• Bulletin of the Korean Mathematical Society
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• v.52 no.3
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• pp.1007-1025
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• 2015

Let $\mathbb{N}_0$ be the set of non-negative integers, and let P(n, l) denote the set of all weak compositions of n with l parts, i.e., $P(n,l)=\{(x_1,x_2,{\cdots},x_l){\in}\mathbb{N}^l_0\;:\;x_1+x_2+{\cdots}+x_l=n\}$. For any element $u=(u_1,u_2,{\cdots},u_l){\in}P(n,l)$, denote its ith-coordinate by u(i), i.e., $u(i)=u_i$. A family $A{\subseteq}P(n,l)$ is said to be t-intersecting if ${\mid}\{i:u(i)=v(i)\}{\mid}{\geq}t$ for all $u,v{\epsilon}A$. A family $A{\subseteq}P(n,l)$ is said to be trivially t-intersecting if there is a t-set T of $[l]=\{1,2,{\cdots},l\}$ and elements $y_s{\in}\mathbb{N}_0(s{\in}T)$ such that $A=\{u{\in}P(n,l):u(j)=yj\;for\;all\;j{\in}T\}$. We prove that given any positive integers l, t with $l{\geq}2t+3$, there exists a constant $n_0(l,t)$ depending only on l and t, such that for all $n{\geq}n_0(l,t)$, if $A{\subseteq}P(n,l)$ is non-trivially t-intersecting, then $${\mid}A{\mid}{\leq}(^{n+l-t-l}_{l-t-1})-(^{n-1}_{l-t-1})+t$$. Moreover, equality holds if and only if there is a t-set T of [l] such that $$A=\bigcup_{s{\in}[l]{\backslash}T}\;A_s{\cup}\{q_i:i{\in}T\}$$, where $$A_s=\{u{\in}P(n,l):u(j)=0\;for\;all\;j{\in}T\;and\;u(s)=0\}$$ and $$q_i{\in}P(n,l)\;with\;q_i(j)=0\;fo\;all\;j{\in}[l]{\backslash}\{i\}\;and\;q_i(i)=n$$.

• Analytical Science and Technology
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• v.14 no.3
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• pp.238-243
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• 2001

The study was carried out to analysis of the pollutant $COD_{Mn}$, T-N, T-P for water quality proximated to sediment in lake of K river basin. water extracted from sediment showed higher $COD_{Mn}$, T-N, T-P datas than water proximated to sediment. Also, water proximated to sediment and water 5-10cm proximated to sediment showed the following data : $COD_{Mn}$, 1.2~1.9mg/L, T-N, 1.3~6.2mg/L, TP, 0.05~0.26mg/L, respectively. From this results, we have known the fact that the pollution degree of sediment have an effect on the water quality in lake and stream.

• Asian-Australasian Journal of Animal Sciences
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• v.13 no.5
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• pp.659-665
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• 2000

A nitrogen (N) balance trial was conducted to examine the effect of N deprivation on subsequent N retention, blood urea nitrogen (BUN) and IGF-I levels and the ratio of IGF binding protein (IGFBP)-3 to IGFBP-l and -2. Pigs in treatment (T) 1 were given diet A (2.39% N) and those in T2 and T3 were given diet B (1.31% N) and excreta were collected (period 1 (P1)). Pigs in T1 continued to receive diet A while diets for T2 and T3 were changed to diets A and C (2.74% N), respectively. The excreta were collected for two more periods (P2 and P3). During P1, pigs in T2 and T3 retained 50% less N (p<0.001) than those in T1. However, pigs provided T2 (p<0.01) and T3 (p<0.05) retained more N than those assigned to T1 during P2. Pigs in T3 tended to retain more (p=0.10) N than those receiving T2 for the same period. The BUN values were lower (p<0.05) for pigs assigned to T2 and T3 than T1 during P1 and P2. Both IGF-I and IGFBP ratios of pigs assigned to T1 were higher (p<0.05) than those given T2 and T3 during P1 but no differences were found during P2 and P3.

• Journal of applied mathematics & informatics
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• v.24 no.1_2
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• pp.437-448
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• 2007

