• Journal of the Chungcheong Mathematical Society
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• v.31 no.1
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• pp.1-12
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• 2018

Let R be a 3!-torsion free noncommutative semiprime ring, and suppose there exists a Jordan derivation $D:R{\rightarrow}R$ such that $D^2(x)[D(x),x]=0$ or $[D(x),x]D^2(x)=0$ for all $x{\in}R$. In this case we have $f(x)^5=0$ for all $x{\in}R$. Let A be a noncommutative Banach algebra. Suppose there exists a continuous linear Jordan derivation $D:A{\rightarrow}A$ such that $D^2(x)[D(x),x]{\in}rad(A)$ or $[D(x),x]D^2(x){\in}rad(A)$ for all $x{\in}A$. In this case, we show that $D(A){\subseteq}rad(A)$.

• Journal of the Korean Mathematical Society
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• v.56 no.3
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• pp.579-594
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• 2019

A colored space is a pair (X, r) of a set X and a function r whose domain is $\(^X_2\)$. Let (X, r) be a finite colored space and $Y,\;Z{\subseteq}X$. We shall write $Y{\simeq}_rZ$ if there exists a bijection $f:Y{\rightarrow}Z$ such that r(U) = r(f(U)) for each $U{\in}\({^Y_2}\)$ where $f(U)=\{f(u){\mid}u{\in}U\}$. We denote the numbers of equivalence classes with respect to ${\simeq}_r$ contained in $\(^X_i\)$ by $a_i(r)$. In this paper we prove that $a_2(r){\leq}a_3(r)$ when $5{\leq}{\mid}X{\mid}$, and show what happens when equality holds.

• Journal of the Korean Wood Science and Technology
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• v.8 no.1
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• pp.22-27
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• 1980

Quantitative assessment of edge blunting of saw-teeth was carried out by TALYSURF. 1. Using the following equation, the real shape of a saw-tooth can be traced on the graph of TALYSURF. ${\frac{{\Delta}h}{h}}={\frac{V{\Delta}_x}{V_x}}$ {${\Delta}h$: vertical distance of stylus h: vertical distance in chart $V{\Delta}_x$: Velocity of stylus $V_x$: velocity of chart} 2. As shown on Fig 2, the error from stylus itself can be calculated by following equation. i) 13.8${\mu}{\leqq}$x<20.4${\mu}$ y=-0.2246x+4.59${\mu}$ ii) 0${\leqq}$x<13.8${\mu}$ y=${\sqrt{(-18{\mu})^2-x^2}}-1.42x+32.7{\mu}}$ 3. The relationship between profile of saw-tooth and error from stylus itself can be calculated by following equation. $E(%)=\frac{f(r){\times}{\frac{4}{18{\mu}}}}{f(R){\times}{\frac{R}{18.5{\mu}}}-f(r){\times}{\frac{r}{18{\mu}}}}{\times}100$ {E(%)${\frac{error\;of\;stylus}{dullness\;of\;saw\;tooth}}{\times}100$ r: radius of stylus tip R: radius of tip which is drawn in graph of talysurf f(r) : error of stylus f(R) : dullness of tip which is drawn in graph of talysurf} 4. The graph of maximum error and profile of saw-tooth was parabola.

• Journal of the Korean Mathematical Society
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• v.50 no.5
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• pp.1105-1127
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• 2013

Let C[0, $t$] denote the function space of real-valued continuous paths on [0, $t$]. Define $X_n\;:\;C[0,t]{\rightarrow}\mathbb{R}^{n+1}$ and $X_{n+1}\;:\;C[0,t]{\rightarrow}\mathbb{R}^{n+2}$ by $X_n(x)=(x(t_0),x(t_1),{\ldots},x(t_n))$ and $X_{n+1}(x)=(x(t_0),x(t_1),{\ldots},x(t_n),x(t_{n+1}))$, respectively, where $0=t_0 <; t_1 <{\ldots} < t_n < t_{n+1}=t$. In the present paper, using simple formulas for the conditional expectations with the conditioning functions $X_n$ and $X_{n+1}$, we evaluate the $L_p(1{\leq}p{\leq}{\infty})$-analytic conditional Fourier-Feynman transforms and the conditional convolution products of the functions, which have the form $fr((v_1,x),{\ldots},(v_r,x)){\int}_{L_2}_{[0,t]}\exp\{i(v,x)\}d{\sigma}(v)$ for $x{\in}C[0,t]$, where $\{v_1,{\ldots},v_r\}$ is an orthonormal subset of $L_2[0,t]$, $f_r{\in}L_p(\mathbb{R}^r)$, and ${\sigma}$ is the complex Borel measure of bounded variation on $L_2[0,t]$. We then investigate the inverse conditional Fourier-Feynman transforms of the function and prove that the analytic conditional Fourier-Feynman transforms of the conditional convolution products for the functions can be expressed by the products of the analytic conditional Fourier-Feynman transform of each function.

