• Bulletin of the Korean Mathematical Society
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• v.53 no.5
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• pp.1385-1394
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• 2016

Let (R, m) be a Noetherian local ring, I, J two ideals of R, and A an Artinian R-module. Let $k{\geq}0$ be an integer and $r=Width_{>k}(I,A)$ the supremum of lengths of A-cosequences in dimension > k in I defined by Nhan-Hoang [9]. It is first shown that for each $t{\leq}r$ and each sequence $x_1,{\cdots},x_t$ which is an A-cosequence in dimension > k, the set $$\Large(\bigcup^{t}_{i=0}Att_R(0:_A(x_1^{n_1},{\ldots},x_i^{n_i})))_{{\geq}k}$$ is independent of the choice of $n_1,{\ldots},n_t$. Let r be the eventual value of $Width_{>k}(0:_AJ^n)$. Then our second result says that for each $t{\leq}r$ the set $\large(\bigcup\limits_{i=0}^{t}Att_R(Tor_i^R(R/I,\;(0:_AJ^n))))_{{\geq}k}$ is stable for large n.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.9 no.1
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• pp.79-90
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• 2005

In this paper we study the numerical solutions of the stochastic differential equations of the form $$du(x,\;t)=f(x,\;t,\;u)dt\;+\;g(x,\;t,\;u)dW(t)\;+\;\sum\limits_{|q|\leq2m}\;A_q(x,\;t)D^qu(x,\;t)dt$$ where $0\;{\leq}\;t\;{\leq}\;T,\;x\;{\in}\;R^{\nu}$, ($R^{nu}$ is the $\nu$-dimensional Euclidean space). Here $u\;{\in}\;R^n$, W(t) is an n-dimensional Brownian motion, $$f\;:\;R^{n+\nu+1}\;{\rightarrow}\;R^n,\;g\;:\;R^{n+\nu+1}\;{\rightarrow}\;R^{n{\times}n},$$, and $$A_q\;:\;R^{\nu}\;{\times}\;[0,\;T]\;{\rightarrow}\;R^{n{\times}n}$$ where ($A_q,\;|\;q\;|{\leq}\;2m$) is a family of square matrices whose elements are sufficiently smooth functions on $R^{\nu}\;{\times}\;[0,\;T]\;and\;D^q\;=\;D^{q_1}_1_{\ldots}_{\ldots}D^{q_{\nu}}_{\nu},\;D_i\;=\;{\frac{\partial}{\partial_{x_i}}}$.

• The Transactions of the Korean Institute of Electrical Engineers C
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• v.55 no.7
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• pp.344-348
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• 2006

The effect of x on microwave dielectric properties of the $(1-x)Mg_4Ta_2O_9-x(TiO_2,\;CaTiO_3,\;SrTiO_3)$ ceramics for microwave components were investigated. All spcecimens prepared by the conventional mixed oxied method and sintered at $1450^{\circ}C$. Microwave dielectric properties of the $(1-x)Mg_4Ta_2O_9-xTiO_2$ ceramics were influenced by $MgTi_2O_5$ phase. Also the microwave dielectric properties of the $(1-x)Mg_4Ta_2O_9-x(TiO_2,\;CaTiO_3,\;SrTiO_3)$ ceramics were dominated with an addition of $CaTiO_3\;and\;SrTiO_3$. The dielectric constant $(\varepsilon_r)$, quality factor $(Q{\times}f_r)$ and temperature coefficient of the resonant frequency $(TCRF,\;\tau_f)$ of the $(1-x)Mg_4Ta_2O_9-x(TiO_2,\;CaTiO_3,\;SrTiO_3)$ ceramics were $12.96\sim70.98,\;5,132\sim186,410GHZ$ and $-35.82\sim+75.96ppm/^{\circ}C$, respectively, and depend on x and addition materials.

• Korean Journal of Soil Science and Fertilizer
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• v.32 no.3
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• pp.215-222
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• 1999

