• 대한수학회지
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• 제34권4호
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• pp.1049-1064
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• 1997

We study the existence and uniqueness of nonnegative singular solution u(x,t) of the semilinear parabolic equation $$ u_t = \Delta u - a \cdot \nabla(u^q) = u^p, $$ defined in the whole space $R^N$ for t > 0, with initial data $M\delta(x)$, a Dirac mass, with M > 0. The exponents p,q are larger than 1 and the direction vector a is assumed to be constant. We here show that a unique singular solution exists for every M > 0 if and only if 1 < q < (N + 1)/(N - 1) and 1 < p < 1 + $(2q^*)$/(N + 1), where $q^* = max{q, (N + 1)/N}$. This result agrees with the earlier one for N = 1. In the proof of this result, we also show that a unique singular solution of a diffusion-convection equation without absorption, $$ u_t = \Delta u - a \cdot \nabla(u^q), $$ exists if and only if 1 < q < (N + 1)/(N - 1).

• 대한수학회논문집
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• 제17권3호
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• pp.535-540
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• 2002

Let X$_1$, X$_2$‥‥,X$\_$n/ be n independent and identically distributed random variables with continuous cumulative distribution function F(x). Let us rearrange the X's in the increasing order X$\_$1:n/ $\leq$ X$\_$2:n/ $\leq$ ‥‥ $\leq$ X$\_$n:n/. We call X$\_$k:n/ the k-th order statistic. Then X$\_$n:n/ - X$\_$n-1:n/ and X$\_$n-1:n/ are independent if and only if f(x) = 1-e(equation omitted) with some c > 0. And X$\_$j/ is an upper record value of this sequence lf X$\_$j/ > max(X$_1$, X$_2$,¨¨ ,X$\_$j-1/). We define u(n) = min(j|j > u(n-1),X$\_$j/ > X$\_$u(n-1)/, n $\geq$ 2) with u(1) = 1. Then F(x) = 1 - e(equation omitted), x > 0 if and only if E[X$\_$u(n+3)/ - X$\_$u(n)/ | X$\_$u(m)/ = y] = 3c, or E[X$\_$u(n+4)/ - X$\_$u(n)/|X$\_$u(m)/ = y] = 4c, n m+1.

• 대한수학회보
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• 제55권5호
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• pp.1441-1462
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• 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.

• Current Research on Agriculture and Life Sciences
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• 제6권
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• pp.171-180
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• 1988

parathion을 rat의 복강내에 매 3일 마다 20회 반복적으로 주사 했을때, 일정한 농도의 parathion을 주사한 rat와 점진적으로 주사량을 증가 시켰을때 rat의 독성정도, 혈액 및 신경조직내 cholinesterase 활성 변화, 혈액내 urea nitrogen 및 creatinine의 함량을 측정한 결과 다음과 같은 성적을 얻었다. 복강내 주사시 rat에 대한 parathion의 $LD_{50}$는 10.5mg/kg였으며 95% 신뢰한계는 6.6~16.8mg/kg였다. 아급성 독성실험에서는 A군이 50%의 폐사율을 보인데 비하여 B군과 C군에서 각각 57% 및 83%의 폐사율을 보여 parathion에 대한 축적효과가 나타났으며 증체량 측정에서도 A군에서 123 g의 증체량을 보인데 비하여 B군과 C군에서 각각 60.7 g, 및 88.4 g 의 증체량을 보여 parathion 투여군에서 체중 증가량이 감소하였다. 혈장내 cholinesterase 활성도는 A군($0.58U/m{\ell}$)에 비해 B군($0.47U/m{\ell}$)과 C군($0.36U/m{\ell}$)에서 각각 19%, 및 38%의 억제를 보였고 AA군($0.31U/m{\ell}$), BB군($0.26U/m{\ell}$) 및 CC군($0.17U/m{\ell}$)에서도 A군에 비해 각각 47%, 55%, 71%까지 유의성(P<.05)있는 감소를 보였다. 척수내 cholinesterase 활성도는 A군(2.484U/g)에 비해 B군(1.87U/g)과 C군(1.29U/g)에서 각각 25%, 및 48%의 억제를 보였고 AA군(1.27U/g), BB군(0.71U/g) 및 CC군(0.25U/g)에서도 A군에 비하여 각각 49%, 71%, 및 90%의 유의성(P<.01)있는 억제를 보였다. 뇌의 cholinesterase 활성도에서는 A군(4.67U/g)에 비해 B군(2.52U/g)과 C군(1.32U1U/g)에서 각각 46%, 및 72%로 억제 되었고 AA군(2.48U/g), BB군(1.08U/g) 및 CC군(0.51U/g)에서는 A군에 비해 각각 47%, 77%, 89%까지 유의성(P<.01)있게 억제되는 축적효과를 보였다. 비단백 질소 화합물이 urea nitrogen과 creatinine 함량은 A군에서 각각 $39.8mg/d{\ell}$와 $1.15mg/d{\ell}$인데 비하여 B군($40.9mg/d{\ell}$, $0.90mg/d{\ell}$) 및 C군($41.4mg/d{\ell}$, $1.08mg/d{\ell}$)에서 유의성 있는 차이를 보이지 않았으나 urea nitrogen 함량은 A군에 비해 B군과 C군에서 다소 증가하는 경향을 보였다.

