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Journal articles on the topic 'Subspaces'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

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1

Baranov, Anton, and Harald Woracek. "Subspaces of de Branges Spaces Generated by Majorants." Canadian Journal of Mathematics 61, no. 3 (2009): 503–17. http://dx.doi.org/10.4153/cjm-2009-026-2.

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Abstract.For a given de Branges space ℋ (E ) we investigate de Branges subspaces defined in terms of majorants on the real axis. If ω is a nonnegative function on ℝ, we consider the subspaceWe show that ℛω (E ) is a de Branges subspace and describe all subspaces of this form. Moreover, we give a criterion for the existence of positive minimal majorants.

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Wang, Junpeng, Xiaotong Liu, and Han-Wei Shen. "High-dimensional data analysis with subspace comparison using matrix visualization." Information Visualization 18, no. 1 (2017): 94–109. http://dx.doi.org/10.1177/1473871617733996.

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Due to the intricate relationship between different dimensions of high-dimensional data, subspace analysis is often conducted to decompose dimensions and give prominence to certain subsets of dimensions, i.e. subspaces. Exploring and comparing subspaces are important to reveal the underlying features of subspaces, as well as to portray the characteristics of individual dimensions. To date, most of the existing high-dimensional data exploration and analysis approaches rely on dimensionality reduction algorithms (e.g. principal component analysis and multi-dimensional scaling) to project high-di

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Neckrasov, Vasiliy. "On Some Properties of Irrational Subspaces." Uniform distribution theory 17, no. 1 (2022): 89–104. http://dx.doi.org/10.2478/udt-2022-0002.

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Abstract In this paper, we discuss some properties of completely irrational subspaces. We prove that there exist completely irrational subspaces that are badly approximable and, moreover, sets of such subspaces are winning in different senses. We get some bounds for Diophantine exponents of vectors that lie in badly approximable subspaces that are completely irrational; in particular, for any vector ξ from two-dimensional badly approximable completely irrational subspace of ℝ d one has ω ⌢ ( ξ ) ≤ 5 - 1 2 \mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\frown$}}\over \omega } \left( \xi \

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4

Sia, Florence, and Rayner Alfred. "Tree-based mining contrast subspace." International Journal of Advances in Intelligent Informatics 5, no. 2 (2019): 169. http://dx.doi.org/10.26555/ijain.v5i2.359.

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All existing mining contrast subspace methods employ density-based likelihood contrast scoring function to measure the likelihood of a query object to a target class against other class in a subspace. However, the density tends to decrease when the dimensionality of subspaces increases causes its bounds to identify inaccurate contrast subspaces for the given query object. This paper proposes a novel contrast subspace mining method that employs tree-based likelihood contrast scoring function which is not affected by the dimensionality of subspaces. The tree-based scoring measure recursively bin

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Wang, Xuan, Chao Sun, Ming Yang Li, and Shao-Dong Zhang. "Detection by Angle-domain subspace with horizontal array in uncertain shallow-water environment." Acta Physica Sinica 71, no. 8 (2022): 1. http://dx.doi.org/10.7498/aps.71.20211742.

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The uncertainty of environmental parameters affects the robustness of detection method in complex shallow water. We define the angle-domain subspaces with horizontal linear array and estimate it in a proper way in the uncertain environment. Based on the angle-domain subspaces, we propose an angle-domain subspace detector and its robust form. Angle-domain subspaces contain the uncertain informations by using the observation matrices in different environmental parameters. The relationship between the horizontal wave number of propagating modes and the sound speed of the bottom and sediment in ha

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Shi, Yanyue, and Na Zhou. "Reducing Subspaces of Some Multiplication Operators on the Bergman Space over Polydisk." Abstract and Applied Analysis 2015 (2015): 1–12. http://dx.doi.org/10.1155/2015/209307.

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We consider the reducing subspaces ofMzNonAα2(Dk), wherek≥3,zN=z1N1⋯zkNk, andNi≠Njfori≠j. We prove that each reducing subspace ofMzNis a direct sum of some minimal reducing subspaces. We also characterize the minimal reducing subspaces in the cases thatα=0andα∈(-1,+∞)∖Q, respectively. Finally, we give a complete description of minimal reducing subspaces ofMzNonAα2(D3)withα>-1.

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LENG, JINSONG, and ZHIHU HUANG. "OUTLIERS DETECTION WITH CORRELATED SUBSPACES FOR HIGH DIMENSIONAL DATASETS." International Journal of Wavelets, Multiresolution and Information Processing 09, no. 02 (2011): 227–36. http://dx.doi.org/10.1142/s0219691311004067.