Platycodon root contains abundant pharmaceutical substances and is widely used as a food and a medicinal herb. This study was conducted to determine the cultural environment and soil morphological characteristics of platycodon. Sampling sites were Keochang 4, Kimhae 7, Haman 6, Chinju 6 and Koseong 3 fields in Kyongnam province and Hongcheong 6 fields in Kangwon province. The average continious cropping year was highest Chinju 8.0-years old, whereas lowest Hongcheon 2.3-years old. The average cropping area and compost application were highest Hongcheon 1.3ha and $108Mg\;ha^{-1}$ respectively than other areas. The slope was in order to Koseong steep slope with 35%. Koechang 28%, Flaman 16%, Chinju 11.7%, Kimhae 11% and Hongcheon 7.5%. The drainage classes was well drained in Koechang. Kimhae, Chinju and Koseong, while it s poorly drained in Hongcheon and Haman. Distribution of topography was highest rolling 37.9% and drainage classes was highest well drained 48.3%. The root disease incidence rate was in the order of Haman 56.8%, Hongcheon 52.5%, Kimhae 36.7%, Koechang 35.3%, Chinju 32.3% and Koseong 30.0%. The yield at the Chinju $36.17Mg\;ha^{-1}$ was higher than that of Koseong $25.00Mg\;ha^{-1}$, Kimhae $13.57Mg\;ha^{-1}$, Koechang $11.75Mg\;ha^{-1}$, Haman $9.50Mg\;ha^{-1}$ and Hongcheon $5.24Mg\;ha^{-1}$. The average temperature was correlated with the disease incidence rate by $Y=3.07X^2-87.16X+649.26(R^2=0.947^{**})$ and yield by $Y=-478.68X^2+13403X-90836(R^2=0.763^*)$. The root disease incidence rate was correlated with drainage classes Y=19.1X-5.26($R^2=0.592{***}$), topography Y=9.68X+10.77($R^2=0.205^{**}$) and slope Y=0.85X+-27.88 ($R^2=0.143^*$). The yield was correlated with drainage classes Y=-10X+42($R^2=0.348^{**}$), topography Y=-5.34X+34.5 ($R^2=0.134^*$) and slope Y=-0.68X+25.48($R^2=0.129^*$). The optimum cultivated land of perennial platycodon was average temperature $14^{\circ}C$, direction of southeast, topography of flat or undulating, slope of 0-6%, well drained.

• Development and Reproduction
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• v.10 no.4
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• pp.271-275
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• 2006

The objective of this study was to examine the early growth of haddock, Melanogrammus aeglefinus larvae from a series of reared specimens for provide information to developmental biology and more information on the aspect of aquaculture in the larvae of this species. Larvae were reared in the laboratory and sampled periodically for developmental study until 67 days after hatching. An increase in total length of fish indicated continuous growth, described by the growth expression of the type $TL=3.5374e^{0.0536X}(r^2=0.8759$, where TL is total length and X is at days after hatching) and $BW=0.0002e^{0.1858X}(r^2=0.8671$, where BW is body weight and X is at days after hatching), respectively. Pattern of body depth and pectoral fin length are instantaneous growth which expression of the type $BD=0.3545e^{0.0778X},\;r^2=0.9563$(where BD is body depth and X is at days after hatching) for body depth growth and the type $PL=0.0111e^{0.1591X},\;r^2=0.9194$(where PL is pectoral fin length and X is at days after hatching) for pectoral fin length growth. The relationship of body depth and total length expressed as $BD=0.2397X-0.5735(r^2=0.9957$, where BD is body depth and X is total length), and pectoral fin length and total length is $PL=0.1929X-1.3767(r^2=0.9882$, where PL is pectoral fin length and X is total length) pectoral fin length against body depth simultaneously recorded for juvenile haddock(PL=0.8117BD-0.9718, $r^2=0.9814$, where PL is pectoral fin length and BD is body depth). Relationship of body depth and body weight was expressed the type of $BD=-9.4734X^2+19.046X+1.3672,\;r^2=0.941$(where BD is body depth and X is body weight), and pectoral fin length and body weight expressed the type of $PL=6.379X^2+14.023X+0.3774,\;r^2=0.9494$(where PL is pectoral fin length and X is body weight). From this point view, growth characteristics of juvenile haddock in this experiment may be useful to establish a successful culture technique for rearing larval haddock.

• Journal of the Korean Ceramic Society
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• v.38 no.3
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• pp.280-286
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• 2001

10 이하의 저유전율을 갖는 (1-x)BaWO$_4$-xMg$_2$SiO$_4$(x=0.1~0.9) 세라믹스의 미세구조와 고주파 유전특성을 조사하였다. (1-x)BaWO$_4$-xMg$_2$SiO$_4$(x=0.1~0.9) 세라믹스는 정방정(tetragonal) 구조를 가진다. 0.1BaWO$_4$-0.9Mg$_2$SiO$_4$세라믹스는 BaWO$_4$와 $Mg_2$SiO$_4$의 상들이 공존하는 혼합상을 보였으며, $Mg_2$SiO$_4$가 이차사으로 형성된 것이 관찰되었다. 120$0^{\circ}C$~140$0^{\circ}C$에서 2시간 동안 소결된 (1-x)BaWO$_4$-xMg$_2$SiO$_4$(x=0.1~0.9) 세라믹스는 $\varepsilon$$_{r}$=6.37~8.21, Q.f=15000~99422 그리고 $ au$$_{f}$=73.9~48.9 ppm/$^{\circ}C$의 고주파 유전특성을 가졌다. $\tau$$_{f}$를 보정하기 위해, CaTiO$_3$(1,5 wt%)가 (1-x)BaWO$_4$-xMg$_2$SiO$_4$(x$\geq$0.9) 세라믹스에 첨가되었다. 135$0^{\circ}C$에서 2시간 동안 소결된 0.1BaWO$_4$-0.9Mg$_2$SiO$_4$+CaTiO$_3$(5 wt%) 세라믹스는 $\varepsilon$$_{r}$=7.3, Q.f=30532 그리고 $\tau$$_{f}$=-30 ppm/$^{\circ}C$의 고주파 유전특성을 얻었다. 얻었다.

