• Communications of the Korean Mathematical Society
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• v.39 no.3
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• pp.693-715
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• 2024

Let n ∈ ℕ, n ≥ 2. An element (x₁, . . . , x_n) ∈ Eⁿ is called a norming point of T ∈ 𝓛(ⁿE) if ||x₁|| = ··· = ||x_n|| = 1 and |T(x₁, . . . , x_n)| = ||T||, where 𝓛(ⁿE) denotes the space of all continuous n-linear forms on E. For T ∈ 𝓛(ⁿE), we define Norm(T) = {(x₁, . . . , x_n) ∈ Eⁿ : (x₁, . . . , x_n) is a norming point of T}. Norm(T) is called the norming set of T. Let $0{\leq}{\theta}{\leq}{\frac{{\pi}}{4}}$ and ${\ell}^2_{{\infty},{\theta}}={\mathbb{R}}^2$ with the rotated supremum norm $${\parallel}(x,y){\parallel}_{({\infty},{\theta})}={\max}\{{\mid}x\;cos\;{\theta}+y\;sin\;{\theta}{\mid},\;{\mid}x\;sin\;{\theta}-y\;cos\;{\theta}|\}$$. In this paper, we characterize the norming set of T ∈ 𝓛(ⁿℓ²_(∞,θ)). Using this result, we completely describe the norming set of T ∈ 𝓛_s(ⁿℓ²_(∞,θ)) for n = 3, 4, 5, where 𝓛_s(ⁿℓ²_(∞,θ)) denotes the space of all continuous symmetric n-linear forms on ℓ²_(∞,θ). We generalizes the results from [9] for n = 3 and ${\theta}={\frac{{\pi}}{4}}$.

• Journal of Korean Society for Atmospheric Environment
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• v.12 no.2
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• pp.141-149
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• 1996

Lateral dispersion parameter(.sigma.$_{y}$) which is an important factor in atmospheric dispersion can be estimated byusing wind direction fluctuation(.sigma.$_{\theta}$). In this paper, we studied the characteristics of the .sigma.$_{\theta}$ in the Chunchon basin and calculated the .sig- ma.$_{y}$ by using the .sigma.$_{\theta}$. We could find some characteristics of the .sigma.$_{\theta}$ which showed small value, when the atmospheric condition was in weak unstable (C class) and neutral (D class). Moreover, when the atmospheric stability was neutral, there was no difference of .sigma.$_{\theta}$ with wind speed. On the other hand, .sigma.$_{\theta}$ showed large values at the strong unstable (A class) and strong stable (F class) condition with low wind speed. In this case, the .sigma.$_{\theta}$ increased as long as averaging time due to the long-period wind direction fluctuation by the terrain effect. In the result of calculation of .sigma.$_{y}$, it was smaller than that of pasquill-Gifford curve. Especially, when the atmospheric condition was in a neutral and stable, .sigma.$_{y}$ showed small increment as the downwind distance increased.creased.

• Korean Journal of Materials Research
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• v.5 no.2
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• pp.184-190
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• 1995

IN 617 was crept under stresses of 107 and 180 MPa with monotonic deformation to strains of $\varepsilon$= 0.03 - 0.30 at 1073K. In order to determine the distances between the subgrain boundaries, the deformed specimens were examined at magnifications of one hundred thousand times by TEM. In cases . where TEM observations were not possible, subgrain angles($\theta$_{s}=sin^{-1}$(b/s))were measured by Kikuchi diffraction lines. The $\theta$_{k}$ converted from s values measured directly by TEM agreed very well with those measured from Kikuchi lines. Therefore, it was found that the $\theta$_{k}$ values could be used in obtaining s, especially in cases where it is impossible to measure s by TEM.

• Fashion & Textile Research Journal
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• v.1 no.4
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• pp.387-392
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• 1999

