• Journal of the Korean Data and Information Science Society
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• v.22 no.6
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• pp.1233-1240
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• 2011

An augmented asymmetric power GARCH(p, q) process is considered and conditions for stationarity, geometric ergodicity and ${\beta}$-mixing property with exponential decay rate are obtained.

• Journal of the Korean Mathematical Society
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• v.60 no.2
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• pp.375-393
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• 2023

Rabinowitz action functional is the Lagrange multiplier functional of the negative area functional to a constraint given by the mean value of a Hamiltonian. In this note we show that on a symplectization there is a one-to-one correspondence between gradient flow lines of Rabinowitz action functional and gradient flow lines of the restriction of the negative area functional to the constraint. In the appendix we explain the motivation behind this result. Namely that the restricted functional satisfies Chas-Sullivan additivity for concatenation of loops which the Rabinowitz action functional does in general not do.

• Korean Journal of Mathematics
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• v.31 no.3
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• pp.313-321
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• 2023

In this paper, we explore the additivity of the map Ω : 𝒜 → 𝒜 that satisfies Ω([ℒ, ℳ]_*)=[Ω (ℳ), ℒ]_* + [ℳ, Ω(ℒ)]_*, where [ℒ, ℳ]_*= ℒℳ^* - ℳ ℒ^*, for all ℒ, ℳ ∈ 𝒜, a prime *-algebra with unit ℐ. Additionally we show that if Ω (αℐ) is self-adjoint operator for α ∈ {1, i} then Ω = 0.

• Journal of applied mathematics & informatics
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• v.41 no.1
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• pp.123-132
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• 2023

We define an operator version of the relative Rényi entropy as the generalization of relative von Neumann entropy, and provide its fundamental properties and the bounds for its trace value. Moreover, we see an effect of the relative Rényi entropy under tensor product, and show the sub-additivity for density matrices.

• Journal of applied mathematics & informatics
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• v.42 no.4
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• pp.985-995
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• 2024

We see fundamental properties of the log-determinant α-divergence including the convexity of weighted geometric mean and the reversed sub-additivity under tensor product. We introduce a symmetrized divergence and show its properties including the boundedness and monotonicity on parameters. Finally, we discuss the barycenter minimizing the weighted sum of symmetrized divergences.

• Korea-Australia Rheology Journal
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• v.11 no.3
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• pp.255-263
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• 1999

Blends of two thermotropic liquid crystalline polymers, HX2000 and Vectra A950, were prepared by melt blending. Effects of transesterification on these blends are investigated by comparing properties of the blends with and without the addition of an inhibitor, in terms of blend miscibility and rheology. Both the uninhibited and inhibited blends are found to be largely immiscible with very limited miscibility in HX2000-rich phase. No strong evidence indicates the occurrence of transesterification in the blends in the solid state. Dynamic rheological behaviour, such as shear storage modulus (G') and shear loss modulus (G") as a function of frequency, of the blends are interpreted by a three-zone model. HX2000 shows terminal-zone and plateau-zone behaviour, whilst Vectra A950 shows plateau-zone and transition-zone behaviour. The un- inhibited blends show plateau-zone behaviour up to 50% Vectra A950 content and the inhibited blends show plateau-zone behaviour up to 60% Vectra A950 content. Compositional dependence of the complex viscosities of the uninhibited and inhibited blends displayed positive deviations from additivity, which is a characteristic feature for the immiscible thermoplastic blends. When under steady shear, both the uninhibited and inhibited blends show shear thinning behaviour and their viscosities decrease monotonically with the addition of Vectra A950. Compositional dependence of the steady shear viscosities of the two sets of blends displayed negative deviations from additivity and the uninhibited blends were more viscous than the inhibited blends for the full composition range. Although limited agreement with the Cox-Merz rule is found for the inhibited blends, these two sets of blends, in general, do not follow the rule due to their liquid crystalline order and two-phase morphology. Despite being immiscible blends, transesterification, such as polymerization, in the blends might occur during the rheological characterization, supported by the facts that uninhibited blends show HX2000-dominant behaviour at lower Vectra A950 content and are more viscous than the inhibited blends. The addition of transesterification inhibitor in such blends is advised if only physical mixing is desired.ired.