Suppose K is a nonempty closed convex nonexpansive retract of a real uniformly convex Banach space E with P as a nonexpansive retraction. Let $T_1,\;T_2\;and\;T_3\;:\;K{\rightarrow}E$ be nonexpansive mappings with nonempty common fixed points set. Let $\{\alpha_n\},\;\{\beta_n\},\;\{\gamma_n\},\;\{\alpha'_n\},\;\{\beta'_n\},\;\{\gamma'_n\},\;\{\alpha'_n\},\;\{\beta'_n\}\;and\;\{\gamma'_n\}$ be real sequences in [0, 1] such that ${\alpha}_n+{\beta}_n+{\gamma}_n={\alpha}'_n+{\beta'_n+\gamma}'_n={\alpha}'_n+{\beta}'_n+{\gamma}'_n=1$, starting from arbitrary $x_1{\in}K$, define the sequence $\{x_n\}$ by $$\{zn=P({\alpha}'_nT_1x_n+{\beta}'_nx_n+{\gamma}'_nw_n)\;yn=P({\alpha}'_nT_2z_n+{\beta}'_nx_n+{\gamma}'_nv_n)\;x_{n+1}=P({\alpha}_nT_3y_n+{\beta}_nx_n+{\gamma}_nu_n)$$ with the restrictions $\sum^\infty_{n=1}{\gamma}_n<\infty,\;\sum^\infty_{n=1}{\gamma}'_n<\infty,\; \sum^\infty_{n=1}{\gamma}'_n<\infty$. (i) If the dual $E^*$ of E has the Kadec-Klee property, then weak convergence of a $\{x_n\}$ to some $x^*{\in}F(T_1){\cap}{F}(T_2){\cap}(T_3)$ is proved; (ii) If $T_1,\;T_2\;and\;T_3$ satisfy condition(A'), then strong convergence of $\{x_n\}$ to some $x^*{\in}F(T_1){\cap}{F}(T_2){\cap}(T_3)$ is obtained.

• Bulletin of the Korean Mathematical Society
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• v.26 no.2
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• pp.169-173
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• 1989

Let V={(x,y,z):f=z$^{n}$ -npz+(n-1)q=0 for n .geq. 3} be a compled analytic subvariety of a polydisc in $C^{3}$ where p=p(x,y) and q=q(x,y) are holomorphic near (x,y)=(0,0) and f is an irreducible Weierstrass polynomial in z of multiplicity n. Suppose that V has an isolated singular point at the origin. Recall that the z-discriminant of f is D(f)=c(p$^{n}$ -q$^{n-1}$) for some number c. Suppose that D(f) is square-free. then we prove that by Theorem 2.1 .mu.(p$^{n}$ -q$^{n-1}$)=.mu.(f)-(n-1)+n(n-2)I(p,q)+1 where .mu.(f), .mu. p$^{n}$ -q$^{n-1}$are the corresponding Milnor numbers of f, p$^{n}$ -q$^{n-1}$, respectively and I(p,q) is the intersection number of p and q at the origin. By one of applications suppose that W$_{t}$ ={(x,y,z):g$_{t}$ =z$^{n}$ -np$_{t}$ $^{n-1}$z+(n-1)q$_{t}$ $^{n-1}$=0} is a smooth family of complex analytic varieties near t=0 each of which has an isolated singularity at the origin, satisfying that the z-discriminant of g$_{t}$ , that is, D(g$_{t}$ ) is square-free. If .mu.(g$_{t}$ ) are constant near t=0, then we prove that the family of plane curves, D(g$_{t}$ ) are equisingular and also D(f$_{t}$ ) are equisingular near t=0 where f$_{t}$ =z$^{n}$ -np$_{t}$ z+(n-1)q$_{t}$ =0.}$ =0.

• 한국생물공학회:학술대회논문집
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• 2003.04a
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• pp.343-347
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• 2003

Power of loess ball on nitrogen and phosphorous removal in wastewater treatment were investigated. flow line A ( anaerobic${\rightarrow}$oxic${\rightarrow}$anoxic(organic source methanol)${\rightarrow}$p-absorption) showed the results of T-P 0.5, T-N 1.0, and COD 10ppm bellow, and flow line B ( oxic${\rightarrow}$anoxic, organic source: methanol${\rightarrow}$p-absorption) showed the results of T-P 0.3, T-N 5.0, and COD 15 ppm bellow. flow line C ( anaerobic${\rightarrow}$oxic${\rightarrow}$anoxic, organic source: wastewater ${\rightarrow}$ p-absorption) showed the results of T-P 0.6, T-N 10, and COD 15 ppm bellow, and flow line D ( oxic${\rightarrow}$anoxic, organic source: methanol${\rightarrow}$p-absorption) showed the results of T-P 1, T-N 8m, and COD 20 ppm bellow. So the results of these experiments showed the probability of loess ball in wastewater treatment.

• Bulletin of the Korean Mathematical Society
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• v.60 no.4
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• pp.905-913
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• 2023

