dordrecht: Springer Netherlands, 1994. http://dx.doi.org/10.1007/978-94-011-0990-1_34.

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Conference papers on the topic "Bounded Symmetric domain"

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Wang, Guoli, Youfu Li, and Weiliang Xu. "Symmetric Dichotomy Based Inverse Dynamics of a High-Speed Flexible Beam." In ASME 1999 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 1999. http://dx.doi.org/10.1115/imece1999-0110.

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Abstract The symmetric acausal/causal dichotomy based model is developed for the internal dynamics of a high-speed flexible beam, and the resultant modeling redundancy is revealed. The efficient scheme of computing the bounded input-state trajectories is proposed to relieve the redundant computational burden of the time-domain inverse dynamic solutions, and its implication to trajectory planning is also investigated.
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ENGLIŠ, MIROSLAV. "QP-SPACES: GENERALIZATIONS TO BOUNDED SYMMETRIC DOMAINS." In Proceedings of the 13th International Conference on Finite or Infinite Dimensional Complex Analysis and Applications. WORLD SCIENTIFIC, 2006. http://dx.doi.org/10.1142/9789812773159_0005.

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TU, ZHEN-HAN. "RIGIDITY OF PROPER HOLOMORPHIC MAPPINGS BETWEEN BOUNDED SYMMETRIC DOMAINS." In Proceedings of a Satellite Conference to the International Congress of Mathematicians in Beijing 2002. WORLD SCIENTIFIC, 2004. http://dx.doi.org/10.1142/9789812702500_0022.

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Balas, Mark J., and Susan A. Frost. "A Stabilization of Fixed Gain Controlled Infinite Dimensional Systems by Augmentation With Direct Adaptive Control." In ASME 2017 Conference on Smart Materials, Adaptive Structures and Intelligent Systems. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/smasis2017-3726.

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Linear infinite dimensional systems are described by a closed, densely defined linear operator that generates a continuous semigroup of bounded operators on a general Hilbert space of states and are controlled via a finite number of actuators and sensors. Many distributed applications are included in this formulation, such as large flexible aerospace structures, adaptive optics, diffusion reactions, smart electric power grids, and quantum information systems. We have developed the following stability result: an infinite dimensional linear system is Almost Strictly Dissipative (ASD) if and only if its high frequency gain CB is symmetric and positive definite and the open loop system is minimum phase, i.e. its transmission zeros are all exponentially stable. In this paper, we focus on infinite dimensional linear systems for which a fixed gain linear infinite or finite dimensional controller is already in place. It is usually true that fixed gain controllers are designed for particular applications but these controllers may not be able to stabilize the plant under all variations in the operating domain. Therefore we propose to augment this fixed gain controller with a relatively simple direct adaptive controller that will maintain stability of the full closed loop system over a much larger domain of operation. This can ensure that a flexible structure controller based on a reduced order model will still maintain closed-loop stability in the presence of unmodeled system dynamics. The augmentation approach is also valuable to reduce risk in loss of control situations. First we show that the transmission zeros of the augmented infinite dimensional system are the open loop plant transmission zeros and the eigenvalues (or poles) of the fixed gain controller. So when the open-loop plant transmission zeros are exponentially stable, the addition of any stable fixed gain controller does not alter the stability of the transmission zeros. Therefore the combined plant plus controller is ASD and the closed loop stability when the direct adaptive controller augments this combined system is retained. Consequently direct adaptive augmentation of controlled linear infinite dimensional systems can produce robust stabilization even when the fixed gain controller is based on approximation of the original system. These results are illustrated by application to a general infinite dimensional model described by nuclear operators with compact resolvent which are representative of distributed parameter models of mechanically flexible structures. with a reduced order model based controller and adaptive augmentation.
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Funk, Maurice, Jean Christoph Jung, and Carsten Lutz. "Actively Learning Concepts and Conjunctive Queries under ELr-Ontologies." In Thirtieth International Joint Conference on Artificial Intelligence {IJCAI-21}. California: International Joint Conferences on Artificial Intelligence Organization, 2021. http://dx.doi.org/10.24963/ijcai.2021/260.

