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Academic literature on the topic 'Compact homogenous spaces'

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Published: 10 March 2023

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Journal articles on the topic "Compact homogenous spaces"

Golasiński, Marek. "On homotopy nilpotency." Glasnik Matematicki 56, no. 2 (December 23, 2021): 391–406. http://dx.doi.org/10.3336/gm.56.2.10.

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We review established and recent results on the homotopy nilpotence of spaces. In particular, the homotopy nilpotency of the loop spaces $\Omega(G/K)$ of homogenous spaces $G/K$ for a compact Lie group $G$ and its closed homotopy nilpotent subgroup $K \lt G$ is discussed.

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Abbas, Fadhil, and Hassan A. Alhayo. "Fuzzy ideal topological vector spaces." Mathematica Slovaca 72, no. 4 (August 1, 2021): 993–1000. http://dx.doi.org/10.1515/ms-2022-0069.

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Abstract In this paper, we introduce the concept of fuzzy ideal topological vector spaces and study the basic properties of fuzzy-I-open and fuzzy-I-closed sets in fuzzy ideal topological vector spaces. Also, we study the properties of fuzzy-I-Hausdorff and fuzzy-I-compact in fuzzy ideal topological vector spaces. Furthermore, we introduce the concepts of fuzzy-I-homogenous space, fuzzy-I-monomorphism space, fuzzy-I-isomorphism space and fuzzy-I-automorphism space. Finally, we introduce the concepts of fuzzy-I-bounded set, fuzzy-I-balanced set, fuzzy-I-symmetric set and study their properties in fuzzy ideal topological vector spaces.

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Rejali, Ali, and Navid Sabzali. "On the homological and algebraical properties of some Feichtinger algebras." Mathematica Slovaca 71, no. 5 (October 1, 2021): 1211–28. http://dx.doi.org/10.1515/ms-2021-0049.

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Abstract Let G be a locally compact group (not necessarily abelian) and B be a homogeneous Banach space on G, which is in a good situation with respect to a homogeneous function algebra on G. Feichtinger showed that there exists a minimal Banach space B min in the family of all homogenous Banach spaces C on G, containing all elements of B with compact support. In this paper, the amenability and super amenability of B min with respect to the convolution product or with respect to the pointwise product are showed to correspond to amenability, discreteness or finiteness of the group G and conversely. We also prove among other things that B min is a symmetric Segal subalgebra of L 1(G) on an IN-group G, under certain conditions, and we apply our results to study pseudo-amenability and some other homological properties of B min on IN-groups. Furthermore, we determine necessary and sufficient conditions on A under which A min $\mathcal{A}_{\min}$ with the pointwise product is an abstract Segal algebra or Segal algebra in A, whenever A is a homogeneous function algebra with an approximate identity. We apply these results to study amenability of some Feichtinger algebras with respect to the pointwise product.

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Ghaani Farashahi, Arash. "A Class of Abstract Linear Representations for Convolution Function Algebras over Homogeneous Spaces of Compact Groups." Canadian Journal of Mathematics 70, no. 1 (February 1, 2018): 97–116. http://dx.doi.org/10.4153/cjm-2016-043-9.

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AbstractThis paper introduces a class of abstract linear representations on Banach convolution function algebras over homogeneous spaces of compact groups. LetGbe a compact group andHa closed subgroup ofG. Letμbe the normalizedG-invariant measure over the compact homogeneous spaceG/Hassociated with Weil's formula and. We then present a structured class of abstract linear representations of the Banach convolution function algebrasLp(G/H,μ).

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Nikiel, J., and E. D. Tymchatyn. "On Homogeneous Images of Compact Ordered Spaces." Canadian Journal of Mathematics 45, no. 2 (April 1, 1993): 380–93. http://dx.doi.org/10.4153/cjm-1993-019-7.

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AbstractWe answer a 1975 question of G R Gordh by showing that if X is a homogeneous compactum which is the continuous image of a compact ordered space then at least one of the following holds(I) X is metrizable, (II) dim X = 0 or (III) X is a union of finitely many pairwise disjoint generalized simple closed curves.We begin to examine the structure of homogeneous 0-dimensional spaces which are continuous images of ordered compacta.

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Berestovskii, V. N., and Y. G. Nikonorov. "О конечных однородных метрических пространствах." Владикавказский математический журнал, no. 2 (June 22, 2022): 51–61. http://dx.doi.org/10.46698/h7670-4977-9928-z.

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This survey is devoted to recently obtained results on finite homogeneousmetric spaces. The main subject of discussion is the classification of regular and semiregular polytopes in Euclidean spacesby whether or not their vertex sets have the normal homogeneity property or the Clifford - Wolf homogeneity property.Every finite homogeneous metric subspace of an Euclidean space represents the vertex set of a compact convex polytope with the isometry group that is transitive on the set of vertices, moreover, all these vertices lie on some sphere. Consequently, the study of such subsets is closely related to the theory of convex polytopes in Euclidean spaces. The normal generalized homogeneity and the Clifford - Wolf homogeneity describe more stronger properties than the homogeneity. Therefore, it is natural to first check the presence of these properties for the vertex sets of regular and semiregular polytopes. In addition to the classification results, the paper contains a description of the main tools for the study of the relevant objects.