The effects of the ratio of warp diameter to filling diameter (${\beta}$-ratio) and warp thread crash on the crimp factor and the yarn curvature were studied theoretically in this paper. The models of 2/2 twill fabric derived square cloth and sinusoidal curved cloth were used for the theoretical analysis. The crimp factors (C) for the models were given theoretically as follows; (1) Derived square cloth(general equation for b) $$C=\frac{(1+{\beta})({\theta}-sin{\theta})}{(1+{\beta})sin{\theta}+{\alpha}}$$ (2) Sihusoidal curved cloth $$C=\frac{(1+{\beta})sin{\theta}\[1+\{\frac{{\pi}(1-cos{\theta})}{4sin{\theta}}\}^2\]+{\alpha}}{(1+{\beta})sin{\theta}+{\alpha}}-1$$ The curvatures(${\kappa}$) for the models were given theoretically as follows; (1) Derived square cloth $${\kappa}=\frac{2}{d_w+d_f}$$ (2) Sinusoidal curved cloth $${\kappa}=\|{^{\;\;\prime\prime} \atop r}(s)\| \\ where \;s=\frac{p^'}{{\pi}}\(u+\frac{k^2u}{4}+\frac{k^2}{8}sin2u\)$$.

• Transactions of the Korean Society of Mechanical Engineers
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• v.16 no.4
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• pp.649-657
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• 1992

Transmission error for a stepping motor-timing belt drive system is investigated experimentally and analytically. From FFT analysis of the experimental results, it is found that the transmission error consists of three periodic errors : (1) error by the stepping motor per one resolution angle theta.$_{m}$, (2) error by the pulley eccentricity per one revolution theta.$_{e}$, and (3) error by the meshing effect between the belt and the pulley teeth per one pitch revoltion theta.$_{p}$. In order to investigate the effects of some design parameters on the transmission error, the dynamic models of the stepping motor-timing belt drive system are derived by Bondgraph. According to the simulation results, as the belt total tension increases, theta.$_{m}$ and theta.$_{e}$ decrease due to the nonlinearity of the belt. In adition, the numerical and experimental results show that theta.$_{m}$ and theta.$_{e}$ of the loaded case are larger than those of the unloaded case. The analytical results are in good accordance with the experimental results.sults.s.sults.

• Korean Journal of Mathematics
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• v.21 no.4
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• pp.429-437
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• 2013

Let $X_1$, $X_2$, ${\cdots}$, $X_n$ be independent and identically distributed random variables having common exponential density with unknown mean ${\mu}$. In the sequential confidence interval estimation for the exponential hazard rate ${\theta}=1/{\mu}$, when the loss function is strictly convex, the following stopping rule is proposed with the half length d of prescribed confidence interval $I_n$ for the parameter ${\theta}$; ${\tau}$ = smallest integer n such that $n{\geq}z^2_{{\alpha}/2}\hat{\theta}^2/d^2+2$, where $\hat{\theta}=(n-1)\bar{X}{_n}^{-1}/n$ is the minimum risk estimator for ${\theta}$ and $z_{{\alpha}/2}$ is defined by $P({\mid}Z{\mid}{\leq}{\alpha}/2)=1-{\alpha}({\alpha}{\in}(0,1))$ Z ~ N(0, 1). For the confidence intervals $I_n$ which is required to satisfy $P({\theta}{\in}I_n){\geq}1-{\alpha}$. These estimated intervals $I_{\tau}$ have the asymptotic consistency of the sequential procedure; $$\lim_{d{\rightarrow}0}P({\theta}{\in}I_{\tau})=1-{\alpha}$$, where ${\alpha}{\in}(0,1)$ is given.

• Journal of the Korean Electrochemical Society
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• v.9 no.1
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• pp.19-28
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• 2006

The phase-shift method for determining the Langmuir, Frumkin, and Temkin adsorption isotherms ($\theta_H\;vs.\;E$) of H for the cathodic $H_2$ evolution reaction (HER) at a Pt/0.1 M KOH solution interface has been proposed and verified using cyclic voltammetric, differential pulse voltammetric, and electrochemical impedance techniques. At the Pt/0.1 M KOH solution interface, the Langmuir and Temkin adsorption isotherms ($\theta_H\;vs.\;E$), the equilibrium constants ($K_H=2.9X10^{-4}mol^{-1}$ for the Langmuir and $K_H=2.9X10^{-3}\exp(-4.6\theta_H)mol^{-1}$ for the Temkin adsorption isotherm), the interaction parameters (g=0 far the Langmuir and g=4.6 for the Temkin adsorption isotherm), the rate of change of the standard free energy of $\theta_H\;with\;\theta_H$ (r=11.4 kJ $mol^{-1}$ for g=4.6), and the standard free energies (${\Delta}G_{ads}^{\circ}=20.2kJ\;mol^{-1}$ for $k_H=2.9\times10^{-4}mol^{-1}$, i.e., the Langmuir adsorption isotherm, and $16.7<{\Delta}G_\theta^{\circ}<23.6kJ\;mol^{-1}$ for $K_H=2.9\times10^{-3}\exp(-4.6\theta_H)mol^{-1}$ and $0.2<\theta_H<0.8$, i.e., the Temkin adsorption isotherm) of H for the cathodic HER are determined using the phase-shift method. At intermediate values of $\theta_H$, i.e., $0.2<\theta_H<0.8$, the Temkin adsorption isotherm ($\theta_H\;vs.\;E$) corresponding to the Langmuir adsorption isotherm ($\theta_H\;vs.\;E$), and vice versa, is readily determined using the constant conversion factors. The phase-shift method and constant conversion factors are useful and effective for determining the Langmuir, Frumkin, and Temkin adsorption isotherms of intermediates for sequential reactions and related electrode kinetic and thermodynamic data at electrode catalyst interfaces.