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We consider the problem to learn a concept or a query in the presence of an ontology formulated in the description logic ELr, in Angluin's framework of active learning that allows the learning algorithm to interactively query an oracle (such as a domain expert). We show that the following can be learned in polynomial time: (1) EL-concepts, (2) symmetry-free ELI-concepts, and (3) conjunctive queries (CQs) that are chordal, symmetry-free, and of bounded arity. In all cases, the learner can pose to the oracle membership queries based on ABoxes and equivalence queries that ask whether a given concept/query from the considered class is equivalent to the target. The restriction to bounded arity in (3) can be removed when we admit unrestricted CQs in equivalence queries. We also show that EL-concepts are not polynomial query learnable in the presence of ELI-ontologies.
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Botelho, Rui M. "Computing Resonant Frequencies and Coupled Mode-Shapes of Structural-Acoustic Systems Using the Finite Element Method." In ASME 2008 Noise Control and Acoustics Division Conference. ASMEDC, 2008. http://dx.doi.org/10.1115/ncad2008-73017.

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This paper examines numerical techniques to compute the resonant frequencies and coupled mode-shapes of general structural-acoustic systems using the finite element method. This information is useful in quantifying the key frequencies and vibration patterns of elastic structures coupled to bounded or unbounded acoustic fluid volumes. This paper reviews and evaluates three finite element solution techniques that deal with the computational difficulties encountered in structural-acoustic eigen-analysis. One of the difficulties stems from the fluid-structure coupling in the finite element equations, which depending on the variable used to discretize the acoustic fluid, either introduces non-symmetric area coupling terms in the mass and stiffness matrices or adds symmetric area coupling terms in the damping matrix. The other difficulty is related to the application of a radiation boundary condition in those structural-acoustic problems involving unbounded acoustic domains. The radiation boundary condition introduces damping terms in the finite element equations that lead to a complex eigen-analysis to determine the resonant frequencies and coupled mode-shapes. The finite element techniques evaluated in this paper consist of subspace projection employing an augmented-symmetric form of the fluid-structure equations as well as new extensions of component mode synthesis (CMS). Basic examples of simplified structural-acoustic systems are used to compare the solution accuracy between the three finite element techniques. Examples consist of simplified one-dimensional (1-D) and two-dimensional (2-D) elastic structures coupled to closed and open acoustic spaces.
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7

Bosshard, Vitor, Benedikt Bünz, Benjamin Lubin, and Sven Seuken. "Computing Bayes-Nash Equilibria in Combinatorial Auctions with Continuous Value and Action Spaces." In Twenty-Sixth International Joint Conference on Artificial Intelligence. California: International Joint Conferences on Artificial Intelligence Organization, 2017. http://dx.doi.org/10.24963/ijcai.2017/18.

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Combinatorial auctions (CAs) are widely used in practice, which is why understanding their incentive properties is an important problem. However, finding Bayes-Nash equilibria (BNEs) of CAs analytically is tedious, and prior algorithmic work has only considered limited solution concepts (e.g. restricted action spaces). In this paper, we present a fast, general algorithm for computing symmetric pure ε-BNEs in CAs with continuous values and actions. In contrast to prior work, we separate the search phase (for finding the BNE) from the verification step (for estimating the ε), and always consider the full (continuous) action space in the best response computation. We evaluate our method in the well-studied LLG domain, against a benchmark of 16 CAs for which analytical BNEs are known. In all cases, our algorithm converges quickly, matching the known results with high precision. Furthermore, for CAs with quasi-linear utility functions and independently distributed valuations, we derive a theoretical bound on ε. Finally, we introduce the new Multi-Minded LLLLGG domain with eight goods and six bidders, and apply our algorithm to finding an equilibrium in this domain. Our algorithm is the first to find an accurate BNE in a CA of this size.
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Cardou, Philippe, Denis Laurendeau, Luc Beaulieu, Luc Be´langer, and Alexandre Carette. "The Dimensional Synthesis of the Linear Delta Robot for a Force-Feedback Device." In ASME 2010 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2010. http://dx.doi.org/10.1115/detc2010-28383.

