• 청정기술
• /
• 제18권4호
• /
• pp.404-409
• /
• 2012

본 연구는 교반강도 및 응집제 주입량의 변화에 따라 플럭의 성장특성이 인의 제거에 미치는 영향을 파악하고자 수행되었다. 본 연구에서는 Al/P 몰비를 1.0, 1.5와 2.0으로 급속혼화강도 G값을 100, 300과 500 $s^{-1}$로 변화시켜 수행하였다. 응집시 발생되는 응집지수(floc size index, FSI)와 크기가 다른 여과지를 이용하여 인의 제거율을 측정하여 성장 특성을 파악하였다. 연구결과 교반강도가 높을수록 용존인의 제거효율이 증가하였으며 Al/P 몰비가 낮을수록 교반강도의 영향이 컸다. T-P의 제거율은 Al/P 몰비 1.0 이하에서는 급속혼화 교반강도가 높을수록 높았으나 Al/P 몰비 1.0 이상에서는 G값 300 $s^{-1}$에서 가장 높은 제거 효율을 나타내었다. Al/P 비 1.0 이하에서는 G값 500 $s^{-1}$에서 가장 큰 FSI값을 나타내었으며, Al/P 몰비 1.0 이상에서는 G값 300 $s^{-1}$에서 가장 큰 FSI값을 나타내었다. 실제하수처리장 유출수를 대상으로 응집에 의한 인 제거에 Al/P 몰비와 급속혼화 강도의 영향은 인공조제수의 결과와 유사하였다.

• Kyungpook Mathematical Journal
• /
• 제48권1호
• /
• pp.15-24
• /
• 2008

Let $N{\geq}1$ and p > 1. Let ${\Omega}$ be a domain of $\mathbb{R}^N$. In this article we shall establish Kato's inequalities for quasilinear degenerate elliptic operators of the form $A_pu$ = divA(x,$\nabla$u) for $u{\in}K_p({\Omega})$, ), where $K_p({\Omega})$ is an admissible class and $A(x,\xi)\;:\;{\Omega}{\times}\mathbb{R}^N{\rightarrow}\mathbb{R}^N$ is a mapping satisfying some structural conditions. If p = 2 for example, then we have $K_2({\Omega})\;= \;\{u\;{\in}\;L_{loc}^1({\Omega})\;:\;\partial_ju,\;\partial_{j,k}^2u\;{\in}\;L_{loc}^1({\Omega})\;for\;j,k\;=\;1,2,{\cdots},N\}$. Then we shall prove that $A_p{\mid}u{\mid}\;\geq$ (sgn u) $A_pu$ and $A_pu^+\;\geq\;(sgn^+u)^{p-1}\;A_pu$ in D'(${\Omega}$) with $u\;\in\;K_p({\Omega})$. These inequalities are called Kato's inequalities provided that p = 2. The class of operators $A_p$ contains the so-called p-harmonic operators $L_p\;=\;div(\mid{{\nabla}u{\mid}^{p-2}{\nabla}u)$ for $A(x,\xi)={\mid}\xi{\mid}^{p-2}\xi$.

• Journal of Applied and Pure Mathematics
• /
• 제4권3_4호
• /
• pp.85-97
• /
• 2022

Let a graph G = (V, E) be a (p, q) graph. Define $${\rho}\;=\;\{\array{{\frac{p}{2}}&p\text{ is even}\\{\frac{p-1}{2}}\;&p\text{ is odd,}}$$ and M = {±1, ±2, ⋯ ± 𝜌} called the set of labels. Consider a mapping λ : V → M by assigning different labels in M to the different elements of V when p is even and different labels in M to p - 1 elements of V and repeating a label for the remaining one vertex when p is odd. The labeling as defined above is said to be a pair mean cordial labeling if for each edge uv of G, there exists a labeling $\frac{{\lambda}(u)+{\lambda}(v)}{2}$ if λ(u) + λ(v) is even and $\frac{{\lambda}(u)+{\lambda}(v)+1}{2}$ if λ(u) + λ(v) is odd such that ${\mid}\bar{\mathbb{S}}_{{\lambda}_1}-\bar{\mathbb{S}}_{{\lambda}^c_1}{\mid}{\leq}1$ where $\bar{\mathbb{S}}_{{\lambda}_1}$ and $\bar{\mathbb{S}}_{{\lambda}^c_1}$ respectively denote the number of edges labeled with 1 and the number of edges not labeled with 1. A graph G for which there exists a pair mean cordial labeling is called a pair mean cordial graph. In this paper, we investigate the pair mean cordial labeling of graphs which are obtained from path and cycle.

