• Journal of the Korean Chemical Society
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• v.23 no.1
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• pp.37-41
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• 1979

The kinetics of the reaction of benzyl m-nitrobenzenesulfonate with m-and p-substituted N,N-dimethylanilines in acetone have been investigated by an electric conductivity method. The effects of substituents on the reactivity of N,N-dimethylaniline and the existence of linear free energy relationship were discussed. The rate constants k were in the range 2.55∼487 $10^{-4}l{\cdot}mol^{-l}{\cdot}sec^{-1} (35^{\circ}C)$ and increased with the electron donating ability of substituents. In the present reaction, the Hammett plot was correlated with ${\sigma}$ substituent constant, especially using the new ${\sigma}$ value of 0.35 in p-MeO and it's ${\rho}$ value was found to be -1.37. r value for the reaction was very large than the value obtained in the reaction of benzyl bromide. $Br{\"{o}}nsted$ linear relationship was shown between rate constant and basicites except for p-MeO resulted from solvent effect. From the Bronsted plot, this reaction was suggested that the cleavage of the C${\cdot}{\cdot}{\cdot}$O bond in the $S_N2$ transition state proceed the bond formation.

• Knee surgery & related research
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• v.30 no.4
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• pp.334-340
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• 2018

Purpose: The purposes of this study were to compare clinical results after total knee arthroplasty (TKA) using the Attune and PFC Sigma knee designs and to investigate whether the use of the Attune prosthesis increased the risk of patellar injury in Asian patients. Materials and Methods: Three hundred knees that underwent TKA using Attune (group A) were compared to 300 knees that underwent TKA using PFC Sigma (group B). The Knee Society Knee Score (KS) and Function Score (FS), and range of motion (ROM) were compared. The residual patellar thickness was compared to evaluate the risk of patellar injury. Results: The postoperative KS and ROM of group A were better than those of group B (93.1 vs. 88.8, p<0.001 and $131.4^{\circ}$ vs. $129.0^{\circ}$, p=0.008, respectively). The postoperative FS did not differ significantly between the two groups (80.9 vs. 78.7, p=0.427). The residual patella was thinner in group A (14.8 mm vs. 15.7 mm, p=0.003), which made up a higher proportion of the high-risk group for patellar fractures with a residual thickness of <12 mm (7.5% vs. 2.1%, p=0.003). Conclusions: TKA using the Attune prosthesis provided more favorable clinical results than TKA using PFC Sigma. However, the risk of injury in the residual patella was increased with use of the Attune prosthesis in Asian patients.

• Communications of the Korean Mathematical Society
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• v.10 no.4
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• pp.881-887
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• 1995

Let f be a measurable function on the unit ball B in $C^n$, then we define a maximal function $M_p(f), 1 \leq p < \infty$, by $$ M_p(f)(\zeta ) = \sup_{\delta > 0}(\frac{1}{\sigma(\beta(\zeta, \delta))} \int_{T(\beta(\zeta, \delta))} $\mid$f(z)$\mid$^p \frac{d\nu(z)}{(1-$\mid$z$\mid$^n})^{1/p} $$ where $\sigma$ denotes the surface area measure on S, the boundary of B, and $T(\beta(\zeta, \delta))$ denotes the tent over the ball $\beta(\zeta, \delta)$. We prove that the maximal operator $M_p$ belongs to the Muckenhoupt class $A_1$.

• Honam Mathematical Journal
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• v.30 no.1
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• pp.9-20
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• 2008

Let ${X_i{\mid}i{\geq}1}$ be a strictly stationary sequence of associated random variables with mean zero and let ${\sigma}^2=EX_1^2+2\sum\limits_{j=2}^\infty{EX_1}{X_j}$ with 0 < ${\sigma}^2$ < ${\infty}$. Set $S_n={\sum\limits^n_{i=1}^\{X_i}$, the precise asymptotics for ${\varepsilon}^{{\frac{2(r-p)}{2-p}}-1}\sum\limits_{n{\geq}1}n^{{\frac{r}{p}}-{\frac{1}{p}}+{\frac{1}{2}}}P({\mid}S_n{\mid}{\geq}{\varepsilon}n^{{\frac{1}{p}}})$,${\varepsilon}^2\sum\limits_{n{\geq}3}{\frac{1}{nlogn}}p({\mid}Sn{\mid}{\geq}{\varepsilon\sqrt{nloglogn}})$ and ${\varepsilon}^{2{\delta}+2}\sum\limits_{n{\geq}1}{\frac{(loglogn)^{\delta}}{nlogn}}p({\mid}S_n{\mid}{\geq}{\varepsilon\sqrt{nloglogn}})$ as ${\varepsilon}{\searrow}0$ are established under the suitable conditions.

