Relevant bibliographies by topics / Invariant subspaces – Research – Analysis

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

Academic literature on the topic 'Invariant subspaces – Research – Analysis'

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Published: 4 June 2021
Last updated: 1 February 2022

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Journal articles on the topic "Invariant subspaces – Research – Analysis"

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Kuznetsov, Sergey P., and Yuliya V. Sedova. "Robust Hyperbolic Chaos in Froude Pendulum with Delayed Feedback and Periodic Braking." International Journal of Bifurcation and Chaos 29, no. 12 (November 2019): 1930035. http://dx.doi.org/10.1142/s0218127419300350.

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We indicate a possibility of implementing hyperbolic chaos using a Froude pendulum that is able to produce self-oscillations due to the suspension on a shaft rotating at constant angular velocity, in the presence of time-delay feedback and of periodic braking by the application of additional frictional force. We formulate a mathematical model and carry out its numerical research. In the parameter space we reveal areas of chaotic and regular dynamics using the analysis of Lyapunov exponents and some other diagnostic tools. It is shown that there are regions in the parameter space where the Poincaré stroboscopic map has an attractor, which is a kind of Smale–Williams solenoid embedded in the infinite-dimensional state space. We confirm the hyperbolicity of the attractor by numerical calculations including the analysis of angles of intersections of stable and unstable invariant subspaces of vectors of small perturbations for trajectories on the attractor and verify the absence of tangencies between these subspaces.
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Rapiejko, Piotr, Zbigniew M. Wawrzyniak, Ryszard S. Jachowicz, and Dariusz Jurkiewicz. "Image analysis in automatic system of pollen recognition." Acta Agrobotanica 59, no. 1 (2012): 385–93. http://dx.doi.org/10.5586/aa.2006.040.

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In allergology practice and research, it would be convenient to receive pollen identification and monitoring results in much shorter time than it comes from human identification. Image based analysis is one of the approaches to an automated identification scheme for pollen grain and pattern recognition on such images is widely used as a powerful tool. The goal of such attempt is to provide accurate, fast recognition and classification and counting of pollen grains by computer system for monitoring. The isolated pollen grain are objects extracted from microscopic image by CCD camera and PC computer under proper conditions for further analysis. The algorithms are based on the knowledge from feature vector analysis of estimated parameters calculated from grain characteristics, including morphological features, surface features and other applicable estimated characteristics. Segmentation algorithms specially tailored to pollen object characteristics provide exact descriptions of pollen characteristics (border and internal features) already used by human expert. The specific characteristics and its measures are statistically estimated for each object. Some low level statistics for estimated local and global measures of the features establish the feature space. Some special care should be paid on choosing these feature and on constructing the feature space to optimize the number of subspaces for higher recognition rates in low-level classification for type differentiation of pollen grains.The results of estimated parameters of feature vector in low dimension space for some typical pollen types are presented, as well as some effective and fast recognition results of performed experiments for different pollens. The findings show the ewidence of using proper chosen estimators of central and invariant moments (M21, NM2, NM3, NM8 NM9), of tailored characteristics for good enough classification measures (efficiency > 95%), even for low dimensional classifiers (≥ 3) for type differentiation of pollens grain.
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Beattie, Christopher, Mark Embree, and John Rossi. "Convergence of Restarted Krylov Subspaces to Invariant Subspaces." SIAM Journal on Matrix Analysis and Applications 25, no. 4 (January 2004): 1074–109. http://dx.doi.org/10.1137/s0895479801398608.

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Omladič, Matjaž. "Perturbation of Invariant Subspaces." Journal of Mathematical Analysis and Applications 197, no. 1 (January 1996): 125–37. http://dx.doi.org/10.1006/jmaa.1996.0011.

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Baranov, Anton, and Yurii Belov. "Synthesizable differentiation-invariant subspaces." Geometric and Functional Analysis 29, no. 1 (February 2019): 44–71. http://dx.doi.org/10.1007/s00039-019-00474-8.

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Djordjević, Slaviša V., Robin E. Harte, and David R. Larson. "Partially hyper invariant subspaces." Operators and Matrices, no. 1 (2012): 97–106. http://dx.doi.org/10.7153/oam-06-07.

