• Journal of applied mathematics & informatics
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• 제28권3_4호
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• pp.1003-1008
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• 2010

In allelic model $X\;=\;(x_1,\;x_2,\;\cdots,\;x_d)$, $$M_f(t)\;=\;f(p(t))\;-\;\int_0^t\;Lf(p(t))ds$$ is a P-martingale for diffusion operator L under the certain conditions. In this note, we define $T_tf\;=\;E_{p_0}^{p^*}\;[f((P(t))]$ for $t\;{\geq}\;0$ for using a new diffusion operator $L^*$ and we show the diffusion relations between $T_t$ and diffusion operator $L^*$.

• Korean Journal of Mathematics
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• 제26권1호
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• pp.75-85
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• 2018

In this paper, we study nonconstant warping functions on an Einstein warped product manifold $M=B{\times}_{f^2}F$ with a warped product metric $g=g_B+f(t)^2g_F$. And we consider a 2-dimensional base manifold B with a metric $g_B=dt^2+(f^{\prime}(t))^2du^2$. As a result, we prove the following: if M is an Einstein warped product manifold with a 2-dimensional base, then there exist generally nonconstant warping functions f(t).

• Bulletin of the Korean Mathematical Society
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• 제33권3호
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• pp.377-383
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• 1996

We consider in this paper the following nonlinear regression model $$ (1.1) y_t = f(x_t, \theta_o) + \in_t, t = 1, \ldots, n, $$ where $y_t$ is the tth response, $x_t$ is m-vector imput variable, $\theta_o$ is a p-vector of unknown parameter belong to a parameter space $\Theta, f:R^m \times \Theta \ to R^1$ is a nonlinear known function, and $\in_t$ are independent unobservable random errors with finite second moment.

• Journal of Environmental Health Sciences
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• 제43권6호
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• pp.525-531
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• 2017

Objectives: The purpose of this experiment is to better understand the nitrogen and phosphorus removal ratio according to operating conditions in an iron electrolysis system consisting of an anoxic basin, aerobic basin, and iron precipitation apparatus. Methods: Iron electrolysis consists of an iron precipitation reactor composed of iron plates in oxic and anoxic basins. We studied the interrelation coefficient between T-N and T-P removal rates and F/M ratio, and the C/N ratio and BOD removal rate. Results: The F/M ratio and the T-N and T-P removal rate per unit area have interrelation coefficients of 0.362 and 0.603, respectively. The removal rate per MLVSS and the T-N and T-P removal rate per unit area have respective interrelation coefficients of 0.49 and 0.59. Conclusions: The removal rate of T-N and T-P increased with the increasing F/M ratio in the influent, and they also linearly increased in proportion to the C/N ratio of influent and BOD removal rate of the reactor.

• Journal of the Korean Mathematical Society
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• 제53권5호
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• pp.1167-1182
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• 2016

Let M be an R-module, where R is a commutative ring with identity 1 and let G(V,E) be a graph. In this paper, we study the graphs associated with modules over commutative rings. We associate three simple graphs $ann_f({\Gamma}(M_R))$, $ann_s({\Gamma}(M_R))$ and $ann_t({\Gamma}(M_R))$ to M called full annihilating, semi-annihilating and star-annihilating graph. When M is finite over R, we investigate metric dimensions in $ann_f({\Gamma}(M_R))$, $ann_s({\Gamma}(M_R))$ and $ann_t({\Gamma}(M_R))$. We show that M over R is finite if and only if the metric dimension of the graph $ann_f({\Gamma}(M_R))$ is finite. We further show that the graphs $ann_f({\Gamma}(M_R))$, $ann_s({\Gamma}(M_R))$ and $ann_t({\Gamma}(M_R))$ are empty if and only if M is a prime-multiplication-like R-module. We investigate the case when M is a free R-module, where R is an integral domain and show that the graphs $ann_f({\Gamma}(M_R))$, $ann_s({\Gamma}(M_R))$ and $ann_t({\Gamma}(M_R))$ are empty if and only if $$M{\sim_=}R$$. Finally, we characterize all the non-simple weakly virtually divisible modules M for which Ann(M) is a prime ideal and Soc(M) = 0.

• Journal of the Korean Mathematical Society
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• 제33권4호
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• pp.763-775
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• 1996

For $Q = [0,S] \times [0,T]$ let C(Q) denote Yeh-Wiener space, i.e., the space of all real-valued continuous functions x(s,t) on Q such that x(0,t) = x(s,0) = 0 for every (s,t) in Q. Yeh [10] defined a Gaussian measure $m_y$ on C(Q) (later modified in [13]) such that as a stochastic process ${x(s,t), (s,t) \epsilon Q}$ has mean $E[x(s,t)] = \smallint_{C(Q)} x(s,t)m_y(dx) = 0$ and covariance $E[x(s,t)x(u,\upsilon)] = min{s,u} min{t,\upsilon}$. Let $C_\omega \equiv C[0,T]$ denote the standard Wiener space on [0,T] with Wiener measure $m_\omega$. Yeh [12] introduced the concept of the conditional Wiener integral of F given X, E(F$\mid$X), and for case X(x) = x(T) obtained some very useful results including a Kac-Feynman integral equation.