• Korean Journal of Optics and Photonics
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• v.5 no.1
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• pp.74-79
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• 1994

The characteristics of the type I and type II SHG in LiB305 crystals grown by TSSG method have been investigated using 1064 nm beam from a Q-switched Nd:YAG laser. The measured phase matching angles and angular acceptance bandwidths were $\theta_m=90^{\circ}, \phi_m=11.6^{\circ}$, <$\delta\theta_{int}L_{1/2}=3.3^{\circ}-cm^{1/2}, \theta\phi_{int}L=0.27^{\circ}-cm^{1/2}$ for type I SHG and $\theta_m=20^{\circ}, \phi_m=90^{\circ}$, TEX>$\delta\theta_{int}L_=0.65^{\circ}-cm, \theta\phi_{int}L^{1/2}=3.5^{\circ}-cm^{1/2}$ for type II SHG, respectively. Thp. type I NCPM temperature of 1064 nm beam was found to be $149^{\circ}C$ with the temperature bandwidth $\DeltaTL$of $4.8^{\circ}C-cm$. An energy conversion efficiency of about 1.8% with 2.6 mm thick LBO crystal at an incident power of TEX>$171 MW/\textrm{cm}^2$ was demonstrated. The measured $d_{32} was 0.74\pm0.05 pm/V$..

• Biomedical Science Letters
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• v.6 no.2
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• pp.83-91
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• 2000

Subconfluent neonatal human epidermal keratinocytes were treated with a concentration 200 ng/$m\ell$ of human recombinant epidermal growth factor (hrEGF), human recombinant insulin-like growth factor-1 (hrIGF-1), and with a combination of hrEGF and hrIGF-1. Cytoplasmic and membrane-associated proteins were extracted and assayed. Proteins were separated by SDS-PAGE, and subjected to the western blot analysis. In the cytoplasmic fraction, the PKC concentration of keratinocyte treated with hrIGF-1 was higher than the control group, but the concentration of control group was the highest than the others in the membrane fraction. In the cytoplasmic fraction, EGF stimulated PKC-$\beta$II, -$\delta$, -$\theta$, and also stimulated PKC-$\alpha$, -$\beta$I, -$\delta$, -$\Im$ and -$\theta$ in the membrane fraction. IGF-1 stimulated PKC-$\beta$I, -$\Im$ and -$\theta$ in the cytoplasmic, PKC-$\alpha$, -$\beta$I, -$\delta$, -$\Im$, - $\varepsilon$ and -$\theta$ in the membrane. In the cells treated with a combination of EGF and IGF-1, PKC-$\alpha$, -$\beta$I, -$\Im$ and -$\theta$ in the cytoplasmic fraction, PKC-$\alpha$, -$\delta$, -$\Im$, -$\varepsilon$ and -$\theta$ in the membrane fraction were stimulated.

• Journal of the Korean Statistical Society
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• v.17 no.2
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• pp.81-92
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• 1988

We observe independent random variable $Y_i \sim N(\theta_i,1), i=1,2,\cdots,k$, and we are interested in detecting the treatment with the largest $\theta_i$. We consider a procedure which infers $\theta_{(k)} \geq max\theta_i (i\neq(k))$ whenever $Y_{(k)} \geq maxY_i+C (i\neq(k))$. The maximum probability of a false inference is found, and it is shown that the inference can be made with the two-sample one-sided critical value for the usual error levels. The result also holds in the case of common unknown variance.