• 융합정보논문지
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• 제9권5호
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• pp.7-13
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• 2019

클라우드 환경이나 빅데이터 환경에서의 역할기반 또는 속성기반의 접근제어에는 계층적 모델을 표현하는 적당한 수학적 구조가 필요하다. 본 논문에서는 역할기반 또는 속성기반의 접근제어의 계층적 모델을 구현할 수 있는 격자함의 대수에서 멀티플라이어와 단순 멀티플라이어의 개념을 정의하고, 모든 멀티플라이어는 단순 멀티플라이어임을 증명한다. 또한 격자함의대수 L의 멀티플라이어와 준동형사상의 관계를 조사하고, 각각의 $u{\in}L$에 대하여 격자 [0, u]와 격자 $[u^{\prime},1]$이 동치임과 $u{\vee}u^{\prime}=1$인 $u{\in}L$에 대하여 L과 $[u,1]{\times}[u^{\prime},1]$이 격자함의대수로써 동치임을 보인다.

• Journal of applied mathematics & informatics
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• 제14권1_2호
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• pp.1-37
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• 2004

We consider the following system of discrete equations $u_i(\kappa)\;=\;{\Sigma{N}{\ell=0}}g_i({\kappa},\;{\ell})f_i(\ell,\;u_1(\ell),\;u_2(\ell),\;{\cdots}\;,\;u_n(\ell)),\;{\kappa}\;{\in}\;\{0,\;1,\;{\cdots}\;,\;T\},\;1\;{\leq}\;i\;{\leq}\;n\;where\;T\;{\geq}\;N\;>\;0,\;1\;{\leq}i\;{\leq}\;n$. Existence criteria for single, double and multiple constant-sign solutions of the system are established. To illustrate the generality of the results obtained, we include applications to several well known boundary value problems. The above system is also extended to that on $\{0,\;1,\;{\cdots}\;\}\;u_i(\kappa)\;=\;{\Sigma{\infty}{\ell=0}}g_i({\kappa},\;{\ell})f_i(\ell,\;u_1(\ell),\;u_2(\ell),\;\cdots\;,\;u_n(\ell)),\;{\kappa}\;{\in}\;\{0,\;1,\;{\cdots}\;\},\;1\;{\leq}\;i\;{\leq}\;n$ for which the existence of constant-sign solutions is investigated.

• Korean Journal of Mathematics
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• 제25권1호
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• pp.1-18
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• 2017

In this paper, we introduce the concepts of ([r, s], [t, u])-interval-valued intuitionistic fuzzy generalized preclosed sets and ([r, s], [t, u])-interval-valued intuitionistic fuzzy generalized preopen sets in the interval-valued intuitionistic smooth topological space and ([r, s], [t, u])-interval-valued intuitionistic fuzzy generalized pre-continuous mappings and then investigate some of their properties.

• 대한수학회보
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• 제51권4호
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• pp.1041-1054
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• 2014

Let $P{\geq}3$ be an integer and let ($U_n$) and ($V_n$) denote generalized Fibonacci and Lucas sequences defined by $U_0=0$, $U_1=1$; $V_0= 2$, $V_1=P$, and $U_{n+1}=PU_n-U_{n-1}$, $V_{n+1}=PV_n-V_{n-1}$ for $n{\geq}1$. In this study, when P is odd, we solve the equations $V_n=kx^2$ and $V_n=2kx^2$ with k | P and k > 1. Then, when k | P and k > 1, we solve some other equations such as $U_n=kx^2$, $U_n=2kx^2$, $U_n=3kx^2$, $V_n=kx^2{\mp}1$, $V_n=2kx^2{\mp}1$, and $U_n=kx^2{\mp}1$. Moreover, when P is odd, we solve the equations $V_n=wx^2+1$ and $V_n=wx^2-1$ for w = 2, 3, 6. After that, we solve some Diophantine equations.

• Asian-Australasian Journal of Animal Sciences
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• 제10권4호
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• pp.364-370
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• 1997

Four local cattle were ($145{\pm}9.7kg$) used in a $4{\times}4$ Latin square design to study the effect of different levels of rumen degradable protein (RDP) in straw based ration on purine derivatives excretion and microbial N supply in cattle. The four rations were formulated at the same amount of energy but varying RDP approximately 50 (U0), 75 (U1), 100 (U2) and 150 (U3) percent levels of RDP requirement for maintenance. They were fed ranged from 101 to 304 g RDP/d. Apparent digestibility of all nutrients increased significantly (p < 0.01) in cattle fed ration U2 than other rations. Rumen $NH_3-N$ concentration increased from 43 to 130 mg/l in response of RDP intake. Purine derivatives excretion increased significantly (p < 0.01) with incremental level of 203 g RDP/d (U2) intake and positively correlated (r=0.69, p < 0.01, n=16) with amount of RDP intake. The rates of rumen microbial N supply were 16.8, 27.2, 39.1 and 32.9 g/d for rations U0, U1, U2 and U3 respectively. Efficiency of microbial N supply (EMNS) per kg of DOMR were 19.0, 25.3, 33.0, and 28.6 g and per MJ of ME. Intake were 0.62, 1.00, 1.44 and 1.21 g for U0, U1, U2 and U3 respectively and highest results were obtained in cattle fed U2 ration. Results of this study suggest that PD excretion and EMNS were increased as incremental level of RDP intake (U2) in local cattle.

• 대한수학회지
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• 제51권1호
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• pp.67-86
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• 2014

Based on an expanded mixed finite element method, we consider the semidiscrete approximations of the solution u of the quasilinear pseudo-parabolic equation defined on ${\Omega}{\subset}R^d$, $1{\leq}d{\leq}3$. We construct the semidiscrete approximations of ${\nabla}u$ and $a(u){\nabla}u+b(u){\nabla}u_t$ as well as u and prove the existence of the semidiscrete approximations. And also we prove the optimal convergence of ${\nabla}u$ and $a(u){\nabla}u+b(u){\nabla}u_t$ as well as u in $L^2$ normed space.