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Apostol, Constantin, Ciprian Foias, and Norberto Salinas. "On stable invariant subspaces." Integral Equations and Operator Theory 8, no. 6 (November 1985): 721–50. http://dx.doi.org/10.1007/bf01213789.

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Turovskii, Yu V. "Volterra Semigroups Have Invariant Subspaces." Journal of Functional Analysis 162, no. 2 (March 1999): 313–22. http://dx.doi.org/10.1006/jfan.1998.3368.

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Chalendar, Isabelle, and Jonathan R. Partington. "Constrained approximation and invariant subspaces." Journal of Mathematical Analysis and Applications 280, no. 1 (April 2003): 176–87. http://dx.doi.org/10.1016/s0022-247x(03)00099-4.

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Kovarik, Zdislav V., and Nagwa Sherif. "Perturbation of invariant subspaces." Linear Algebra and its Applications 64 (January 1985): 93–113. http://dx.doi.org/10.1016/0024-3795(85)90269-1.

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Dissertations / Theses on the topic "Invariant subspaces – Research – Analysis"

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Caglar, Mert. "Invariant Subspaces Of Positive Operators On Riesz Spaces And Observations On Cd0(k)-spaces." Phd thesis, METU, 2005. http://etd.lib.metu.edu.tr/upload/12606391/index.pdf.

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The present work consists of two main parts. In the first part, invariant subspaces of positive operators or operator families on locally convex solid Riesz spaces are examined. The concept of a weakly-quasinilpotent operator on a locally convex solid Riesz space has been introduced and several results that are known for a single operator on Banach lattices have been generalized to families of positive or close-to-them operators on these spaces. In the second part, the so-called generalized Alexandroff duplicates are studied and CDsigma, gamma(K, E)-type spaces are investigated. It has then been shown that the space CDsigma, gamma(K, E) can be represented as the space of E-valued continuous functions on the generalized Alexandroff duplicate of K.
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Hokamp, Samuel A. "Weak*-Closed Unitarily and Moebius Invariant Spaces of Bounded Measurable Functions on a Sphere." Bowling Green State University / OhioLINK, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1562943150719334.

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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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Chen, Yahao. "Geometric analysis of differential-algebraic equations and control systems : linear, nonlinear and linearizable." Thesis, Normandie, 2019. http://www.theses.fr/2019NORMIR04.

