• Bulletin of the Korean Mathematical Society
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• v.46 no.3
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• pp.521-534
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• 2009

In this paper we present new large-update primal-dual interior point algorithms for $P_*$ linear complementarity problems(LAPS) based on a class of kernel functions, ${\psi}(t)={\frac{t^{p+1}-1}{p+1}}+{\frac{1}{\sigma}}(e^{{\sigma}(1-t)}-1)$, p $\in$ [0, 1], ${\sigma}{\geq}1$. It is the first to use this class of kernel functions in the complexity analysis of interior point method(IPM) for $P_*$ LAPS. We showed that if a strictly feasible starting point is available, then new large-update primal-dual interior point algorithms for $P_*$ LAPS have $O((1+2+\kappa)n^{{\frac{1}{p+1}}}lognlog{\frac{n}{\varepsilon}})$ complexity bound. When p = 1, we have $O((1+2\kappa)\sqrt{n}lognlog\frac{n}{\varepsilon})$ complexity which is so far the best known complexity for large-update methods.

• Journal of Environmental Science International
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• v.9 no.5
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• pp.415-422
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• 2000

In this study the removal possibility of nutrients of T-P, NH3-N, NO3-N and T-N is examined through a positive experimental study using submerged biofilter of media packing channel method. From the analysis of nutrients removal efficiency for each run of the collected sample following results are obtained. Firstly the result of N/P surveying for inflow shows serious value that excess the limit value of 20 as the values are in the range of 12.0~42.7 and the average is 25.73. Secondly the highest concentration of the incoming NH3-N reaches double of the standard since the concentrations of NH3-N and NO3-N for inflow shows 0.06mg/$\ell$ and 2.5~3.8mg/$\ell$ respectively and the average removal rate which passed the submerged biofilter adopted in this study is a satisfactory level. Next the average removal rate of T-P of 51.5% shows the possiblity of entrophication removal since the removal rate of T-P of 66.8~68.8% in relative low temperature period of RUN 1~2 appeared higher than in RUN 3~6 and T-N shows relatively poor result with the average removal rate of 34.1% And it is known that the bigger BOD/P and BOD/N are the more removal rate increases from the examination result of the relation between BOD/P and BOD/N and the treatment water T-P and T-N to decide the relation with the concentration of organic matters and though that the appropriate proportion is necessary for effective removal of nitrogen and phsophorus.

• Communications of the Korean Mathematical Society
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• v.32 no.1
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• pp.193-200
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• 2017

Given a pair p, q of relative prime positive integers, we have uniquely determined positive integers x, y, u and v such that vx-uy = 1, p = x + y and q = u + v. Using this property, we show that$${\sum\limits_{1{\leq}i{\leq}x,1{\leq}j{\leq}v}}\;{t^{(i-1)q+(j-1)p}\;-\;{\sum\limits_{1{\leq}k{\leq}y,1{\leq}l{\leq}u}}\;t^{1+(k-1)q+(l-1)p}$$ is the Alexander polynomial ${\Delta}_{p,q}(t)$ of a torus knot t(p, q). Hence the number $N_{p,q}$ of non-zero terms of ${\Delta}_{p,q}(t)$ is equal to vx + uy = 2vx - 1. Owing to well known results in knot Floer homology theory, our expanding formula of the Alexander polynomial of a torus knot provides a method of algorithmically determining the total rank of its knot Floer homology or equivalently the complexity of its (1,1)-diagram. In particular we prove (see Corollary 2.8); Let q be a positive integer> 1 and let k be a positive integer. Then we have $$\begin{array}{rccl}(1)&N_{kq}+1,q&=&2k(q-1)+1\\(2)&N_{kq}+q-1,q&=&2(k+1)(q-1)-1\\(3)&N_{kq}+2,q&=&{\frac{1}{2}}k(q^2-1)+q\\(4)&N_{kq}+q-2,q&=&{\frac{1}{2}}(k+1)(q^2-1)-q\end{array}$$ where we further assume q is odd in formula (3) and (4). Consequently we confirm that the complexities of (1,1)-diagrams of torus knots of type t(kq + 2, q) and t(kq + q - 2, q) in [5] agree with $N_{kq+2,q}$ and $N_{kq+q-2,q}$ respectively.