• Korean journal of applied entomology
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• v.45 no.3 s.144
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• pp.327-331
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• 2006

This study was carried out to determine the economic injury level of the rice leaffolder,Cnaphalocrocis medinalis G.. The damage aspects of rice plant (at tilling stage) by leaf folders at different larval density per plant were studied in pot experiment (24 cm in diameter, 18 cm in height). One leaf folder consumed 6-7 leaves during larval stage. The damage by leaf folders was simulated by cutting off 0, 10, 30, 50, 70, and 90% of leaves before and after heading stage July 15th (at panicle initiation stage) and August 15th (at milk stage), respectively. When leaves were cut before the heading of rice, the linear relationships between the leaf cutting rate (X) and each factors of yield (Y) were as following; for grain maturity it was Y = -9.379X + 83.630 ($R^{2}=0.493$),\;Y = 0.139X + 0.490 ($R^{2}=0.925$) for yield, and Y = -4.880X + 81.116 ($R^{2}=0.665$) for head rice. When leaves were cut after the heading of rice, it was Y = -23.0l4X + 83.589 ($R{2}=0.915$), for grain maturity, Y=0.141X + 3.466 ($R^{2}=0.842$) for yield, and Y = -13.795X + 81.964 ($R^{2}=0.898$) for head rice. We found that when leaf cutting after the heading stage caused more damage than before the heading in terms of yield and yield components. Based on theses results the economic threshold level was estimated to be 30% and 7% leaf loss before and after heading stage.

• Communications of the Korean Mathematical Society
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• v.23 no.3
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• pp.333-342
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• 2008

We introduce weak Armendariz ideals which are a generalization of ideals have the weakly insertion of factors property (or simply weakly IFP) and investigate their properties. Moreover, we prove that, if I is a weak Armendariz ideal of R, then I[x] is a weak Armendariz ideal of R[x]. As a consequence, we show that, R is weak Armendariz if and only if R[x] is a weak Armendariz ring. Also we obtain a generalization of [8] and [9].

• Bulletin of the Korean Mathematical Society
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• v.45 no.1
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• pp.59-66
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• 2008

Keskin and Harmanci defined the family B(M,X) = ${A{\leq}M|{\exists}Y{\leq}X,{\exists}f{\in}Hom_R(M,X/Y),\;Ker\;f/A{\ll}M/A}$. And Orhan and Keskin generalized projective modules via the class B(M, X). In this note we introduce X-local summands and X-hollow modules via the class B(M, X). Let R be a right perfect ring and let M be an X-lifting module. We prove that if every co-closed submodule of any projective module P contains Rad(P), then M has an indecomposable decomposition. This result is a generalization of Kuratomi and Chang's result [9, Theorem 3.4]. Let X be an R-module. We also prove that for an X-hollow module H such that every non-zero direct summand K of H with $K{\in}B$(H, X), if $H{\oplus}H$ has the internal exchange property, then H has a local endomorphism ring.

• Journal of the Korean Society of Clothing and Textiles
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• v.9 no.1
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• pp.17-27
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• 1985

In order to investigate the warmth retaining properties of fabrics some characteristics such as thickness. porosity, packing density, thermal conductivity, moisture regain and air permeability were measured and experimental results were analysed statistically to relate the warmth retaining properties with those characteristics. From the analysis, the following results were obtained. 1. When the warmth retaining properties of fabrics (Y) are dependent variable and thickness ($x_1$), porosity ($x_2$), packing density ($x_3$), thermal conductivity ($x_4$), moisture regain ($x_5$) and air permeability ($x_6$) are independent variables, the regression equation of warmth retaining properties can be represented as follows. 1) Y= 1.6005+46.817$x_1$, (R=0.9487) 2)Y=-1.4187+26.5072$x_1$+0.2055$x_2$(R=0.9704) 3) Y= -3.6908+17.4482$x_1$+0.1782$x_2$+28.3243$x_3$ (R=0.9756) 4) Y=0.9202+16.9553$x_1$+0. 1167$x_2$+30.3577$x_3$+1.8884$x_4$ (R=0.9792) 5) Y=0.9353+17.2266$x_1$+0.1177$x_2$+28.9821$x_3$-1.8302$x_4$+0.0151$x_5$ (R=0.9792) 6) Y=0.7583+17.2343$x_1$+0.1196$x_2$+28.8830$x_3$-1.8336$x_4$+0.0187$x_5$0.0004$x_5$ (R=0.9792) 2. The warmth retaining properties of fabrics are merely affected by adding thermal conductivity, moisture regain and multiple regression equation which contains thickness, porosity and packing density as variables. Therefore the multiple regression which contains thickness, porosity and packing density as variables Y=-3.6908+17.4482$x_1$+0.1782$x_2$+28.3243$x_3$ is highly practical.