• Communications for Statistical Applications and Methods
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• v.16 no.5
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• pp.841-849
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• 2009

Let {$X_n$, n ${\ge}$ 1} be a negatively associated sequence of identically distributed random variables with mean zeros and positive finite variances. Set $S_n$ = ${\Sigma}^n_{i=1}\;X_i$. Suppose that 0 < ${\sigma}^2=EX^2_1+2{\Sigma}^{\infty}_{i=2}\;Cov(X_1,\;X_i)$ < ${\infty}$. We prove that, if $EX^2_1(log^+{\mid}X_1{\mid})^{\delta}$ < ${\infty}$ for any 0< ${\delta}{\le}1$, then $\lim_{{\epsilon}\downarrow0}{\epsilon}^{2{\delta}}\sum_{{n=2}}^{\infty}\frac{(logn)^{\delta-1}}{n^2}ES^2_nI({\mid}S_n{\mid}\geq{\epsilon}{\sigma}\sqrt{nlogn}=\frac{E{\mid}N{\mid}^{2\delta+2}}{\delta}$, where N is the standard normal random variable. We also prove that if $S_n$ is replaced by $M_n=max_{1{\le}k{\le}n}{\mid}S_k{\mid}$ then the precise rate still holds. Some results in Fu and Zhang (2007) are improved to the complete moment case.

• Journal of the Korean earth science society
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• v.27 no.6
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• pp.695-700
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• 2006

We present B, V, I time series CCD photometry for the variable star TU UMi to classify its variable type. The observations were performed using 61cm telescope equipped with 2K CCD camera at Sobaeksan Optical Astronomy Observatory (SOAO). Judging from the amplitude ratio $({\Delta}i/{\Delta}v)$ and color variation $({\Delta}(b-v),\;{\Delta}(v-i))$. TU UMi should be a W UMa type eclipsing binary. We obtained two primary times of minimum lights (HJD 2453848.0446, HJD 2453848.2309) from our observations and determined new orbital elements (Min I=HJD 2452500.1344+0.37708907${\times}$E) for TU UMi.

• Journal of the Korean Chemical Society
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• v.53 no.2
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• pp.118-124
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• 2009

The values of critical micelle concentration (CMC) and counter ion binding constants (B) in a micellar state of CPC (1-hexadecylpyridinium chloride) with Brij 35 (polyoxyethylene(23) lauryl ether) in water were determined as a function of ${\alpha}_1$ (the overall mole fraction of CPC) by the use of electric conductivity method. Various thermodynamic parameters ($X_i,\;{\gamma}_i,\;C_i,\;a_{i}^{M},\;\beta,\;and\;{\Delta}H_{mix}$) were calculated and analyzed by means of the equations derived from the non-ideal mixed micellar model. And thermodynamic parameters (${\Delta}{G^o}_m,\;{\Delta}{H^o}_m,\;and\;{\Delta}{S^o}_m$) for the micellization of CPC/Brij 35 mixtures were also calculated from the temperature dependence of the CMC values. The values of ${\Delta}{G^o}_m$ are all negative, but the values of ${\Delta}{S^o}_m$ and ${\Delta}{H^o}_m$ are positive or negative, depending on the measured temperature and ${\alpha}_1$.

• Journal of Environmental Health Sciences
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• v.10 no.1
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• pp.1-12
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• 1984

The stochastic characteristics of the daily range of water temperature variation was analyzed by employing the techniques of autocorrelation coefficient, autoreggresive model and crosscorrelation model. These time series included daily observations on maximum and minimum values of water temperature and air temperature. The measurement was made by automatic recording instrument at Gu-yee and Dook-do in Han River, and at Waegwan and Gu-mi in Nackdong River in 1981. As a result of this study, it was found that (1) The correlogram of daily water temperature ranges $\Delta AT_i$ and daily air temperature $\Delta AT_i$ at Gu-mi and Gu-yee showed the exponential curves. (2) The most high frequency values of $\Delta AT_i$ and $\Delta WT_i$ were 11$\circ$C and 0.5${\circ}C$ respectively at every measuring site. (3) The correlation coefficients between the daily mean air temperature AT$_i$ and the daily mean water temperature were fairly high as 0.966 at Dook-do and 0.949 at Gu-yee, but the correlation coefficients between $\Delta AT_i$ and $\Delta WT_i$ were very low as 0.1074 at Gu-yee and 0.0324 at Dook-Do.