• Journal of Applied and Pure Mathematics
• /
• 제5권3_4호
• /
• pp.237-253
• /
• 2023

Let a graph G = (V, E) be a (p, q) graph. Define $${\rho}=\{\array{{\frac{p}{2}} & \;\;p\text{ is even} \\ {\frac{p-1}{2}} & \;\;p\text{ is odd,}$$ and M = {±1, ±2, … ± ρ} called the set of labels. Consider a mapping λ : V → M by assigning different labels in M to the different elements of V when p is even and different labels in M to p - 1 elements of V and repeating a label for the remaining one vertex when p is odd. The labeling as defined above is said to be a pair mean cordial labeling if for each edge uv of G, there exists a labeling ${\frac{{\lambda}(u)+{\lambda}(v)}{2}}$ if λ(u) + λ(v) is even and ${\frac{{\lambda}(u)+{\lambda}(v)+1}{2}}$ if λ(u) + λ(v) is odd such that ${\mid}{\bar{{\mathbb{S}}}}_{\lambda}{_1}-{\bar{{\mathbb{S}}}}_{{\lambda}^c_1}{\mid}{\leq}1$ where ${\bar{{\mathbb{S}}}}_{\lambda}{_1}$ and ${\bar{{\mathbb{S}}}}_{{\lambda}^c_1}$ respectively denote the number of edges labeled with 1 and the number of edges not labeled with 1. A graph G for which there exists a pair mean cordial labeling is called a pair mean cordial graph. In this paper, we investigate the pair mean cordial labeling behavior of few graphs including the closed helm graph, web graph, jewel graph, sunflower graph, flower graph, tadpole graph, dumbbell graph, umbrella graph, butterfly graph, jelly fish, triangular book graph, quadrilateral book graph.

• 한국농공학회지
• /
• 제20권1호
• /
• pp.4592-4598
• /
• 1978

The purpose of this research is to find out mathemetically an economical intake water depth in the design of head works through the derivation of some formulas. For the performance of the purpose the following formulas were found out for the design intake water depth in each flow type of intake sluice, such as overflow type and orifice type. (1) The conditional equations of !he economical intake water depth in .case that weir body is placed on permeable soil layer ; (a) in the overflow type of intake sluice, {{{{ { zp}_{1 } { Lh}_{1 }+ { 1} over {2 } { Cp}_{3 }L(0.67 SQRT { q} -0.61) { ( { d}_{0 }+ { h}_{1 }+ { h}_{0 } )}^{- { 1} over {2 } }- { { { 3Q}_{1 } { p}_{5 } { h}_{1 } }^{- { 5} over {2 } } } over { { 2m}_{1 }(1-s) SQRT { 2gs} }+[ LEFT { b+ { 4C TIMES { 0.61}^{2 } } over {3(r-1) }+z( { d}_{0 }+ { h}_{0 } ) RIGHT } { p}_{1 }L+(1+ SQRT { 1+ { z}^{2 } } ) { p}_{2 }L+ { dcp}_{3 }L+ { nkp}_{5 }+( { 2z}_{0 }+m )(1-s) { L}_{d } { p}_{7 } ] =0}}}} (b) in the orifice type of intake sluice, {{{{ { zp}_{1 } { Lh}_{1 }+ { 1} over {2 } C { p}_{3 }L(0.67 SQRT { q} -0.61)}}}} {{{{ { ({d }_{0 }+ { h}_{1 }+ { h}_{0 } )}^{ - { 1} over {2 } }- { { 3Q}_{1 } { p}_{ 6} { { h}_{1 } }^{- { 5} over {2 } } } over { { 2m}_{ 2}m' SQRT { 2gs} }+[ LEFT { b+ { 4C TIMES { 0.61}^{2 } } over {3(r-1) }+z( { d}_{0 }+ { h}_{0 } ) RIGHT } { p}_{1 }L }}}} {{{{+(1+ SQRT { 1+ { z}^{2 } } ) { p}_{2 } L+dC { p}_{4 }L+(2 { z}_{0 }+m )(1-s) { L}_{d } { p}_{7 }]=0 }}}} where, z=outer slope of weir body (value of cotangent), h1=intake water depth (m), L=total length of weir (m), C=Bligh's creep ratio, q=flood discharge overflowing weir crest per unit length of weir (m3/sec/m), d0=average height to intake sill elevation in weir (m), h0=freeboard of weir (m), Q1=design irrigation requirements (m3/sec), m1=coefficient of head loss (0.9∼0.95) s=(h1-h2)/h1, h2=flow water depth outside intake sluice gate (m), b=width of weir crest (m), r=specific weight of weir materials, d=depth of cutting along seepage length under the weir (m), n=number of side contraction, k=coefficient of side contraction loss (0.02∼0.04), m2=coefficient of discharge (0.7∼0.9) m'=h0/h1, h0=open height of gate (m), p1 and p4=unit price of weir body and of excavation of weir site, respectively (won/㎥), p2 and p3=unit price of construction form and of revetment for protection of downstream riverbed, respectively (won/㎡), p5 and p6=average cost per unit width of intake sluice including cost of intake canal having the same one as width of the sluice in case of overflow type and orifice type respectively (won/m), zo : inner slope of section area in intake canal from its beginning point to its changing point to ordinary flow section, m: coefficient concerning the mean width of intak canal site,a : freeboard of intake canal. (2) The conditional equations of the economical intake water depth in case that weir body is built on the foundation of rock bed ; (a) in the overflow type of intake sluice, {{{{ { zp}_{1 } { Lh}_{1 }- { { { 3Q}_{1 } { p}_{5 } { h}_{1 } }^{- {5 } over {2 } } } over { { 2m}_{1 }(1-s) SQRT { 2gs} }+[ LEFT { b+z( { d}_{0 }+ { h}_{0 } )RIGHT } { p}_{1 }L+(1+ SQRT { 1+ { z}^{2 } } ) { p}_{2 }L+ { nkp}_{5 }}}}} {{{{+( { 2z}_{0 }+m )(1-s) { L}_{d } { p}_{7 } ]=0 }}}} (b) in the orifice type of intake sluice, {{{{ { zp}_{1 } { Lh}_{1 }- { { { 3Q}_{1 } { p}_{6 } { h}_{1 } }^{- {5 } over {2 } } } over { { 2m}_{2 }m' SQRT { 2gs} }+[ LEFT { b+z( { d}_{0 }+ { h}_{0 } )RIGHT } { p}_{1 }L+(1+ SQRT { 1+ { z}^{2 } } ) { p}_{2 }L}}}} {{{{+( { 2z}_{0 }+m )(1-s) { L}_{d } { p}_{7 } ]=0}}}} The construction cost of weir cut-off and revetment on outside slope of leeve, and the damages suffered from inundation in upstream area were not included in the process of deriving the above conditional equations, but it is true that magnitude of intake water depth influences somewhat on the cost and damages. Therefore, in applying the above equations the fact that should not be over looked is that the design value of intake water depth to be adopted should not be more largely determined than the value of h1 satisfying the above formulas.

