• Communications of the Korean Mathematical Society
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• v.37 no.3
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• pp.851-864
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• 2022

We define a kind of sectional curvature and 𝛿-invariants for statistical manifolds. For statistical submanifolds the sum of the squared mean curvature and the squared dual mean curvature is bounded below by using the 𝛿-invariant. This inequality can be considered as a generalization of the so-called Chen inequality for Riemannian submanifolds.

• Honam Mathematical Journal
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• v.27 no.3
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• pp.389-397
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• 2005

Let K be an absolutely real abelian number field with $G=Gal(K/{\mathbb{Q}})$. Let E be a subfield of K and ${\Delta}=Gal(K/E)$. Let $C_K$ and $C_E$ be the group of circular units of K and E respectively. In [G], Greither has shown that if G is cyclic then $C_K^{\Delta}=C_E$. In this paper we show that the same result holds in function field case.

• The Korean Journal of Applied Statistics
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• v.4 no.1
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• pp.1-11
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• 1991

It is of great interest to consider the homogeniety of covariance matrices in MANOVA of discriminant analysis. If we lock at the problem of testing hypothesis, H : $\Sigma_1 = \Sigma_2$ from an invariance point of view where $\Sigma_i$ are the covariance matrix of two independent p-variate distribution, the testing problem is invariant under the group of nonsingular transformations and the hypothesis becomes H : $\delta_1 = \delta_2 = \cdots = \delta_p = 1$ where $\delta = (\delta_1, \delta_2, \cdots, \delta_p)$ is a vector of latent roots of $\Sigma$. Bias-corrected estimators of eigenvalues and sampling distribution of the test statistics proposed are obtained. Pooled-bootstrap method also considered for Bartlett's modified likelihood ratio statistics.

• Bulletin of the Korean Mathematical Society
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• v.47 no.4
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• pp.815-823
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• 2010

Let ${\tau}\;{\neq}\;\delta_0$ be either a power bounded radial measure with compact support on the unit disc D with $\tau(D)\;=\;1$ such that there is a $\delta$ > 0 so that ${\mid}\hat{\tau}(s){\mid}\;{\neq}\;1$ for every $s\;{\in}\;\Sigma(\delta)$ \ {0,1}, or just a radial probability measure on D. Here, we provide a decomposition of the set X = {$h\;{\in}\;L^{\infty}(D)\;{\mid}\;lim_{n{\rightarrow}{\infty}}\;h\;*\;\tau^n$ exists}. Let $\tau_1$, ..., $\tau_n$ be measures on D with above mentioned properties. Here, we prove that if $f\;{in}\;L^{\infty}(D^n)$ satisfies an invariant volume mean value property with respect to $\tau_1$, ..., $\tau_n$, then f is n-harmonic.

• Journal of the Korean Ceramic Society
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• v.32 no.5
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• pp.635-641
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• 1995

The effects of A-site substitution with alkaline-earth ions (Ca, Sr and Ba) on the perovskite-phase formation and dielectric properties for Pb1-xMx(Zn1/3Nb2/3)O3 (0.0 x 0.5)-based relaxors were studied. Considerable improvements in the sinterability and the extent fo perovskite formation were observed with increasing the A-site substitution (x) and sintering temperature. The maximum dielectric permittivity appeared at x=0.1 for Sr and Ba substitutiion, while the relative dielectric permittivity was almost invariant in the case of Ca ion substitution. Curie temperature decreased with increasing relative amount of Sr and Ba ions but was almost invariant in case of Ca ion substitution. With increasing the amount of x, the diffuseness parameter ($\delta$) increased but the maximum dielectric constant decreased, demonstrating an enhanced diffuse phase transition (DPT) in the presence of alkaline-earth cations.

• Bulletin of the Korean Mathematical Society
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• v.33 no.1
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• pp.57-64
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• 1996

Let $(X, B, \mu)$ be a probability space. Then we say $\tau : X \to X$ is a measure-preserving transformation if $\mu(\tau^{-1} E) = \mu(E)$. and we call it an ergodic transformation if $\mu(\tau^{-1}E\DeltaE) = 0$ for a measurable subset E implies $\mu(E) = 0$. An equivalent definition is that constant functions are the only $\tau$-invariant functions.