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Detecting outliers in high dimensional datasets is quite a difficult data mining task. Mining outliers in subspaces seems to be a promising solution, because outliers may be embedded in some interesting subspaces. Due to the existence of many irrelevant dimensions in high dimensional datasets, it is of great importance to eliminate the irrelevant or unimportant dimensions and identify outliers in interesting subspaces with strong correlation. Normally, the correlation among dimensions can be determined by traditional feature selection techniques and subspace-based clustering methods. The dimen

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Fatehi, Kavan, Mohsen Rezvani, Mansoor Fateh, and Mohammad-Reza Pajoohan. "Subspace Clustering for High-Dimensional Data Using Cluster Structure Similarity." International Journal of Intelligent Information Technologies 14, no. 3 (2018): 38–55. http://dx.doi.org/10.4018/ijiit.2018070103.

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This article describes how recently, because of the curse of dimensionality in high dimensional data, a significant amount of research has been conducted on subspace clustering aiming at discovering clusters embedded in any possible attributes combination. The main goal of subspace clustering algorithms is to find all clusters in all subspaces. Previous studies have mostly been generating redundant subspace clusters, leading to clustering accuracy loss and also increasing the running time of the algorithms. A bottom-up density-based approach is suggested in this article, in which the cluster s

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Wang, Xing, Jun Wang, Carlotta Domeniconi, Guoxian Yu, Guoqiang Xiao, and Maozu Guo. "Multiple Independent Subspace Clusterings." Proceedings of the AAAI Conference on Artificial Intelligence 33 (July 17, 2019): 5353–60. http://dx.doi.org/10.1609/aaai.v33i01.33015353.

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Multiple clustering aims at discovering diverse ways of organizing data into clusters. Despite the progress made, it’s still a challenge for users to analyze and understand the distinctive structure of each output clustering. To ease this process, we consider diverse clusterings embedded in different subspaces, and analyze the embedding subspaces to shed light into the structure of each clustering. To this end, we provide a two-stage approach called MISC (Multiple Independent Subspace Clusterings). In the first stage, MISC uses independent subspace analysis to seek multiple and statistical ind

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Gopinath, S., G. Kowsalya, K. Sakthivel, and S. Arularasi. "A Proposed Clustering Algorithm for Efficient Clustering of High-Dimensional Data." Journal of Information Technology and Cryptography 1, no. 1 (2023): 14–21. http://dx.doi.org/10.48001/joitc.2023.1114-21.

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To partition transaction data values, clustering algorithms are used. To analyse the relationships between transactions, similarity measures are utilized. Similarity models based on vectors perform well with low-dimensional data. High-dimensional data values are clustered using subspace clustering techniques. Clustering high-dimensional data is difficult due to the curse of dimensionality. Projective clustering seeks out projected clusters in subsets of a data space's dimensions. In high-dimensional data space, a probability model represents predicted clusters. A model-based fuzzy projection c

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11

Zou, Yang. "Minimal Reducing Subspaces of 3-order Slant Toeplitz Operator on Hardy Space over the Disc." Mathematics Letters 11, no. 1 (2025): 1–9. https://doi.org/10.11648/j.ml.20251101.11.

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The reducing subspace problem and the invariant subspace problem of an operator are two core problems in operator theory. There are lots of works on reducing subspaces and invariant subspaces of Toeplitz operators in recent years. A slant Toeplitz operator is a generalization of Toeplitz operator. In this paper, we study minimal reducing subspaces of the third-order slant Toeplitz operator with the symbol &lt;i&gt;z&lt;SUP&gt;N&lt;/SUP&gt;&lt;/i&gt;. By classifying &lt;I&gt;N&lt;/I&gt; into three cases, we give a complete description of minimal r

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FERNIQUE, THOMAS, and MATHIEU SABLIK. "Weak colored local rules for planar tilings." Ergodic Theory and Dynamical Systems 39, no. 12 (2018): 3322–46. http://dx.doi.org/10.1017/etds.2018.20.

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A linear subspace $E$ of $\mathbb{R}^{n}$ has colored local rules if there exists a finite set of decorated tiles whose tilings are digitizations of $E$. The local rules are weak if the digitizations can slightly wander around $E$. We prove that a linear subspace has weak colored local rules if and only if it is computable. This goes beyond previous results, all based on algebraic subspaces. We prove an analogous characterization for sets of linear subspaces, including the set of all the linear subspaces of $\mathbb{R}^{n}$.

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Kowynia, Joanna. "The unicity of best approximation in a space of compact operators." MATHEMATICA SCANDINAVICA 108, no. 1 (2011): 146. http://dx.doi.org/10.7146/math.scand.a-15164.

