Academic literature on the topic 'Complex Structure Moduli'

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Journal articles on the topic "Complex Structure Moduli"

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ISIDRO, JOSÉ M. "COMPLEX MODULI OF PHYSICAL QUANTA." Modern Physics Letters A 20, no. 12 (2005): 869–74. http://dx.doi.org/10.1142/s0217732305017196.

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Classical mechanics can be formulated using a symplectic structure on classical phase space, while quantum mechanics requires a complex-differentiable structure on that same space. Complex-differentiable structures on a given real manifold are often not unique. This paper is devoted to analysing the dependence of the notion of a quantum on the complex-differentiable structure chosen on classical phase space.
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ISIDRO, JOSÉ M. "MODULI OF QUANTA." International Journal of Geometric Methods in Modern Physics 03, no. 02 (2006): 177–86. http://dx.doi.org/10.1142/s0219887806001089.

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The classical phase of the matrix model of 11-dimensional M-theory is complex, infinite-dimensional Hilbert space. As a complex manifold, the latter admits a continuum of nonequivalent, complex-differentiable structures that can be placed in 1-to-1 correspondence with families of coherent states in the Hilbert space of quantum states. The moduli space of nonbiholomorphic complex structures on classical phase space turns out to be an infinite-dimensional symmetric space. We argue that each choice of a complex differentiable structure gives rise to a physically different notion of an elementary
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García-Bellido, Juan, and Raúl Rabadán. "Complex structure moduli stability in toroidal compactifications." Journal of High Energy Physics 2002, no. 05 (2002): 042. http://dx.doi.org/10.1088/1126-6708/2002/05/042.

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Allcock, Daniel, James A. Carlson, and Domingo Toledo. "A complex hyperbolic structure for moduli of cubic surfaces." Comptes Rendus de l'Académie des Sciences - Series I - Mathematics 326, no. 1 (1998): 49–54. http://dx.doi.org/10.1016/s0764-4442(97)82711-5.

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Emam, Moataz H., H. H. Salah, and Safinaz Salem. "Brane-worlds and the Calabi–Yau complex structure moduli." Classical and Quantum Gravity 37, no. 19 (2020): 195007. http://dx.doi.org/10.1088/1361-6382/ab9515.

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Kamiyama, Yasuhiko, and Shuichi Tsukuda. "On Deformations of the Complex Structure on the Moduli Space of Spatial Polygons." Canadian Mathematical Bulletin 45, no. 3 (2002): 417–21. http://dx.doi.org/10.4153/cmb-2002-043-8.

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AbstractFor an integer n ≥ 3, let Mn be the moduli space of spatial polygons with n edges. We consider the case of odd n. Then Mn is a Fano manifold of complex dimension n − 3. Let ΘMn be the sheaf of germs of holomorphic sections of the tangent bundle TMn. In this paper, we prove Hq(Mn, ΘMn) = 0 for all q ≥ 0 and all odd n. In particular, we see that the moduli space of deformations of the complex structure on Mn consists of a point. Thus the complex structure on Mn is locally rigid.
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Milton, G. W. "Exact band structure for the scalar wave equation with periodic complex moduli." Physica B: Condensed Matter 338, no. 1-4 (2003): 186–89. http://dx.doi.org/10.1016/s0921-4526(03)00484-8.

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RADNELL, DAVID, and ERIC SCHIPPERS. "QUASISYMMETRIC SEWING IN RIGGED TEICHMÜLLER SPACE." Communications in Contemporary Mathematics 08, no. 04 (2006): 481–534. http://dx.doi.org/10.1142/s0219199706002210.

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One of the basic geometric objects in conformal field theory (CFT) is the moduli space of Riemann surfaces whose n boundaries are "rigged" with analytic parametrizations. The fundamental operation is the sewing of such surfaces using the parametrizations to identify points. An alternative model is the moduli space of n-punctured Riemann surfaces together with local biholomorphic coordinates at the punctures. We refer to both of these moduli spaces as the "rigged Riemann moduli space".By generalizing to quasisymmetric boundary parametrizations, and defining rigged Teichmüller spaces in both the
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CURIO, GOTTFRIED, and VERA SPILLNER. "ON THE MODIFIED KKLT PROCEDURE: A CASE STUDY FOR THE P11169[18] MODEL." International Journal of Modern Physics A 22, no. 20 (2007): 3463–92. http://dx.doi.org/10.1142/s0217751x07037019.