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Dans la première partie de cette thèse, nous étudions les équations différentielles algébriques (en abrégé EDA) linéaires et les systèmes de contrôles linéaires associés (en abrégé SCEDA). Les problèmes traités et les résultats obtenus sont résumés comme suit : 1. Relations géométriques entre les EDA linéaires et les systèmes de contrôles génériques SCEDO. Nous introduisons une méthode, appelée explicitation, pour associer un SCEDO à n'importe quel EDA linéaire. L'explicitation d'une EDA est une classe des SCEDO, précisément un SCEDO défini, à un changement de coordonnées près, une transformation de bouclage près et une injection de sortie près. Puis nous comparons les « suites de Wong » d'une EDA avec les espaces invariants de son explicitation. Nous prouvons que la forme canonique de Kronecker FCK d'une EDA linéaire et la forme canonique de Morse FCM d'un SCEDO, ont une correspondance une à une et que leurs invariants sont liés. De plus, nous définissons l'équivalence interne de deux EDA et montrons sa particularité par rapport à l'équivalence externe en examinant les relations avec la régularité interne, i.e., l'existence et l'unicité de solutions. 2. Transformation d'un SCEDA linéaire vers sa forme canonique via la méthode d'explicitation avec des variables de driving. Nous étudions les relations entre la forme canonique par bouclage FCFB d'un SCEDA proposée dans la littérature et la forme canonique de Morse pour les SCEDO. Premièrement, dans le but de relier SCEDA avec les SCEDO, nous utilisons une méthode appelée explicitation (avec des variables de driving). Cette méthode attache à une classe de SCEDO avec deux types d'entrées (le contrôle original et le vecteur des variables de driving) à un SCEDA donné. D'autre part, pour un SCEDO linéaire classique (sans variable de driving) nous proposons une forme de Morse triangulaire FMT pour modifier la construction de la FCM. Basé sur la FMT nous proposons une forme étendue FMT et une forme étendue de FCM pour les SCEDO avec deux types d'entrées. Finalement, un algorithme est donné pour transformer un SCEDA dans sa FCFB. Cet algorithme est construit sur la FCM d'un SCEDO donné par la procédure d'explicitation. Un exemple numérique illustre la structure et l'efficacité de l'algorithme. Pour les EDA non linéaires et les SCEDA (quasi linéaires) nous étudions les problèmes suivants : 3. Explicitations, analyse externe et interne et formes normales des EDA non linéaires. Nous généralisons les deux procédures d'explicitation (avec ou sans variables de driving) dans le cas des EDA non linéaires. L'objectif de ces deux méthodes est d'associer un SCEDO non linéaire à une EDA non linéaire telle que nous puissions l'analyser à l'aide de la théorie des EDO non linéaires. Nous comparons les différences de l'équivalence interne et externe des EDA non linéaires en étudiant leurs relations avec l'existence et l'unicité d'une solution (régularité interne). Puis nous montrons que l'analyse interne des EDA non linéaire est liée à la dynamique nulle en théorie classique du contrôle non linéaire. De plus, nous montrons les relations des EDAS de forme purement semi-explicite avec les 2 procédures d'explicitations. Finalement, une généralisation de la forme de Weierstrass non linéaire FW basée sur la dynamique nulle d'un SCEDO non linéaire donné par la méthode d'explicitation est proposée
In the first part of this thesis, we study linear differential-algebraic equations (shortly, DAEs) and linear control systems given by DAEs (shortly, DAECSs). The discussed problems and obtained results are summarized as follows. 1. Geometric connections between linear DAEs and linear ODE control systems ODECSs. We propose a procedure, named explicitation, to associate a linear ODECS to any linear DAE. The explicitation of a DAE is a class of ODECSs, or more precisely, an ODECS defined up to a coordinates change, a feedback transformation and an output injection. Then we compare the Wong sequences of a DAE with invariant subspaces of its explicitation. We prove that the basic canonical forms, the Kronecker canonical form KCF of linear DAEs and the Morse canonical form MCF of ODECSs, have a perfect correspondence and their invariants (indices and subspaces) are related. Furthermore, we define the internal equivalence of two DAEs and show its difference with the external equivalence by discussing their relations with internal regularity, i.e., the existence and uniqueness of solutions. 2. Transform a linear DAECS into its feedback canonical form via the explicitation with driving variables. We study connections between the feedback canonical form FBCF of DAE control systems DAECSs proposed in the literature and the famous Morse canonical form MCF of ODECSs. In order to connect DAECSs with ODECSs, we use a procedure named explicitation (with driving variables). This procedure attaches a class of ODECSs with two kinds of inputs (the original control input and the vector of driving variables) to a given DAECS. On the other hand, for classical linear ODECSs (without driving variables), we propose a Morse triangular form MTF to modify the construction of the classical MCF. Based on the MTF, we propose an extended MTF and an extended MCF for ODECSs with two kinds of inputs. Finally, an algorithm is proposed to transform a given DAECS into its FBCF. This algorithm is based on the extended MCF of an ODECS given by the explication procedure. Finally, a numerical example is given to show the structure and efficiency of the proposed algorithm. For nonlinear DAEs and DAECSs (of quasi-linear form), we study the following problems: 3. Explicitations, external and internal analysis, and normal forms of nonlinear DAEs. We generalize the two explicitation procedures (with or without driving variable) proposed in the linear case for nonlinear DAEs of quasi-linear form. The purpose of these two explicitation procedures is to associate a nonlinear ODECS to any nonlinear DAE such that we can use the classical nonlinear ODE control theory to analyze nonlinear DAEs. We discuss differences of internal and external equivalence of nonlinear DAEs by showing their relations with the existence and uniqueness of solutions (internal regularity). Then we show that the internal analysis of nonlinear DAEs is closely related to the zero dynamics in the classical nonlinear control theory. Moreover, we show relations of DAEs of pure semi-explicit form with the two explicitation procedures. Furthermore, a nonlinear generalization of the Weierstrass form WE is proposed based on the zero dynamics of a nonlinear ODECS given by the explicitation procedure
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Thompson, Derek Allen. "Restrictions to Invariant Subspaces of Composition Operators on the Hardy Space of the Disk." 2014. http://hdl.handle.net/1805/3881.