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Chebyshev subspaces of $\mathcal{K}(c_0,c_0)$ are studied. A $k$-dimensional non-interpolating Chebyshev subspace is constructed. The unicity of best approximation in non-Chebyshev subspaces is considered.

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14

Saxon, Stephen A., та William H. Ruckle. "Reducing the classical multipliers ℓ∞, C0 and bv0". Proceedings of the Edinburgh Mathematical Society 40, № 2 (1997): 345–52. http://dx.doi.org/10.1017/s0013091500023786.

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For R ∈ {bv0, c0, ℓ∞} a multiplier of FK spaces, the classical sectional convergence theorems permit the reduction of R to any of its dense barrelled subspaces as a simple consequence of the Closed Graph Theorem. (Cf. the Bachelis/Rosenthal reduction of R = ℓ∞ to its dense barrelled subspace m0.) A natural modern setting permits the reduction of R to any of the larger class of dense βφ subspaces. Bennett and Kalton's FK setting remarkably reduced R = ℓ∞ to any of its dense subspaces. This extreme reduction also obtains in the modern βφ setting since, surprisingly, every dense subspace of ℓ∞ is

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15

Liu, Junfeng. "On Invariant Subspaces for the Shift Operator." Symmetry 11, no. 6 (2019): 743. http://dx.doi.org/10.3390/sym11060743.

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In this paper, we improve two known invariant subspace theorems. More specifically, we show that a closed linear subspace M in the Hardy space H p ( D ) ( 1 ≤ p < ∞ ) is invariant under the shift operator M z on H p ( D ) if and only if it is hyperinvariant under M z , and that a closed linear subspace M in the Lebesgue space L 2 ( ∂ D ) is reducing under the shift operator M e i θ on L 2 ( ∂ D ) if and only if it is hyperinvariant under M e i θ . At the same time, we show that there are two large classes of invariant subspaces for M e i θ that are not hyperinvariant subspaces for M e i θ a

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16

Yamskulna, Gaywalee. "Mathieu–Zhao subspaces of vertex algebras." Journal of Algebra and Its Applications 18, no. 12 (2019): 1950225. http://dx.doi.org/10.1142/s0219498819502256.

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We introduce a notion of Mathieu–Zhao subspaces of vertex algebras. Among other things, we show that for a vertex algebra [Formula: see text] and its subspace [Formula: see text] that contains [Formula: see text], [Formula: see text] is a Mathieu–Zhao subspace of [Formula: see text] if and only if the quotient space [Formula: see text] is a Mathieu–Zhao subspace of a commutative associative algebra [Formula: see text]. As a result, one can study the famous Jacobian conjecture in terms of Mathieu–Zhao subspaces of vertex algebras. In addition, for a [Formula: see text]-type vertex operator alge

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17

Ren, Guojing, and Huaqing Sun. "J-Self-Adjoint Extensions for a Class of Discrete Linear Hamiltonian Systems." Abstract and Applied Analysis 2013 (2013): 1–19. http://dx.doi.org/10.1155/2013/904976.

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This paper is concerned with formallyJ-self-adjoint discrete linear Hamiltonian systems on finite or infinite intervals. The minimal and maximal subspaces are characterized, and the defect indices of the minimal subspaces are discussed. All theJ-self-adjoint subspace extensions of the minimal subspace are completely characterized in terms of the square summable solutions and boundary conditions. As a consequence, characterizations of all theJ-self-adjoint subspace extensions are given in the limit point and limit circle cases.

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18

Wang, Guo-Hua, Jia-Fu Pang, Yong-Yang Jin, and Bo Ren. "Invariant Subspaces of Short Pulse-Type Equations and Reductions." Symmetry 16, no. 6 (2024): 760. http://dx.doi.org/10.3390/sym16060760.

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In this paper, we extend the invariant subspace method to a class of short pulse-type equations. Complete classification results with invariant subspaces from 2 to 5 dimensions are provided. The key step is to take subspaces of solutions of linear ordinary differential equations as invariant subspaces that nonlinear operators admit. Some concrete examples and corresponding reduced systems are presented to illustrate this method.

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IZUCHI, KEI JI, KOU HEI IZUCHI, and YUKO IZUCHI. "SPLITTING INVARIANT SUBSPACES IN THE HARDY SPACE OVER THE BIDISK." Journal of the Australian Mathematical Society 102, no. 2 (2016): 205–23. http://dx.doi.org/10.1017/s1446788716000203.

