• Communications of the Korean Mathematical Society
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• v.33 no.4
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• pp.1141-1158
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• 2018

Hahn difference operator $D_{q,{\omega}}$ which is defined by $$D_{q,{\omega}}g(t)=\{{\frac{g(gt+{\omega})-g(t)}{t(g-1)+{\omega}}},{\hfill{20}}\text{if }t{\neq}{\theta}:={\frac{\omega}{1-q}},\\g^{\prime}({\theta}),{\hfill{83}}\text{if }t={\theta}$$ received a lot of interest from many researchers due to its applications in constructing families of orthogonal polynomials and in some approximation problems. In this paper, we investigate sufficient conditions for stability of the abstract linear Hahn difference equations of the form $$D_{q,{\omega}}x(t)=A(t)x(t)+f(t),\;t{\in}I$$, and $$D^2{q,{\omega}}x(t)+A(t)D_{q,{\omega}}x(t)+R(t)x(t)=f(t),\;t{\in}I$$, where $A,R:I{\rightarrow}{\mathbb{X}}$, and $f:I{\rightarrow}{\mathbb{X}}$. Here ${\mathbb{X}}$ is a Banach algebra with a unit element e and I is an interval of ${\mathbb{R}}$ containing ${\theta}$.

• Bulletin of the Korean Mathematical Society
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• v.56 no.2
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• pp.419-437
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• 2019

This paper investigates skew ${\Theta}-{\lambda}$-constacyclic codes over $R=F_0{\oplus}F_1{\oplus}{\cdots}{\oplus}F_{k-1}$, where $F{_i}^{\prime}s$ are finite fields. The structures of skew ${\lambda}$-constacyclic codes over finite commutative semi-simple rings and their duals are provided. Moreover, skew ${\lambda}$-constacyclic codes of arbitrary length are studied under a new definition. We also show that a skew cyclic code of arbitrary length over finite commutative semi-simple rings is equivalent to either a cyclic code over R or a quasi-cyclic code over R.

• Journal of Biosystems Engineering
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• v.4 no.1
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• pp.1-23
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• 1979

The use of barley seeder attached to rotary tiller in the rural area has a significant meaning not only for the solution of labor peak season, but also for the increase of land utilization efficiency. The facts that presently being used barley seeders are all based on the mechanical principles of the reverse rotation, center drive and are all using forward rotating tine, which is used to be easily and heavily worn out when it rotates reversely, raise problem of recommending them to rural area in Korea. Therefore, the main objective of the study was to develop new type of rotary tine attachable to barley seeders. To attain the objective the following approaches were applied. (1) The kinematic analysis of reverse rotating barley seeders. (2) The studies on the soil bin and artificial soil. (3) The comparative experiment on the power requirement of prototype tine. The results obtained from the studies are summarized as follow: 1. The kinematic analysis of barley seeder attached to rotary tiller: The following results were obtained from the kinematic analysis for deriving general formulae of the motion and velocity characterizing the rotary tine of barley seeders presently being used by farmers. a) The position vector (P) of edge point (P) in the rotary tine of reverse rotating, center drive was obtained by the following formula. $$P=(vt+Rcos wt)i+Rsin wt j+ \{ Rcos \theta r sin \alpha cos (wt- \beta +\theta r) +Rsin \theta r sin \alpha sin (wt-\beta + \theta r) \} lk $$ b) The velocity of edge point $(P^')$ of reverse rotating, center drive rotary tine was obtained by the following formula. $$(P^')=(V-wR sin wt)i+(w\cdot Rcoswt)j + \{ -w\cdot Rcos \theta r\cdot sin \alpha \cdot sin (wt-\beta +\theta r) + w\cdot Rsin \theta r\cdot sin \alpha \cdot cos (wt- \beta + \theta r \} k $$ c) In order to reduce the power requirement of rotary tine, the angle between holder and edge point was desired to be reduced. d) In order to reduce the power requirement, the edge point of rotary tine should be moved from the angle at the begining of cutting to center line of machine, and the additional cutting width should be also reduced. 2. The studies on the soil bin and artificial soil: In order to measure the power requirement of various cutting tines under the same physical condition of soil, the indoor experiments Viere conducted by filling soil bin with artificially made soil similar to the common paddy soil and the results were as follows: a) When the rolling frequencies$(x)$ of the artificial soil were increased, the densIty$(Y)$ was also increased as follows: $$y=1.073200 +0.070780x - 0.002263x^2 (g/cm^3)$$ b) The absolute hardness $(Y)$ of soil had following relationship with the rolling frequencies$(x)$ and were increased as the rolling frequencies were increased. $$Y=37.74 - \frac {0.64 + 0.17x-0. 0054x^2} {(3.36-0.17x + 0.0054x^2)^3} (kg/cm^3)$$ c) The density of soil had significant effect on the cohesion and angle of internal friction of soil. For instance, the soil with density of 1.6 to 1.75 had equivalent density of sandy loam soil with 29.5% of natural soil moisture content. d) The coefficient of kinetiic friction of iron plate on artificial soil was 0.31 to 0.41 and was comparable with that of the natural soil. e) When the pulling speed of soil bin was the 2nd forward speed of power tiller, the rpm of driving shaft of rotary was similar to that of power tiller, soil bin apparatus is indicating the good indoor tester. 3. The comparative experiment on the power requirement of prototype tine of reverse rotating rotary: According to the preliminary test of rotary tine developed with various degrees of angle between holder and edge pcint due to the kinematic analysis, comparative test between prototype rotary tine with $30 ^\circ $ and $10 ^\circ$ of it and presently being used rotary tine was carried out 2nd the results were as follows: a) The total cutting torque was low when the angle between holder and edge point was reduced. b) $\theta r$ (angle between holder and edge point) of rotary tine seemed to be one: of the factors maximizing the increase of torque. c) As the angle between holder and edge point ($\theta r$) of rotary tine was $30 ^\circ $ rather than $45 ^\circ $, the angle of rotation during cutting soil was reduced and the total cutting torque was accordingly reduced about 10%, and the reduction efficiency of total cutting torque was low when the angle between holder and edge point ($\theta r$) of rotary tine was $10 ^\circ $, which indicates that the proper angle between holder and edge point of rotary tine should be larger than $10 ^\circ $ and smaller than $30 ^\circ $ . From above results, it could be concluded that the use of the prototype rotary tine which reduced the angle between holder and edge point to $30 ^\circ $, insted of $45 ^\circ $, is disirable not only decreasing the power requirements, but also increasing the durabie hour of it. Also forward researches are needed, WIlich determine the optimum tilted angle of rotary brocket, and rearrangement of the rotary tine on the rotary boss.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.14 no.4
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• pp.941-951
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• 1994