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Indiana University-Purdue University Indianapolis (IUPUI)
Invariant subspaces are a natural topic in linear algebra and operator theory. In some rare cases, the restrictions of operators to different invariant subspaces are unitarily equivalent, such as certain restrictions of the unilateral shift on the Hardy space of the disk. A composition operator with symbol fixing 0 has a nested sequence of invariant subspaces, and if the symbol is linear fractional and extremally noncompact, the restrictions to these subspaces all have the same norm and spectrum. Despite this evidence, we will use semigroup techniques to show many cases where the restrictions are still not unitarily equivalent.
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Popov, Alexey. "Invariant subspaces of certain classes of operators." Phd thesis, 2011. http://hdl.handle.net/10048/1906.

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The first part of the thesis studies invariant subspaces of strictly singular operators. By a celebrated result of Aronszajn and Smith, every compact operator has an invariant subspace. There are two classes of operators which are close to compact operators: strictly singular and finitely strictly singular operators. Pelczynski asked whether every strictly singular operator has an invariant subspace. This question was answered by Read in the negative. We answer the same question for finitely strictly singular operators, also in the negative. We also study Schreier singular operators. We show that this subclass of strictly singular operators is closed under multiplication by bounded operators. In addition, we find some sufficient conditions for a product of Schreier singular operators to be compact. The second part studies almost invariant subspaces. A subspace Y of a Banach space is almost invariant under an operator T if TY is a subspace of Y+F for some finite-dimensional subspace F ("error"). Almost invariant subspaces of weighted shift operators are investigated. We also study almost invariant subspaces of algebras of operators. We establish that if an algebra is norm closed then the dimensions of "errors" for the operators in the algebra are uniformly bounded. We obtain that under certain conditions, if an algebra of operators has an almost invariant subspace then it also has an invariant subspace. Also, we study the question of whether an algebra and its closure have the same almost invariant subspaces. The last two parts study collections of positive operators (including positive matrices) and their invariant subspaces. A version of Lomonosov theorem about dual algebras is obtained for collections of positive operators. Properties of indecomposable (i.e., having no common invariant order ideals) semigroups of nonnegative matrices are studied. It is shown that the "smallness" (in various senses) of some entries of matrices in an indecomposable semigroup of positive matrices implies the "smallness" of the entire semigroup.
Mathematics
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Kaschner, Scott R. "Superstable manifolds of invariant circles." 2013. http://hdl.handle.net/1805/3749.

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Indiana University-Purdue University Indianapolis (IUPUI)
Let f:X\rightarrow X be a dominant meromorphic self-map, where X is a compact, connected complex manifold of dimension n > 1. Suppose there is an embedded copy of \mathbb P^1 that is invariant under f, with f holomorphic and transversally superattracting with degree a in some neighborhood. Suppose also that f restricted to this line is given by z\rightarrow z^b, with resulting invariant circle S. We prove that if a ≥ b, then the local stable manifold W^s_loc(S) is real analytic. In fact, we state and prove a suitable localized version that can be useful in wider contexts. We then show that the condition a ≥ b cannot be relaxed without adding additional hypotheses by resenting two examples with a < b for which W^s_loc(S) is not real analytic in the neighborhood of any point.
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Books on the topic "Invariant subspaces – Research – Analysis"

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Radjavi, Heydar. Invariant subspaces. 2nd ed. Mineola, N.Y: Dover Publications, 2003.

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Radjavi, Heydar. Invariant Subspaces. Springer, 2011.

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Invariant Subspaces. Springer, 2011.

