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Relevant bibliographies by topics / Isotropic subspace

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Academic literature on the topic 'Isotropic subspace'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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Journal articles on the topic "Isotropic subspace"

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Hakimi Poroch, Mahdieh. "Bounds on subspace codes based on totally isotropic subspace in symplectic spaces and extended symplectic spaces." Asian-European Journal of Mathematics 12, no. 05 (2019): 1950069. http://dx.doi.org/10.1142/s1793557119500694.

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In this paper, we propose the Sphere-packing bound, Singleton bound and Gilbert–Varshamov bound on the subspace codes [Formula: see text] based on totally isotropic subspaces in symplectic space [Formula: see text] and on the subspace codes [Formula: see text] based on totally isotropic subspace in extended symplectic space [Formula: see text].

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Gao, You, Liyum Zhao, and Gang Wang. "Bounds on subspace codes based on totally isotropic subspaces in unitary spaces." Discrete Mathematics, Algorithms and Applications 08, no. 04 (2016): 1650056. http://dx.doi.org/10.1142/s1793830916500567.

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In this paper, the Sphere-packing bound, Singleton bound, Wang–Xing–Safavi-Naini bound, Johnson bound and Gilbert–Varshamov bound on the subspace codes [Formula: see text] based on [Formula: see text]-dimensional totally isotropic subspaces in unitary space [Formula: see text] over finite fields [Formula: see text] are presented. Then, we prove that [Formula: see text] codes based on [Formula: see text]-dimensional totally isotropic subspaces in unitary space [Formula: see text] attain the Wang–Xing–Safavi-Naini bound if and only if they are certain Steiner structures in [Formula: see text].

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3

Xu, Xiao-Ming, and Yile Zhao. "J-Self-Adjoint Projections in Krein Spaces." Journal of Function Spaces 2020 (March 16, 2020): 1–7. http://dx.doi.org/10.1155/2020/6725969.

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Let ℋ be a Krein space with fundamental symmetry J. Starting with a canonical block-operator matrix representation of J, we study the regular subspaces of ℋ. We also present block-operator matrix representations of the J-self-adjoint projections for the regular subspaces of ℋ, as well as for the regular complements of the isotropic part in a pseudo-regular subspace of ℋ.

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Nielsen, Jørgen. "The distribution of volume reductions induced by isotropic random projections." Advances in Applied Probability 31, no. 04 (1999): 985–94. http://dx.doi.org/10.1017/s0001867800009563.

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In this paper, isotropic random projections of d-sets in ℝ n are studied, where a d-set is a subset of a d-dimensional affine subspace which satisfies certain regularity conditions. The squared volume reduction induced by the projection of a d-set onto an isotropic random p-subspace is shown to be distributed as a product of independent beta-distributed random variables, for d ≤ p. One of the proofs of this result uses Wilks' lambda distribution from multivariate normal theory. The result is related to Cauchy's and Crofton's formulae in stochastic geometry. In particular, it can be used to giv

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Nielsen, Jørgen. "The distribution of volume reductions induced by isotropic random projections." Advances in Applied Probability 31, no. 4 (1999): 985–94. http://dx.doi.org/10.1239/aap/1029955254.

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In this paper, isotropic random projections of d-sets in ℝn are studied, where a d-set is a subset of a d-dimensional affine subspace which satisfies certain regularity conditions. The squared volume reduction induced by the projection of a d-set onto an isotropic random p-subspace is shown to be distributed as a product of independent beta-distributed random variables, for d ≤ p. One of the proofs of this result uses Wilks' lambda distribution from multivariate normal theory. The result is related to Cauchy's and Crofton's formulae in stochastic geometry. In particular, it can be used to give

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6

Ikramov, Kh D. "Calculating the Isotropic Subspace of a Symmetric Quasi-Definite Matrix." Moscow University Computational Mathematics and Cybernetics 42, no. 3 (2018): 97–99. http://dx.doi.org/10.3103/s027864191803007x.

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Forte, Sandra, and Maurizio Vianello. "Restricted Invariants on the Space of Elasticity Tensors." Mathematics and Mechanics of Solids 11, no. 1 (2006): 48–82. http://dx.doi.org/10.1177/1081286505046483.

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A linear function defined on the space of elasticity tensors is a restricted invariant under a group of rotations G if it has an invariant restriction to a proper subspace which is larger than the set left fixed by the action of G itself. A necessary and sufficient condition for a function to be a restricted invariant is given using concepts related with isotypic decomposition, Haar integration and G -dependence. The result is applied to characterize isotropic and transversely isotropic restricted invariants.

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GAUDRON, ÉRIC, and GAËL RÉMOND. "Espaces adéliques quadratiques." Mathematical Proceedings of the Cambridge Philosophical Society 162, no. 2 (2016): 211–47. http://dx.doi.org/10.1017/s0305004116000438.

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AbstractWe study quadratic forms defined on an adelic vector space over an algebraic extension K of the rationals. Under the sole condition that a Siegel lemma holds over K, we provide height bounds for several objects naturally associated to the quadratic form, such as an isotropic subspace, a basis of isotropic vectors (when it exists) or an orthogonal basis. Our bounds involve the heights of the form and of the ambient space. In several cases, we show that the exponents of these heights are best possible. The results improve and extend previously known statements for number fields and the f

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Kiderlen, Markus. "On projected thick sections of stationary point processes and Boolean models." Advances in Applied Probability 28, no. 02 (1996): 335. http://dx.doi.org/10.1017/s0001867800048308.

