• Communications for Statistical Applications and Methods
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• v.17 no.4
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• pp.507-513
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• 2010

Let {$X_i,-{\infty}$ < 1 < $\infty$} be a doubly infinite sequence of identically distributed and negatively associated random variables with mean zero and finite variance and {$a_i,\;-{\infty}$ < i < ${\infty}$} be an absolutely summable sequence of real numbers. Define a moving average process as $Y_n={\sum}_{i=-\infty}^{\infty}a_{i+n}X_i$, n $\geq$ 1 and $S_n=Y_1+{\cdots}+Y_n$. In this paper we prove that E|$X_1$|$^rh$($|X_1|^p$) < $\infty$ implies ${\sum}_{n=1}^{\infty}n^{r/p-2-q/p}h(n)E{max_{1{\leq}k{\leq}n}|S_k|-{\epsilon}n^{1/p}}{_+^q}<{\infty}$ and ${\sum}_{n=1}^{\infty}n^{r/p-2}h(n)E{sup_{k{\leq}n}|k^{-1/p}S_k|-{\epsilon}}{_+^q}<{\infty}$ for all ${\epsilon}$ > 0 and all q > 0, where h(x) > 0 (x > 0) is a slowly varying function, 1 ${\leq}$ p < 2 and r > 1 + p/2.

• Honam Mathematical Journal
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• v.42 no.1
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• pp.139-150
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• 2020

Let p be a prime number with p > 3, p ≡ 3 (mod 4) and let n be a positive integer. In this paper, we prove that the Diophantine equation (5pn² - 1)^x + (p(p - 5)n² + 1)^y = (pn)^z has only the positive integer solution (x, y, z) = (1, 1, 2) where pn ≡ ±1 (mod 5). As an another result, we show that the Diophantine equation (35n² - 1)^x + (14n² + 1)^y = (7n)^z has only the positive integer solution (x, y, z) = (1, 1, 2) where n ≡ ±3 (mod 5) or 5 | n. On the proofs, we use the properties of Jacobi symbol and Baker's method.

• The Journal of the Korea Contents Association
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• v.10 no.8
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• pp.274-282
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• 2010

The purpose of this study was to examine the types of implant, the type of bone graft, periodontal status and the distribution of implant among patients in a region. The subjects in this study were 299 patients who received implant treatment Busan area. The number of their implants was 871 in total. The findings of the study were as follows: As for the type of implant, home-made implants accounted for 83.6 percent, and imported ones represented 16.4 percent. Regarding bone graft, The presence or absence of disease made a significant difference to that($x^2$=14.66, p<.01). As to periodontal status by gender, age and disease, the periodontal state was better among those who were female(y=-2.73, p<.01), who were younger(F=14.20, p<.001) and who had no disease(t=-4.67, p<.001). The intergroup gaps were statistically significant. Concerning the distribution of implant, The distribution of implant was statistically significantly different($x^2$=33.14, p<.01). Age made a statistically significant difference to that($x^2$=74.09, p<.001). As to links between periodontal status and the number of implant, The intergroup gaps were statistically significant($x^2$=38.28, p<.01).

• Food Science of Animal Resources
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• v.32 no.5
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• pp.678-684
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• 2012

The melanin pigment in human skin is a major defense mechanism against ultraviolet light to the skin, but darken skin color. Tyrosinase is mainly responsible for melanin biosynthesis (melanogenesis) in animals and enzymatic browning (melanosis) in plants. The purpose of this study was to optimize the fermented milk process for the melanin formation inhibition by using Lactobacillus plantarum M23 with tyrosinase inhibitory activity. We used 4-factor-3-level central composite design combining with response surface methodology. Yeast extract concentration (%, $X_1$), addition of grape (%, $X_2$), incubation temperature ($^{\circ}C$, $X_3$) and incubation time (h, $X_4$) was used as an independent factor, on the other hand, pH (pH, $Y_1$), overall palatability (score, $Y_2$) and tyrosinase inhibitory activity (%, $Y_3$) was used as a dependant factor. Based on the optimization for the highest tyrosinase inhibitory activity with pH 4.4, the expected data of pH, palatability and tyrosinase inhibitory activity with 14.8 h incubation at $37.1^{\circ}C$ by the addition of 0.127% of yeast extract, 2.95% of grape was 4.42, 7.06 and 86.65%, but the real data was 4.35, 6.86 and 84.05%, respectively. Based on the previous results, fermented milk using Lactobacillus plantarum M23 with the tyrosinase inhibitory activity could contribute for the whitening and antiaging of human skin.