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Henry, Helson, Yadav B. S. 1931-, Singh Udita Narayana 1917-1989, University of Delhi. Dept. of Mathematics., and International Conference on "Invariant Subspaces and Allied Topics" (1986 : Dept. of Mathematics, University of Delhi), eds. Invariant subspaces and allied topics. New Delhi: Narosa Pub. House, 1990.

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(Editor), A. Aizpuru-Tomas, and F. Leon-Saavedra (Editor), eds. Advanced Courses Of Mathematical Analysis I: Proceedings Of The First International School, Cádiz, Spain 22 27 September 2002. World Scientific Publishing Company, 2004.

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Book chapters on the topic "Invariant subspaces – Research – Analysis"

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Sz.-Nagy, Béla, Hari Bercovici, Ciprian Foias, and László Kérchy. "Regular Factorizations and Invariant Subspaces." In Harmonic Analysis of Operators on Hilbert Space, 289–330. New York, NY: Springer New York, 2010. http://dx.doi.org/10.1007/978-1-4419-6094-8_7.

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Rovnyak, James. "Invariant Subspaces and Models for Linear Operators." In Gian-Carlo Rota on Analysis and Probability, 93–96. Boston, MA: Birkhäuser Boston, 2003. http://dx.doi.org/10.1007/978-1-4612-2070-1_14.

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Dyakonov, Konstantin M. "Continuous and Compact Embeddings Between Star-invariant Subspaces." In Complex Analysis, Operators, and Related Topics, 65–76. Basel: Birkhäuser Basel, 2000. http://dx.doi.org/10.1007/978-3-0348-8378-8_6.

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Rota, G. C. "Note on the Invariant Subspaces of Linear Operators." In Gian-Carlo Rota on Analysis and Probability, 67–69. Boston, MA: Birkhäuser Boston, 2003. http://dx.doi.org/10.1007/978-1-4612-2070-1_6.

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Tikhonov, Alexey. "Inner-outer Factorization for Weighted Schur Class Functions and Corresponding Invariant Subspaces." In Spectral Theory and Analysis, 125–34. Basel: Springer Basel, 2011. http://dx.doi.org/10.1007/978-3-7643-9994-8_8.

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Beyn, Wolf-Jürgen, Winfried Kleß, and Vera Thümmler. "Continuation of Low-Dimensional Invariant Subspaces in Dynamical Systems of Large Dimension." In Ergodic Theory, Analysis, and Efficient Simulation of Dynamical Systems, 47–72. Berlin, Heidelberg: Springer Berlin Heidelberg, 2001. http://dx.doi.org/10.1007/978-3-642-56589-2_3.

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Constantinescu, Tiberiu. "Schur Analysis for Matrices with a Finite Number of Negative Squares." In Advances in Invariant Subspaces and Other Results of Operator Theory, 87–108. Basel: Birkhäuser Basel, 1986. http://dx.doi.org/10.1007/978-3-0348-7698-8_7.

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Fernández-Morales, H. R., A. G. García, and G. Pérez-Villalón. "Generalized Sampling in $${L}^{2}({\mathbb{R}}^{d})$$ Shift-Invariant Subspaces with Multiple Stable Generators." In Multiscale Signal Analysis and Modeling, 51–80. New York, NY: Springer New York, 2012. http://dx.doi.org/10.1007/978-1-4614-4145-8_3.

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"Invariant subspaces." In Linear Analysis, 226–32. Cambridge University Press, 1999. http://dx.doi.org/10.1017/cbo9781139168472.017.

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"Invariant subspaces for contractions." In Introduction to Banach Algebras, Operators, and Harmonic Analysis, 160–65. Cambridge University Press, 2003. http://dx.doi.org/10.1017/cbo9780511615429.017.

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Conference papers on the topic "Invariant subspaces – Research – Analysis"

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Peña, Marta, Ferran Puerta, Xavier Puerta, Theodore E. Simos, George Psihoyios, and Ch Tsitouras. "A Sufficient Condition for Stability of Controlled Invariant Subspaces." In Numerical Analysis and Applied Mathematics. AIP, 2007. http://dx.doi.org/10.1063/1.2790164.