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Ikawa, Osamu. "Equivariant minimal immersions of compact Riemannian homogeneous spaces into compact Riemannian homogeneous spaces." Tsukuba Journal of Mathematics 17, no. 1 (June 1993): 169–88. http://dx.doi.org/10.21099/tkbjm/1496162138.

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Gorbachev, Dmitry Viktorovich. "Nikol’skii constants for compact homogeneous spaces." Chebyshevskii sbornik 22, no. 4 (2021): 99–112. http://dx.doi.org/10.22405/2226-8383-2021-22-4-99-112.

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Gorbatsevich, V. V. "Stable cohomology of compact homogeneous spaces." Mathematical Notes 83, no. 5-6 (June 2008): 735–43. http://dx.doi.org/10.1134/s0001434608050192.

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Dissertations / Theses on the topic "Compact homogenous spaces"

Odell, Carl Richard. "Kernel approximation on compact homogeneous spaces." Thesis, University of Leicester, 2012. http://hdl.handle.net/2381/27598.

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This thesis is concerned with approximation on compact homogeneous spaces. The first part of the research involves a particular kind of compact homogeneous space, the hypersphere, S ͩˉ¹ embedded in R ͩ. It is a calculation of three integrals associated with approximation using radial basis functions, calculating the Fourier-Gegenbauer coefficients for two such functions. The latter part of the research is a calculation of an error bound for compact homogeneous spaces when interpolating with a G-invariant kernel, a generalisation of a result already known for spheres.

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Kadyrov, Shirali. "Entropy and Escape of Mass in Non-Compact Homogeneous Spaces." The Ohio State University, 2010. http://rave.ohiolink.edu/etdc/view?acc_num=osu1272027404.

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Bletz-Siebert, Oliver. "Homogeneous spaces with the cohomology of sphere products and compact quadrangles." Doctoral thesis, [S.l. : s.n.], 2002. http://deposit.ddb.de/cgi-bin/dokserv?idn=966590341.

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Rauße, Christian [Verfasser], and Christoph [Akademischer Betreuer] Böhm. "Simplicial complexes of compact homogeneous spaces / Christian Rauße ; Betreuer: Christoph Böhm." Münster : Universitäts- und Landesbibliothek Münster, 2017. http://d-nb.info/1142528421/34.

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Ebert, Svend. "Wavelets on Lie groups and homogeneous spaces." Doctoral thesis, Technische Universitaet Bergakademie Freiberg Universitaetsbibliothek "Georgius Agricola", 2011. http://nbn-resolving.de/urn:nbn:de:bsz:105-qucosa-78988.

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Within the past decades, wavelets and associated wavelet transforms have been intensively investigated in both applied and pure mathematics. They and the related multi-scale analysis provide essential tools to describe, analyse and modify signals, images or, in rather abstract concepts, functions, function spaces and associated operators. We introduce the concept of diffusive wavelets where the dilation operator is provided by an evolution like process that comes from an approximate identity. The translation operator is naturally defined by a regular representation of the Lie group where we want to construct wavelets. For compact Lie groups the theory can be formulated in a very elegant way and also for homogeneous spaces of those groups we formulate the theory in the theory of non-commutative harmonic analysis. Explicit realisation are given for the Rotation group SO(3), the k-Torus, the Spin group and the n-sphere as homogeneous space. As non compact example we discuss diffusive wavelets on the Heisenberg group, where the construction succeeds thanks to existence of the Plancherel measure for this group. The last chapter is devoted to the Radon transform on SO(3), where the application on diffusive wavelets can be used for its inversion. The discussion of a variational spline approach provides criteria for the choice of points for measurements in concrete applications.

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Zeekoei, Elroy Denovanne. "A study of Dunford-Pettis-like properties with applications to polynomials and analytic functions on normed spaces / Elroy Denovanne Zeekoei." Thesis, North-West University, 2011. http://hdl.handle.net/10394/7586.

