• Title/Summary/Keyword: PHI

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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.

Micro PIV Measurement of Two-Fluid Flow with Different Refraction Indices (미소입자영상유속계를 이용한 굴절률이 다른 두 유체 유동 측정)

  • Kim, Byoung-Jae;Liu, Ying Zheng;Sung, Hyung-Jin
    • 유체기계공업학회:학술대회논문집
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    • 2003.12a
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    • pp.107-114
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    • 2003
  • The influence of property difference in refraction index on micro PIV measurement of two-fluid flow in a microchannel was analyzed. The difference of measurement planes in two fluids would bring misunderstanding of the physics. The objective-imaging system for two-fluid flow measurement was presented, and the condition for measurement of valid velocity profile across two-fluid interface was derived. A micro PIV experimental system was set up to measure two-fluid flow inside a Y-shape microchannel. Under the conditions, three cases of two-fluid flow of glycerol solutions at different concentration (${\phi}$), e.g., (${\phi}=0\;and\;{\phi}=0.2,\;{\phi}=0.1\;and\;{\phi}=0.5,\;{\phi}=0\;and\;{\phi}=0.6$, were measured. Close agreement of experimental and numerical results was found.

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AUTOMORPHISM GROUPS ON CERTAIN REINHARDT DOMAINS

  • Kang, Hyeonbae
    • Bulletin of the Korean Mathematical Society
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    • v.30 no.2
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    • pp.171-177
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    • 1993
  • In this paper, we show that Greene-Krantz's conjecture is true for certain class of domains. In fact, we give a complete classification of automorphism groups of domains of the form (Fig.) where the function .phi. is a real valued $C^{\infty}$ function in a neighborhood of [0,1] which satisfies the following conditions; (1) .phi.(0)=.phi.'(0)=0 and .phi.(1)=1, (2) .phi.(t) is increasing and convex for t>0.vex for t>0.

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REMARKS ON THE REIDEMEISTER NUMBER OF A G-MAP

  • Cho, Sung Ki;Kweon, Dae Seop
    • Korean Journal of Mathematics
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    • v.6 no.2
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    • pp.165-172
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    • 1998
  • For a G-map ${\phi}:X{\rightarrow}X$, we define and characterize the Reidemeister number $R_G({\phi})$ of ${\phi}$. Also, we prove that $R_G({\phi})$ is a G-homotopy invariance and we obtain a lower bound of $R_G({\phi})$.

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HARMONIC TRANSFORMATIONS OF THE HYPERBOLIC PLANE

  • Park, Joon-Sik
    • Journal of the Chungcheong Mathematical Society
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    • v.22 no.4
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    • pp.771-776
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    • 2009
  • Let (H, g) denote the upper half plane in $R^2$ with the Riemannian metric g := ($(dx)^2$ + $(dy)^2$)$/y^2$. First of all we get a necessary and sufficient condition for a diffeomorphism $\phi$ of (H, g) to be a harmonic map. And, we obtain the fact that if a diffeomorphism $\phi$ of (H, g) is a harmonic function, then the following facts are equivalent: (1) $\phi$ is a harmonic map; (2) $\phi$ is an affine transformation; (3) $\phi$ is an isometry (motion).

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On asymptotic Stability in nonlinear differential system

  • An, Jeong-Hyang
    • Journal of Korea Society of Industrial Information Systems
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    • v.11 no.5
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    • pp.62-66
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    • 2006
  • We investigate various $\Phi(t)-stability$ of comparison differential equations and we abtain necessary and/or sufficient conditions for the uniform asymptotic and exponential asymptotic stability of the nonlinear differential equation x'=f(t, x).

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Effects of SPS Mold on the Properties of Sintered and Simulated SiC-ZrB2 Composites

  • Lee, Jung-Hoon;Kim, In-Yong;Kang, Myeong-Kyun;Jeon, Jun-Soo;Lee, Seung-Hoon;Jeon, An-Gyun;Shin, Yong-Deok
    • Journal of Electrical Engineering and Technology
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    • v.8 no.6
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    • pp.1474-1480
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    • 2013
  • Silicon carbide (SiC)-zirconium diboride ($ZrB_2$) composites were prepared by subjecting a 60:40 vol% mixture of ${\beta}$-SiC powder and $ZrB_2$ matrix to spark plasma sintering (SPS) in 15 $mm{\Phi}$ and 20 $mm{\Phi}$ molds. The 15 $mm{\Phi}$ and 20 $mm{\Phi}$ compacts were sintered for 60 sec at $1500^{\circ}C$ under a uniaxial pressure of 50 MPa and argon atmosphere. Similar composites were simulated using $Flux^{(R)}$ 3D computer simulation software. The current and power densities of the specimen sections of the simulated SiC-$ZrB_2$ composites were higher than those of the mold sections of the 15 $mm{\Phi}$ and 20 $mm{\Phi}$ mold simulated specimens. Toward the centers of the specimen sections, the current densities in the simulated SiC-$ZrB_2$ composites increased. The power density patterns of the specimen sections of the simulated SiC-$ZrB_2$ composites were nearly identical to their current density patterns. The current densities of the 15 $mm{\Phi}$ mold of the simulated SiC-$ZrB_2$ composites were higher than those of the 20 $mm{\Phi}$ mold in the center of the specimen section. The volume electrical resistivity of the simulated SiC-$ZrB_2$ composite was about 7.72 times lower than those of the graphite mold and the punch section. The power density, 1.4604 $GW/m^3$, of the 15 $mm{\Phi}$ mold of the simulated SiC-$ZrB_2$ composite was higher than that of the 20 $mm{\Phi}$ mold, 1.3832 $GW/m^3$. The $ZrB_2$ distributions in the 20 $mm{\Phi}$ mold in the sintered SiC-$ZrB_2$ composites were more uniform than those of the 15 $mm{\Phi}$ mold on the basis of energy-dispersive spectroscopy (EDS) mapping. The volume electrical resistivity of the 20 $mm{\Phi}$ mold of the sintered SiC-$ZrB_2$ composite, $6.17{\times}10^{-4}{\Omega}cm$, was lower than that of the 15 $mm{\Phi}$ mold, $9.37{\times}10^{-4}{\Omega}{\cdot}cm$, at room temperature.