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Brennan, Sean N. "Dimensionless Sensitivity Methods to Identify Vehicle Cornering Stiffness From Yaw Rate Measurements." In ASME 2003 International Mechanical Engineering Congress and Exposition. ASMEDC, 2003. http://dx.doi.org/10.1115/imece2003-41609.

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A simplified method of identifying a dynamic model is presented that utilizes explicit and implicit coupling between Bode parameter sensitivities. This focus of this work is the identification, in real-time, of the Cornering Stiffness parameter. This parameter governs the tire-road interaction within the simplified bicycle model description of vehicle chassis dynamics at highway speeds. This novel sensitivity coupling method, discovered earlier as sensitivity invariance in circuit network analysis, explicitly limits the possible parameter gradients of the system model to a very small subspace. By constraining the parameter identification or adaptation to solely this possible subspace, a simplified and efficient parameter identification can be obtained at a reduced computational and modelling cost. Both simulation and experimental implementation on a research vehicle under changing road conditions are presented.
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Yang, Dan, and Venkataramana Ajjarapu. "Critical Eigenvalues Tracing for Power System Analysis via Continuation of Invariant Subspaces and Projected Arnoldi Method." In 2007 IEEE Power Engineering Society General Meeting. IEEE, 2007. http://dx.doi.org/10.1109/pes.2007.385842.

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Nayak, Jyothi S., M. Indiramma, and N. Nagarathna. "Modeling self-Principal Component Analysis for age invariant face recognition." In 2012 IEEE International Conference on Computational Intelligence and Computing Research (ICCIC). IEEE, 2012. http://dx.doi.org/10.1109/iccic.2012.6510277.

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Boos, E. E. "Gauge invariant classes of Feynman diagrams and applications for calculations." In ADVANCED COMPUTING AND ANALYSIS TECHNIQUES IN PHYSICS RESEARCH: VII International Workshop; ACAT 2000. AIP, 2001. http://dx.doi.org/10.1063/1.1405303.

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Kerdoncuff, Tanguy, Rémi Emonet, and Marc Sebban. "Metric Learning in Optimal Transport for Domain Adaptation." In Twenty-Ninth International Joint Conference on Artificial Intelligence and Seventeenth Pacific Rim International Conference on Artificial Intelligence {IJCAI-PRICAI-20}. California: International Joint Conferences on Artificial Intelligence Organization, 2020. http://dx.doi.org/10.24963/ijcai.2020/299.

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Domain Adaptation aims at benefiting from a labeled dataset drawn from a source distribution to learn a model from examples generated from a different but related target distribution. Creating a domain-invariant representation between the two source and target domains is the most widely technique used. A simple and robust way to perform this task consists in (i) representing the two domains by subspaces described by their respective eigenvectors and (ii) seeking a mapping function which aligns them. In this paper, we propose to use Optimal Transport (OT) and its associated Wassertein distance to perform this alignment. While the idea of using OT in domain adaptation is not new, the original contribution of this paper is two-fold: (i) we derive a generalization bound on the target error involving several Wassertein distances. This prompts us to optimize the ground metric of OT to reduce the target risk; (ii) from this theoretical analysis, we design an algorithm (MLOT) which optimizes a Mahalanobis distance leading to a transportation plan that adapts better. Extensive experiments demonstrate the effectiveness of this original approach.
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Pelegri, Assimina, and Baoxiang Shan. "Dynamic Analysis of Soft Tissues Using a State Space Model." In ASME 2008 Summer Bioengineering Conference. American Society of Mechanical Engineers, 2008. http://dx.doi.org/10.1115/sbc2008-193695.