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Recall that a Banach space X has the Dunford-Pettis property if every weakly compact operator defined on X takes weakly compact sets into norm compact sets. Some valuable characterisations of Banach spaces with the Dunford-Pettis property are: X has the DPP if and only if for all Banach spaces Y, every weakly compact operator from X to Y sends weakly convergent sequences onto norm convergent sequences (i.e. it requires that weakly compact operators on X are completely continuous) and this is equivalent to “if (xn) and (x*n) are sequences in X and X* respectively and limn xn = 0 weakly and limn x*n = 0 weakly then limn x*n xn = 0". A striking application of the Dunford-Pettis property (as was observed by Grothendieck) is to prove that if X is a linear subspace of L() for some finite measure  and X is closed in some Lp() for 1 ≤ p < , then X is finite dimensional. The fact that the well known spaces L1() and C() have this property (as was proved by Dunford and Pettis) was a remarkable achievement in the early history of Banach spaces and was motivated by the study of integral equations and the hope to develop an understanding of linear operators on Lp() for p ≥ 1. In fact, it played an important role in proving that for each weakly compact operator T : L1()  L1() or T : C()  C(), the operator T2 is compact, a fact which is important from the point of view that there is a nice spectral theory for compact operators and operators whose squares are compact. There is an extensive literature involving the Dunford-Pettis property. Almost all the articles and books in our list of references contain some information about this property, but there are plenty more that could have been listed. The reader is for instance referred to [4], [5], [7], [8], [10], [17] and [24] for information on the role of the DPP in different areas of Banach space theory. In this dissertation, however, we are motivated by the two papers [7] and [8] to study alternative Dunford-Pettis properties, to introduce a scale of (new) alternative Dunford-Pettis properties, which we call DP*-properties of order p (briefly denoted by DP*P), and to consider characterisations of Banach spaces with these properties as well as applications thereof to polynomials and holomorphic functions on Banach spaces. In the paper [8] the class Cp(X, Y) of p-convergent operators from a Banach space X to a Banach space Y is introduced. Replacing the requirement that weakly compact operators on X should be completely continuous in the case of the DPP for X (as is mentioned above) by “weakly compact operators on X should be p-convergent", an alternative Dunford-Pettis property (called the Dunford-Pettis property of order p) is introduced. More precisely, if 1 ≤ p ≤ , a Banach space X is said to have DPPp if the inclusion W(X, Y)  Cp(X, Y) holds for all Banach spaces Y . Here W(X, Y) denotes the family of all weakly compact operators from X to Y. We now have a scale of “Dunford-Pettis like properties" in the sense that all Banach spaces have the DPP1, if p < q, then each Banach space with the DPPq also has the DPPp and the strongest property, namely the DPP1 coincides with the DPP. In the paper [7] the authors study a property on Banach spaces (called the DP*-property, or briey the DP*P) which is stronger than the DPP, in the sense that if a Banach space has this property then it also has DPP. We say X has the DP*P, when all weakly compact sets in X are limited, i.e. each sequence (x*n)  X * in the dual space of X which converges weak* to 0, also converges uniformly (to 0) on all weakly compact sets in X. It turns out that this property is equivalent to another property on Banach spaces which is introduced in [17] (and which is called the *-Dunford-Pettis property) as follows: We say a Banach space X has the *-Dunford-Pettis property if for all weakly null sequences (xn) in X and all weak* null sequences (x*n) in X*, we have x*n(xn) n 0. After a thorough study of the DP*P, including characterisations and examples of Banach spaces with the DP*P, the authors in [7] consider some applications to polynomials and analytic functions on Banach spaces. Following an extensive literature study and in depth research into the techniques of proof relevant to this research field, we are able to present a thorough discussion of the results in [7] and [8] as well as some selected (relevant) results from other papers (for instance, [2] and [17]). This we do in Chapter 2 of the dissertation. The starting point (in Section 2.1 of Chapter 2) is the introduction of the so called p-convergent operators, being those bounded linear operators T : X  Y which transform weakly p-summable sequences into norm-null sequences, as well as the so called weakly p-convergent sequences in Banach spaces, being those sequences (xn) in a Banach space X for which there exists an x  X such that the sequence (xn - x) is weakly p-summable. Using these concepts, we state and prove an important characterisation (from the paper [8]) of Banach spaces with DPPp. In Section 2.2 (of Chapter 2) we continue to report on the results of the paper [7], where the DP*P on Banach spaces is introduced. We focus on the characterisation of Banach spaces with DP*P, obtaining among others that a Banach space X has DP*P if and only if for all weakly null sequences (xn) in X and all weak* null sequences (x*n) in X*, we have x*n(xn) n 0. An important characterisation of the DP*P considered in this section is the fact that X has DP*P if and only if every T  L(X, c0) is completely continuous. This result proves to be of fundamental importance in the study of the DP*P and its application to results on polynomials and holomorphic functions on Banach spaces. To be able to report on the applications of the DP*P in the context of homogeneous polynomials and analytic functions on Banach spaces, we embark on a study of “Complex Analysis in Banach spaces" (mostly with the focus on homogeneous polynomials and analytic functions on Banach spaces). This we do in Chapter 3; the content of the chapter is mostly based on work in the books [23] and [14], but also on the work in some articles such as [15]. After we have discussed the relevant theory of complex analysis in Banach spaces in Chapter 3, we devote Chapter 4 to considering properties of polynomials and analytic functions on Banach spaces with DP*P. The discussion in Chapter 4 is based on the applications of DP*P in the paper [7]. Finally, in Chapter 5 of the dissertation, we contribute to the study of “Dunford-Pettis like properties" by introducing the Banach space property “DP*P of order p", or briefly the DP*Pp for Banach spaces. Using the concept “weakly p-convergent sequence in Banach spaces" as is defined in [8], we define weakly-p-compact sets in Banach spaces. Then a Banach space X is said to have the DP*-property of order p (for 1 ≤ p ≤ ) if all weakly-p-compact sets in X are limited. In short, we say X has DP*Pp. As in [8] (where the DPPp is introduced), we now have a scale of DP*P-like properties, in the sense that all Banach spaces have DP*P1 and if p < q and X has DP*Pq then it has DP*Pp. The strongest property DP*P coincides with DP*P. We prove characterisations of Banach spaces with DP*Pp, discuss some examples and then consider applications to polynomials and analytic functions on Banach spaces. Our results and techniques in this chapter depend very much on the results obtained in the previous three chapters, but now we have to find our own correct definitions and formulations of results within this new context. We do this with some success in Sections 5.1 and 5.2 of Chapter 5. Chapter 1 of this dissertation provides a wide range of concepts and results in Banach spaces and the theory of vector sequence spaces (some of them very deep results from books listed in the bibliography). These results are mostly well known, but they are scattered in the literature - they are discussed in Chapter 1 (some with proof, others without proof, depending on the importance of the arguments in the proofs for later use and depending on the detail with which the results are discussed elsewhere in the literature) with the intention to provide an exposition which is mostly self contained and which will be comfortably accessible for graduate students. The dissertation reflects the outcome of our investigation in which we set ourselves the following goals: 1. Obtain a thorough understanding of the Dunford-Pettis property and some related (both weaker and stronger) properties that have been studied in the literature. 2. Focusing on the work in the paper [8], understand the role played in the study of difierent classes of operators by a scale of properties on Banach spaces, called the DPPp, which are weaker than the DP-property and which are introduced in [8] by using the weakly p-summable sequences in X and weakly null sequences in X*. 3. Focusing on the work in the paper [7], investigate the DP*P for Banach spaces, which is the exact property to answer a question of Pelczynsky's regarding when every symmetric bilinear separately compact map X x X  c0 is completely continuous. 4. Based on the ideas intertwined in the work of the paper [8] in the study of a scale of DP-properties and the work in the paper [7], introduce the DP*Pp on Banach spaces and investigate their applications to spaces of operators and in the theory of polynomials and analytic mappings on Banach spaces. Thereby, not only extending the results in [7] to a larger family of Banach spaces, but also to find an answer to the question: “When will every symmetric bilinear separately compact map X x X  c0 be p-convergent?"
Thesis (M.Sc. (Mathematics))--North-West University, Potchefstroom Campus, 2012.

