• Title, Summary, Keyword: numerical range

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ON NUMERICAL RANGE AND NUMERICAL RADIUS OF CONVEX FUNCTION OPERATORS

  • Zaiz, Khaoula;Mansour, Abdelouahab
    • Korean Journal of Mathematics
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    • v.27 no.4
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    • pp.879-898
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    • 2019
  • In this paper we prove some interesting inclusions concerning the numerical range of some operators and the numerical range of theirs ranges with a convex function. Further, we prove some inequalities for the numerical radius. These inclusions and inequalities are based on some classical convexity inequalities for non-negative real numbers and some operator inequalities.

A NOTE ON THE NUMERICAL RANGE OF AN OPERATOR

  • Yang, Youngoh
    • Bulletin of the Korean Mathematical Society
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    • v.21 no.1
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    • pp.27-30
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    • 1984
  • The concepts of the numerical range of an operator on a Hillbert space and on a Banach space were introduced by Toeplitz in 1918 and Bauer in 1962 respectively. Bauer's paper was concerned only with finite dimensional Banach spaces, but the concept of numerical range that he introduced is available without restriction of the dimension [1, 2]. In this paper, we define a C-algebra spatial numerical range of an operator on C-algebra valued inner product modules introduced by Paschke [4], and give analogous results on these modules as those on Banach spaces.

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A Numerical Analysis of Hydraulic Hammer Compaction (유압식 햄머다짐의 수치해석적 연구)

  • 박인준;박양수;김수일
    • Proceedings of the Korean Geotechical Society Conference
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    • pp.183-190
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    • 2000
  • Effective range of Hydraulic Hammer Compaction was studied by numerical analysis instead of empirical method. Numerical analyses were carried out with commercial FEM code, ABAQUS, and verified by comparing the numerical results with field tests of Hydraulic Hammer Compaction. Most of material properties were evaluated by data from laboratory and in-situ tests. Vertical effective range was estimated by distribution curve of plastic strain energy dissipated through soil layers under dynamic load and these results were in good agreement with field tests. Based on verification, the effects of governing properties of Hydraulic Hammer Compaction such as number of hit can be determined by numerical analyses. In addition, vertical effective range can also be determined by Menard's empirical equation using the external work at converging time of plastic strain energy in numerical analysis. This implies that the minimum energy of Hydraulic Hammer Compaction for improvement can be determined by Menard's equation.

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SPATIAL NUMERICAL RANGES OF ELEMENTS OF $C^*$-ALGEBRAS

  • Takahasi, Sin-Ei
    • Bulletin of the Korean Mathematical Society
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    • v.37 no.3
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    • pp.537-542
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    • 2000
  • When A is a subalgebra of a $C^*$-algebra, the spatial numerical range of element of A can be described in terms of positive linear functionals on the $C^*$-algebra.

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MAPPING PRESERVING NUMERICAL RANGE OF OPERATOR PRODUCTS ON C*-ALGEBRAS

  • MABROUK, MOHAMED
    • Bulletin of the Korean Mathematical Society
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    • v.52 no.6
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    • pp.1963-1971
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    • 2015
  • Let $\mathcal{A}$ and $\mathcal{B}$ be two unital $C^*$-algebras. Denote by W(a) the numerical range of an element $a{\in}\mathcal{A}$. We show that the condition W(ax) = W(bx), ${\forall}x{\in}\mathcal{A}$ implies that a = b. Using this, among other results, it is proved that if ${\phi}$ : $\mathcal{A}{\rightarrow}\mathcal{B}$ is a surjective map such that $W({\phi}(a){\phi}(b){\phi}(c))=W(abc)$ for all a, b and $c{\in}\mathcal{A}$, then ${\phi}(1){\in}Z(B)$ and the map ${\psi}={\phi}(1)^2{\phi}$ is multiplicative.

Numerical Analysis of Wintertime Air Pollution in East Asia Region Using Long-Range Transport Model

  • Jang, Eun-Suk
    • Environmental Sciences Bulletin of The Korean Environmental Sciences Society
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    • v.4 no.2
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    • pp.103-110
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    • 2000
  • In order to understand the wintertime intermittent characteristics of the trans-boundary air pollutant transport observed in East Asia, a numerical simulation of the long-range transport of pollutants was applied using an atmospheric transport model(STEM-II). The numerical simulation was carried out for the entire month of January 1997 and specific atmospheric aerosol (including sulfate, nitrate, and other ion compounds0 observation data were compared from four observation sites(Cheju Island, Kanghwa Island, Dazaifu, and Fukue Island). The observation data revealed that concentration peaks were intermittently observed at 3 to 4-day intervals plus the four observation sites exhibited a very similar spatial variation. The horizontal and spatial scale of the heavily polluted air masses was analyzed based on numerical results. The mechanism of the intermittent transport of air pollutants was clearly explained by a comparison of the observed data with the numerical output. It was found that the wind pattern variations associated with the synoptic scale pressure system changes play an extremely important role in the transport of pollutants in this region.

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Numerical Range Criteria for Classification of Value Engineering Proposals based on Value Improvement Types (VE제안의 가치향상 유형별 수치적 범위기준 제시)

  • Nam, Keong-Woo;Jang, Myunghoun
    • Journal of Advanced Engineering and Technology
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    • v.11 no.4
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    • pp.287-294
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    • 2018
  • Since its introduction in Korea, design VE has widely been used as a means to enhance values in the construction industry. However, a greater emphasis is still placed on cost reduction in approach attitudes and performance evaluations on the implementation of design VE. In this regard, this study presented a performance evaluation method for cost, function, and value of VE proposals. Numerical criteria on the increase and decrease of cost and function that can classify the value enhancement type of VE proposals were proposed based on the performance evaluation method. It is expected that the use of numerical criteria for the type classification of VE proposal, and cost and performance evaluation method proposed in this study will make it possible to conduct a clear and more intuitive evaluation of VE proposal. However, it is appropriate to use the numerical criteria as a guideline to apply the new performance evaluation method for VE proposals. Therefore, it is necessary to conduct a statistical analysis with a wider range of users after the repeated application of the findings of this study, and thus to carry out research for presenting the numerical criteria for various types of users.

Numerical Investigation of Ring Groove Effect in a Centrifugal Compressor (원심압축기의 링 그루브 효과에 관한 수치해석적 연구)

  • Park, Chi-Yong;Choi, Young-Seok;Lee, Kyoung-Yong;Yoon, Joon-Yong
    • The KSFM Journal of Fluid Machinery
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    • v.14 no.2
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    • pp.11-16
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    • 2011
  • This paper presents a numerical study of casing treatments on a centrifugal compressor stage to improve stability and the surge margin. High efficiency, a high pressure ratio, and a wide operating range are required for a high performance centrifugal compressor. In the present study, a ring groove arrangement was applied to the transonic centrifugal compressor. According to the numerical analysis using a commercial code ANSYS-CFX, the unstable phenomena limiting the range of the centrifugal compressors were compared with and without a ring groove. Although the ring groove decreased the efficiency, but increased the operating range by suppressing a flow separation at the leading-edge of the impeller especially near shroud part. Newly designed ring groove arrangement improved the compressor performance and increased the operating range of the compressor.