Suppose that M is a strictly convex hypersurface in the (n + 1)-dimensional Euclidean space 𝔼ⁿ⁺¹ with the origin o in its convex side and with the outward unit normal N. For a fixed point p ∈ M and a positive constant t, we put 𝚽_t the hyperplane parallel to the tangent hyperplane 𝚽 at p and passing through the point q = p - tN(p). We consider the region cut from M by the parallel hyperplane 𝚽_t, and denote by I_p(t) the (n + 1)-dimensional volume of the convex hull of the region and the origin o. Then Schneider's characterization theorem for ellipsoids states that among centrally symmetric, strictly convex and closed surfaces in the 3-dimensional Euclidean space 𝔼³, the ellipsoids are the only ones satisfying I_p(t) = 𝜙(p)t, where 𝜙 is a function defined on M. Recently, the characterization theorem was extended to centrally symmetric, strictly convex and closed hypersurfaces in 𝔼ⁿ⁺¹ satisfying for a constant 𝛽, I_p(t) = 𝜙(p)t^𝛽. In this paper, we study the volume I_p(t) of a strictly convex and complete hypersurface in 𝔼ⁿ⁺¹ with the origin o in its convex side. As a result, first of all we extend the characterization theorem to strictly convex and closed (not necessarily centrally symmetric) hypersurfaces in 𝔼ⁿ⁺¹ satisfying I_p(t) = 𝜙(p)t^𝛽. After that we generalize the characterization theorem to strictly convex and complete (not necessarily closed) hypersurfaces in 𝔼ⁿ⁺¹ satisfying I_p(t) = 𝜙(p)t^𝛽.

• Journal of applied mathematics & informatics
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• v.38 no.5_6
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• pp.591-600
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• 2020

This work is a continuation of our investigations for p-adic analogue of the alternating form Dirichlet L-functions $$L_E(s,{\chi})={\sum\limits_{n=1}^{\infty}}{\frac{(-1)^n{\chi}(n)}{n^s}},\;Re(s)>0$$. Let L_p,E(s, t; χ) be the p-adic Euler L-function of two variables. In this paper, for any α ∈ ℂ_p, |α|_p ≤ 1, we give a power series expansion of L_p,E(s, t; χ) in terms of the variable t. From this, we derive a power series expansion of the generalized Euler polynomials with negative index, that is, we prove that $$E_{-n,{\chi}}(t)={\sum\limits_{m=0}^{\infty}}\(\array{-n\\m}\)E_{-(m+n),{\chi}^{t^m}},\;n{\in}{\mathbb{N}}$$, where t ∈ ℂ_p with |t|_p < 1. Some further properties for L_p,E(s, t; χ) has also been shown.

• Journal of Environmental Science International
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• v.31 no.11
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• pp.989-992
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• 2022

This study was conducted to investigate the efficacy of larval stages of three species, namely, Tenebrio molitor, Protaetia brevitarsis seulensis, and Ptecticus tenebrifer larvae, in degrading poultry manure, specially, broiler and duck manure. The survival rates of larvae were also noted. For the experiment, T. molitor (n=300), P. brevitarsis seulensis (n=60), and P. tenebrifer (n=300) hatched larvae were randomly divided into six groups with three replicates. The degaradation efficacy tests were then performed for 30 days in a laboratory. The test groups were as follows: T1, 110 g broiler manure + T. molitor larvae (n=50); T2, 110 g duck manure + T. molitor larvae (n=50); T3, 125 g broiler manure + P. brevitarsis seulensis larvae (n=10); T4, 125 g duck manure + P. brevitarsis seulensis larvae (n=10); T5, 105 g broiler manure + P. tenebrifer larvae (n=50); and T6, 105 g duck manure + P. tenebrifer larvae (n=50). The groups showed significant efficacy in degrading broiler and duck manure (p<0.05). The highest survival rates were recorded for T. molitor larvae in both manure types [T1 (92.67%) and T2 (50%)], followed by P. brevitarsis seulensis larvae (T4, 40%) and P. tenebrifer larvae (T6, 14.67%) in duck manure. Next, the survival rates of P. brevitarsis seulensis (T3) and Ptecticus tenebrifer larvae (T5) in broiler manure were 0%. In conclusion, these results point to the feasibility of using insect larvae to degrade broiler and duck manure.

• Journal of the Korean Mathematical Society
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• v.34 no.4
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• pp.1029-1036
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• 1997

Let ${A_t)}_{t>0}$ be a dilation group given by $A_t = exp(-P log t)$, where P is a real $n \times n$ matrix whose eigenvalues has strictly positive real part. Let $\nu$ be the trace of P and $P^*$ denote the adjoint of pp. Suppose that $K$ is a function defined on $R^n$ such that $$\mid$K(x)$\mid$ \leq k($\mid$x$\mid$_Q)$ for a bounded and decreasing function $k(t) on R_+$ satisfying $k \diamond $\mid$\cdot$\mid$_Q \in \cup_{\varepsilon >0}L^1((1 + $\mid$x$\mid$)^\varepsilon dx)$ where $Q = \int_{0}^{\infty} exp(-tP^*) exp(-tP)$ dt and the norm $$\mid$\cdot$\mid$_Q$ stands for $$\mid$x$\mid$_Q = \sqrt{}, x \in R^n$. For $f \in L^1(R^n)$, define $mf(x) = sup_{t>0}$\mid$K_t * f(x)$\mid$$ where $K_t(X) = t^{-\nu}K(A_{1/t}^* x)$. Then we show that $m$ is a bounded operator of $L^1(R^n) into L^{1, \infty}(R^n)$.