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Pediconi, Francesco. "Geometric aspects of locally homogeneous Riemannian spaces." Doctoral thesis, 2020. http://hdl.handle.net/2158/1197175.

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The subject of this thesis is the study of some geometric problems arising in the context of locally and globally homogeneous Riemannian spaces. In particular, we are mainly interested in investigate the interplay between curvature conditions and the compactness of some classes of locally homogeneous spaces, with respect to appropriate topologies.

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Bletz-Siebert, Oliver [Verfasser]. "Homogeneous spaces with the cohomology of sphere products and compact quadrangles / vorgelegt von Oliver Bletz-Siebert." 2002. http://d-nb.info/966590341/34.

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Books on the topic "Compact homogenous spaces"

Spaces of constant curvature. 6th ed. Providence, R.I: AMS Chelsea Pub., 2011.

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1938-, Griffiths Phillip, and Kerr Matthew D. 1975-, eds. Hodge theory, complex geometry, and representation theory. Providence, Rhode Island: Published for the Conference Board of the Mathematical Sciences by the American Mathematical Society, 2013.

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Epstein, Charles L., and Rafe Mazzeo. Holder Estimates for General Models. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691157122.003.0009.

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This chapter presents the Hölder estimates for general model problems. It first estimates solutions to heat equations for both the homogeneous Cauchy problem and the inhomogeneous problem, obtaining first and second derivative estimates in the latter case, before discussing a general result describing the off-diagonal and long-time behavior of the solution kernel for the general model. It also states a proposition summarizing the properties of the resolvent operator as an operator on the Hölder spaces. In contrast to the case of the heat equation, there is no need to assume that the data has compact support in the x-variables to prove estimates when k > 0.

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Epstein, Charles L., and Rafe Mazzeo. The Semi-group on. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691157122.003.0012.

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This chapter deals with the semi-group on the space Β‎⁰(P). It first describes the boundary behavior of elements of the adjoint operator at points in the interiors of hypersurface boundary components before discussing the null-space of the adjoint under the hypothesis that a generalized Kimura diffusion operator, L, meets bP cleanly. It then examines long time asymptotics, along with a lemma in which P is a compact manifold with corners and L is a generalized Kimura diffusion on P. It also considers the existence of irregular solutions to the homogeneous equations Lu = f, for functions that do not belong to the range of the generator of a C⁰-semi-group on Β‎⁰(P).

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Epstein, Charles L., and Rafe Mazzeo. Existence of Solutions. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691157122.003.0010.

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This chapter proves existence of solutions to the inhomogeneous problem using the Schauder estimate and analyzes a generalized Kimura diffusion operator, L, defined on a manifold with corners, P. The discussion centers on the solution w = v + u, where v solves the homogeneous Cauchy problem with v(x, 0) = f(x) and u solves the inhomogeneous problem with u(x, 0) = 0. The chapter first provides definitions for the Wright–Fisher–Hölder spaces on a general compact manifold with corners before explaining the steps involved in the existence proof. It then verifies the induction hypothesis and treats the k = 0 case. It also shows how to perform the doubling construction for P and considers the existence of the resolvent operator and a contraction semi-group. Finally, it discusses the problem of higher regularity.

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Book chapters on the topic "Compact homogenous spaces"

Onishchik, A. L. "Compact Homogeneous Spaces." In Encyclopaedia of Mathematical Sciences, 172–210. Berlin, Heidelberg: Springer Berlin Heidelberg, 1993. http://dx.doi.org/10.1007/978-3-642-57999-8_11.