• Bulletin of the Korean Chemical Society
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• v.32 no.8
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• pp.2711-2716
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• 2011

para-Substituted phenoxide derivatives of Pd(II) having an NCN pincer, Pd(NCN)($OC_6H_4$-p-X) (NCN = 2,6-$(CH_2NMe_2)_2C_6H_3$; X = $NO_2$ (1), Me (2)) were prepared by the reaction of Pd(NCN)($OSO_2CF_3$) with equi-molar amount of $NaOC_6H_4$-p-X. Treatment of Pd(NCN)($OSO_2CF_3$) with an excess amount of $NaOC_6H_4$-p-Me affords the hydrogen-bonding adduct complex 3 ($2{\cdot}HOC_6H_4$-p-Me). Complex 3 can also be obtained from benzene solution of 2 in the presence of free $HOC_6H_4$-p-Me. Complex 1 does not undergo adduct formation with $HOC_6H_4-p-NO_2$ neither from metathesis reaction of Pd(NCN)($OSO_2CF_3$) with an excess amount of $NaOC_6H_4-p-NO_2$ nor from treatment of 1 with free $HOC_6H_4-p-NO_2$. Complex 3 undergoes fast exchange of the coordinated p-cresolate with the hydrogen-bonding p-cresol. Complex 2 undergoes ${\sigma}$-ligand exchange reaction with $HOC_6H_4-p-NO_2$ to give 1. The exchange reaction, however, is irreversible as readily anticipated from their respective $pK_a$ values of the phenol derivatives. Reaction of 2 with diphenyliodium chloride quantitatively produced Pd(NCN)Cl and PhI along with liberation of O-phenylated product $PhOC_6H_4$-p-Me which was identified by GC/MS spectroscopy.

• Journal of the Microelectronics and Packaging Society
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• v.7 no.4
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• pp.1-5
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• 2000

Properties of AC applied hot pressed ($Pb_{1-x}Sn_{x}$) Te thermoelectrics were investigated. Mechanical alloying process used to produce alloyed powder to reduce the inhomogeneity and to avoid vaporization of constituents. It showed an increase in the mechanical alloying time with increasing of Sn contents in ($Pb_{1-x}Sn_{x}$)Te. ($Pb_{1-x}Sn_{x}$)Te were sintered at 873 to 923K for 1-4 minutes, under 150 kgf/$\textrm{cm}^2$ by AC applied hot pressng method. The short sintering time of AC applied hot pressing process could reduce the vaporization of Te. The density of ($Pb_{1-x}Sn_{x}$) Te was more dependent on the sintering temperature than the sintering time. The p-n transition was observed at x=0.1 but only p type conduction behavior was observed at more than 20 mol% of Sn compositions. The maximum value of Seebeck coefficient is 250 $\mu$V/K for x=0.2 at 500K. As the amount of Sn increases, the peak value of Seebeck coefficient drops and shifts to higher temperature and the peak value of electrical conductivity decreased with increasing temperature.

• Journal of Korean Academy of Nursing
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• v.37 no.7
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• pp.1091-1097
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• 2007

Purpose: This study was done to survey health behaviors in people at risk for a Cerebrovascular Accident(CVA). Method: From November 21 to December 29, 2005, a questionnaire survey was conducted with 171 people at risk for a Cerebrovascular Accident(LDL of above 130mg/dl & homocysteine of above $15.0{\mu}mol/L$). Their physical composition was measured and blood was collected. Results: 1. Of the subjects, 34.5% were smokers, 61.4% were drinkers, 56.7% did not exercise regularly, 57.3% did not control their weight, 26.9% preferred eating meat, and 32.2% preferred salty food. 2. The gender was different between smoking status($X^2=10.734$, p= .001), and drinking status($X^2=7.185$, p= .007), and the age was different between smoking status($X^2=6.656$, p=.010), and drinking status($X^2=10.722$, p= .001). The $HbA_1C$ level was different for regular exercise($X^2=4.824$, p=.028) and the HDL-cholesterol was different for meat-eating preference($X^2=7.928$, p= .005). The observance of troubling signs was different for a salty food preference($X^2=4.313$, p= .038). Conclusion: It is necessary to develop programs for taking care of people at risk for a Cerebrovascular Accident and test the effects of the programs in order to reduce the risk factors of CVA and enhance health behavior promotion.