• 대한수학회지
• /
• 제54권2호
• /
• pp.575-598
• /
• 2017

This paper introduces and studies a generalization of the classical Struve function of order p given by $$_aS_{p,c}(x):=\sum\limits_{k=0}^{\infty}\frac{(-c)^k}{{\Gamma}(ak+p+\frac{3}{2}){\Gamma}(k+\frac{3}{2})}(\frac{x}{2})^{2k+p+1}$$. Representation formulae are derived for $_aS_{p,c}$. Further the function $_aS_{p,c}$ is shown to be a solution of an (a + 1)-order differential equation. Monotonicity and log-convexity properties for the generalized Struve function $_aS_{p,c}$ are investigated, particulary for the case c = -1. As a consequence, $Tur{\acute{a}}n$-type inequalities are established. For a = 2 and c = -1, dominant and subordinant functions are obtained for the Struve function $_2S_{p,-1}$.

• 대한수학회보
• /
• 제55권5호
• /
• pp.1441-1462
• /
• 2018

In this paper, we investigate the fractional p&q-Kirchhoff type system $$\{M_1([u]^p_{s,p})(-{\Delta})^s_pu+V_1(x){\mid}u{\mid}^{p-2}u\\{\hfill{10}}={\ell}k^{-1}F_u(x,\;u,\;v)+{\lambda}{\alpha}(x){\mid}u{\mid}^{m-2}u,\;x{\in}{\Omega}\\M_2([u]^q_{s,q})(-{\Delta})^s_qv+V_2(x){\mid}v{\mid}^{q-2}v\\{\hfill{10}}={\ell}k^{-1}F_v(x,u,v)+{\mu}{\alpha}(x){\mid}v{\mid}^{m-2}v,\;x{\in}{\Omega},\\u=v=0,\;x{\in}{\partial}{\Omega},$$ where ${\Omega}{\subset}{\mathbb{R}}^N$ is an unbounded domain with smooth boundary ${\partial}{\Omega}$, and $0<s<1<p{\leq}q$ and sq < N, ${\lambda},{\mu}>0$, $1<m{\leq}k<p^*_s$, ${\ell}{\in}R$, while $[u]^t_{s,t}$ denotes the Gagliardo semi-norm given in (1.2) below. $V_1(x)$, $V_2(x)$, $a(x):{\mathbb{R}}^N{\rightarrow}(0,\;{\infty})$ are three positive weights, $M_1$, $M_2$ are continuous and positive functions in ${\mathbb{R}}^+$. Using variational methods, we prove existence of infinitely many high-energy solutions for the above system.