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Wolf, Joseph. "Compact Lie groups and homogeneous spaces." In Harmonic Analysis on Commutative Spaces, 119–40. Providence, Rhode Island: American Mathematical Society, 2007. http://dx.doi.org/10.1090/surv/142/06.

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Hamrouni, Hatem, and Firas Sadki. "Self-Chabauty-isolated Locally Compact Groups." In Geometric and Harmonic Analysis on Homogeneous Spaces, 57–70. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-26562-5_2.

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Volchkov, Valery V., and Vitaly V. Volchkov. "Analogies for Compact Two-point Homogeneous Spaces." In Offbeat Integral Geometry on Symmetric Spaces, 111–34. Basel: Springer Basel, 2013. http://dx.doi.org/10.1007/978-3-0348-0572-8_4.

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Ohno, Shinji, Takashi Sakai, and Hajime Urakawa. "Biharmonic Homogeneous Submanifolds in Compact Symmetric Spaces." In Hermitian–Grassmannian Submanifolds, 323–33. Singapore: Springer Singapore, 2017. http://dx.doi.org/10.1007/978-981-10-5556-0_27.

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Zheng, Xue-An. "Harmornic Analysis on Compact Lie Groups and Compact Homogeneous Spaces in China." In Harmonic Analysis in China, 266–86. Dordrecht: Springer Netherlands, 1995. http://dx.doi.org/10.1007/978-94-011-0141-7_16.

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Levesley, Jeremy. "Tangent Space Methods for Approximation on Compact Homogeneous Manifolds." In Recent Progress in Multivariate Approximation, 211–24. Basel: Birkhäuser Basel, 2001. http://dx.doi.org/10.1007/978-3-0348-8272-9_16.

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Pesenson, Isaac. "Parseval Space-Frequency Localized Frames on Sub-Riemannian Compact Homogeneous Manifolds." In Frames and Other Bases in Abstract and Function Spaces, 413–33. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-55550-8_17.

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Guivarc’h, Yves, and C. R. E. Raja. "Polynomial Growth, Recurrence and Ergodicity for Random Walks on Locally Compact Groups and Homogeneous Spaces." In Random Walks, Boundaries and Spectra, 65–74. Basel: Springer Basel, 2011. http://dx.doi.org/10.1007/978-3-0346-0244-0_4.

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"STRUCTURES OF COMPACT LIE GROUPS." In Almost Complex Homogeneous Spaces and Their Submanifolds, 1–26. WORLD SCIENTIFIC, 1987. http://dx.doi.org/10.1142/9789814503235_0001.

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Conference papers on the topic "Compact homogenous spaces"

Cooley, W. Glenn, and Anthony Palazotto. "Finite Element Analysis of Functionally Graded Shell Panels Under Thermal Loading." In ASME 2005 International Mechanical Engineering Congress and Exposition. ASMEDC, 2005. http://dx.doi.org/10.1115/imece2005-82776.

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Functionally Graded Materials (FGM) have continuous variation of material properties from one surface to another unlike a composite which has stepped (or discontinuous) material properties. The gradation of properties in an FGM reduces the thermal stresses, residual stresses, and stress concentrations found in traditional composites. An FGM’s gradation in material properties allows the designer to tailor material response to meet design criteria. For example, the Space Shuttle utilizes ceramic tiles as thermal protection from heat generated during re-entry into the Earth’s atmosphere. However, these tiles are prone to cracking at the tile / superstructure interface due to differences in thermal expansion coefficients. An FGM made of ceramic and metal can provide the thermal protection and load carrying capability in one material thus eliminating the problem of cracked tiles found on the Space Shuttle. This paper will explore analysis of shell panels under thermal loading and compare performance of traditional homogeneous materials to FGMs using ABAQUS [1] finite element software. First, theoretical development of FGMs is presented. Second, finite element modeling technique for FGMs is discussed for a thermal stress analysis. Third, homogeneous curved panels made of ceramic and metal are analyzed under thermal loading. Finally, FGM curved panels created from a mixture of ceramic and metal are analyzed. FGM performance is compared to the homogeneous materials in order to explore the effect continuously grading material properties has on structural performance.

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Fishman, Louis. "Symbol Analysis and the Construction of One-Way Forward and Inverse Wave Propagation Theories." In Numerical Simulation and Analysis in Guided-Wave Optics and Opto-Electronics. Washington, D.C.: Optica Publishing Group, 1989. http://dx.doi.org/10.1364/gwoe.1989.se3.

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The analysis and fast, accurate numerical computation of the wave equations of classical physics are often quite difficult for rapidly changing, multidimensional environments extending over many wavelengths. This is particularly so for ocean seismo-acoustic environments characterized by a refractive index field with a compact region of arbitrary (n-dimensional) variability superimposed upon a transversely inhomogeneous ((n-1)-dimensional) background profile. For such environments, the entire domain is in the scattering regime, with the subsequent absence of an “asymptotically free” region. While classical, macroscopic methods have resulted in direct wave field approximations, derivations of approximate wave equations, and discrete numerical approximations, mathematicians studying linear partial differential equations have developed a sophisticated, microscopic phase space analysis centered about the theory of pseudo-differential and Fourier integral operators. In conjunction with the global functional integral techniques pioneered by Wiener (Brownian motion) and Feynman (quantum mechanics), and so successfully applied today in quantum field theory and statistical physics, the n-dimensional classical physics propagators can be both represented explicitly and computed directly. The phase space, or microscopic, methods and path (functional) integral representations provide the appropriate framework to extend homogeneous Fourier methods to inhomogeneous environments, in addition to suggesting the basis for the formulation and solution of corresponding arbitrary-dimensional nonlinear inverse problems.