• Journal of the Korean Mathematical Society
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• v.47 no.1
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• pp.135-163
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• 2010

Motivated by [Science in China (Ser. A Mathematics) 36 (2006), no. 7, 721?732], this article deals with the following discrete type BVP $\LARGE\left\{{{\;{\Delta}[{\phi}({\Delta}x(n))]\;+\;f(n,\;x(n\;+\;1),{\Delta}x(n),{\Delta}x(n + 1))\;=\;0,\;n\;{\in}\;[0,N],}}\\{\;{x(0)-{\sum}^m_{i=1}{\alpha}_ix(n_i) = A,}}\\{\;{x(N+2)-\;{\sum}^m_{i=1}{\beta}_ix(n_i)\;=\;B.}}\right.$ The sufficient conditions to guarantee the existence of at least three positive solutions of the above multi-point boundary value problem are established by using a new fixed point theorem obtained in [5]. An example is presented to illustrate the main result. It is the purpose of this paper to show that the approach to get positive solutions of BVPs by using multifixed-point theorems can be extended to treat nonhomogeneous BVPs. The emphasis is put on the nonlinear term f involved with the first order delta operator ${\Delta}$x(n).

• Journal of the Korean Mathematical Society
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• v.55 no.6
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• pp.1381-1388
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• 2018

Let ${\Delta}$ be a simplicial complex, $I_{\Delta}$ its Stanley-Reisner ideal and $K[{\Delta}]$ its Stanley-Reisner ring over a field K. Assume that ${\Gamma}(R)$ denotes the zero-divisor graph of a commutative ring R. Here, first we present a condition on two reduced Noetherian rings R and R', equivalent to ${\Gamma}(R){\cong}{\Gamma}(R{^{\prime}})$. In particular, we show that ${\Gamma}(K[{\Delta}]){\cong}{\Gamma}(K^{\prime}[{\Delta}^{\prime}])$ if and only if ${\mid}Ass(I_{\Delta}){\mid}={\mid}Ass(I_{{{\Delta}^{\prime}}}){\mid}$ and either ${\mid}K{\mid}$, ${\mid}K^{\prime}{\mid}{\leq}{\aleph}_0$ or ${\mid}K{\mid}={\mid}K^{\prime}{\mid}$. This shows that ${\Gamma}(K[{\Delta}])$ contains little information about $K[{\Delta}]$. Then, we define the squarefree zero-divisor graph of $K[{\Delta}]$, denoted by ${\Gamma}_{sf}(K[{\Delta}])$, and prove that ${\Gamma}_{sf}(K[{\Delta}){\cong}{\Gamma}_{sf}(K[{\Delta}^{\prime}])$ if and only if $K[{\Delta}]{\cong}K[{\Delta}^{\prime}]$. Moreover, we show how to find dim $K[{\Delta}]$ and ${\mid}Ass(K[{\Delta}]){\mid}$ from ${\Gamma}_{sf}(K[{\Delta}])$.

• The Journal of the Petrological Society of Korea
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• v.27 no.1
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• pp.1-15
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• 2018

The characteristics of the rock cleavage of Jurassic Geochang granite were analysed using the distribution of microcrack lengths and spacings. The length and spacing-cumulative diagrams for the six directions of rock cleavages were arranged in increasing order ($H2{\rightarrow}R1$) on the density (${\rho}$) of microcrack length. The various parameters were extracted through the combination of above two types of diagrams. The evaluation for the six directions of rock cleavages was performed using the four groups (I~IV) of parameters such as (I) intersection angle (${\alpha}-{\beta}$), exponent difference (${\lambda}_S-{\lambda}_L$), length of line (ol and ll'), length ratio (ol/os and ll'/sl'), mean length ((ss'+ll')/2), area of right-angled triangle (${\Delta}oaa_a^{\prime}$ and ${\Delta}obb_a^{\prime}$) and area difference (${\Delta}obb^{\prime}-{\Delta}oaa^{\prime}$ and ${\Delta}obb_a^{\prime}-{\Delta}oaa_a^{\prime}$), (II) length of line (oa and os) and area (${\Delta}oaa^{\prime}$), (III) length of line (sl') and length ratio (ss'/ll') and (IV) length of line (ob, ss' and ls') and area (${\Delta}obb^{\prime}$, ${\Delta}ll^{\prime}s^{\prime}$, ${\Delta}ss^{\prime}l^{\prime}$ and ⏢ll'ss'). The results of correlation analysis between the values of parameters for three rock cleavages and those for three planes are as follows. The values of parameters for three rock cleavages are in orders of (I) H(hardway, (H1 + H2)/2) < G(grain, (G1 + G2)/2) < R(rift, (R1 + R2)/2), (II) R < G < H, (III) G < H < R and (IV) H < G < R. On the contrary, the values of parameters for three planes are in orders of (I) R' < G' < H', (II) H' < G' < R' and (III and IV) R' < H' < G'. Especially the values of parameters belonging to group I and group II show mutual reverse orders. In conclusion, this type of correlation analysis is useful for discriminating three quarrying planes.