The resilient behavior of subbase materials, locally used in Korea. were evaluated in this study by performing laboratory MR tests. The variations of the MR value according to LVDT's location in experiments and moisture conditions, respectively, were evaluated. And, in order to determine the relevant MR characteristics of the prototype materials, laboratory model tests containing smaller particles than those of the prototype were conducted. Based on above results, the relationship of the MR and the bulk stress (${\theta}$) was suggested. The case using internal LVDT. gave much larger $M_R$ value than that using external LVDT, since the external LVDT somewhat overestimates the resilient strain. The measured $M_R$ in damp conditions ($S_r$=40%) was larger than that in wet conditions ($S_r$=70%) by about 10%. The relationship between the $M_R$ and the void ratio was linear according to particle size effect. The relationship of the $M_R$ and the bulk stress (${\theta}$) on subbase materials in damp conditions to be used in Korea could be recommended as $M_R=3960{\cdot}{\theta}^{0.60}$ psi.

• Journal of the Korean Electrochemical Society
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• v.10 no.3
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• pp.219-228
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• 2007

The phase-shift method and correlation constants, i.e., the electrochemical impedance spectroscopy (EIS) techniques for studying linear relationships between the behaviors (${\varphi}\;vs.\;E$) of the phase shift ($0^{\circ}{\leq}-{\varphi}{\leq}90^{\circ}$) for the optimum intermediate frequency and those (${\theta}\;vs.\;E$) of the fractional surface coverage ($1{\geq}{\theta}{\geq}0$), have been proposed and verified to determine the Langmuir, Frumkin, and Temkin adsorption isotherms (${\theta}\;vs.\;E$) of H for the cathodic $H_2$ evolution reaction (HER) at noble and transition-metal/aqueous solution interfaces. At the Pt/0.1 MKOH aqueous solution interface, the Langmuir, Frumkin, and Temkin adsorption isotherms (${\theta}\;vs.\;E$), equilibrium constants ($K=5.6{\times}10^{-10}\;mol^{-1}\;at\;0{\leq}{\theta}<0.81$, $K=5.6{\times}10^{-9}{\exp}(-4.6{\theta})\;mol^{-1}\;at\;0.2<{\theta}<0.8$, and $K=5.6{\times}10^{-10}{\exp}(-12{\theta})\;mol^{-1}\;at\;0.919<{\theta}{\leq}1$, interaction parameters (g = 4.6 for the Temkin and g = 12 for the Frumkin adsorption isotherm), rates of change of the standard free energy ($r=11.4\;kJ\;mol^{-1}$ for g=4.6 and $r=29.8\;kJ\;mol^{-1}$ for g=12), and standard free energies (${\Delta}G_{ads}^0=52.8\;kJ\;mol^{-1}\;at\;0{\leq}{\theta}<0.81,\;49.4<{\Delta}G_{\theta}^0<56.2\;kJ\;mol^{-1}\;at\;0.2<{\theta}<0.8$ and $80.1<{\Delta}_{\theta}^0{\leq}82.5\;kJ\;mol^{-1}\;at\;0.919<{\theta}{\leq}1$) of OH for the anodic $O_2$ evolution reaction (OER) are also determined using the phase-shift method and correlation constants. The adsorption of OH transits from the Langmuir to the Frumkin adsorption isotherm (${\theta}\;vs.E$), and vice versa, depending on the electrode potential (E) or the fractional surface coverage (${\theta}$). At the intermediate values of ${\theta}$, i.e., $0.2<{\theta}<0.8$, the Temkin adsorption isotherm (${\theta}\;vs.