• Tuberculosis and Respiratory Diseases
• /
• 제62권6호
• /
• pp.499-505
• /
• 2007

배 경: TREM-1은 중성구, 단핵구, 대식세포 표면에 존재하는 세포표면수용체로, 세균에 의해 그 발현이 증가하여 여러 염증전달물질을 증폭시키는 역할을 한다. 저자들은 삼출성흉수를 가진 환자의 혈청과 흉수에서 soluble (s) TREM-1을 측정하여 흉수의 원인진단에 대한 유용성을 알아보고자 하였다. 방 법: 2003년 3월부터 2006년 12월까지 삼출성흉수로 입원한 환자 45명을 대상으로 하여, 혈청과 흉수에서 human sTREM-1 항체를 사용하여 면역점적법(immunoblot assay)으로 sTREM-1을 측정하였다. 원인질환에 따라 결핵성, 부폐렴성, 악성흉수로 나누어 비교하였다. 결 과: 혈청 sTREM-1은 원인질환 별로 유의한 차이를 보이지 않았으나, 흉수 sTREM-1은 원인질환별로 유의한 차이를 보였으며(p=0.011), 특히 부폐렴성흉수의 sTREM-1이 결핵성흉수와(p<0.05) 악성흉수보다 유의하게 높았다(p<0.05). 부폐렴성흉수를 진단하는 데 흉수 sTREM-1의 유용성을 평가하고자 ROC 곡선을 그린 결과 곡선밑면적은 0.818이고 (p=0.001), 흉수 sTREM-1의 cutoff 값을 103.5pg/mL로 하였을 때 민감도가 73%, 특이도가 81%이었다. 결 론: 흉수의 sTREM-1은 삼출성흉수 중 부폐렴성흉수를 진단하는 유용한 지표로 판단된다.

• 대한임상검사과학회지
• /
• 제49권2호
• /
• pp.128-134
• /
• 2017

Der p 1과 Der p 2는 알레르기 질환과 관련된 집먼지 진드기의 핵심적인 알러젠이다. 본 연구에서는 Der p 1과 Der p 2가 단구에서 S100A8과 S10A9을 분비시키는지를 확인하였고, 분비된 S100A8과 S10A9이 호중구의 세포고사 조절기전에 작용하는지를 연구하였다. Der p 1과 Der p 2는 정상인의 단구에서 S100A8과 S10A9을 유의하게 증가시켰고, S100A8과 S10A9은 정상인과 알레르기 질환 호중구의 자발적 세포고사를 억제 시켰다. 호중구의 Lyn, Akt, ERK는 S100A8과 S10A9을 시간별로 처리하였을 때 활성화하였다. 본 연구를 통하여 단구와 호중구에서 Der p 1과 Der p 2의 역할을 규명하였고, 나아가 관련된 알레르기 병인기전을 이해하는데 유용할 것이다.

• Biomolecules & Therapeutics
• /
• 제29권5호
• /
• pp.492-497
• /
• 2021

Levels of sphingosine 1-phosphate (S1P), an intercellular signaling molecule, reportedly increase in the bronchoalveolar lavage fluids of patients with asthma. Although the type 4 S1P receptor, S1P₄ has been detected in mast cells, its functions have been poorly investigated in an allergic asthma model in vivo. S1P₄ functions were evaluated following treatment of CYM50358, a selective antagonist of S1P₄, in an ovalbumin-induced allergic asthma model, and antigen-induced degranulation of mast cells. CYM50358 inhibited antigen-induced degranulation in RBL-2H3 mast cells. Eosinophil accumulation and an increase of Th2 cytokine levels were measured in the bronchoalveolar lavage fluid and via the inflammation of the lungs in ovalbumin-induced allergic asthma mice. CYM50358 administration before ovalbumin sensitization and before the antigen challenge strongly inhibited the increase of eosinophils and lymphocytes in the bronchoalveolar lavage fluid. CYM50358 administration inhibited the increase of IL-4 cytokines and serum IgE levels. Histological studies revealed that CYM50358 reduced inflammatory scores and PAS (periodic acid-Schiff)-stained cells in the lungs. The pro-allergic functions of S1P₄ were elucidated using in vitro mast cells and in vivo ovalbumin-induced allergic asthma model experiments. These results suggest that S1P₄ antagonist CYM50358 may have therapeutic potential in the treatment of allergic asthma.