• 대한수학회보
• /
• 제52권3호
• /
• pp.1007-1025
• /
• 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 $$q_i{\in}P(n,l)\;with\;q_i(j)=0\;fo\;all\;j{\in}[l]{\backslash}\{i\}\;and\;q_i(i)=n$$.

• 분석과학
• /
• 제14권3호
• /
• pp.238-243
• /
• 2001

K 수계 6개 지점의 호소 퇴적물과 근접된 수질에 대해 $COD_{Mn}$, T-N, T-P, pH를 측정분석 하였다. 퇴적물로부터 분리된 수질이 퇴적물과 근접한 수질보다 COD, T-N, T-P 모두 높은 값을 나타내었으며 그 다음으로 퇴적층 바로 위의 수질이 높은 값을 나타내었다. 직상수와 최상수의 $COD_{Mn}$, T-N, T-P에 대한 수질분석 결과는 1.2~19.0mg/L, T-N, 1.3~6.2mg/L, T-P, 0.05~0.26mg/L의 농도범위를 나타내었다. 이상의 결과로부터 퇴적물이 호소내 수질오염에 영향을 미치는 요인임을 알 수 있었다.

• 대한수학회보
• /
• 제26권2호
• /
• pp.169-173
• /
• 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.

• Journal of applied mathematics & informatics
• /
• 제38권5_6호
• /
• pp.591-600
• /
• 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.

• Asian-Australasian Journal of Animal Sciences
• /
• 제13권5호
• /
• pp.659-665
• /
• 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
• /
• 제24권1_2호
• /
• pp.437-448
• /
• 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.

• 한국생물공학회:학술대회논문집
• /
• 한국생물공학회 2003년도 생물공학의 동향(XII)
• /
• pp.343-347
• /
• 2003

황토볼을 이용하여 폐수처리를 한 결과 다음과 같은 결과를 보였다. 흐름도 A에서는 T-P 0.5ppm이하, T-N 1.0 ppm이하, COD 10ppm 이하였으며, 흐름도 B에서는 T-P 0.3ppm이하, T-N 5.0 ppm이하, COD 15 ppm 이하의 결과를 보여 주었다. 흐름도 C에서는 T-P 0.6ppm이하, T-N 10 ppm이하, COD 15 ppm 이하였으며, 흐름도 D에서는 T-P 1 ppm, T-N 8 ppm이하, COD 20ppm 이하의 결과를 보여 주었다. BOD는 각 흐름도 A, B, C, D에서 COD보다 높은 경우에는 6 ppm, 낮은 경우에는 3 ppm 정도의 차이를 보였다. SS는 각 공정에 따라 그다지 큰 차이를 보이고 있지 않으며, 1.0 처리 용량 Ton/day으로 계산 할 경우에 5 - 20 g/day 정도를 보이고 있다. 이러한 결과치는 하수종말처리장(특별대책지역 및 잠실수중보권지역)의 2 ppm 및 폐수처리시설(농공단지, 오${\cdot}$폐수처리시설 포함)의 T-P 8 ppm, T-N 질소성분 60 ppm이내의 탄소원 COD 40 ppm 이내의 기준에 해당하는 수치의 좋은 결과로 황토볼을 이용한 폐수처리 시스템의 가능성을 보여주고 있다.

• 대한수학회보
• /
• 제60권4호
• /
• pp.905-913
• /
• 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.

• 한국환경과학회지
• /
• 제31권11호
• /
• pp.989-992
• /
• 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.

• 대한수학회지
• /
• 제34권4호
• /
• pp.1029-1036
• /
• 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 $L^1(R^n) into L^{1, \infty}(R^n)$.