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We probe the existence of supersymmetric vacua of the type IIB orientifold of the elliptic Calabi–Yau space P11169[18] where generically two complex structure moduli zi, the dilaton τ and the two Kähler moduli Ti are stabilized by fluxes and gaugino condensates. The usual KKLT procedure, which integrates out the complex structure moduli and the dilaton, actually has to be modified, such that one keeps the dependence on τ. We derive explicitly the resulting effective superpotential W eff (τ) for the dilaton for various flux combinations. As this is actually a nonholomorphic quantity one must pr
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Fialowski, Alice, and Michael Penkava. "Moduli spaces of low-dimensional Lie superalgebras." International Journal of Mathematics 32, no. 09 (2021): 2150059. http://dx.doi.org/10.1142/s0129167x21500592.

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In this paper, we study moduli spaces of low-dimensional complex Lie superalgebras. We discover a similar pattern for the structure of these moduli spaces as we observed for ordinary Lie algebras, namely, that there is a stratification of the moduli space by projective orbifolds. The moduli spaces consist of some families as well as some singleton elements. The different strata are linked by jump deformations, which gives a unique manner of decomposing the moduli space which is consistent with deformation theory.
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Dissertations / Theses on the topic "Complex Structure Moduli"

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De, Notariis Kevin. "Light hyperweak new gauge bosons from kinetic mixing in string models." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2019. http://amslaurea.unibo.it/19491/.

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String theory is at the moment our best candidate for a unified quantum theory of gravity, aiming to reconcile all the known (and unknown) interactions with gravity as well as provide insights for currently mysterious phenomena that the Standard Model and the modern Cosmology are not able to explain. In fact, it is believed that most of the problems associated to the Standard Model can indeed be resolved in string theory. Supersymmetry is supposed to be an elegant solution to the Hierarchy problem (even though more and more stringent bounds in this direction are being placed by the fact that w
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Choe, Sehyo Charley. "Models of complex adaptive systems with underlying network structure." Thesis, University of Oxford, 2007. https://ora.ox.ac.uk/objects/uuid:1cb8cb96-d27f-4543-9065-0e38a4297435.

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This thesis explores the effect of different types of underlying network structure on the dynamical behaviour of a competitive population - a situation encountered in many real-world complex systems. In the first part of the thesis, I focus on generic, but abstract, multi-agent systems. I start by presenting analytic and numerical results for a population of heterogeneous, decision-making agents competing for some limited global resource, in which connections arise unintentionally between agents as a by-product of their strategy choices. I show that accounting for the resulting groups of stron
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Sun, Daning. "Structured policies for complex production and inventory models." Thesis, University of British Columbia, 1990. http://hdl.handle.net/2429/31002.

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For inventory models minimizing the long-run average cost over an infinite horizon, the existence of optimal policies was an open question for a long time. Consider a deterministic, continuous time inventory system satisfies the following conditions: the production network is acyclic, the joint setup cost function is monotone, the holding cost and the backlogging cost rates are nonnegative, the demand rates are constant over time, the production rates are infinite or finite non-increasing, and backlogging may be allowed or not. For this very general extension of the Wilson-Harris EOQ model, we
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Leon, Ralph Daniel. "Module structure of a Hilbert space." CSUSB ScholarWorks, 2003. https://scholarworks.lib.csusb.edu/etd-project/2469.

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This paper demonstrates the properties of a Hilbert structure. In order to have a Hilbert structure it is necessary to satisfy certain properties or axioms. The main body of the paper is centered on six questions that develop these ideas.
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Bonnet, Jacques. "Analyses structure fonction du module de déubiquitination du complexe SAGA." Phd thesis, Université de Strasbourg, 2012. http://tel.archives-ouvertes.fr/tel-00870969.