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Let $H^{2}$ be the Hardy space over the bidisk. It is known that Hilbert–Schmidt invariant subspaces of $H^{2}$ have nice properties. An invariant subspace which is unitarily equivalent to some invariant subspace whose continuous spectrum does not coincide with $\overline{\mathbb{D}}$ is Hilbert–Schmidt. We shall introduce the concept of splittingness for invariant subspaces and prove that they are Hilbert–Schmidt.

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20

Kalenov, N. E., and A. N. Sotnikov. "Architecture of the Common Digital Space of Scientific Knowledge." Information resources of Russia, no. 5 (2020): 5–8. http://dx.doi.org/10.51218/0204-3653-2020-5-5-8.

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The architecture of the Common Digital Space of Scientific Knowledge (CDSSK) is determined by its functions and objectives. CDSSK includes a set of subspaces related to various scientific fields. The unity of subspaces is provided by unified principles for constructing subspaces and ontological connections between their objects. Each subspace includes digital objects, metadata containing facts related to objects, and subject ontologies that provide advanced searches and navigation through space. All information is reflected in the CDSSK according to the rules of the "semantic WEB". The content

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ASSADI, AMANOLLAH, MOHAMAD ALI FARZANEH, and HAJI MOHAMMAD MOHAMMADINEJAD. "ON THE DECOMPOSITION OF OPERATORS WITH SEVERAL ALMOST-INVARIANT SUBSPACES." Bulletin of the Australian Mathematical Society 99, no. 2 (2019): 274–83. http://dx.doi.org/10.1017/s0004972718001363.

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We seek a sufficient condition which preserves almost-invariant subspaces under the weak limit of bounded operators. We study the bounded linear operators which have a collection of almost-invariant subspaces and prove that a bounded linear operator on a Banach space, admitting each closed subspace as an almost-invariant subspace, can be decomposed into the sum of a multiple of the identity and a finite-rank operator.

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22

YU, BAI-YUN, and ZHI-BIAO SHU. "CONSTRUCTION OF DUAL g-FRAMES FOR CLOSED SUBSPACES." International Journal of Wavelets, Multiresolution and Information Processing 09, no. 06 (2011): 947–64. http://dx.doi.org/10.1142/s0219691311004390.

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In this paper, we introduce dual g-frames for a closed subspace in a separable Hilbert space and also give a characterization. Generally dual g-frames for a closed subspace are non-commutative. Therefore, we construct dual g-frames for closed subspaces from two aspects and give the corresponding formulas, respectively. Finally, we give a necessary and sufficient condition for commutative dual g-frame pairs for closed subspaces under certain conditions.

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Fadeev, Alexey M., Igor V. Ilin, Anastasia I. Levina, Alissa S. Dubgorn, and Polina A. Rukina. "Digitalization as a Factor for Development of the Target Arctic Subspaces." Arctic and North, no. 58 (March 17, 2025): 84–101. https://doi.org/10.37482/issn2221-2698.2025.58.84.

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The Arctic zone of the Russian Federation is a rich, attractive, but hard-to-reach region. The authors of the article believe that the current level of development of digital and data technologies can make a constructive contribution to overcoming some of the challenges of Arctic conquest. Since the Russian Arc-tic is a complexly structured macro-region, the authors rely on the division of the Arctic into seven target subspaces. The paper identifies the requirements of the target Arctic subspaces for digital technologies that could facilitate the process of Arctic exploration. The paper used t

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Wang, Shi Heng. "Semi-Orthogonal Parseval Wavelets Frames on Local Fields and Applications in Manufacturing Science." Advanced Materials Research 712-715 (June 2013): 2464–68. http://dx.doi.org/10.4028/www.scientific.net/amr.712-715.2464.

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Manufacturing science focuses on understanding problems from the perspective of the stakeholders involved and then applying manufacturing science as needed. We investigate semi-orthogonal frame wavelets and Parseval frame wavelets in with a dilation factor. We show that every affine subspace is the orthogonal direct sum of at most three purely non-reducing subspaces. This result is obtained through considering the basicquestion as to when the orthogonal complement of an afffine subspace in another one is still affine subspace.The definition of multiple pseudofames for subspaces with integer tr

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Bagchi, Susmit. "On the Topological Structure and Properties of Multidimensional (C, R) Space." Symmetry 12, no. 9 (2020): 1542. http://dx.doi.org/10.3390/sym12091542.