\;E$) correlating with the Langmuir or the Frumkin adsorption isotherm (${\theta}\;vs.\;E$), and vice versa, is readily determined using the correlation constants. The phase-shift method and correlation constants are accurate and reliable techniques to determine the adsorption isotherms and related electrode kinetic and thermodynamic parameters. They are useful and effective ways to study the adsorptions of intermediates (H, OH) for the sequential reactions (HER, OER) at the interfaces.

• Journal of the Korean Society for Heat Treatment
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• v.5 no.1
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• pp.13-22
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• 1992

The thermal stability of duplex high Mn-steel structure have been investigated using 15%Mn~1.0~2.4%C steels which are composed of ${\gamma}$-and ${\theta}$-phases in the range of temperature from 900 to $1100^{\circ}C$, and time from 50 to 300h. The results are as follows ; 1) The grain growth in single-phase region proceeds by grain boundary migration and the relation between mean radius $\bar{r}$ and annealing time t is described as follows ; $\bar{r}^2-{\bar{r}_0}^2=k_0{\cdot}t$ 2) The grain growth of duplex, (${\gamma}+{\theta}$), strucrure is slower than that single phase because the chemical composition of ${\gamma}$-and ${\theta}$-phases differs esch others. 3) The grain of (${\gamma}+{\theta}$) duplex structure grow slowly in a mode of Ostwald ripening. Because grain boundaries of ${\gamma}$-phase migrate under a restriction of pinning by ${\theta}$-phases. 4) In the duplex structures. the dispersed structures change to the dual-structures, as the volume fraction of the dispersed second-phase increase. Consequently, the growth-law, which is controlled by boundary-diffusion change to that of the volume diffusion-mechanism.

• Journal of Biosystems Engineering
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• v.13 no.3
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• pp.1-10
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• 1988

Fraser, Dombrowski, Tanasawa 그리고 Momono 등(等)이 분구(噴口)에 대(對)한 중자도구(中子導溝) 단면적(斷面積)의 비(比)에 기초을 두고 있는 Nozzle Parameter가 클수록 유량계수(流量係數)는 증가(增加)한다고 보고(報告)하였다. 그러나 노즐의 구조(構造)는 중자도구(中子導溝) 및 와실(渦室)의 형상(形狀)에 따라서 특성(特性)을 가지고 있고 구조(構造)의 특성(特性)은 유량계수(流量係數), 분무각(噴霧角) 및 살포도(撒布度)에 지대한 영향을 미친다. 노즐구조(構造)에 관(關)한 이론분석(理論分析)의 결과(結果)는 다음과 같다. 중자도구변(中子導溝邊)(d), 중자(中子)두께(t) 및 중자도구각(中子導溝角)(${\theta}$) 등(等)의 관계(關係)가 와실유선각(渦室流線角)(${\theta}_c$)에 미치는 영향은 $$tan({\theta}_c)=\frac{t{\cdot}sin^2{\theta}}{d-t{\cdot}sin{\theta}{\cdot}(1-cos{\theta})}$$ 또한 와실유선각(渦室流線角)(${\theta}_c$)이 중자도구각(中子導溝角)(${\theta}$)과 일치(一致)하는 관계(關係)는 $\frac{d}{t}=sin{\theta}$이다. 와실유선각(渦室流線角)과 와실형상(渦室形狀)과의 관계(關係)는 $$tan({\theta}_c){\qeq_-}\frac{r_c-r_g}{L_c}$$ 이며 와실유선각(渦室流線角)은 와실유선회전반경(渦室流線回轉半徑)과 와실(渦室)길이의 비(比)에 의(依)하여 변화(變化)함을 시사(示唆)한다. Swirl core가 Swirl plate보다는 생산비(生産費)의 고려없이 압력손실(壓力損失) 및 마찰손실 면(面)에서 더욱 합리적(合理的)으로 고려(考慮)된다.

