• Title/Summary/Keyword: Hilbert

Search Result 888, Processing Time 0.086 seconds

ON THE THREE OPERATOR SPACE STRUCTURES OF HILBERT SPACES

  • Shin, Dong-Yun
    • Communications of the Korean Mathematical Society
    • /
    • v.11 no.4
    • /
    • pp.983-996
    • /
    • 1996
  • In this paper, we show that $\Vert \xi \Vert_r = \Vert \sum_{i \in I}x_i x^*_i \Vert^{\frac{1}{2}}, \Vert \xi \Vert_c = \Vert \sum_{i \in I}x^*_ix_i \Vert^{\frac{1}{2}}$ for $\xi = \sum_{i \in I}x_i e_i$ in $M_n(H)$, that subspaces as Hilbert spaces are subspaces as column and row Hilbert spaces, and that the standard dual of column (resp., row) Hilbert spaces is the row (resp., column) Hilbert spaces differently from [1,6]. We define operator Hilbert spaces differently from [10], show that our definition of operator Hilbert spaces is the same as that in [10], show that subspaces as Hilbert spaces are subspaces as operator Hilbert spaces, and for a Hilbert space H we give a matrix norm which is not an operator space norm on H.

  • PDF

Fast Hilbert R-tree Bulk-loading Scheme using GPGPU (GPGPU를 이용한 Hilbert R-tree 벌크로딩 고속화 기법)

  • Yang, Sidong;Choi, Wonik
    • Journal of KIISE
    • /
    • v.41 no.10
    • /
    • pp.792-798
    • /
    • 2014
  • In spatial databases, R-tree is one of the most widely used indexing structures and many variants have been proposed for its performance improvement. Among these variants, Hilbert R-tree is a representative method using Hilbert curve to process large amounts of data without high cost split techniques to construct the R-tree. This Hilbert R-tree, however, is hardly applicable to large-scale applications in practice mainly due to high pre-processing costs and slow bulk-load time. To overcome the limitations of Hilbert R-tree, we propose a novel approach for parallelizing Hilbert mapping and thus accelerating bulk-loading of Hilbert R-tree on GPU memory. Hilbert R-tree based on GPU improves bulk-loading performance by applying the inversed-cell method and exploiting parallelism for packing the R-tree structure. Our experimental results show that the proposed scheme is up to 45 times faster compared to the traditional CPU-based bulk-loading schemes.

MODULES WHOSE CLASSICAL PRIME SUBMODULES ARE INTERSECTIONS OF MAXIMAL SUBMODULES

  • Arabi-Kakavand, Marzieh;Behboodi, Mahmood
    • Bulletin of the Korean Mathematical Society
    • /
    • v.51 no.1
    • /
    • pp.253-266
    • /
    • 2014
  • Commutative rings in which every prime ideal is an intersection of maximal ideals are called Hilbert (or Jacobson) rings. We propose to define classical Hilbert modules by the property that classical prime submodules are intersections of maximal submodules. It is shown that all co-semisimple modules as well as all Artinian modules are classical Hilbert modules. Also, every module over a zero-dimensional ring is classical Hilbert. Results illustrating connections amongst the notions of classical Hilbert module and Hilbert ring are also provided. Rings R over which all modules are classical Hilbert are characterized. Furthermore, we determine the Noetherian rings R for which all finitely generated R-modules are classical Hilbert.

CENTRAL HILBERT ALGEBRAS

  • Jun, Young-Bae;Park, Chul-Hwan
    • The Pure and Applied Mathematics
    • /
    • v.15 no.3
    • /
    • pp.309-313
    • /
    • 2008
  • The notion of central Hilbert algebras and central deductive systems is introduced, and related properties are investigated. We show that the central part of a Hilbert algebra is a deductive system. Conditions for a subset of a Hilbert algebra to be a deductive system are given. Conditions for a subalgebra of a Hilbert algebra to be a deductive system are provided.

  • PDF

THE WOVEN FRAME OF MULTIPLIERS IN HILBERT C* -MODULES

  • Irani, Mona Naroei;Nazari, Akbar
    • Communications of the Korean Mathematical Society
    • /
    • v.36 no.2
    • /
    • pp.257-266
    • /
    • 2021
  • In this paper, by using the sequence of adjointable operators from C*-algebra 𝓐 into Hilbert 𝓐-module E, the woven frames of multipliers in Hilbert C*-modules are introduced. Meanwhile, we study the effect of operators on these frames and, also we construct the new woven frame of multipliers in Hilbert 𝓐-module 𝓐. Finally, compositions of woven frames of multipliers in Hilbert C*-modules are studied.