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Generally, the linear topological spaces successfully generate Tychonoff product topology in lower dimensions. This paper proposes the construction and analysis of a multidimensional topological space based on the Cartesian product of complex and real spaces in continua. The geometry of the resulting space includes a real plane with planar rotational symmetry. The basis of topological space contains cylindrical open sets. The projection of a cylindrically symmetric continuous function in the topological space onto a complex planar subspace maintains surjectivity. The proposed construction show

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Makuta, Owidiusz, Błażej Kuzaka, and Remigiusz Augusiak. "Fully non-positive-partial-transpose genuinely entangled subspaces." Quantum 7 (February 9, 2023): 915. http://dx.doi.org/10.22331/q-2023-02-09-915.

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Genuinely entangled subspaces are a class of subspaces in the multipartite Hilbert spaces that are composed of only genuinely entangled states. They are thus an interesting object of study in the context of multipartite entanglement. Here we provide a construction of multipartite subspaces that are not only genuinely entangled but also fully non-positive-partial-transpose (NPT) in the sense that any mixed state supported on them has non-positive partial transpose across any bipartition. Our construction originates from the stabilizer formalism known for its use in quantum error correction. To

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Shenawy, Sameh, Uday Chand De, Nasser Bin Turki, Suliman Alsaeed, and Abdallah Abdelhameed Syied. "Investigation of Pseudo-Ricci Symmetric Spacetimes in Gray’s Subspaces." Journal of Mathematics 2021 (August 16, 2021): 1–6. http://dx.doi.org/10.1155/2021/6188097.

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In the present paper, we focused our attention to study pseudo-Ricci symmetric spacetimes in Gray’s decomposition subspaces. It is proved that PRS n spacetimes are Ricci flat in trivial, A , and B subspaces, whereas perfect fluid in subspaces I , I ⊕ A , and I ⊕ B , and have zero scalar curvature in subspace A ⊕ B . Finally, it is proved that pseudo-Ricci symmetric GRW spacetimes are vacuum, and as a consequence of this result, we address several corollaries.

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LEVAN, NHAN, and CARLOS S. KUBRUSLY. "TIME-SHIFTS GENERALIZED MULTIRESOLUTION ANALYSIS OVER DYADIC-SCALING REDUCING SUBSPACES." International Journal of Wavelets, Multiresolution and Information Processing 02, no. 03 (2004): 237–48. http://dx.doi.org/10.1142/s0219691304000494.

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A Generalized Multiresolution Analysis (GMRA) associated with a wavelet is a sequence of nested subspaces of the function space ℒ2(ℝ), with specific properties, and arranged in such a way that each of the subspaces corresponds to a scale 2m over all time-shifts n. These subspaces can be expressed in terms of a generating-wandering subspace — of the dyadic-scaling operator — spanned by orthonormal wavelet-functions — generated from the wavelet. In this paper we show that a GMRA can also be expressed in terms of subspaces for each time-shift n over all scales 2m. This is achieved by means of "el

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Liu, Wenhao, and Yang Yang. "The 7-Round Subspace Trail-Based Impossible Differential Distinguisher of Midori-64." Security and Communication Networks 2021 (November 9, 2021): 1–15. http://dx.doi.org/10.1155/2021/6269604.

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This paper analyzes the subspace trail of Midori-64 and uses the propagation law and mutual relationship of the subspaces of Midori-64 to provide a 6-round Midori-64 subspace trail-based impossible differential key recovery attack. The data complexity of the attack is 2 54.6 chosen plaintexts, and the computational complexity is 2 58.2 lookup operations. Its overall complexity is less than that of the known 6-round truncated impossible differential distinguisher. This distinguisher is also applicable to Midori-128 with a secret S -box. Additionally, utilizing the properties of subspaces, we pr

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Sangwisat, Juthamas, and Siripong Sirisuk. "Some Properties of Subspaces over Residue Class Rings." Progress in Applied Science and Technology 14, no. 2 (2024): 12–15. http://dx.doi.org/10.60101/past.2024.253316.

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Let denote the residue class ring where is a prime number and is a positive integer. For , a free submodule of the -module that has a basis is called a subspace of . In this paper, we present some properties of subspaces regarding their dimensions and the joins of subspaces of .

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Bose, Snehasish, P. Muthukumar, and Jaydeb Sarkar. "Beurling type invariant subspaces of composition operators." Journal of Operator Theory 86, no. 2 (2021): 425–38. http://dx.doi.org/10.7900/jot.2020may15.2286.

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The aim of this paper is to answer the following question concerning invariant subspaces of composition operators: characterize φ, holomorphic self maps of D, and inner functions θ∈H∞(D) such that the Beurling type invariant subspace θH2 is an invariant subspace for Cφ. We prove the following result: Cφ(θH2)⊆θH2 if and only if θ∘φθ∈S(D). This classification also allows us to recover or improve some known results on Beurling type invariant subspaces of composition operators.