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Pour faciliter l'initiation de la transcription par l'ARN Polymérase II, le complexe co-activateur de la transcription SAGA possède une activité d'acétylation des histones H3 et une activité de déubiquitination des histones H2B, catalysée chez l'homme par l'enzyme USP22. Mon travail de thèse a porté sur l'étude de la régulation de cette activité de déubiquitination.Au sein de SAGA, USP22 interagit fortement avec trois protéines pour former un module structural appelé module de déubiquitination (DUBm). Nous avons montré que la formation d'un tel module était requise pour activer USP22. D'autre
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Guo, Xu. "Checking the adequacy of regression models with complex data structure." HKBU Institutional Repository, 2014. https://repository.hkbu.edu.hk/etd_oa/90.

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In this thesis, we investigate the model checking problem for parametric regression model with missing response at random and nonignorable missing response. Besides, we also propose a hypothesis-adaptive procedure which is based on the dimension reduction theory. Finally, to extend our methods to missing response situation, we consider the dimension reduction problem with missing response at random. The .rst part of the thesis introduces the model checking for parametric models with response missing at random which is a more general missing mechanism than missing completely at random. Di.eren
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Forsman, Åsa. "Identification of simple structures in complex substance transport models /." Linköping : Faculty of Arts and Sciences, Univ, 2002. http://www.bibl.liu.se/liupubl/disp/disp2002/stat1s.pdf.

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Chauvet, Jocelyn. "Introducing complex dependency structures into supervised components-based models." Thesis, Montpellier, 2019. http://www.theses.fr/2019MONTS008/document.

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Une forte redondance des variables explicatives cause de gros problèmes d'identifiabilité et d'instabilité des coefficients dans les modèles de régression. Même lorsque l'estimation est possible, l'interprétation des résultats est donc extrêmement délicate. Il est alors indispensable de combiner à leur vraisemblance un critère supplémentaire qui régularise l'estimateur. Dans le sillage de la régression PLS, la stratégie de régularisation que nous considérons dans cette thèse est fondée sur l'extraction de composantes supervisées. Contraintes à l'orthogonalité entre elles, ces composantes doive
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Levy, Marc. "Shareholders' control in complex corporate structures." Doctoral thesis, Universite Libre de Bruxelles, 2012. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/209768.

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In this global world, many firms present a complex shareholding structure with<p>indirect participation, such that it may become difficult to assess a firm’s controllers.<p>Furthermore, if there are numerous dominant shareholders, the control can be shared between<p>them. Determining who has the most influence is often a difficult task. To measure this<p>influence, game theory allows the modeling of voting games and the computing of the<p>Banzhaf index. This thesis develops models to measure the Banzhaf indices in any ownership structure (pyramidal ownership structures and cross-ownership stru
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Hang, Huajiang Engineering &amp Information Technology Australian Defence Force Academy UNSW. "Prediction of the effects of distributed structural modification on the dynamic response of structures." Awarded by:University of New South Wales - Australian Defence Force Academy. Engineering & Information Technology, 2009. http://handle.unsw.edu.au/1959.4/44275.

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The aim of this study is to investigate means of efficiently assessing the effects of distributed structural modification on the dynamic properties of a complex structure. The helicopter structure is normally designed to avoid resonance at the main rotor rotational frequency. However, very often military helicopters have to be modified (such as to carry a different weapon system or an additional fuel tank) to fulfill operational requirements. Any modification to a helicopter structure has the potential of changing its resonance frequencies and mode shapes. The dynamic properties of the modifie
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Books on the topic "Complex Structure Moduli"

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Complex manifolds and deformation of complex structures. Springer-Verlag, 1986.

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Complex manifolds and deformation of complex structures. Springer-Verlag, 1986.

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Laeven, Luc. Complex ownership structures and corporate valuations. International Monetary Fund, Research Dept., 2007.

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Laeven, Luc. Complex ownership structures and corporate valuations. National Bureau of Economic Research, 2006.

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Moduli spaces of Riemann surfaces. American Mathematical Society, 2013.

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service), SpringerLink (Online, ed. Evolutionary Games in Complex Topologies: Interplay Between Structure and Dynamics. Springer Berlin Heidelberg, 2012.

