• Geomechanics and Engineering
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• v.1 no.3
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• pp.205-218
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• 2009

The bearing capacity factor $N_{\gamma}$ is computed for a rough conical footing placed over horizontal ground surface. The axisymmetric lower bound limit analysis formulation, in combination with finite elements and linear programming, proposed recently by the authors is used in this study. The variation of $N_{\gamma}$ with cone apex angle (${\beta}$), in a range of $30^{\circ}-180^{\circ}$, is obtained for different values of ${\phi}$; where ${\phi}$ is soil friction angle. For ${\phi}<30^{\circ}$, the magnitude of $N_{\gamma}$ is found to decrease continuously with an increase in ${\beta}$ from $30^{\circ}$ to $180^{\circ}$. On the other hand, for ${\phi}>30^{\circ}$, the minimum magnitude of $N_{\gamma}$ is found to occur generally between ${\beta}=120^{\circ}$ and ${\beta}=150^{\circ}$. In all the cases, it is noticed that the magnitude of $N_{\gamma}$ becomes maximum for ${\beta}=30^{\circ}$. For a given diameter of the cone, the area of the plastic zone reduces generally with an increase in ${\beta}$. The obtained values of $N_{\gamma}$ are found to compare quite well with those available in literature.

• Journal of Biosystems Engineering
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• v.3 no.1
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• pp.1-19
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• 1978

Power tiller is a major unit of agricultural machinery being used on farms in Korea. About 180.000 units are introduced by 1977 and the demand for power tiller is continuously increasing as the farm mechanization progress. Major farming operations done by power tiller are the tillage, pumping, spraying, threshing, and hauling by exchanging the corresponding implements. In addition to their use on a relatively mild slope ground at present, it is also expected that many of power tillers could be operated on much inclined land to be developed by upland enlargement programmed. Therefore, research should be undertaken to solve many problems related to an effective untilization of power tillers on slope ground. The major objective of this study was to find out the travelling and tractive characteristics of power tillers being operated on general slope ground.In order to find out the critical travelling velocity and stability limit of slope ground for the side sliding and the dynamic side overturn of the tiller and tiller-trailer system, the mathematical model was developed based on a simplified physical model. The results analyzed through the model may be summarized as follows; (1) In case of no collision with an obstacle on ground, the equation of the dynamic side overturn developed was: $$\sum_n^{i=1}W_ia_s(cos\alpha cos\phi-{\frac {C_1V^2sin\phi}{gRcos\beta})-I_{AB}\frac {v^2}{Rr}}=0$$ In case of collision with an obstacle on ground, the equation was: $$\sum_n^{i=1}W_ia_s\{cos\alpha(1-sin\phi_1)-{\frac {C_1V^2sin\phi}{gRcos\beta}\}-\frac {1}{2}I_{TP} \( {\frac {2kV_2} {d_1+d_2}\)-I_{AB}{\frac{V^2}{Rr}} \( \frac {\pi}{2}-\frac {\pi}{180}\phi_2 \} = 0 $$ (2) As the angle of steering direction was increased, the critical travelling veloc\ulcornerities of side sliding and dynamic side overturn were decreased. (3) The critical travelling velocity was influenced by both the side slope angle .and the direct angle. In case of no collision with an obstacle, the critical velocity $V_c$ was 2.76-4.83m/sec at $\alpha=0^\circ$, $\beta=20^\circ$ ; and in case of collision with an obstacle, the critical velocity $V_{cc}$ was 1.39-1.5m/sec at $\alpha=0^\circ$, $\beta=20^\circ$ (4) In case of no collision with an obstacle, the dynamic side overturn was stimu\ulcornerlated by the carrying load but in case of collision with an obstacle, the danger of the dynamic side overturn was decreased by the carrying load. (5) When the system travels downward with the first set of high speed the limit {)f slope angle of side sliding was $\beta=5^\circ-10^\circ$ and when travels upward with the first set of high speed, the limit of angle of side sliding was $\beta=10^\circ-17.4^\circ$ (6) In case of running downward with the first set of high speed and collision with an obstacle, the limit of slope angle of the dynamic side overturn was = $12^\circ-17^\circ$ and in case of running upward with the first set of high speed and collision <>f upper wheels with an obstacle, the limit of slope angle of dynamic side overturn collision of upper wheels against an obstacle was $\beta=22^\circ-33^\circ$ at $\alpha=0^\circ -17.4^\circ$, respectively. (7) In case of running up and downward with the first set of high speed and no collision with an obstacle, the limit of slope angle of dynamic side overturn was $\beta=30^\circ-35^\circ$ (8) When the power tiller without implement attached travels up and down on the general slope ground with first set of high speed, the limit of slope angle of dynamic side overturn was $\beta=32^\circ-39^\circ$ in case of no collision with an obstacle, and $\beta=11^\circ-22^\circ$ in case of collision with an obstacle, respectively.

• Journal of Korean Society of Steel Construction
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• v.14 no.3
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• pp.403-411
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• 2002

This paper described the ultimate strength and deformation limit of welded T-joints in cold-formed square hollow sections. Previous studies showed that the T-joint has an obvious peak load. with the failure mode of chord-web buckling at a ratio of branch width to chord width ($\beta$) of above 0.8. Similar to a T-joint with chord-flange failure mode, the strength at a certain deformation limit can be regarded as the ultimate strength of a T-joint Based on the experimental results including tests done by Kato and Zhao, the deformation limit was proposed as 3%B for $10.7{\leq}2{\gamma}(B/T){\leq}42.3$ and $0.8{\leq}{\beta}{\leq}1.0$. The strength formula of CIDECT and those of other researchers were also compared with the test results. Finally, the strength formula based on the column buckling was proposed.