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For a stationary point process X of convex particles in ℝ d the projected thick section process X(L) on a q-dimensional linear subspace L is considered. Formulae connecting geometric functionals, e.g. the quermass densities of X and X(L), are presented. They generalize the classical results of Miles (1976) and Davy (1976) which hold only in the isotropic case.

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Kiderlen, Markus. "On projected thick sections of stationary point processes and Boolean models." Advances in Applied Probability 28, no. 2 (1996): 335. http://dx.doi.org/10.2307/1428046.

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For a stationary point process X of convex particles in ℝd the projected thick section process X(L) on a q-dimensional linear subspace L is considered. Formulae connecting geometric functionals, e.g. the quermass densities of X and X(L), are presented. They generalize the classical results of Miles (1976) and Davy (1976) which hold only in the isotropic case.

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Dissertations / Theses on the topic "Isotropic subspace"

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Dorosh, Anastasiia. "Direction-of-Arrival Estimation in Spherically Isotropic Noise." Thesis, Linnéuniversitetet, Institutionen för fysik och elektroteknik (IFE), 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-28603.

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Today the multisensor array signal processing of noisy measurements has received much attention. The classical problem in array signal processing is determining the location of an energy-radiating source relative to the location of the array, in other words, direction-of-arrival (DOA) estimation. One is considering the signal estimation problem when together with the signal(s) of interest some noise and interfering signals are present. In this report a direction-of-arrival estimation system is described based on an antenna array for detecting arrival angles in azimuth plane of signals pitched

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Landon, Jonathan Charles. "Development of an Experimental Phased-Array Feed System and Algorithms for Radio Astronomy." BYU ScholarsArchive, 2011. https://scholarsarchive.byu.edu/etd/2794.

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Phased array feeds (PAFs) are a promising new technology for astronomical radio telescopes. While PAFs have been used in other fields, the demanding sensitivity and calibration requirements in astronomy present unique new challenges. This dissertation presents some of the first astronomical PAF results demonstrating the lowest noise temperature and highest sensitivity at the time (66 Kelvin and 3.3 m^2/K, respectively), obtained using a narrowband (425 kHz bandwidth) prototype array of 19 linear co-polarized L-band dipoles mounted at the focus of the Green Bank 20 Meter Telescope at the Nation

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Elzinga, Randall J. "The Minimum Witt Index of a Graph." Thesis, 2007. http://hdl.handle.net/1974/682.

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An independent set in a graph G is a set of pairwise nonadjacent vertices, and the maximum size, alpha(G), of an independent set in G is called the independence number. Given a graph G and weight matrix A of G with entries from some field F, the maximum dimension of an A-isotropic subspace, known as the Witt index of A, is an upper bound on alpha(G). Since any weight matrix can be used, it is natural to seek the minimum upper bound on the independence number of G that can be achieved by a weight matrix. This minimum, iota_F^*(G), is called the minimum Witt index of G over F, and the resulting

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Book chapters on the topic "Isotropic subspace"

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Harder, Günter, and A. Raghuram. "Eisenstein Cohomology." In Eisenstein Cohomology for GL and the Special Values of Rankin-Selberg L-Functions. Princeton University Press, 2019. http://dx.doi.org/10.23943/princeton/9780691197890.003.0006.

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This chapter provides the Eisenstein cohomology. It begins with the Poincaré duality and maximal isotropic subspace of boundary cohomology. Here, the chapter considers the compatibility of duality isomorphisms with the connecting homomorphism. It then states and proves the main result on rank-one Eisenstein cohomology. Thereafter, the chapter presents a theorem of Langlands: the constant term of an Eisenstein series. It draws some details from the Langlands–Shahidi method in this context. Induced representations are examined, as are standard intertwining operators. The chapter finally illustrates the Eisenstein series, the constant term of an Eisenstein series, and the holomorphy of the Eisenstein series at the point of evaluation.

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"The variety of maximal totally isotropic subspaces." In The Algebraic and Geometric Theory of Quadratic Forms. American Mathematical Society, 2008. http://dx.doi.org/10.1090/coll/056/17.

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Conference papers on the topic "Isotropic subspace"

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Zhou, Tianyuan, João Sedoc, and Jordan Rodu. "Getting in Shape: Word Embedding SubSpaces." In Twenty-Eighth International Joint Conference on Artificial Intelligence {IJCAI-19}. International Joint Conferences on Artificial Intelligence Organization, 2019. http://dx.doi.org/10.24963/ijcai.2019/761.

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Many tasks in natural language processing require the alignment of word embeddings. Embedding alignment relies on the geometric properties of the manifold of word vectors. This paper focuses on supervised linear alignment and studies the relationship between the shape of the target embedding. We assess the performance of aligned word vectors on semantic similarity tasks and find that the isotropy of the target embedding is critical to the alignment. Furthermore, aligning with an isotropic noise can deliver satisfactory results. We provide a theoretical framework and guarantees which aid in the

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Elsayed, Mostafa S. A., and Damiano Pasini. "Characterization and Performance Optimization of 2D Lattice Materials With Hexagonal Bravais Lattice Symmetry." In ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2009. http://dx.doi.org/10.1115/detc2009-87540.

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The current paper examines the static performance of 2D infinite lattice materials with hexagonal Bravais lattice symmetry. Two novel microscopic cell topologies are proposed. The first topology is a semi-regular lattice that has the modified Schafli symbol 34.6, which describes the type of regular polygons surrounding the joints of the lattice. Here, 34.6 indicates four (4) regular triangles (3) successively surrounding a node followed by a regular hexagon (6). The second topology is an irregular lattice that is referred here as Double Hexagonal Triangulation (DHT). The lattice material is co

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