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David, Goss. Basic structures of function field arithmetic. Springer, 1998.

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Basic structures of function field arithmetic. Springer, 1996.

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Simple models of complex nuclei: The shell model and interacting boson model. Harwood Academic Publishers, 1993.

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Daw, Murray S. Atomic-scale modeling of the structure and dynamics of dislocations in complex alloys at high temperatures. National Aeronautics and Space Administration, Glenn Research Center, 2003.

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Book chapters on the topic "Complex Structure Moduli"

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Lange, Herbert, and Christina Birkenhake. "Moduli Spaces of Abelian Varieties with Endomorphism Structure." In Complex Abelian Varieties. Springer Berlin Heidelberg, 1992. http://dx.doi.org/10.1007/978-3-662-02788-2_11.

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Birkenhake, Christina, and Herbert Lange. "Moduli Spaces of Abelian Varieties with Endomorphism Structure." In Complex Abelian Varieties. Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-662-06307-1_11.

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Stronge, William James, and Tongxi Yu. "More Complex Configurations." In Dynamic Models for Structural Plasticity. Springer London, 1993. http://dx.doi.org/10.1007/978-1-4471-0397-4_6.

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Filieri, Antonio, Marcelo F. Frias, Corina S. Păsăreanu, and Willem Visser. "Model Counting for Complex Data Structures." In Model Checking Software. Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-23404-5_15.

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Gardner, Robert H. "Neutral Models and the Analysis of Landscape Structure." In Modelling Complex Ecological Dynamics. Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-05029-9_15.

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Belov, Mikhail V., and Dmitry A. Novikov. "Structural Models of Complex Activity." In Studies in Systems, Decision and Control. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-48610-5_3.

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Dette, Holger, and Jens Wagener. "Least Squares Estimation in High Dimensional Sparse Heteroscedastic Models." In Robustness and Complex Data Structures. Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-35494-6_9.

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Li, Xue-Zhi, Junyuan Yang, and Maia Martcheva. "Age Structured Models on Complex Networks." In Interdisciplinary Applied Mathematics. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-42496-1_5.

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Wermuth, Nanny, and David R. Cox. "Concepts and a Case Study for a Flexible Class of Graphical Markov Models." In Robustness and Complex Data Structures. Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-35494-6_20.

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Kulah, S., U. Aridogan, and I. Basdogan. "Investigation of an Active Structural Acoustic Control System on a Complex 3D Structure." In Topics in Modal Analysis, Volume 7. Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4614-6585-0_68.

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Conference papers on the topic "Complex Structure Moduli"

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Bharadwaj, N. Ashwin, James T. Allison, and Randy H. Ewoldt. "Early-Stage Design of Rheologically Complex Materials via Material Function Design Targets." In ASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/detc2013-13462.

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Rheological material properties are high-dimensional function-valued quantities, such as frequency-dependent viscoelastic moduli or non-Newtonian shear viscosity. Here we describe a process to model and optimize design targets for such rheological material functions. For linear viscoelastic systems, we demonstrate that one can avoid specific a priori assumptions of spring-dashpot topology by writing governing equations in terms of a time-dependent relaxation modulus function. Our approach embraces rheological design freedom, connecting system-level performance to optimal material functions tha
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Hatami-Marbini, Hamed, and Catalin R. Picu. "On Structure and Elastic Fields of Random Fiber Networks." In ASME 2010 First Global Congress on NanoEngineering for Medicine and Biology. ASMEDC, 2010. http://dx.doi.org/10.1115/nemb2010-13058.

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Random filamentous networks and their response to the applied load can be considered as a model to study the mechanical properties of biological systems such as cytoskeleton of a cell and connective tissues. A mathematical model for the actual and complex deformation of these networks under stress is developed using a micromechanics approach. We recently studied the effect of various micro-structural parameters such as fiber length, mean segment length and fiber flexibility on the network deformation field at various length scales. The network elasticity is mapped into a two dimensional hetero
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De Santis, Gianluca, Federica Boschetti, Alex B. Lennon, Patrick J. Prendergast, Pascal Verdonck, and Benedict Verhegghe. "How an Eukaryotic Cell Senses the Substrate Stiffness? An Exploration Using a Finite Element Model With Cytoskeleton Modelled as Tensegrity Structure." In ASME 2009 Summer Bioengineering Conference. American Society of Mechanical Engineers, 2009. http://dx.doi.org/10.1115/sbc2009-206448.