• Applied Biological Chemistry
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• v.33 no.1
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• pp.39-42
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• 1990

The properties of amylose of cow pea starch were investigated. Amylose content of cow pea was 25.1 % and iodine binding capacity was 20.2 %. The ${\beta}-amylolysis$ limit of the amylose was 82.3%. The limiting viscosity number of the amylose fraction was 204 ml/g and the corresponding average degree of polymerization was 1,510 glucose units. The percent distribution of molecular weight of the amylose by gel chromatography was $1{\times}10^4$(0.7 %), $1{\times}10^4{\sim}4{\times}10^4$(4.1 %), $4{\times}10^4{\sim}5{\times}10^5$(44.6 %), $5{\times}10^5{\sim}4{\times}10^7$(49.6 % ).

• The Mathematical Education
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• v.10 no.1
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• pp.6-8
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• 1972

Metacompact인 부분 집합들을 5가지 형으로 분류하여 $\beta$-metacompact인 집합과 그 집합에 관하여 폐집합인 집합들과의 관계를 규명하였고, 위상공간의 임의의 부분집합의 Point finite filter를 정의하여 이 filter가 limit point를 갖는 조건과 이 집합이 $\beta$-metacompact인 조건과를 비교하였다. 다음에 5가지형의 metacompact들 사이의 관계를 조사하여 다음과 같은 관계를 얻었다. (1) $\beta$-metacompact ($\beta$-countably metacompact)인 부분집합의 내점들의 폐 부분집합은 $\alpha$-metacompact ($\alpha$-countably metacompact) 이다. (2) $\sigma$-metacompact of 이고, $\alpha$-countably metacompact인 부분집합은 $\alpha$-metacompact이다.

• Korean Journal of Food Science and Technology
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• v.24 no.6
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• pp.568-573
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• 1992

Molecular structural properties of Japonica and Tongil type waxy rice starches were compared. The general properties including water-binding capacity, swelling power at $80^{\circ}C$, intrinsic viscosity, leach loss at $98^{\circ}C$ and ${\beta}-amylolysis$ limit were similar but the chain length was slightly different between the two starches. Similar elution profiles on Sephadex G-50 were obtained when the starches were treated with ${\beta}-amylase$. The pullulanase treated starches however showed different elution patterns each other. The ${\beta}-amylolysis$ of acid-treated (2 days) starches linearly increased as hydrolysis time prolonged. When the acid-treated starches were hydrolyzed with ${\beta}-amylase$ or pullulanase, the elution profiles on Sepharose CL-2B were considerably different from those of native starches.

• Applied Biological Chemistry
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• v.43 no.4
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• pp.241-246
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• 2000

In order to investigate structural properties of Chindo black rice(grown in Chindo, Chonnam) starch and its amylopectin, Chindo black rice was investigated in comparison to Shinsun waxy rice. The maximum absorbance wave and intrinsic viscosity of Chindo black rice starch and Shinsun waxy rice starch were 523 nm, 521 nm and 183 ml/g, 178 ml/g, respectively. ${\beta}-amylolysis$ limit(%) of Chindo black rice and Shinsun waxy rice starch were 62.8% and 60.3%, respectively. Chindo black rice was determined to be a waxy rice due to the results of iodine reaction and elution profile on Sephroce CL-2B. The chain of amylopectins in Chindo black rice distributed fraction 1$(F_1)$ of above degree of polymerization$({\overline{DP}})$ 55, fraction 2$(F_2)$ of ${\overline{DP}} $40{\sim}50$ and fraction 3$(F_3)$ of ${\overline{DP}} $15{\sim}20$, and the ratio of $F_3$ to $F_2$ for Chindo black rice was higher than that for Shinsun waxy rice. The super long chain of amylopectin in Chindo black rice was consisted much more than that of Shinsun waxy rice. ${\beta}-limit$ dextrins in Chindo black rice amylopectin distributed $F_1$ of above ${\overline{DP}} 55, $F_2$ of ${\overline{DP}} $30{\sim}45$ and $F_3$ of ${\overline{DP}} $10{\sim}20$. Little difference was shown between elution patterns of the pullulanase treated ${\beta}-limit$ dextrins of Chindo black rice amylopectin and Shinsun waxy rice amylopectin. These results suggest that Chindo black rice starch was similar to Shinsun waxy rice starch.

• Proceedings of the Materials Research Society of Korea Conference
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• 1996.11a
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• pp.23-23
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• 1996

• Communications for Statistical Applications and Methods
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• v.21 no.4
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• pp.327-334
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• 2014

Various modified GARCH(1, 1) models have been found adequate in many applications. We are interested in their continuous time versions and limiting properties. We first define a stochastic integral that includes useful continuous time versions of modified GARCH(1, 1) processes and give sufficient conditions under which the process is exponentially ergodic and ${\beta}$-mixing. The central limit theorem for the process is also obtained.

• East Asian mathematical journal
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• v.4
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• pp.57-73
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• 1988

The subclasses S*($\alpha,\beta,\mu$) and C*($\alpha,\beta,\mu$) ($0\leqq\alpha<1,\;0<\beta\leqq1$ and $0\leqq\mu\leqq1$) of T the class of analytic and univalent functions of the form $$f(z)=z-\sum\limit^{\infty}_{n=2}\mid a_n\mid z^n$$ have been considered. Sharp results concerning coefficients, distortion of functions belonging to S*($\alpha,\beta,\mu$) and C*($\alpha,\beta,\mu$) are determined along with a representation formula for the functions in S*($\alpha,\beta,\mu$). Furthermore, it is shown that the classes S*($\alpha,\beta,\mu$) and C*($\alpha,\beta,\mu$) are closed under arithmetic mean and convex linear combinations. Also in this paper, we find extreme points and support points for these classes.