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Rivas Sanz, Juan Luis de las, Miguel Fernández-Maroto, Enrique Rodrigo González, and Victor Pérez-Eguíluz. "Detecting opportunities: neighbourhood data dynamics for urban regeneration in Valladolid (Spain)." In Virtual City and Territory. Barcelona: Centre de Política de Sòl i Valoracions, 2016. http://dx.doi.org/10.5821/ctv.8126.

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Urban regeneration has become a priority for urban planning in Spain, because it is one of the best ways to foster a more sustainable, compact and mixed-use urban model, founded in the improvement of existing city. The Master Plan of Valladolid (Spain) has been an opportunity to tackle this objective by a thorough study of existing urban fabrics, in order to program future actions and projects. The built city was divided into units, and each of them was carefully analysed in order to identify opportunities for improvement, such as vacant spaces or deprived areas. Every regeneration action was then designed to also generate a positive impact on its surroundings, which requires knowing the needs and structural deficits of each neighbourhood. That’s why a homogeneous “neighbourhood data system” was created, in order to propose the most appropriate action for each case. However, "measuring" the city is a difficult task. There are different official sources of urban data, but they are not oriented to this kind of evaluation. For instance, census data have lost accuracy due to its new methodology (2011), and their level of disaggregation is often inadequate. Other sources such as Cadastre are aimed at tax purposes and they must therefore be reinterpreted.

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Liu, Decheng, Nannan Wang, Chunlei Peng, Jie Li, and Xinbo Gao. "Deep Attribute Guided Representation for Heterogeneous Face Recognition." In Twenty-Seventh International Joint Conference on Artificial Intelligence {IJCAI-18}. California: International Joint Conferences on Artificial Intelligence Organization, 2018. http://dx.doi.org/10.24963/ijcai.2018/116.

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Heterogeneous face recognition (HFR) is a challenging problem in face recognition, subject to large texture and spatial structure differences of face images. Different from conventional face recognition in homogeneous environments, there exist many face images taken from different sources (including different sensors or different mechanisms) in reality. Motivated by human cognitive mechanism, we naturally utilize the explicit invariant semantic information (face attributes) to help address the gap of different modalities. Existing related face recognition methods mostly regard attributes as the high level feature integrated with other engineering features enhancing recognition performance, ignoring the inherent relationship between face attributes and identities. In this paper, we propose a novel deep attribute guided representation based heterogeneous face recognition method (DAG-HFR) without labeling attributes manually. Deep convolutional networks are employed to directly map face images in heterogeneous scenarios to a compact common space where distances mean similarities of pairs. An attribute guided triplet loss (AGTL) is designed to train an end-to-end HFR network which could effectively eliminate defects of incorrectly detected attributes. Extensive experiments on multiple heterogeneous scenarios (composite sketches, resident ID cards) demonstrate that the proposed method achieves superior performances compared with state-of-the-art methods.

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Fernández-Maroto, Miguel. "Stages in the configuration of urban form in urban development planning: the emerging role of open spaces as sustainability mechanism. The case of Valladolid (Spain)." In 24th ISUF 2017 - City and Territory in the Globalization Age. Valencia: Universitat Politècnica València, 2017. http://dx.doi.org/10.4995/isuf2017.2017.5241.

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Along the last five decades and through three different stages, the urban development plans —general plans— of Valladolid, a medium-sized Spanish city, show an interesting evolution in the way of configuring the global urban form and controlling urban development that we can also find in other similar Spanish cities. In the sixties and seventies, plans proposed “autonomous” expansive schemes foreseeing a huge rate of urban growth, so they defined wide areas to be urbanised through new transport infrastructures and typical zoning mechanisms. In the eighties, after decay in urban and economic development and during the transition to democracy, the new local governments focused on the existing city and fostered a more controlled urban growth. However, plans continued to employ the same tools to manage future urban form —definition of transport infrastructures and sectors to be urbanised—, although they looked for more “controllable” forms, such as radio-concentric ones, aiming at a gradual and homogeneous implementation —compact city—. When real-estate market recovered in early nineties, this strategy revealed its weaknesses: fragmented urban fringe and tendency to a congestive model, reinforced when a new generation of expansive plans drove these schemes out of the limits they were conceived with. However, an alternative and more sustainable model had already emerged, as some new urban planning tools proposed a change of perspective: managing global urban form not through future urbanised spaces, but through open ones, generating an “empty” network able to give coherence to the whole urban structure in a metropolitan scale.