• Journal of the Korean Mathematical Society
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• v.55 no.3
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• pp.593-604
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• 2018

Recently, a new version of expansiveness which is closely attached to some certain weak version of hyperbolicity was given for $C^1$ vector fields as following: a $C^1$ vector field X will be called rescaling expansive on a compact invariant set ${\Lambda}$ of X if for any ${\epsilon}$ > 0 there is ${\delta}$ > 0 such that, for any $x,\;y{\in}{\Lambda}$ and any time reparametrization ${\theta}:{\mathbb{R}}{\rightarrow}{\mathbb{R}}$, if $d({\varphi}_t(x),\,{\varphi}_{{\theta}(t)}(y)){\leq}{\delta}{\parallel}X({\varphi}_t(x)){\parallel}$ for all $t{\in}{\mathbb{R}}$, then ${\varphi}_{{\theta}(t)}(y){\in}{\varphi}_{(-{\epsilon},{\epsilon})}({\varphi}_t(x))$ for all $t{\in}{\mathbb{R}}$. In this paper, some equivalent definitions for rescaled expansiveness are given.

• The Journal of Asian Finance, Economics and Business
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• v.7 no.5
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• pp.291-304
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• 2020

This paper examines the factors that drive temporal income diversification in rural areas of the Mekong River Delta in Vietnam, based on a framework that conceptualized diversification as a function of a household's capacity to diversify and incentives (both push and pull factors) to diversify. Drawing from five rounds of the Vietnam Living Standard Measurement Surveys covering a 13-year span (1993-2006), two panel datasets made from five cross-sectional samples are used for the analyses. The data are drawn from the Vietnam General Statistics Office. Both tobit model and Ordinary Least Squares model with random and fixed effects are applied. The main points emerging from the analysis is that income diversification is strongly influenced by household labor capacity. The relationship between household labor capacity and increasing insertion in non-farming wage activities is not driven by unobserved time-invariant factors such as household ability and motivation, but is instead driven by the higher labor capacity of households. In terms of the other household capacity variables, the effect of farm size is much larger in terms of retaining households in traditional occupations as compared to pushing them towards non-farm wage employment. Other variables such as household access to financial capital do not play an important role.

• Journal of the Korean Crystal Growth and Crystal Technology
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• v.22 no.1
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• pp.29-35
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• 2012

Special attention in the role of convection in vapor crystal growth has been paid since some single crystals under high gravity acceleration of $10g_0$ appear considerably larger than those under normal gravity acceleration ($1g_0$). With increasing the gravity acceleration from $1g_0$ up to $10g_0$, the total molar flux for ${\Delta}T$ = 30 K increases by a factor of 4, while for ${\Delta}T$ = 90, by a factor of 3. The maximum molar fluxes for three different gravity levels of $1g_0$, $4g_0$ and $10g_0$, appear approximately in the neighborhood of y = 0.5 cm, and the molar fluxes show asymmetrical patterns, which indicate the occurrence of either one single or more than one convective cell. As the gravitational level is enhanced form $1g_0$ up to $10g_0$, the intensity of convection is increased significantly through the maximum molar fluxes for ${\Delta}T$ = 30 K and 90 K. At $10g_0$, the maximum total molar flux is nearly invariant for for ${\Delta}T$ = 30 K and 90 K. The total molar flux increases with increasing the gravity acceleration, for $1g_0{\leq}g_y{\leq}10g_0$, and decreases with increasing the partial pressure of component B, a noble gas called as Kr (Krypton), $P_B$. The ${{\mid}U{\mid}}_{max}$ is directly proportional to the gravity acceleration for 20 Torr $P_B{\leq}300$ Torr. As the partial pressure of $P_B$ (Torr) decreases from 300 Torr to 20 Torr, the slopes of the ${{\mid}U{\mid}}_{max}s$ versus the gravity accelerations increase from 0.29 sec to 0.54 sec, i.e. by a factor of 2. The total molar flux of $Hg_2Cl_2$ is first order exponentially decayed with increasing the partial pressure of component B, $P_B$ (Torr) from 20 Torr up to 300 Torr.

• Journal of Institute of Control, Robotics and Systems
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• v.17 no.4
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• pp.289-294
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• 2011

Digital redesign is yet another efficient tool to convert a pre-designed analog controller into a sampled-data one to maintain the analog closed-loop performance in the sense of state matching. A rising difficulty in developing a digital redesign technique for trackers with time-varying references is the unavailability of a closed-form discrete-time model of a system, even if it is linear time-invariant. A way to resolve this is to approximate the time-varying reference as a piecewise constant one, which deteriorates the state matching performance. Another remedy may be to decrease a sampling period, which however could numerically destabilize the optimization-based digital redesign condition. In this paper, we develop a digital redesign condition for time-varying trackers by approximating the time-varying reference through a triangular hold and by introducing delta-operated discrete-time models. It is shown that the digitally redesigned sampled-data tracker recovers the performance of the pre-designed analog tracker under a fast sampling limit. Simulation results on the formation flying of satellites convincingly show the effectiveness of the development.