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Mammalian cells in vivo are connected to the ECM (or other substrate, SS) or other cells having elastic moduli ranging from 10 to 10000 Pa. Several experimental evidences relate cell processes (e.g. changes of spreading area, cytoskeletal filament assembling, focal adhesion complex (FAC)) to SS stiffness, but how a passive substrate affects these cell processes is still unknown [1,2].
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Nouh, M. "Structural Intensity Analysis of Periodic Elastic Structures With Frequency Stop Bands." In ASME 2016 Conference on Smart Materials, Adaptive Structures and Intelligent Systems. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/smasis2016-9277.

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Periodic elastic structures consisting of self-repeating geometric or material arrangements exhibit unique wave propagation characteristics culminating in frequency stop bands, i.e. ranges of frequency where elastic waves can propagate the periodic medium. Such features make periodic structures appealing for a wide range of vibration suppression and noise control applications. Stop bands in periodic media are achieved via Bragg scattering of elastic which is attributed to impedance mismatches between the different constituents of the self-repeating cells. Stop band frequencies can be numerical
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Vijith, P. P., and Suresh Rajendran. "Horizontal and Torsional Modes of an Ultra Large Container Ship (ULCS)." In ASME 2020 39th International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2020. http://dx.doi.org/10.1115/omae2020-18659.

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Abstract The hydro elastic responses of flexible structures under fluid loading is an important concern during the design of large ocean structures. The two-way coupling between the structural responses and the hydrodynamic loads is a complex problem in large flexible floating structures since the structures can vibrate in longitudinal, vertical, horizontal, or torsional modes. The antisymmetric distortion modes may be coupled depending on the location of the centroid and the shear centre. In the case of thin walled open structures, horizontal and torsional vibrations are usually coupled due t
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Shirotori, H. "Phenomenological models of raft structure." In SLOW DYNAMICS IN COMPLEX SYSTEMS: 3rd International Symposium on Slow Dynamics in Complex Systems. AIP, 2004. http://dx.doi.org/10.1063/1.1764162.

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Barquero, Gala, Loli Burgueño, Javier Troya, and Antonio Vallecillo. "Extending Complex Event Processing to Graph-structured Information." In MODELS '18: ACM/IEEE 21th International Conference on Model Driven Engineering Languages and Systems. ACM, 2018. http://dx.doi.org/10.1145/3239372.3239402.

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Wang, X. Q., Ricardo A. Perez, and Marc P. Mignolet. "Nonlinear Reduced Order Modeling of Complex Wing Models." In 54th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference. American Institute of Aeronautics and Astronautics, 2013. http://dx.doi.org/10.2514/6.2013-1520.

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Gordon, Robert, and Joseph Hollkamp. "Coupled Structural-Acoustic Response Prediction with Complex Modal Models." In 50th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference. American Institute of Aeronautics and Astronautics, 2009. http://dx.doi.org/10.2514/6.2009-2307.

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Russell, Steven G. "Complex Potential Stress Field Models for Damage Evaluation in Composites." In 2018 AIAA/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference. American Institute of Aeronautics and Astronautics, 2018. http://dx.doi.org/10.2514/6.2018-1472.

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Reports on the topic "Complex Structure Moduli"

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Radnell, David. A Complex Structure on the Moduli Space of Rigged Riemann Surfaces. Journal of Geometry and Symmetry in Physics, 2012. http://dx.doi.org/10.7546/jgsp-5-2006-82-94.

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Makarenko, S. I., and K. V. Ushanev. Program imitating model of formation of a traffic of complex structure. Science and Innovation Center Publishing House, 2017. http://dx.doi.org/10.12731/ofernio.2014.20514.