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Bouza Cora, María Belén, and Santiago Barge Ferreiros. "Centro Etnográfico Mandeo. Hormigón y memoria. *** Ethnographic Center Mandeo. Concrete and memory." In 8º Congreso Internacional de Arquitectura Blanca - CIAB 8. Valencia: Universitat Politècnica València, 2018. http://dx.doi.org/10.4995/ciab8.2018.7385.

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En un entorno natural de gran valor paisajístico en la cuenca del río Mandeo, el centro, destinado a formación y divulgación, se concibe como una ‘cabaña’ que se integra en el bosque que lo rodea sin restarle protagonismo. El proyecto desarrolla el programa en una sucesión de volúmenes conectados entre sí, que pueden funcionar de forma autónoma o conjuntamente, lo que confiere al edificio una gran versatilidad de uso. La utilización del hormigón autocompactante (inyectado desde las partes inferiores de muros y cubiertas) en la configuración de los volúmenes, ha hecho posible la homogeneidad y compacidad y ha permitido asimismo resolver, con un único material, tanto la envolvente como la estructura del conjunto.***Located in the remarkable landscape of the Mandeo River basin, the Ethnographic Center is a space for education and information, and is conceived as a primitive ‘cabin’ that melds with the surrounding woods. The program is organized in a series of volumes that are interconnected, and that can function independently or jointly, a feature that gives the building a great versatility of use. The use of the self-compacting concrete (sprayed from the lower parts of the walls and roofs) to configure the walls has allowed to make them compact and homogeneous and has also allowed to resolve, with a single material, both the enclosure and the structure of the whole complex.

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Beretta, Gian Paolo, and Nicolas G. Hadjiconstantinou. "Steepest Entropy Ascent Models of the Boltzmann Equation: Comparisons With Hard-Sphere Dynamics and Relaxation-Time Models for Homogeneous Relaxation From Highly Non-Equilibrium States." In ASME 2013 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/imece2013-64905.

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We present a family of steepest entropy ascent (SEA) models of the Boltzmann equation. The models preserve the usual collision invariants (mass, momentum, energy), as well as the non-negativity of the phase-space distribution, and have a strong built-in thermodynamic consistency, i.e., they entail a general H-theorem valid even very far from equilibrium. This family of models features a molecular-speed-dependent collision frequency; each variant can be shown to approach a corresponding BGK model with the same variable collision frequency in the limit of small deviation from equilibrium. This includes power-law dependence on the molecular speed for which the BGK model is known to have a Prandtl number that can be adjusted via the power-law exponent. We compare numerical solutions of the constant and velocity-dependent collision frequency variants of the SEA model with the standard relaxation-time model and a Monte Carlo simulation of the original Boltzmann collision operator for hard spheres for homogeneous relaxation from near-equilibrium and highly non-equilibrium states. Good agreement is found between all models in the near-equilibrium regime. However, for initial states that are far from equilibrium, large differences are found; this suggests that the maximum entropy production statistical ansatz is not equivalent to Boltzmann collisional dynamics and needs to be modified or augmented via additional constraints or structure.

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Schäpel, Jan-Simon, Rudibert King, Fatma Yücel, Fabian Völzke, Christian Oliver Paschereit, and Rupert Klein. "Fuel Injection Control for a Valve Array in a Shockless Explosion Combustor." In ASME Turbo Expo 2018: Turbomachinery Technical Conference and Exposition. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/gt2018-75295.

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Approximate constant volume combustion (aCVC) is a promising way to optimize the combustion process in a gas turbine, which would exceed the gain in efficiency resulting from optimizing other components significantly. This work deals with a recently proposed approach: shockless explosion combustion (SEC). Compared to already known concepts, such as pulsed detonation combustion (PDC), it overcomes several disadvantages, e.g., sharp pressure transitions and entropy generation due to shock waves. For an SEC, accurate fuel stratification is required to achieve a quasi-homogeneous auto-ignition. In an atmospheric test rig quasi-homogeneous ignitions were achieved previously in non-resonant operation. To achieve a resonant operation, which goes along with a higher firing frequency, lower ignition and injection times are required. For this purpose, an array of solenoid valves was designed to allow for highly dynamic operation within short filling time spans. Using a novel mixed-integer control approach, these solenoid valves were actuated such that a desired fuel profile was generated. In this paper, the mentioned test rig was used for non-reacting fuel measurements to compare the quality of the axial fuel stratification achieved by using the valve array with the one achieved by using a slower proportional valve. In the experimental investigation the actuation with the valve array proved to adjust the required fuel stratification with the same quality as the actuation with the proportional valve, which was already successfully applied to the reactive set-up. Hence, the mixed-integer controlled valve array is considered a useful concept for upcoming resonant reactive SEC investigations.

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Darabi, Mehdi, and Rajamohan Ganesan. "Exact 3-D Stress and Stiffness Analysis of Functionally Graded Sandwich Plates Using Sampling Surfaces Method." In ASME 2014 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/imece2014-38400.