Prediction of the Successful Defibrillation using Hilbert-Huang Transform (Hilbert-Huang 변환을 이용한 제세동 성공 예측)

  • Jang, Yong-Gu;Jang, Seung-Jin;Hwang, Sung-Oh;Yoon, Young-Ro
    • Journal of the Institute of Electronics Engineers of Korea SC
    • /
    • v.44 no.5
    • /
    • pp.45-54
    • /
    • 2007
  • Time/frequency analysis has been extensively used in biomedical signal processing. By extracting some essential features from the electro-physiological signals, these methods are able to determine the clinical pathology mechanisms of some diseases. However, this method assumes that the signal should be stationary, which limits its application in non-stationary system. In this paper, we develop a new signal processing method using Hilbert-Huang Transform to perform analysis of the nonlinear and non-stationary ventricular fibrillation(VF). Hilbert-Huang Transform combines two major analytical theories: Empirical Mode Decomposition(EMD) and the Hilbert Transform. Hilbert-Huang Transform can be used to decompose natural data into independent Intrinsic Mode Functions using the theories of EMD. Furthermore, Hilbert-Huang Transform employs Hilbert Transform to determine instantaneous frequency and amplitude, and therefore can be used to accurately describe the local behavior of signals. This paper studied for Return Of Spontaneous Circulation(ROSC) and non-ROSC prediction performance by Support Vector Machine and three parameters(EMD-IF, EMD-FFT) extracted from ventricular fibrillation ECG waveform using Hilbert-Huang transform. On the average results of sensitivity and specificity were 87.35% and 76.88% respectively. Hilbert-Huang Transform shows that it enables us to predict the ROSC of VF more precisely.

A Study of Three-Dimensional Measurement By Transmission Deflectometry and Hilbert Transform (Hilbert 변환과 투과형 편향법을 이용한 3차원 측정연구)

  • Na, Silin;Yu, Younghun
    • Korean Journal of Optics and Photonics
    • /
    • v.27 no.2
    • /
    • pp.61-66
    • /
    • 2016
  • We used transmission deflectometry to measure the three-dimensional shapes of optical components, and we used the Hilbert transform to retrieve the phases from measured deformed fringe images. Deflectometry is useful for measuring large-scale samples, and specular samples. We have retrieved the phases from deformed fringe images and Hilbert-transformed images, and have used the least-squares method to find the height information. We have verified that phase retrieval using Hilbert transform is useful by computer simulation and experiment.

Improved Linearizer for use in Real Zero SSB Receiver (Real Zero SSB 수신기에서 개선된 Linearizer 구현)

  • 홍교영;김종한;김유창;김원후
    • The Journal of Korean Institute of Communications and Information Sciences
    • /
    • v.24 no.7A
    • /
    • pp.1016-1021
    • /
    • 1999
  • In order to obtain a demodulated signal from RZ-SSB signal, it is important to design a linearizer which cancels the high-order distortions after FM demodulation. Since the NTT's linearizer must include a Hilbert transform, the characteristics of the linearizer are determined by the characteristics of Hilbert transform and it is very complicated to design and realize especially in the low frequency range. In the case of the proposed linearizer, the high-order distortion can be reduced without using any Hilbert transform. Furthemore, unlike the conventional RZ-SSB Demodulator, the proposed linearizer can be realized easily.

  • PDF

HILBERT-SCHMIDT INTERPOLATION FOR OPERATORS IN TRIDIAGONAL ALGEBRAS

  • Kang, Joo-Ho;Kim, Ki-Sook
    • Journal of applied mathematics & informatics
    • /
    • v.10 no.1_2
    • /
    • pp.227-233
    • /
    • 2002
  • Given operators X and Y acting on a Hilbert space H, an interpolating operator is a bounded operator A such that AX = Y. An interpolating operator for n-operators satisfies the equation AX$\sub$i/=Y$\sub$i/, for i=1,2, ‥‥, R. In this article, we investigate Hilbert-Schmidt interpolation for operators in tridiagonal algebras.

A STRONG LAW OF LARGE NUMBERS FOR AANA RANDOM VARIABLES IN A HILBERT SPACE AND ITS APPLICATION

  • Ko, Mi-Hwa
    • Honam Mathematical Journal
    • /
    • v.32 no.1
    • /
    • pp.91-99
    • /
    • 2010
  • In this paper we introduce the concept of asymptotically almost negatively associated random variables in a Hilbert space and obtain the strong law of large numbers for a strictly stationary asymptotically almost negatively associated sequence of H-valued random variables with zero means and finite second moments. As an application we prove a strong law of large numbers for a linear process generated by asymptotically almost negatively random variables in a Hilbert space with this result.