• Journal of Ecology and Environment
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• v.33 no.2
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• pp.165-173
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• 2010

Soil respiration ($R_S$) is a critical component of the annual carbon balance of forests, but few studies thus far have attempted to evaluate empirical regression models in $R_S$. The principal objectives of this study were to evaluate the relationship between $R_S$ rates and soil temperature (ST) and soil water content (SWC) in soil from a cool-temperate deciduous broad-leaved forest, and to evaluate empirical regression models for the prediction of $R_S$ using ST and SWC. We have been measuring $R_S$, using an open-flow gas-exchange system with an infrared gas analyzer during the snowfree season from 1999 to 2001 at the Takayama Forest, Japan. To evaluate the empirical regression models used for the prediction of $R_S$, we compared a simple exponential regression (flux = $ae^{bt}$Eq. [1]) and two polynomial multiple-regression models (flux = $ae^{bt}{\times}({\theta}{\nu}-c){\times}(d-{\theta}{\nu})^f:$ Eq. [2] and flux = $ae^{bt}{\times}(1-(1-({\theta}{\nu}/c))^2)$: Eq. [3]) that included two variables (ST: t and SWC: ${\theta}{\nu}$) and that utilized hourly data for $R_S$. In general, daily mean $R_S$ rates were positively well-correlated with ST, but no significant correlations were observed with any significant frequency between the ST and $R_S$ rates on periods of a day based on the hourly $R_S$ data. Eq. (2) has many more site-specific parameters than Eq. (3) and resulted in some significant underestimation. The empirical regression, Eq. (3) was best explained by temporal variations, as it provided a more unbiased fit to the data compared to Eq. (2). The Eq. (3) (ST $\times$ SWC function) also increased the predictive ability as compared to Eq. (1) (only ST exponential function), increasing the $R^2$ from 0.71 to 0.78.

• Journal of KIISE
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• v.43 no.2
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• pp.229-236
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• 2016

Theta join is one of the essential and important types of queries in database systems. As the amount of data needs to be processed increases, processing theta joins with a single machine becomes impractical. Therefore, theta join algorithms using distributed computing frameworks have been studied widely. Although one of the state-of-the-art theta-join algorithms uses M-Bucket-I heuristic, it is hard to use since running time of M-Bucket-I heuristic, which computes a mapping from a record to a reducer (i.e., reducer mapping), is O(n) where n is the size of input data. In this paper, we propose MBI-I algorithm which reduces the running time of M-Bucket-I heuristic to $O(r_{max}log\;n)$ and gives the same result as M-Bucket-I heuristic does. We also conducted several experiments to show algorithm and confirmed that our algorithm can improve the performance of a theta join by 10%.

• Journal of the Korean Mathematical Society
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• v.55 no.3
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• pp.593-604
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• 2018

Recently, a new version of expansiveness which is closely attached to some certain weak version of hyperbolicity was given for $C^1$ vector fields as following: a $C^1$ vector field X will be called rescaling expansive on a compact invariant set ${\Lambda}$ of X if for any ${\epsilon}$ > 0 there is ${\delta}$ > 0 such that, for any $x,\;y{\in}{\Lambda}$ and any time reparametrization ${\theta}:{\mathbb{R}}{\rightarrow}{\mathbb{R}}$, if $d({\varphi}_t(x),\,{\varphi}_{{\theta}(t)}(y)){\leq}{\delta}{\parallel}X({\varphi}_t(x)){\parallel}$ for all $t{\in}{\mathbb{R}}$, then ${\varphi}_{{\theta}(t)}(y){\in}{\varphi}_{(-{\epsilon},{\epsilon})}({\varphi}_t(x))$ for all $t{\in}{\mathbb{R}}$. In this paper, some equivalent definitions for rescaled expansiveness are given.