• Journal of Environmental Health Sciences
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• v.22 no.3
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• pp.49-55
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• 1996

Water parsley(Oenanthe javanica(Blume) DC) was raised with varying population density(S) in the laboratory aquarium unit to determine the growth equation. The population density was measure after 7 days. The resultant growth curve was well fit to the equation 1/S = A+B (1/S0) with a high correlation coefficient ($R^2$ = 0.999). The maximum specific absorption rate was $9.011 \times 10^{-5}$ kg $NO_x-N/kg$ water parsley$\cdot$day and $1.31 \times 10^{-5}$ kg $PO_4-P/kg$ water parsley$\cdot$day when the average population density was $2.62 kg/m^2$. The relationship between population density and nutrient absorption rate, the absorption rate of $NO_x-N$ was 5.04~5.24 mg/l$\cdot$day when the population density was $7.51~10.0 $mg/m^2\cdot day$ and the absorption rate of $PO_4-P$ was 0.56~0.78 mg/l$\cdot$day when the population density was 5.02~10.0 $kg/m^2\cdot day$. Taking into account the nutrient absorption rate and growth rate, the population density between $7.0 kg/m^2\cdot day$ and $8.0 kg/m^2 \cdot day$ was selected. The removal rate of nutrient was investigated after 7 days culture. Removal rate of $NO_x-N$ was 95.6~99.95% with initial concentration of 35 mg $NO_x-N/l$, and the removal rate of $PO_4-P$ was also high, indicating 80.24~98.9% with initial concentration of 5.95 mg $PO_x-P/l$.

• Communications of the Korean Mathematical Society
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• v.9 no.3
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• pp.539-545
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• 1994

Let $q = p^r$, where p is a prime. A polynomial $f(x) \in GF(q)[x]$ is called a permutation polynomial (PP) over GF(q) if the numbers f(a) where $a \in GF(Q)$ are a permutation of the a's. In other words, the equation f(x) = a has a unique solution in GF(q) for each $a \in GF(q)$. More generally, $f(x_1, \cdots, x_n)$ is a PP in n variables if $f(x_1,\cdots,x_n) = \alpha$ has exactly $q^{n-1}$ solutions in $GF(q)^n$ for each $\alpha \in GF(q)$. Mullen ([3], [4], [5]) has studied the concepts of local permutation polynomials (LPP's) over finite fields. A polynomial $f(x_i, x_2, \cdots, x_n) \in GF(q)[x_i, \codts,x_n]$ is called a LPP if for each i = 1,\cdots, n, f(a_i,\cdots,x_n]$ is a PP in $x_i$ for all $a_j \in GF(q), j \neq 1$.Mullen ([3],[4]) found a set of necessary and three variables over GF(q) in order that f be a LPP. As examples, there are 12 LPP's over GF(3) in two indeterminates ; $f(x_1, x_2) = a_{10}x_1 + a_{10}x_2 + a_{00}$ where $a_{10} = 1$ or 2, $a_{01} = 1$ or x, $a_{00} = 0,1$, or 2. There are 24 LPP's over GF(3) of three indeterminates ; $F(x_1, x_2, x_3) = ax_1 + bx_2 +cx_3 +d$ where a,b and c = 1 or 2, d = 0,1, or 2.

• Journal of the Korean Mathematical Society
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• v.43 no.4
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• pp.691-701
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• 2006

In this paper, we construct a new exotic smooth 4-manifold X which is homeomorphic, but not diffeomorphic, to ${\mathbb{C}}\mathbb{P}^2{\sharp}13\overline{\mathbb{C}\mathbb{P}}^2$. Moreover the manifold X has vanishing Seiberg-Witten invariants for all $Spin^c$-structures of X and has no symplectic structure.