• Journal of Aquaculture
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• v.10 no.3
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• pp.261-271
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• 1997

Ammonia removal capacities of five submerged filter media, 2~3mm sand, 30~50mm gravel, 20~40mm coral sand, polythylene net, and corrugated plastic plate in a seawater recirculating system were tested. A rotating biological contactor (RBC) was also tested for comparison. Oxygen consumption rates were measured along with the ammonia removal efficiencies. The ammonia concentrations in the system were maintained from 0.052 to 0.904 mg/l (mean 0.338$\pm$0.219 mg/l) and the water temperature was ranged from 19.2 to $21.4^{\circ}C\;(mean 20.2^{\circ}C\pm0.58^{\circ}C$). The 1/2-order kinetic model (Y:g/$m^3$/day) and the mean ammonia removal rates (g/$m^3$/day) of the filter media were : Sand : Y=135.5X0.5-25.1(r2=0.8110), 45.1 Coral sand : Y=125.1X0.5-33.0 (r2=0.7307), 31.8 Polyethylene net : Y=87.4X0.5-20.1 (r2=0.6780), 25.2 Corrugated plastic plate : Y=87.4X0.5-20.1(r2=0.5206), 19.2 Gravel : Y=4307X0.5-5.5 (r2=0.2596), 17.1 RBC : Y=127.6X0.5-33.4 (r2=0.7146), 32.8 where X is the concentration of ammonia. Oxygen consumption rates well corresponded to the ammonia removal capacities of each filter medium, thus the sands showing the highest value (442g/$m^3$/day) followed by coral sands (291.1g/$m^3$/day), polyethylene nets (236.9g/$m^3$/day), gravels (135.6g/$m^3$/day) and corrugated plastic plates (134.2g/$m^3$/day). Oxygen consumption rate of the RBC was unable to measure because of the characteristics of the structure.

• Communications of the Korean Mathematical Society
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• v.33 no.1
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• pp.103-125
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• 2018

Let R be a 5!-torsion free semiprime ring, and let $D:R{\rightarrow}R$ be a Jordan derivation on a semiprime ring R. Then $[D(x),x]D(x)^2=0$ if and only if $D(x)^2[D(x), x]=0$ for every $x{\in}R$. In particular, let A be a Banach algebra with rad(A) and if D is a continuous linear Jordan derivation on A, then we show that $[D(x),x]D(x)2{\in}rad(A)$ if and only if $D(x)^2[D(x),x]{\in}rad(A)$ for all $x{\in}A$ where rad(A) is the Jacobson radical of A.

• Korean Journal of Soil Science and Fertilizer
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• v.35 no.5
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• pp.264-271
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• 2002

Nitrogen releasing characteristics of polymer-coated urea(PCU) that made acrylic synthetic resins were studied in incubated soil, water and paddy soil. Also, their correlations and degradation patterns of coating material were tested. Releasing rate of nitrogen from PCU decreased with increasing coating rate. N001(coating rate 8.5%) and N003(coasting rater 6.3%) were low releasing amount at the early stage, whereas N005(coating rate 4.8%) was released over 80% within 20 days. Relationship of the releasing rate between incubated soil($25^{\circ}C$) and paddy soil could be described as follows : $Y=-0.0011X^2+2.2931X-50.264(R^2=0.9884)$ for N001, $Y=-0.0016X^2+1.1587X+5.5064(R^2=0.9805)$ for N003 and $Y=-0.03X^2+6.499X-243.22(R^2=0.9422)$ for N005, respectively (Y: release rate at field condition, X: experiment period). Relationship of the releasing rate between incubated water($30^{\circ}C$) and paddy soil can be described as follows : $Y=0.0011X^2+2.2601X-25.329(R^2=0.9884)$ for N001, $Y=-0.0306X^2+4.4994X-76.307(R^2=0.955)$ for N003 and $Y=-0.0164X^2+3.7764X-108.22(R^2=0.9422)$ for N005. After 150 days, coating materials of N001, N003, and N005 in incubated soil were degraded approximately 23%, 22% and 15%, respectively. Also The scanning electron microscope examination of coating material revealed that particle surface became gradually shattered with the time after the soil treatment.