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Baumann, William T., Richard L. Moose, Hugh F. VanLandigham, Mauro J. Caputi, Stephen H. Jones, and Bhaskar Gorti. Active Control of Generalized Complex Modal Structures in a Stochastic Environment. Defense Technical Information Center, 1992. http://dx.doi.org/10.21236/ada251910.

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Riveros, Guillermo, Felipe Acosta, Reena Patel, and Wayne Hodo. Computational mechanics of the paddlefish rostrum. Engineer Research and Development Center (U.S.), 2021. http://dx.doi.org/10.21079/11681/41860.

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Purpose – The rostrum of a paddlefish provides hydrodynamic stability during feeding process in addition to detect the food using receptors that are randomly distributed in the rostrum. The exterior tissue of the rostrum covers the cartilage that surrounds the bones forming interlocking star shaped bones. Design/methodology/approach – The aim of this work is to assess the mechanical behavior of four finite element models varying the type of formulation as follows: linear-reduced integration, linear-full integration, quadratic-reduced integration and quadratic-full integration. Also presented i
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Chambers, D. Model-based flaw localization from perturbations in the dynamic response of complex mechanical structures. Office of Scientific and Technical Information (OSTI), 2009. http://dx.doi.org/10.2172/948655.

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Hofer, Martin, Tomas Sako, Arturo Martinez Jr., et al. Applying Artificial Intelligence on Satellite Imagery to Compile Granular Poverty Statistics. Asian Development Bank, 2020. http://dx.doi.org/10.22617/wps200432-2.

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This study outlines a computational framework to enhance the spatial granularity of government-published poverty estimates, citing data from the Philippines and Thailand. Computer vision techniques were applied on publicly available medium resolution satellite imagery, household surveys, and census data from the two countries. The results suggest that even using publicly accessible satellite imagery, predictions generally aligned with the distributional structure of government-published poverty estimates after calibration. The study further examines the robustness of the resulting estimates to
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Khalifa, Hesham. Modular fabrication and characterization of complex silicon carbide composite structures Advanced Reactor Technologies (ART) Research Final Report (Feb 2015 – May 2017). Office of Scientific and Technical Information (OSTI), 2017. http://dx.doi.org/10.2172/1373739.

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Yan, Yujie, and Jerome F. Hajjar. Automated Damage Assessment and Structural Modeling of Bridges with Visual Sensing Technology. Northeastern University, 2021. http://dx.doi.org/10.17760/d20410114.

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Recent advances in visual sensing technology have gained much attention in the field of bridge inspection and management. Coupled with advanced robotic systems, state-of-the-art visual sensors can be used to obtain accurate documentation of bridges without the need for any special equipment or traffic closure. The captured visual sensor data can be post-processed to gather meaningful information for the bridge structures and hence to support bridge inspection and management. However, state-of-the-practice data postprocessing approaches require substantial manual operations, which can be time-c
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Qi, Fei, Zhaohui Xia, Gaoyang Tang, et al. A Graph-based Evolutionary Algorithm for Automated Machine Learning. Web of Open Science, 2020. http://dx.doi.org/10.37686/ser.v1i2.77.

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As an emerging field, Automated Machine Learning (AutoML) aims to reduce or eliminate manual operations that require expertise in machine learning. In this paper, a graph-based architecture is employed to represent flexible combinations of ML models, which provides a large searching space compared to tree-based and stacking-based architectures. Based on this, an evolutionary algorithm is proposed to search for the best architecture, where the mutation and heredity operators are the key for architecture evolution. With Bayesian hyper-parameter optimization, the proposed approach can automate th
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Ivanova, Iryna, and Elena Afanasieva. MODEL OF INTERACTION BETWEEN ADVERTISING, PR AND JOURNALISM. Ivan Franko National University of Lviv, 2021. http://dx.doi.org/10.30970/vjo.2021.49.11060.

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The article is an overview of the journalism – PR – advertising relationship at the terminological, empirical-analytical and practical levels. It traces the state of the discussion of these correlations in the post-soviet media such as Ukraine. The study describes that domesticating the importance of the appropriate partnership between the three communication technologies. The thesis is that journalism, advertising and PR create a mutual connection that takes place in an atmosphere of PR and advertising permissiveness and deepens with the development of digitalization, Social network developme
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