• Title, Summary, Keyword: Hilbert

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ON THE THREE OPERATOR SPACE STRUCTURES OF HILBERT SPACES

  • Shin, Dong-Yun
    • Communications of the Korean Mathematical Society
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    • v.11 no.4
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    • pp.983-996
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    • 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.

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MODULES WHOSE CLASSICAL PRIME SUBMODULES ARE INTERSECTIONS OF MAXIMAL SUBMODULES

  • Arabi-Kakavand, Marzieh;Behboodi, Mahmood
    • Bulletin of the Korean Mathematical Society
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    • v.51 no.1
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    • pp.253-266
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    • 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
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    • v.15 no.3
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    • pp.309-313
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    • 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.

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THE WOVEN FRAME OF MULTIPLIERS IN HILBERT C* -MODULES

  • Irani, Mona Naroei;Nazari, Akbar
    • Communications of the Korean Mathematical Society
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    • v.36 no.2
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    • pp.257-266
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    • 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
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    • v.44 no.5
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    • pp.45-54
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    • 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
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    • v.27 no.2
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    • pp.61-66
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    • 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.

A POINT STAR-CONFIGURATION IN ℙn HAVING GENERIC HILBERT FUNCTION

  • Shin, Yong-Su
    • Journal of the Chungcheong Mathematical Society
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    • v.28 no.1
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    • pp.119-125
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    • 2015
  • We find a necessary and sufficient condition for which a point star-configuration in $\mathbb{P}^n$ has generic Hilbert function. More precisely, a point star-configuration in $\mathbb{P}^n$ defined by general forms of degrees $d_1,{\ldots},d_s$ with $3{\leq}n{\leq}s$ has generic Hilbert function if and only if $d_1={\cdots}=d_{s-1}=1$ and $d_s=1,2$. Otherwise, the Hilbert function of a point star-configuration in $\mathbb{P}^n$ is NEVER generic.

SOME EXAMPLES OF THE UNION OF TWO LINEAR STAR-CONFIGURATIONS IN ℙ2 HAVING GENERIC HILBERT FUNCTION

  • Shin, Yong Su
    • Journal of the Chungcheong Mathematical Society
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    • v.26 no.2
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    • pp.403-409
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    • 2013
  • In [20] and [22], the author proved that the union of two linear star-configurations in $\mathbb{P}^2$ of type $t{\times}s$ with $3{\leq}t{\leq}10$ and $t{\leq}s$ has generic Hilbert function. In this paper, we prove that the union of two linear star-configurations in $\mathbb{P}^2$ of type $t{\times}s$ with $3{\leq}t$ and $({a\atop2})-1{\leq}s$ has also generic Hilbert function.

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

  • Ko, Mi-Hwa
    • Honam Mathematical Journal
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    • v.32 no.1
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    • pp.91-99
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    • 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.

On deductive systems of hilbert algebras

  • Hong, Sung-Min;Jun, Young-Bae
    • Communications of the Korean Mathematical Society
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    • v.11 no.3
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    • pp.595-600
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    • 1996
  • We give a characterization of a deductive system. We introduce the concept of maximal deductive systems and show that every bounded Hilbert algebra with at least two elements contains at least one maximal deductive system. Moreover, we introduce the notion of radical and semisimple in a Hilbert algebra and prove that if H is a bounded Hilbert algebra in which every element is an involution, then H is semisimple.

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