• Journal of the Korean Ceramic Society
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• v.40 no.6
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• pp.513-518
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• 2003

La/sub 2/3-x/Li/sub 3x/□/sub 1/3-2x/TiO₃ compounds with x=0.13 and 0.12 were prepared by slow cooling (x=0.13) and rapid quenching (x=0.12) into the liquid nitrogen after sintering at 1350℃ for 6 h. Their crystal structure has been determined by Rietveld refinement of both the powder neutron and X-ray diffraction data. From neutron diffraction data, we found that the main phase was not tetragonal (P4/mmm), but trigonal (R3cH). The refinement of neutron diffraction for the slow cooled samples were in a good agreement with a new model; a mixture of trigonal (R3cH, 45.7 wt％), tetragonal (p4/mmm, 37.0 wt％), and Li/sub 0.57/Ti/sub 0.86/O₂(pbnm, 17.2 wt%), but the quenched sample was found not to contain tetragonal (p4/mmm). X-ray diffraction data couldn't be well fitted because of the Poor scattering factor of lithium ions and the similar reflection patterns among trigonal (R3cH), tetragonal (p4/mmm), and cubic (Pm3m). We also knew that one transport bottlenecks is destroyed by one La vacancy in the case of trigonal (R3cH).

• Korean Journal of Soil Science and Fertilizer
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• v.33 no.1
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• pp.24-31
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• 2000

This study was conducted to determine the effect of soil physical characteristics on rhizome rot incidence of platycodon. Sampling sites were Keochang 4, Kimhae 7, Haman 6, Chinju 6 and Koseong 3 fields in Kyongnam province and Hongcheon 6 fields in Kangwon province. The root disease incidence rate was correlated with soil depth Y=-0.747X+88.19($R^2=0.394^{***}$), soil hardness Y=4.36X+8.93($R^2=0.201^*$), bulk density Y=104.7X-80.99($R^2=0.295^{**}$), clay content Y=1.24X+14.14($R^2=0.196^*$), porosity Y=-3.11X+215.9($R^2=0.220^*$) and silt content Y=-0.75X+67.85($R^2=0.178^*$). The yield was correlated with soil depth Y=0.263X+0.971($R^2=0.105^*$), clay content Y=-0.688X+32.74($R^2=0.158^*$), porosity Y=1.974X-93.19($R^2=0.231^{**}$) and silt content Y=53.05X-108.65($R^2=0.232^*$), The optimum cultivated land of perennial platycodon was soil depth over 1m, soil hardness under $5kg\;cm^{-2}$, bulk density $1.0Mg\;m^{-3}$, moisture content 13~17%. clay content 5~10%, porosity 58~63%, silt content 38~64% and soil texture of silt loam.

• Communications of the Korean Mathematical Society
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• v.32 no.3
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• pp.535-542
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• 2017

Let R be an associative ring and ${\alpha},{\beta}:R{\rightarrow}R$ ring homomorphisms. An additive mapping $d:R{\rightarrow}R$ is called an (${\alpha},{\beta}$)-derivation of R if $d(xy)=d(x){\alpha}(y)+{\beta}(x)d(y)$ is fulfilled for any $x,y{\in}R$, and an additive mapping $D:R{\rightarrow}R$ is called a generalized (${\alpha},{\beta}$)-derivation of R associated with an (${\alpha},{\beta}$)-derivation d if $D(xy)=D(x){\alpha}(y)+{\beta}(x)d(y)$ is fulfilled for all $x,y{\in}R$. In this note, we intend to generalize a theorem of Vukman [5], and a theorem of Daif and El-Sayiad [2].