• Journal of applied mathematics & informatics
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• v.28 no.3_4
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• pp.977-986
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• 2010

Let $X_1$, $X_2$, $\cdots$ be identically distributed negatively associated random variables with $EX_1\;=\;0$ and $E|X_1|^3$ < $\infty$. In this paper we prove $lim_{{\epsilon\downarrow}0}\;\frac{1}{-\log\;\epsilon}\sum\limits_{n=1}^\infty\frac{1}{n^2}ES_n^2I\{|S_n|\;{\geq}\;{\sigma\epsilon}n\}\;=\;2$ and $lim_{\epsilon\downarrow0}\;\epsilon^{2-p}\sum\limits_{n=1}^\infty\frac{1}{n^p}$ $E|S_n|^pI\{|S_n|\;{\geq}\;{\sigma\epsilon}n\}\;=\;\frac{2}{2-p}$ for 0 < p < 2, where $S_n\;=\;\sum\limits_{i=1}^{n}X_i$ and 0 < $\sigma^2\;=\;EX_1^2\;+\;\sum\limits_{i=2}^{\infty}Cov(X_1,\;X_i)$ < $\infty$. We consider some results of i.i.d. random variables obtained by Liu and Lin(2006) under negative association assumption.

• Bulletin of the Korean Chemical Society
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• v.27 no.5
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• pp.718-724
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• 2006

The heterogeneous association behaviour of various concentration binary mixtures of mono alkyl ethers of ethylene glycol with ethyl alcohol were investigated by dielectric measurement in benzene solutions over the entire concentration range at 25 ${^{\circ}C}$. The values of static dielectric constant $\epsilon_0$ of the mixtures were measured at 1 MHz using a four terminal dielectric liquid test fixture and precision LCR meter. The high frequency limiting dielectric constant $\epsilon_\infty$ values were determined by measurement of refractive index $n_D$ ($\epsilon_\infty\;=\;n_D\;^2$). The measured values of $\epsilon_0$ and $\epsilon_\infty$ were used to evaluate the values of excess dielectric constant $\epsilon^E$, effective Kirkwood correlation factor $g^{eff}$ and corrective correlation factor $g_f$ of the binary polar mixtures to obtain qualitative and quantitative information about the H-bond complex formation. The non-linear behaviour of the observed $\epsilon_0$ values of the polar molecules and their mixtures in benzene solvent confirms the variation in the associated structures with change in polar mixture constituents concentration and also by dilution in non-polar solvents. Appearance of the maximum in $\epsilon^E$ values at different concentration of the polar mixtures suggest the formation of stable adduct complex, which depends on the molecular size of the mono alkyl ethers of ethylene glycol. Further, the observed $\epsilon^E$ < 0 also confirms the heterogeneous H-bond complex formation reduces the effective number of dipoles in these polar binary mixtures. In benzene solutions these polar molecules shows the maximum reduce in effective number of dipoles at 50 percent dilutions. But ethyl alcohol rich binary polar mixtures in benzene solvent show the maximum reduce in effective number of dipoles in benzene rich solutions.

• Proceedings of the KIEE Conference
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• 1994.07b
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• pp.1289-1291
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• 1994

Dielectric properties of $C_{22}$-Quinolium(TCNQ) Langmuir-Blodgett (LB) films were studied as a function of frequency(10Hz-13MHz) and annealing temperature($20{\sim}240^{\circ}C$). A complex dielectric constant ${\epsilon}^*={\epsilon}'-i{\epsilon}"$, in general, shows the frequency dependence of orientational polarization in the measured frequency range. A dielectric permittivity ${\epsilon}'$ at 10Hz is around 8.2 and decreases very slowly as the frequency increases up to 1 MHz, and then suddenly drops above this frequency, while a dielectric loss factor ${\epsilon}"$ reaches a maximum near 1 MHz. Its annealing temperature dependence at 10Hz shows that ${\epsilon}'$ and ${\epsilon}"$ increase as the temperature increases upto $180^{\circ}C$, even though there is a little drop near $120{\sim}160^{\circ}C$. Both ${\epsilon}'$ and ${\epsilon}"$ drop quickly above $180^{\circ}C$. which may be thought of a destruction of the LB films. Another fact of the annealing temperature dependence of the dielectric constant is an occurrence of the new dielectric dispersion below 100Hz. This low frequency dispersion is getting clear above $80^{\circ}C$.

• Communications of the Korean Mathematical Society
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• v.33 no.3
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• pp.1025-1037
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• 2018

We consider an ill-posed problem for the heat equation $u_{xx}=u_t$ in the quarter plane {x > 0, t > 0}. We propose a new method to compute the heat flux $h(t)=u_x(1,t)$ from the boundary temperature g(t) = u(1, t). The operator $g{\mapsto}h=Hg$ is unbounded in $L^2({\mathbb{R}})$, so we approximate h(t) by $h_{\delta}(t)=u_x(1+{\delta},\;t)$, ${\delta}{\rightarrow}0$. When noise is present, the data is $g_{\epsilon}$ leading to a corresponding heat $h_{{\delta},{\epsilon}}$. We obtain an estimate of the error ${\parallel}h-h_{{\delta},{\epsilon}}{\parallel}$, as well as the error when $h_{{\delta},{\epsilon}}$ is approximated by the trapezoidal rule. With an a priori choice rule ${\delta}={\delta}({\epsilon})$ and ${\tau}={\tau}({\epsilon})$, the step size of the trapezoidal rule, the main theorem gives the error of the heat flux as a function of noise level ${\epsilon}$. Numerical examples show that the proposed method is effective and stable.