• Journal of the Korean Chemical Society
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• v.25 no.4
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• pp.246-252
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• 1981

Assuming krypton molecules adsorbed on graphite surface as 2D gas, the interaction energy of Kr-graphite and the Henry's constant are calculated analytically by the Fourier series expansion method. 2D virial cofficients, $B_{2D}$ and $C_{2D}$, are also calculated to obtain 2D equation of state, and hence adsorption isotherms. The isotherms so obtained are compared with experimental results reported by Putnam and Fort. The pairwise additivity of Lennard-Jones(12, 6) interaction energy is also assumed, and parameters therein are taken as; ${\varepsilon}_{gs}$/k = 70 K, ${\sigma}_{gs}$ = 0.35 nm, ${\varepsilon}_{gg}$/k = 170 K, and ${\sigma}_{gg}$ = 0.37 nm.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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• 2002.07a
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• pp.119-122
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• 2002

The calculated and measured dielectric constant of (1-x)(Al$\sub$1/2/Ta$\sub$1/2/)O$_2$-x(Mg$\sub$1/3/Ta$\sub$2/3/)O$_2$(O$\leq$x$\leq$1.0) solid solutions were investigated by variations of ionic polarizability and crystal structure. (Al$\sub$1/2/Ta$\sub$1/2/)O$_2$ and (Mg$\sub$1/3/Ta$\sub$2/3/)O$_2$were orthorhombic and tetragonal trirutile structure, respectively. When (Al$\sub$1/2/Ta$\sub$1/2/)O$_2$ was substituted by (Mg$\sub$1/3/Ta$\sub$2/3/)O$_2$, the phase transformed to tetragonal structure over 60 mole%. Because the ionic radius of (Mg$\sub$1/3/Ta$\sub$2/3/)O$_2$was slightly bigger than one of (A1$\sub$1/2/Ta$\sub$1/2)O$_2$, the cell parameters increased with an increase of (Mg$\sub$1/3/Ta$\sub$2/3/)O$_2$ substitution. The measured dielectric constant increased with an increase of (Mg$\sub$1/3/Ta$\sub$2/3/)O$_2$ substitution and coincided with dielectric mixing rule and the calculated dielectric constant with the molecular additivity rule. There were some differences between the measured and the calculated dielectric constant. The reason of the lowered dielectric constant comparing with the calculated one was compressed stress due to the electronic structure of tantalum.

• Polymer(Korea)
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• v.28 no.6
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• pp.460-467
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• 2004

The polymer blends of waste poly(vinyl chloride) (RPVC) and waste polyethylene (RPE) were prepared by melt mixing. Their morphologies and rheological properties were investigated and torque changes were also measured. Comparing the torques calculated by the log additivity rule with measured torque changes, the polymer blends showed the large negative deviation behavior (NDB) due to their incompatibility. The shear viscosities of the blends decreased with increasing shear rates, showing shear thinning behavior. The shear viscosity of the blends with compatibilizer was larger than that of the blends without compatibilizer. SEM micrographs of the strands after measurement showed that the domain size of the blends was slightly enlarged with increasing the shear rate. Also, RPVC domain size was larger in the core-sections of the strands from capillary viscometer than in the surface region.

• Journal of the Korean Institute of Electrical and Electronic Material Engineers
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• v.16 no.2
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• pp.108-112
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• 2003

The calculated and measured dielectric constants of (1-x)(A $l_{1}$2/ T $a_{1}$2/) $O_2$-x(M $g_{1}$3/ T $a_{2}$3/) $O_2$ (0$\leq$x$\leq$1.0) solid solutions were investigated by variations of ionic polarizability and crystal structure. (A $l_{1}$2/ T $a_{1}$2/) $O_2$ and (M $g_{1}$3/ T $a_{2}$3/) $O_2$ were orthorhombic and tetragonal trirutile structure, respectively. When (A $l_{1}$2/ T $a_{1}$2/) $O_2$ was substituted by (M $g_{1}$3/ T $a_{2}$3/) $O_2$, the phase transformed to tetragonal structure over 60 mole. Because the total ionic radius of [(Mg+2Ta)/3]$^{4+}$ was slightly bigger than one of [(Al+Ta)/2]$^{4+}$, the lattice parameters increased with an increase of (M $g_{1}$3/ T $a_{2}$3/) $O_2$ substitution. The measured dielectric constant increased with an increase of (M $g_{1}$3/ T $a_{2}$3/) $O_2$ substitution and coincided with dielectric mixing rule and the calculated dielectric constant with the molecular additivity rule. There were some differences between the measured and the calculated dielectric constant. The reason of the lowered dielectric constant comparing with the calculated one was compressed stress due to the electronic structure of tantalum.