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Nagi, Sajid, Dhruba Kumar Bhattacharyya, and Jugal K. Kalita. "A Preview on Subspace Clustering of High Dimensional Data." INTERNATIONAL JOURNAL OF COMPUTERS & TECHNOLOGY 6, no. 3 (2013): 441–48. http://dx.doi.org/10.24297/ijct.v6i3.4466.

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When clustering high dimensional data, traditional clustering methods are found to be lacking since they consider all of the dimensions of the dataset in discovering clusters whereas only some of the dimensions are relevant. This may give rise to subspaces within the dataset where clusters may be found. Using feature selection, we can remove irrelevant and redundant dimensions by analyzing the entire dataset. The problem of automatically identifying clusters that exist in multiple and maybe overlapping subspaces of high dimensional data, allowing better clustering of the data points, is known

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Laaksonen, Jorma, and Erkki Oja. "Learning Subspace Classifiers and Error-Corrective Feature Extraction." International Journal of Pattern Recognition and Artificial Intelligence 12, no. 04 (1998): 423–36. http://dx.doi.org/10.1142/s0218001498000270.

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Subspace methods are a powerful class of statistical pattern classification algorithms. The subspaces form semiparametric representations of the pattern classes in the form of principal components. In this sense, subspace classification methods are an application of classical optimal data compression techniques. Additionally, the subspace formalism can be given a neural network interpretation. There are learning versions of the subspace classification methods, in which error-driven learning procedures are applied to the subspaces in order to reduce the number of misclassified vectors. An algor

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Menghi, Nicholas, Kemal Kacar, and Will Penny. "Multitask learning over shared subspaces." PLOS Computational Biology 17, no. 7 (2021): e1009092. http://dx.doi.org/10.1371/journal.pcbi.1009092.

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This paper uses constructs from machine learning to define pairs of learning tasks that either shared or did not share a common subspace. Human subjects then learnt these tasks using a feedback-based approach and we hypothesised that learning would be boosted for shared subspaces. Our findings broadly supported this hypothesis with either better performance on the second task if it shared the same subspace as the first, or positive correlations over task performance for shared subspaces. These empirical findings were compared to the behaviour of a Neural Network model trained using sequential

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Demianowicz, Maciej. "Universal construction of genuinely entangled subspaces of any size." Quantum 6 (November 10, 2022): 854. http://dx.doi.org/10.22331/q-2022-11-10-854.

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We put forward a simple construction of genuinely entangled subspaces – subspaces supporting only genuinely multipartite entangled states – of any permissible dimensionality for any number of parties and local dimensions. The method uses nonorthogonal product bases, which are built from totally nonsingular matrices with a certain structure. We give an explicit basis for the constructed subspaces. An immediate consequence of our result is the possibility of constructing in the general multiparty scenario genuinely multiparty entangled mixed states with ranks up to the maximal dimension of a gen

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Adamu, M. Y., and E. Suleiman. "Linear Subspaces of Solutions Applied to Hirota Bilinear Equations." Aceh International Journal of Science and Technology 1, no. 2 (2012): 40–46. http://dx.doi.org/10.13170/aijst.1.2.125.

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Abstract - Linear subspace of solution is applied to Boussinesq and Kadomtseve-Petviashvili (KP) equations using Hirota bilinear transformation. A sufficient and necessary condition for the existence of linear subspaces of exponential travelling wave solutions to Hirota bilinear equations is applied to show that multivariate polynomials whose zeros form a vector space can generate the desire Hirota bilinear equations with given linear subspaces of solutions and formulate such multivariate polynomials by using multivariate polynomials which have one and only one zero.Keywords: Hirota bilinear f

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Astashkin, S. V. "ON SUBSPACES OF AN ORLICZ SPACE SPANNED BY INDEPENDENT IDENTICALLY DISTRIBUTED FUNCTIONS." Доклады Российской академии наук. Математика, информатика, процессы управления 512, no. 1 (2023): 65–68. http://dx.doi.org/10.31857/s2686954323600246.

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Subspaces of an Orlicz space LM generated by probabilistically independent copies of a function \(f \in {{L}_{M}}\), \(\int_0^1 {f(t){\kern 1pt} dt} = 0\), are studied. In terms of dilations of f, we get a characterization of strongly embedded subspaces of this type and obtain conditions that guarantee that the unit ball of such a subspace has equi-absolutely continuous norms in LM. A class of Orlicz spaces such that for all subspaces generated by independent identically distributed functions these properties are equivalent and can be characterized by Matuszewska–Orlicz indices is determined.