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Research on the biomechanical behavior of soft tissues has drawn a lot of recent attention due to its application in tumor pathology, rehabilitation, surgery and biomaterial implants. In this study a finite element (FE) model is applied to represent soft tissues and phantoms with complex geometry and heterogeneous material properties. A solid 3D mixed u-p element S8P0 (8-node for displacement and 1-node for internal pressure) is implemented to capture the near-incompressibility inherent in soft tissues. A dynamic analysis of soft tissues’ response to excitation is explored in which, the second order differential equation representing the soft tissues in FE necessitates a time-consuming numerical solution procedure. Moreover, the second-order representation is complicated in estimating the tissue mechanical properties by inverse procedure. Thus, a state space (SS) model is used to equivalently represent soft tissues by transforming the second-order differential equation into a system of linear first-order differential equations. The linear and time-invariant SS representation of soft tissues for general dynamic analysis can reduce the computational cost and a provide framework for the “forward” simulation and “inverse” identification of soft tissues.
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Carrera, E., A. G. de Miguel, and A. Pagani. "Micro-, Meso- and Macro-Scale Analysis of Composite Laminates by Unified Theory of Structures." In ASME 2017 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/imece2017-71311.

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In the present research, an advanced methodology for the multi-scale analysis of composite structures is proposed. It is based on the Carrera Unified Formulation (CUF), according to which any theory of structures, either 2D plate/shell or 1D beam, can be expressed as a degenerate case of Elasticity by using generalized expansions of the fundamental unknown fields. By using an extensive index notation, CUF allows the governing equations of the problem under consideration, and eventually the related finite element arrays, to be stated in terms of fundamental nuclei, which are invariant of the theory approximation order and the analysis scale. In this manner, micro-, meso-, and macro-scale models of composite structures can be formulated with ease and in a unified way, without the need of changing the model paradigms from one scale to the other. The capability of the proposed methodology based on CUF is assessed and the results demonstrate the validity of the approach, whose mathematical formalism is scale-independent, but allows for the simultaneous analysis of composites from global to very local scales in an accurate manner.
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Xu, Xiao, Qingjun Zhao, Weiwei Luo, Fei Tang, and Xiaolei Sun. "Research on the Matching Relationship Between HPT and LPT of One and One-Half Vaneless Contra-Rotating Turbines." In ASME Turbo Expo 2016: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/gt2016-56141.

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Abstract:
The vaneless contra-rotating turbine (VCRT) has the potential to improve the thrust-to-weight ratio for future high performance propulsion systems. Without the inter-stage vane, the variation of the high pressure turbine (HPT) exit swirl, under off-design conditions, can introduce more significant effects on the operation of the low pressure turbine (LPT). This study performed both analytical and numerical work investigating the matching relationship between the two stages of one and one-half stage (1+1/2) VCRTs. The significant difference of 1+1/2 VCRTs from conventional turbines, under choking geometry-fixed conditions, was found the flow capacity at the station between HPT and LPT is not invariant. The matching relationship between HPT and LPT is indeed how the flow capacity at the station between the two stages varies for different matching conditions. Influenced by the variation of the flow capacity, both the total pressure ratio of HPT and the corrected mass flow rate at the inlet of LPT are confined by the matching relationship. The corrected rotational speeds of the two stages define different matching conditions. A correlation, defining the matching conditions that LPT can work with constant incidence, was also derived. With aid of the correlation, the matching conditions can be controlled assuring LPT work with stable high efficiency. In the end, an application of incorporating the matching relationship into the investigation of engine performances is demonstrated, in which, a turbojet performance cycle analysis was performed. This paper has established a framework guiding how to obtain the matching relationship between the two stages of 1+1/2 VCRTs and incorporate it into the investigation of engine performances.
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10

Kurudamannil, Jubal, and Rama Yedavalli. "Improved Robust Stability Bounds for Sampled Data Time Delay Systems." In ASME 2015 Dynamic Systems and Control Conference. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/dscc2015-9959.

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Abstract:
This paper presents improved bounds on the perturbations of continuous time plant matrix for robust stability in a sampled data time delay system framework using discrete Lyapunov stability criterion. The proposed improvement on the bounds is achieved using the state transformations as a vehicle. Several state transformation approaches are explored that result in improved bounds. In addition to the sampling period, time delay induced by the controller (in the form static output feedback) in the network is also incorporated in the analysis via state augmentation. The proposed robustness analysis is carried out for various classes of perturbations such as time invariant perturbations, as well as for structured and unstructured perturbations. The proposed methodologies are illustrated with the help of examples along with a discussion of future research directions in this area.
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