• Transactions of the Korean Society of Mechanical Engineers
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• v.9 no.1
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• pp.1-9
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• 1985

In-plane tension fatigue tests (R = 0.05) were carried out to investigate the initiation and propagation behaviors of micro-surface-fatigue cracks on smooth surfaces of a mild steel. Also, the investigations of saturated cyclic strain which can be obtained by the fatigue tests have been made via the cyclic strain intensity factor, .DELTA. $K_{\epsilon}$/, for the purpose of unifying two approaches of the study of fatigue; the one approach is based on the fracture mechanics concept and the other on lowcycle fatigue concept. Some of the results are as follows; The growth rate, d(2a)/dN, of small cracks cannot be represented by one straight line as a function of .DELTA.K for various of the nominal stress range, .DELTA..sigma., and is higher than that of a larger through crack. The rearrangement of the d(2a)/dN by .DELTA..epsilon..root..pi.s( = .DELTA. $K_{\epsilon}$/) with the stress range .DELTA..epsilon. in .DELTA.K replaced by .DELTA..epsilon., strain range, gives one straight line of the .DELTA. $K_{\epsilon}$-d(2a)/dN relation for various values of stress range .DELTA.$_{\epsilon}$../.X>../.

• Nuclear Engineering and Technology
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• v.36 no.3
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• pp.248-262
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• 2004

Turbulence models are separately assessed for a three dimensional thermal-hydraulic analysis of the integral reactor SMART. Seven models (mixing length, k-l, standard $k-{\epsilon},\;k-{\epsilon}-f{\mu},\;k-{\epsilon}-v2$, RRSM, and ERRSM) are investigated for flat plate channel flow, rotating channel flow, and square sectioned U-bend duct flow. The results of these models are compared to the DNS data and experiment data. The results are assessed in terms of many aspects such as economical efficiency, accuracy, theorization, and applicability. The standard $k-{\epsilon}$ model (high Reynolds model), the $k-{\epsilon}-v2$ model, and the ERRSM (low Reynolds models) are selected from the assessment results. The standard $k-{\epsilon}$ model using small grid numbers predicts the channel flow with higher accuracy in comparison with the other eddy viscosity models in the logarithmic layer. The elliptic-relaxation type models, $k-{\epsilon}-v2$, and ERRSM have the advantage of application to complex geometries and show good prediction for near wall flows.

• Journal of Power System Engineering
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• v.2 no.1
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• pp.31-38
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• 1998

A diffuser, an important equipment to change kinetic energy into pressure energy, has been studied for a long time. Though experimental and theoretical researches have been done, the understanding of energy transfer and detailed mechanism of energy dissipation is unclear. As far as numerical prediction of diffuser flows are concerned, various numerical studies have also been done. On the contrary, many turbulence models have constraint to the applicability of diffuser-like complex flows, because of anisotropy of turbulence near the wall and of local nonequilibrium induced by an adverse pressure gradient. The existing $k-{\epsilon}$ turbulence models have some problems in the case of being applied to complex turbulent flows. The purpose of this paper is to test the applicability of the nonlinear $k-{\epsilon}$ model concerning diffuser-like flows with expansion and streamline curvature. The results show that the nonlinear $k-{\epsilon}$ turbulence model predicted well the coefficient of pressure, velocity profiles and turbulent kinetic energy distributions, however the shear stress prediction was failed.

• Journal of applied mathematics & informatics
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• v.26 no.1_2
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• pp.375-381
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• 2008

Boundedness for the set of all the $\epsilon$-approximate solutions for convex optimization problems are considered. We give necessary and sufficient conditions for the sets of all the $\epsilon$-approximate solutions of a convex optimization problem involving finitely many convex functions and a convex semidefinite problem involving a linear matrix inequality to be bounded. Furthermore, we give examples illustrating our results for the boundedness.

• Transactions of the Korean Society of Mechanical Engineers
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• v.10 no.4
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• pp.487-493
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• 1986

본 연구에서는 K-.epsilon. 모델을 사용하여 마찰감소 현상이 있는 저어널베어링 내 의 흐름을 해석하였다.

• Korean Journal of Mathematics
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• v.28 no.3
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• pp.573-585
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• 2020

We introduced the concepts of the generalized accumulation points and the generalized density of a subset of the Euclidean space in [1] and [2]. Using those concepts, we introduce the concepts of the generalized closure, the generalized interior, the generalized exterior and the generalized boundary of a subset and investigate some properties of these sets. The generalized boundary of a subset is closely related to the classical boundary. Finally, we also introduce and study a concept of the thickness of a subset.