• Communications of the Korean Mathematical Society
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• v.32 no.4
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• pp.971-977
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• 2017

For $p{\in}{\mathbb{N}}^{\ast}$ let ${\Sigma}_{p,0}$ denote the class of meromorphic functions of the form $g(z) ={\frac{1}{z^p}}+a_0+a_1z+{\cdots}$, $z{\in}U$. In the present paper we introduce a new subclass of the class ${\Sigma}_{p,0}$, using the subordination and the operator $J^n_{p,{\lambda}}$. This class will be denoted by $B^n_{p,{\lambda}}({\alpha},h)$ and we study some inclusion properties of this subclass.

• Journal of the Korean Mathematical Society
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• v.56 no.4
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• pp.985-1000
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• 2019

Let k be an integer with $k{\geq}3$. Define $h(k)=[{\frac{k+1}{2}}]$, ${\sigma}(k)={\min}\(2^{h(k)-1},\;{\frac{1}{2}}h(k)(h(k)+1)\)$. Suppose that ${\lambda}_1,{\ldots},{\lambda}_5$ are non-zero real numbers, not all of the same sign, satisfying that ${\frac{{\lambda}_1}{{\lambda}_2}}$ is irrational. Then for any given real number ${\eta}$ and ${\varepsilon}>0$, the inequality $${\mid}{\lambda}_1p^2_1+{\lambda}_2p^2_2+{\lambda}_3p^2_3+{\lambda}_4p^2_4+{\lambda}_5p^k_5+{\eta}{\mid}<({\max_{1{\leq}j{\leq}5}}p_j)^{-{\frac{3}{20{\sigma}(k)}}+{\varepsilon}}$$ has infinitely many solutions in prime variables $p_1,{\ldots},p_5$. This gives an improvement of the recent results.

• Korean Journal of Mathematics
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• v.13 no.1
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• pp.43-50
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• 2005

We introduce the Joint spectrum on the complex Banach space and on the complex Hilbert space and the tensor product spectrums on the tensor product spaces. And we will show ${\sigma}[P(T_1,T_2,{\ldots},T_n)]={\sigma}(T_1{\otimes}T_2{\otimes}{\cdots}{\otimes}T_n)$ on $X_1{\overline{\otimes}}X_2{\overline{\otimes}}{\cdots}{\overline{\otimes}}X_n$ for a polynomial P.

• Journal of the Korean Statistical Society
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• v.19 no.2
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• pp.182-185
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• 1990

Let a p-component vector y have a p-variate normal distribution $N(b\theta, \Sigma), \Sigma$ unknown, b specified, then for testing $\theta = 0$ against general $\theta$, Khatri and Rao (1987) derive a certain t test and obtain its power function. This paper presents a direct derivation of this power function in terms of the original variates unlike Khatri and Rao (1987) who resort to the canonical transformations of the original variates and the conditional distributions.

• Bulletin of the Korean Mathematical Society
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• v.33 no.1
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• pp.29-33
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• 1996

In this paper we shall generalize a Clary theorem by using the local spectral theory; If $ T \in L(H)$ has property $(\beta)$ and A is any operator such that $A \prec T$, then $\sigma(T) \subseteq \sigma(A)$.

• The Korean Journal of Applied Statistics
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• v.23 no.6
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• pp.1035-1045
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• 2010

Products and/or services should be objectively verified in terms of the technological and use-conditional considerations before entering a market. Every organization or company tries to find the better procedure and method for checking the core needs of customers based on their experience in the market and looks for continuous ways to evaluate the power of products and services(PoP). They also prefer the overall evaluation of indices that could reflect various customer needs, rather than a separate evaluation index for each characteristic of the product or service. S. Ko (2008) proposes a Multi-characteristics Sigma Level(MSL) that can simultaneously evaluate many characteristics of a product or service. In this research, using MSL and a new Blue Ocean Index(BOI), an application of NPS, mobile phone field test is considered from a practical and statistical point of view.