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We perform the dimensional synthesis of a parallel manipulator to be used as a force-feedback device in a virtual reality application for surgeon training in prostate brachytherapy. For such brachytherapy operations, the characteristics of the required workspace point towards the architecture of the linear DELTA robot to be used as the force-feedback device to the surgeon. In this paper, we address the dimensional synthesis of the linear DELTA robot for the prescribed workspace. To this end, we propose the minimum relative kinematic sensitivity as an objective function, a kinematic performance index that is different from most of the commonly used metrics, i.e., manipulability and dexterity. The minimum relative kinematic sensitivity represents the ratio of the minimum to the maximum effect of a unity-bounded set of actuator displacements on the moving-platform pose. These extremum sensitivities are computed independently over the prescribed workspace. Thence, the dimensional synthesis problem consists in finding the robot dimensions that maximize the minimum relative kinematic sensitivity, so it is guaranteed within a narrow interval over the prescribed workspace. This optimization problem is nonconvex, which poses a challenge from the computational point of view. However, because of symmetry in the mechanism and other simplifications, the number of optimization variables is reduced to four. This allows a reasonably fine discretization of the search domain, giving the designers confidence that the ensuing local optimum is close to the global optimum.
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9

Liu, Yachong, Ankang Hu, Fenglei Han, and Yu Lu. "Numerical Method Research on Nonlinear Roll System of Large Container Ship." In ASME 2015 34th International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/omae2015-41493.

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When dealing with the ship-roll problem, the roll motion is mainly regarded as a single degree-of-freedom dynamical system, and the nonlinear properties are reflected in the nonlinear damping term and restoring moment term. Previous studies have shown that transverse chaotic phenomenon means the damage of ship-roll stability which will lead to ship capsizing, and for ultra large container ships, the wind area above water surface can not be neglected, which turns the ship-roll system into asymmetric dynamical system. The concept of safe basin is usually used to express the boundedness of motion. It is defined as the set of bounded solution to dynamical system, and the erosion phenomenon of safe basin is normally explained as the global instability. This concept was firstly brought out by Thompson [1] when he studied the problem of ship capsizing and then was applied to different fields of engineering. Based on this background, the following three tasks are completed in this paper. a) For the calculation of chaos threshold, two numerical methods, namely, Pade approximation and Gauss-Legendre integration are adopted, analyzed and compared. b) One 9200TEU container ship is selected and the chaos threshold is calculated by virtue of Gauss-Legendre method. As numerical verification, the gradually erosion phenomenon of ship’s safe basin is observed and phase trajectories of points located in broken domain are traced; c) When encountered with crosswind (When winds are not parallel to or directly against the line of travel, the wind is said to have a crosswind component; that is, the force can be separated into two vector components, a crosswind component and a headwind or tailwind component.), the symmetry of ship-roll system begin to break. In the last part of this paper, the effect of crosswind on safe basin, asymmetry, and stability are studied.
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Reports on the topic "Bounded Symmetric domain"

1

Clerc, Jean-Louis. Geometry of the Shilov Boundary of a Bounded Symmetric Domain. GIQ, 2012. http://dx.doi.org/10.7546/giq-10-2009-11-55.

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2

Clerc, Jean-Louis. Geometry of the Shilov Boundary of a Bounded Symmetric Domain. Journal of Geometry and Symmetry in Physics, 2012. http://dx.doi.org/10.7546/jgsp-13-2009-25-74.

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