• YAKHAK HOEJI
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• v.23 no.1
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• pp.51-55
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• 1979

"Ha-Neul-Ta-Ri" (Trichosanthes kirilowii Max., Cucurbitaceae) cultivated in Korea and used in popular medicine, was investigated for sterol composition of the seed oil. This seed oil contains unusual sterols having ${\delta}^{7, 22}_-$, ${\delta}^{7, 24}_-$ and ${\delta}^{7, 22, 25}_-$ di and trienols. ${\delta}^{7, 22}_-$ Stigmastadienol and ${\delta}^{7, 22, 25}_-$ Stigmastatrienol were identified as the major sterols in the seed oil of Trichosanthes kirilowii by gas loiquid chromatographic analysis. The results showed that contents of the seed sterols were campesterol 1.0-1.2%, stigmasterol 1.5-1.7%, ${\delta}^{7}_-$ campstenol 0.6-0.8%, sitosterol 10.6-11.4%, ${\delta}^{7, 22}_-$ stigmastadienol 39.1-41.8%, ${\delta}^{7, 22, 25}_-$ stigmastatrienol 28.9-29.3%, ${\delta}^{7, 25}_-$ stigmastadienol 14.9-15.5% and ${\delta}^{7, 24}_-$ stigmastadienol 0.7-1.0%.

• Journal of the korean academy of Pediatric Dentistry
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• v.39 no.3
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• pp.257-266
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• 2012

The objective of this in vitro study was to monitor the amount of remineralization of decalcified enamel according to the number of fluoride varnish application using quantitative light-induced fluorescence-D and polarizing microscope. Artificial white lesion induced on the sound 72 teeth, $CavityShield^{TM}$ (Group I), $FluroDose^{TM}$ (Group II) and $Flor-Opal^{(R)}$ Varnish (Group III) were applied 1, 2 or 3 times every two weeks. The following results was obtained: 1. In group I, II and III, ${\Delta}L$ were increased. From regression analysis of ${\Delta}L$ by the number of application, the equation was y = 3.878x + 90.612 in group I, y = 3.133x + 37.168 in group II, and y = 3.509x + 82.322 in group III(p < 0.05). 2. In group I, II and III, ${\Delta}D$ were decreased. From regression analysis of ${\Delta}D$ by the number of application, the equation was y = -2.336x + 107.235 in group I, y = -2.158x + 101.620 in group II, and y = -1.940x + 94.806 in group III(p < 0.05). 3. The Pearson correlation value between the ${\Delta}L$ and ${\Delta}D$ was -0.673 in group I, -0.574 in group II, and -0.431 in group III(p < 0.05).

• Journal of Electrical Engineering and Technology
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• v.6 no.3
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• pp.384-390
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• 2011

To evaluate the condition of stator winding insulation in generators that have been operated for a long period of time, diagnostic tests were performed on the stator bars of a 500 MW, 22 kV generator under accelerated thermal and electrical aging procedures. The tests included measurements of AC current (${\Delta}I$), dissipation factor ($tan{\delta}$), partial discharge (PD) magnitude, and capacitance (C). In addition, the AC current test was performed on the stator winding of a 350 MW, 24 kV generator under operation to confirm insulation deterioration. The values of ${\Delta}I$, ${\Delta}tan{\delta}$, and PD magnitude in one stator bar indicated serious insulation deterioration. In another stator bar, the ${\Delta}I$ measurements showed that the insulation was in good condition, whereas the values of ${\Delta}tan{\delta}$ and PD magnitude indicated an incipient stage of insulation deterioration. Measurements of ${\Delta}I$ and PD magnitude in all three phases (A, B, C) of the remaining generator stator windings showed that they were in good condition, although the ${\Delta}tan{\delta}$ measurements suggested that the condition of the insulation should be monitored carefully. Overall analysis of the results suggested that the generator stator windings were in good condition. The patterns of PD magnitude in all three phases (A, B, C) were attributed to internal discharge.