• Communications of the Korean Mathematical Society
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• 제16권4호
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• pp.621-626
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• 2001

Let { $A_{>o}$ t= exp(M log t)} $_{t}$ be a dilation group where M is a real n$\times$n matrix whose eigenvalues has strictly positive real part, and let $\rho$be an $A_{t}$ -homogeneous distance function defined on ( $R^{n}$ ). Suppose that K is a function defined on ( $R^{n}$ ) such that /K(x)/$\leq$ (No Abstract.see full/text) for a decreasing function defined on (t) on R+ satisfying where wo(x)=│log│log (x)ll. For f$\in$ $L_{1}$ ( $R^{n}$ ), define f(x)=sup t>0 Kt*f(x)=t-v K(Al/tx) and v is the trace of M. Then we show that \ulcorner is a bounded operator of $L_{-{1}( $R^{n}$ ) into $L^1$,$\infty$( $R^{n}$).

• Bulletin of the Korean Mathematical Society
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• 제56권2호
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• pp.439-450
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• 2019

Let R be a ring with unity. Given modules $M_R$ and $_RN$, $M_R$ is said to be absolutely $_RN$-pure if $M{\otimes}N{\rightarrow}L{\otimes}N$ is a monomorphism for every extension $L_R$ of $M_R$. For a module $M_R$, the subpurity domain of $M_R$ is defined to be the collection of all modules $_RN$ such that $M_R$ is absolutely $_RN$-pure. Clearly $M_R$ is absolutely $_RF$-pure for every flat module $_RF$, and that $M_R$ is FP-injective if the subpurity domain of M is the entire class of left modules. As an opposite of FP-injective modules, $M_R$ is said to be a test for flatness by subpurity (or t.f.b.s. for short) if its subpurity domain is as small as possible, namely, consisting of exactly the flat left modules. Every ring has a right t.f.b.s. module. $R_R$ is t.f.b.s. and every finitely generated right ideal is finitely presented if and only if R is right semihereditary. A domain R is $Pr{\ddot{u}}fer$ if and only if R is t.f.b.s. The rings whose simple right modules are t.f.b.s. or injective are completely characterized. Some necessary conditions for the rings whose right modules are t.f.b.s. or injective are obtained.

• Asian-Australasian Journal of Animal Sciences
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• 제2권3호
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• pp.370-371
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• 1989

• Journal of the Korean Society of Fisheries and Ocean Technology
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• 제31권1호
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• pp.29-44
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• 1995

A model experiment on the pair midwater trawl net applicable to 800 PS class Korean pair bottom trawlers was carried out in the special-prepared experimental thank. the tank was prepared as a reverse trapezoid shape in its vertical section by digging out flat soil. The dimension of the tank showed the 9.6 W$\times$43.0 L(m) of the upper fringe and the 4.8 W$\times$38.0 L(m) of the bottom with 3.0m in depth. The depth of water was maintained 2.7m during experiment. The model net was prepared based on the Tauti's similarity law of fishing gear in 1/30 scale considering the dimension of the experimental tank. Mouth performance of the model net during towing were determined by the photographs taken in front of the net mouth with the combinations of towing velocity, warp length and distance between paired boats. The results obtained can be summarized as follows: 1. Vertical opening of the model nets A and B was varied in the range of 0.18~0.88 m and 0.21~0.78 m (which can be converted into 5.4~26.4m and 6.3~23.4 m in the full-scale net) respectively, and was varied predominantly by towing speed. Vertical opening (H which is appendixed m for the model net. f for the full-scale net. A and B for the types of the model net) can be expressed as the function of towing velocity$V_t$as in the model net $V_t$ : m/ sec)$H_{mA}$=1.67$e^{-1.65V_t}$ $H_{mB}$=1.15$e^{-1.13V_t}$, in the full-scale net ($V_t$ : k't) $H_{fA}$=50.27$e^-0.37V_t$ $H_{fB}$=34.46$e^{-0.26Vt}$. 2. Horizontal opening of the model nets An and b was varied in the range of 1.03~1.54m and 1.04~1.55 m (which can be converted into 30.9~46.2 m and 31.2~46.5m in the full-scale net) respectively, and was varied predominantly by distance between paired boats. Horizontal opening (W, appendixes are as same as the former) an be expressed as the function of distance between paired boats $D_b$as in the model net $W_{mA}$=0.69+0.09$D_b$ $W{mB}$=0.73+0.09$D_b$, in the full-scale net $W_{fA}$=20.81+0.09$D_b$ $W_{fB}$=22.11+0.09$D_b$ 3. Net opening area of the model net A and B was varied in the range of 0.28~1.04 $m^2$ and 0.33~0.94$m^2$(which can be converted into 252~936$m^2$ and 297~846$m^2$ in the full-scale net) respectively, and was varied predominantly by towing velocity. Net opening area ($S$, appendixes are as same as the former) van be expressed as the function of towing velocity$V_t$ as in the model net $v_t$ : m/sec) $S_{Ma}$=2.01$e^{-1.54V_T}$ $S_{mA}$=1.40$e^{-1.65V_t}$, in the full-scale net ($V_t$ : k't) $S_{fA}$=1.807$e^-0.35V_t$ $S_{fA}$=1.265$e^{-0.24V_t}$. 4. Filtering volume of the model nets A and B was varied in the range of 0.32~0.55 $m^3$ and 0.37~0.55$m^3$(which can be converted into 8.640~14.850 $m^3$ and 9.990~14.850$m3$in the full~scale net) respectively, and was predominantly varied by towing speed. filtering volume of the model net-A showed the maximum at the towing speed 0.69 m/sec(3 k't in the full-scale net), compared with that of the model net B showed at 0.92 m/sec(4 k't in the full-scale net).