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Muñoz, María. "A note on the theorem of Baturov." Bulletin of the Australian Mathematical Society 76, no. 2 (2007): 219–25. http://dx.doi.org/10.1017/s0004972700039617.

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D.P. Baturov proved in ‘Subspaces of function spaces’ Vestnik Moskov University Series I (1987) that Lindelöf degree equals extent for subspaces of Cp(Χ) when Χ is a Lindelöf Σ-space. We prove that if the Lindelöf degree of the subspace is “big enough” the equality is true for a topological space Χ not necessarily Lindelöf Σ.

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Zhang, Huan, Wei Leng, Xiaolin Han, and Weidong Sun. "MOON: A Subspace-Based Multi-Branch Network for Object Detection in Remotely Sensed Images." Remote Sensing 15, no. 17 (2023): 4201. http://dx.doi.org/10.3390/rs15174201.

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The effectiveness of training-based object detection heavily depends on the amount of sample data. But in the field of remote sensing, the amount of sample data is difficult to meet the needs of network training due to the non-cooperative imaging modes and complex imaging conditions. Moreover, the imbalance of the sample data between different categories may lead to the long-tail problem during the training. Given that similar sensors, data acquisition approaches, and data structures could make the targets in different categories possess certain similarities, those categories can be modeled to

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Zhang, Xin, Hongfeng Guo, and Yuming Xu. "Finite Unions ofD-Spaces and Applications of Nearly Good Relation." Discrete Dynamics in Nature and Society 2013 (2013): 1–4. http://dx.doi.org/10.1155/2013/808262.

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Some results are obtained on finite unions ofD-spaces. It is proved that if a space is the union of finitely many locally compactD-subspaces, then it is aD-space. It follows that a space is aD-space if it is the union of finitely many locally compact submetacompact subspaces. And a space is aD-space if it is the union of aD-subspace with a locally compactD-subspace. This partially answers one problem raised by Arhangel’skii. At last, some examples are given to exhibit the applications of nearly good relation to discoverD-classes.

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Eiermann, Michael, and Oliver G. Ernst. "Geometric aspects of the theory of Krylov subspace methods." Acta Numerica 10 (May 2001): 251–312. http://dx.doi.org/10.1017/s0962492901000046.

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The development of Krylov subspace methods for the solution of operator equations has shown that two basic construction principles underlie the most commonly used algorithms: the orthogonal residual (OR) and minimal residual (MR) approaches. It is shown that these can both be formulated as techniques for solving an approximation problem on a sequence of nested subspaces of a Hilbert space, an abstract problem not necessarily related to an operator equation. Essentially all Krylov subspace algorithms result when these subspaces form a Krylov sequence. The well-known relations among the iterates

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DOGRA, SHOVAN, and MADHUMANGAL PAL. "Picture Fuzzy Subspace of a Crisp Vector Space." Kragujevac Journal of Mathematics 47, no. 4 (2003): 577–97. http://dx.doi.org/10.46793/kgjmat2304.577d.

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In this paper, the notion of picture fuzzy subspace of a crisp vector space is established and some related properties are explored on the basis of some basic operations (intersection, Cartesian product, union, (θ, ϕ, ψ)-cut etc.) on picture fuzzy sets. Direct sum of two picture fuzzy subspaces is initiated here over the direct sum of two crisp vector spaces. Also, the concepts of picture fuzzy linear transformation and picture fuzzy linearly independent set of vectors are introduced and some corresponding results are presented. Isomorphism between two picture fuzzy subspaces is developed here

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43

Balinsky, Alexander A., та Anatolij K. Prykarpatski. "On the Finite Dimensionality of Closed Subspaces in Lp(M, dμ) ∩ Lq(M, dν)". Axioms 10, № 4 (2021): 275. http://dx.doi.org/10.3390/axioms10040275.

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Finding effective finite-dimensional criteria for closed subspaces in Lp, endowed with some additional functional constraints, is a well-known and interesting problem. In this work, we are interested in some sufficient constraints on closed functional subspaces, Sp⊂Lp, whose finite dimensionality is not fixed a priori and can not be checked directly. This is often the case in diverse applications, when a closed subspace Sp⊂Lp is constructed by means of some additional conditions and constraints on Lp with no direct exemplification of the functional structure of its elements. We consider a clos

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Seshadri, P., S. Yuchi, G. T. Parks, and S. Shahpar. "Supporting multi-point fan design with dimension reduction." Aeronautical Journal 124, no. 1279 (2020): 1371–98. http://dx.doi.org/10.1017/aer.2020.50.