• Korean Journal of Environmental Agriculture
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• v.22 no.1
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• pp.1-6
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• 2003

The yearly average water qualities of the Whang river, which flows into the Hapcheon lake, were COD $3.1{\sim}4.2\;mg/L$, T-N $2.460{\sim}3.550\;mg/L$ and T-P $0.111{\sim}0.201\;mg/L$ during $1996{\sim}2001$. The yearly average COD concentration of Hapcheon lake was increased from 1.9 mg/L (in 1996) to 2.7 mg/L (in 2000). However, T-N and T-P concentration of Hapcheon lake did not show increasing trend over the 6 year period During $1996{\sim}2001$, the yearly average concentrations of T-N, T-P were $1.383{\sim}1.792\;mg/L$, $0.018{\sim}0.023\;mg/L$ respectively. The correlation coefficients between chlorophyll ${\alpha}$ and T-N, T-P, rainfall intensity, water temperature were 0.382, 0.372, 0.589, and 0.526, respectively. Therefore, the rainfall and water temperature appeared to play an important role far the variations of chlolophyll ${\alpha}$ concentration in the Hapcheon lake. Trophic state of the Hapcheon lake were evaluated to be in the range of mesotrophic to eutrophic.

• Journal of Wetlands Research
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• v.11 no.3
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• pp.81-88
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• 2009

The cows manure has been used as fertilizers in farmland because of enough nutrients. However, excess nutrients can be washed off during a storm and affected on nearby waterbodies. In this paper, the runoff characteristics from farmland were studied to determine the watershed runoff rate. As results of estimating, watershed runoff rates with short-term runoff are BOD 0.6%, CODcr 0.3 %, CODMn 0.1 %, T-N 0.8 % and T-P 1.0 % On the other hand, they with long-term runoff are BOD 3.6 %, CODcr 1.0 %, CODMn 0.9 %, T-N 4.9 % and T-P 4.8 %. It is clean that the watershed runoff rates increase according to the rainfall runoff time.

• Journal of applied mathematics & informatics
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• v.28 no.3_4
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• pp.753-762
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• 2010

Let K be a nonempty closed convex subset of a real Hilbert space H. Let T : K $\rightarrow$ K be a nonexpansive mapping with a nonempty fixed point set Fix(T). Let f : K $\rightarrow$ K be a contraction mapping. Let {$\alpha_n$} and {$\beta_n$} be sequences in (0, 1) such that $\lim_{x{\rightarrow}0}{\alpha}_n=0$, (0.1) $\sum_{n=0}^{\infty}\;{\alpha}_n=+{\infty}$, (0.2) 0 < a ${\leq}\;{\beta}_n\;{\leq}$ b < 1 for all $n\;{\geq}\;0$. (0.3) Then it is proved that the modified Krasnoselski-Mann iterative sequence {$x_n$} given by {$x_0\;{\in}\;K$, $y_n\;=\;{\alpha}_{n}f(x_n)+(1-\alpha_n)x_n$, $n\;{\geq}\;0$, $x_{n+1}=(1-{\beta}_n)y_n+{\beta}_nTy_n$, $n\;{\geq}\;0$, (0.4) converges strongly to a point p $\in$ Fix(T} which satisfies the variational inequality

$\leq$ 0, z $\in$ Fix(T). (0.5) This result improves and extends the corresponding results of Yao et al[Y.Yao, H. Zhou, Y. C. Liou, Strong convergence of a modified Krasnoselski-Mann iterative algorithm for non-expansive mappings, J Appl Math Com-put (2009)29:383-389.

• Journal of Korean Neurosurgical Society
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• v.65 no.6
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• pp.779-789
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• 2022

Objective : To analyze the effects of the number and shape of fenestrations on the mechanical strength of pedicle screws and the effects of bone cement augmentation (BCA) on the pull-out strength (POS) of screws used in conventional BCA. Methods : For the control group, a conventional screw was defined as C1, a screw with cannulated end-holes was defined as C2, a C2 screw with six pinholes was defined as C3, and the control group type was set. Among the experimental screws, T1 was designed using symmetrically placed thru-hole type fenestrations with an elliptical shape, while T2 was designed with half-moon (HM)-shaped asymmetrical fenestrations. T3 and T4 were designed with single HM-shaped fenestrations covering three pitches and five pitches, respectively. T5 and T6 were designed with 0.6-mm and 1-mm wider fenestrations than T3. BCA was performed by injecting 3 mL of commercial bone cement in the screw, and mechanical strength and POS tests were performed according to ASTM F1717 and ASTM F543 standards. Synthetic bone (model #1522-505) made of polyurethane foam was used as a model of osteoporotic bone, and radiographic examinations were performed using computed tomography and fluoroscopy. Results : In the fatigue test, at 75% ultimate load, fractures occurred 7781 and 9189 times; at 50%, they occurred 36122 and 82067 times; and at 25%, no fractures occurred. The mean ultimate load for each screw type was 219.1±52.39 N for T1, 234.74±15.9 N for T2, 220.70±59.23 N for T3, 216.45±32.4 N for T4, 181.55±54.78 N for T5, and 216.47±29.25 N for T6. In comparison with C1, T1, T2, T3, T4, and T6 showed significantly different ultimate load values (p<0.05). However, when the values for C2 and the fenestrated screws were evaluated with an unpaired t test, the ultimate load value of C2 significantly differed only from that of T2 (p=0.025). The ultimate load value of C3 differed significantly from those of T1 and T2 (C3 vs. T1 : p=0.048; C3 vs. T2 : p<0.001). Linear correlation analysis revealed a significant correlation between the fenestration area and the volume of bone cement (Pearson's correlation coefficient r=0.288, p=0.036). The bone cement volume and ultimate load significantly correlated with each other in linear correlation analysis (r=0.403, p=0.003). Conclusion : Fenestration yielded a superior ultimate load in comparison with standard BCA using a conventional screw. In T2 screws with asymmetrical two-way fenestrations showed the maximal increase in ultimate load. The fenestrated screws can be expected to show a stable position for the formation of the cement mass.