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In the present work, the three-dimensional analysis for the deflection and stress distributions of functionally graded ceramic–metal sandwich plates is developed based on the method of sampling surfaces (SaS). In accordance with this method, into each layer of the plate, reference surfaces that are not equally spaced and are parallel to the mid-surface of the plate are introduced, and the displacement vectors of these surfaces are chosen as unknown functions. Such a choice allows the representation of the governing equations of the proposed higher order layer-wise plate theory in a very compact form and also permits the derivation of strain–displacement relationships correctly describing all motions including the rigid-body motions of the functionally graded plate. Hence the 3D elasticity problem of the thick plate is efficiently solved. The material properties of sandwich plate’s face layer are assumed to be that of a two-constituent material that vary continuously through the thickness of the face sheet according to a power law distribution of the volume fraction of the constituents. The core layer is homogeneous and made of an isotropic ceramic material. The effects of the volume fraction of the material constituents and their distribution on the deflections and, in particular, the 3-D stress distributions as well as the effects of the length-to-width and length-to-thickness ratios of the plate are investigated. Comparison of the results of the present work with the results available in existing literature is carried out for a benchmark problem. It is shown that considering large number of SaS, which are located at interfaces and Chebyshev polynomial nodes, the accuracy of the solutions can be improved significantly wherein the error will approach zero value as the total number of surfaces in each layer become very large.

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Gómez Gómez, Julián Andres, Camilo E. Moncada Guayazán, Sebastián Roa Prada, and Hernando Gonzalez Acevedo. "Design and Experimental Validation of a LQG Control System for the Stabilization of a 2DOF Commercial Gimbal Using Physical Modelling Techniques." In ASME 2020 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2020. http://dx.doi.org/10.1115/imece2020-24137.

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Abstract Gimbals are mechatronic systems well known for their use in the stabilization of cameras which are under the effect of sudden movements. Gimbals help keeping cameras at previously defined fixed orientations, so that the captured images have the highest quality. This paper focuses on the design of a Linear Quadratic Gaussian, LQG, controller, based on the physical modeling of a commercial Gimbal with two degrees of freedom (2DOF), which is used for first-person applications in unmanned aerial vehicle (UAV). This approach is proposed to make a more realistic representation of the system under study, since it guarantees high accuracy in the simulation of the dynamic response, as compared to the prediction of the mathematical model of the same system. The development of the model starts by sectioning the Gimbal into a series of interconnected links. Subsequently, a fixed reference system is assigned to each link body and the corresponding homogeneous transformation matrices are established, which will allow the calculation of the orientation of each link and the displacement of their centers of mass. Once the total kinetic and potential energy of the mechanical components are obtained, Lagrange’s method is utilized to establish the mathematical model of the mechanical structure of the Gimbal. The equations of motion of the system are then expressed in state space form, with two inputs, two outputs and four states, where the inputs are the torques produced by each one of the motors, the outputs are the orientation of the first two links, and the states are the aforementioned orientations along with their time derivatives. The state space model was implemented in MATLAB’s Simulink environment to compare its prediction of the transient response with the prediction obtained with the representation of the same system using MATLAB’s SimMechanics physical modelling interface. The mathematical model of each one of the three-phase Brushless DC motors is also expressed in state space form, where the three inputs of each motor model are the voltages of the corresponding motor phases, its two outputs are the angular position and angular velocity, and its four states are the currents in two of the phases, the orientation of the motor shaft and its rate of change. This model is experimentally validated by performing a switching sequence in both the simulation model and the physical system and observing that the transient response of the angular position of the motor shaft is in accordance with the theoretical model. The control system design process starts with the interconnection of the models of the mechanical components and the models of the Brushless DC Motor, using their corresponding state space representations. The resulting model features six inputs, two outputs and eight states. The inputs are the voltages in each phase of the two motors in the Gimbal, the outputs are the angular positions of the first two links, and the states are the currents in two of the phases for each motor and the orientations of the first two links, along with their corresponding time derivatives. An optimal LQG control system is designed using MATLAB’s dlqr and Kalman functions, which calculate the gains for the control system and the gains for the states estimated by the observer. The external excitation in each of the phases is carried out by pulse width modulation. Finally, the transient response of the overall system is evaluated for different reference points. The simulation results show very good agreement with the experimental measurements.

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Reports on the topic "Compact homogenous spaces"

Baltagi, Badi H., Georges Bresson, Anoop Chaturvedi, and Guy Lacroix. Robust dynamic space-time panel data models using ε-contamination: An application to crop yields and climate change. CIRANO, January 2023. http://dx.doi.org/10.54932/ufyn4045.

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This paper extends the Baltagi et al. (2018, 2021) static and dynamic ε-contamination papers to dynamic space-time models. We investigate the robustness of Bayesian panel data models to possible misspecification of the prior distribution. The proposed robust Bayesian approach departs from the standard Bayesian framework in two ways. First, we consider the ε-contamination class of prior distributions for the model parameters as well as for the individual effects. Second, both the base elicited priors and the ε-contamination priors use Zellner (1986)’s g-priors for the variance-covariance matrices. We propose a general “toolbox” for a wide range of specifications which includes the dynamic space-time panel model with random effects, with cross-correlated effects `a la Chamberlain, for the Hausman-Taylor world and for dynamic panel data models with homogeneous/heterogeneous slopes and cross-sectional dependence. Using an extensive Monte Carlo simulation study, we compare the finite sample properties of our proposed estimator to those of standard classical estimators. We illustrate our robust Bayesian estimator using the same data as in Keane and Neal (2020). We obtain short run as well as long run effects of climate change on corn producers in the United States.

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