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AbstractMotivated by the idea of turbomachinery active subspace performance maps, this paper studies dimension reduction in turbomachinery 3D CFD simulations. First, we show that these subspaces exist across different blades—under the same parametrisation—largely independent of their Mach number or Reynolds number. This is demonstrated via a numerical study on three different blades. Then, in an attempt to reduce the computational cost of identifying a suitable dimension reducing subspace, we examine statistical sufficient dimension reduction methods, including sliced inverse regression, slice

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Qin, Jun, ChuTing Wang, and GuiHe Qin. "A Multilevel Image Thresholding Method Based on Subspace Elimination Optimization." Mathematical Problems in Engineering 2019 (June 25, 2019): 1–11. http://dx.doi.org/10.1155/2019/6706590.

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Multilevel thresholding is to find the thresholds to segment the image with grey levels. Usually, the thresholds are so determined that some indicator functions of the segmented image are optimized. To improve the computational efficiency, we presented an optimization method for multilevel thresholding. First, the solution space is divided into subspaces. Second, the subspaces are searched to obtain their current local optimal value. Third, the subspaces that are of worse current optimal value are eliminated. Then, the next round of elimination is exerted in the remainder. The elimination is r

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Saab, Elias. "On the weak*-Radon Nikodym property." Bulletin of the Australian Mathematical Society 37, no. 3 (1988): 323–32. http://dx.doi.org/10.1017/s0004972700026939.

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We say that a certain property in a Banach space E is stable by subspaces if every closed subspace of E enjoys the same property. It is well known that the Radon-Nikodym property is stable by subspaces while the Weak Radon-Nikodym property is not. In his recent memoir, Talagrand investigated the stability of the Weak*Radon-Nikodym property which is a generalization of the Weak Radon-Nikodym property and showed that under Axiom L, the Weak*Radon-Nikodym property is stable by subspaces. It is still an open problem whether or not this result holds without this extra set theoretical hypothesis. In

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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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Zhuraev, Tursunbay F., and Qamariddin R. Zhuvonov. "Subspaces dimensional properties that are boundary sets of the probability measures space, defined in an infinite compactum X." Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mekhanika, no. 89 (2024): 32–50. http://dx.doi.org/10.17223/19988621/89/3.

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In this note, we consider dimensional properties of the subspace of probability measure spaces P(X) for which transfinite dimensional functions ind, Ind and dim are defined. It is shown that countability of a compact set X is equivalent to the existence of dimensions indP x  ( ) , IndP x  ( ) , dimP x  ( ) , indP x f ( ) , IndP x f ( ) and dimP x f ( ) for the subspaces P x  ( ) , P x f ( ) , P x n ( ) respectively. It is also noted that for any compact C-space of the subspaces P x n ( ) , P x  ( ) , P x f ( ) the space P x( ) are compact C-spaces. If for an infinite compact set X the sub

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Poloni, Federico, and NataÅ¡a StrabiÄ. "Principal Pivot Transforms of Quasidefinite Matrices and Semidefinite Lagrangian Subspaces." Electronic Journal of Linear Algebra 31 (February 5, 2016): 200–231. http://dx.doi.org/10.13001/1081-3810.3132.

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Lagrangian subspaces are linear subspaces that appear naturally in control theory applications, and especially in the context of algebraic Riccati equations. We introduce a class of semidefinite Lagrangian subspaces and show that these subspaces can be represented by a subset I â {1, 2, . . . , n} and a Hermitian matrix X â C nÃn with the property that the submatrix X II is negative semidefinite and the submatrix X I c I c is positive semidefinite. A matrix X with these definiteness properties is called I-semidefinite and it is a generalization of a quasidefinite matrix. Under mild hypoth

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Raynaud, Yves. "A note on symmetric basic sequences in Lp(Lq)." Mathematical Proceedings of the Cambridge Philosophical Society 112, no. 1 (1992): 183–94. http://dx.doi.org/10.1017/s0305004100070869.

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Subspaces of Lp spanned by symmetric independent identically distributed random variables were identified as Orlicz spaces by Bretagnolle and Dacunha-Castelle[1], who showed that, conversely, in the case p ≤ 2, every p-convex, 2-concave Orlicz space is isomorphic to a subspace of Lp. This was extended by Dacunha-Castelle [3] to subspaces of Lp with symmetric basis, which appear as ‘p-means’ of Orlicz spaces (see [9] for the corresponding finite-dimensional result, and [12] for the case of rearrangement invariant function spaces). On the contrary the only subspaces with symmetric basis of Lp fo

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