• Magazine of the Korean Society of Agricultural Engineers
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• v.31 no.3
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• pp.93-102
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• 1989

With an objective to provide basic information for the management and the prediction of eutrophication in lentic water Systems, total amount of Kjeldahl nitrogen(T-N) and phosphorous(T-P) from irrigated water and drained water from flooded paddies were investigated during the rice growing period of 1988. A 29.3 ha paddies near Jungnam-myun, HwaSung-gun, Gyungi Province, Korea was instrumented for measuring runoff and sampling irrigated water and drained water from paddies. The following conclusions may be drawn from the result of this study. 1.During 115 days of investigation, T-N load for paddies was 362.6kg and T-P 63.44kg.These would be converted to 12.4kg T-N/ha and 2.17kg T-P/ha, respectively. 2.The T-N and T-P loadings in different periods showed a significant difference. The 25% of T-N loading was drained soon after fertilization period and 60% was drained during the rainy season from July 5 to July 24. 3.Annual loadings from paddies could be calculated to 30kg T-N/ha/year and 52kg T-P/ha/year considering non-measurement periods. 4.After the rainy season, the nutrient loads from drained water showed much less than those from irrigated water, and it may be suggested that the paddies would act as a stabilization pond. 5.The average concentrations of nutrients at 0.9km downstream from investigated paddies were 2.02(T-N) mg/l and 0.52(T-P) mg/I, which were 1.82(T-N) mg/l and 0.056(T-P)mg/l lower than those of drained water from paddies.

• Journal of Ocean Engineering and Technology
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• v.7 no.2
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• pp.131-140
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• 1993

To study the corrosion fatigue begavior of T.M.C.P. steel, the rotary bending fatigue test with the change of concentration of NaCl solution was carried out. Fatigue life in the corrosion environment is decreased markedly in comparision with that in the air. Fatigue limit in the air was about 225 MPa. In case of 3.5% NaCl solution fatigue life could be expressed as .sigma./sub f/=10,392 * (N/sub f/)/sup -o.2923 . According to the paris's rule, crack growth rates could be expressed as da/dN=2.62.*10/sup -7/ .DELTA. K/sup 1.09/(3.5% NaCl solution), da/dN=1.95 *10/sup -7 .DELTA. K/sup 1.05/(1% NaCl solution), da/dN=2.62 * 10/sup -7/.DELTA./sup 0.72/(0.01% NaCl solution) with da/dN expressed in mm/cycle and .DELTA.K in MPa.GAMMA.m. The crack growth rate in the corrosion environment was highest under 3.5% NaCl solution.

• Journal of Wetlands Research
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• v.17 no.4
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• pp.391-401
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• 2015

In this study, divided into small category groups for the residential area it was carried out monitoring for the runoff during precipitation. Based on the results analyzed according to the nonpoint sources Housing leakage characteristics. Analysis of the rainfall runoff and concentration of each type of exclusive detached house with apartments, in the majority of precipitation types runoff concentrations were higher in early. In the case of a difference of two points per runoff rate rainfall it was largely investigation. The average runoff is estimated loadings of BOD $101.1kg/km^2$, SS $232.2kg/km^2$, T-N $18.2kg/km^2$, T-P $2.0kg/km^2$ detached house case, if the apartment was estimated at point BOD $108.82kg/km^2$, SS $329.18kg/km^2$, T-N $57.67kg/km^2$, T-P $4.21kg/km^2$. The average EMCs is BOD BOD 6.6 mg/L, SS 12.8 mg/L, T-N 1.518 mg/L, T-P 0.099 mg/L detached house case, if the apartment was estimated at point BOD 6.3 mg/L, COD 11.2mg/L, SS 14.5 mg/L, T-N 3.1 mg/L, T-P 0.2 mg/L. The initial 30 percentage calculated based on the initial results, the total flow of 30% if the outflow of detached house showed a net percentage difference to T-P 1.04 > T-N 0.97 > BOD 0.90 > SS 0.80. The apartment area showed the percentage difference in the water quality in the order of BOD 1.49 > T-P 1.40 > SS 1.30 > T-N 0.96 per item.