• Journal for History of Mathematics
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• v.23 no.4
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• pp.17-30
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• 2010

The aim of this paper is to classify mathematical revolutions by discussing the concept of revolution, and to suggest criteria to judge mathematical revolutions. I examine the relation between the types and the criteria of mathematical revolutions, and explore what types of revolutions several instances of changes in mathematical knowledge are.

• Journal of Biosystems Engineering
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• v.9 no.2
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• pp.37-47
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• 1984

Using the soil bin systems, this study was carried out to analyze the effects of the angular and tilling speed of the rotary shaft with the edge curves which were $30^{\circ}$ and $40^{\circ}$, and the edged blade which were single and double, on the torque requirement of rotary tillage. In the analyses, we developed the mathematical models for the torque requirments of rotary tillage, and analyzed the optimum conditions of each variable for the minimum tillage torque requriements. The results of the study were summarized as follows. 1. The required tilling torque by one rotary blade has the minimum value when the tilling speed of the rotary blade was low, and the revolution of the rotary blade was fast, in general. 2. The torque requirements of single edged blade was decreased to about 81% in comparing with that of double edged blade of which the edge curved angle was $40^{\circ}$ and the tilling speed was 29.40 cm/sec. But, for the mean values, the maximum torque requirements were decreased to 45%, and the mean torque requirements were decreased to 35%. 3. For the edge curved angle, the torque requirements of ${\theta}=40^{\circ}$ were 48% more than that of ${\theta}=30^{\circ}$ in the maximum tilling torque in case that the rotary blade were double edged blade. but, there was not a difference when the rotary blades were single edged blade. The mean tilling torques of ${\theta}=40^{\circ}$ were 6% more when the rotary blade was double edged blade, and were 11% less at single edged blade, than that of ${\theta}=30^{\circ}$. 4. In order to reduce the torque requirements for tilling, the optimum revolutions of the rotary shaft were analyzed as that 204-240 rpm for the double edged blade and 280-320 rpm for the single edged blade.

• Korean Journal of Agricultural Science
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• v.11 no.1
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• pp.160-175
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• 1984

This study was carried out to analyze the effects of the revolution and forwarding speed of the rotary blade and the edge curves which were $30^{\circ}$ and $40^{\circ}$, on the power requirement of rotary tillage. In this study, the revolutions of the rotary blade considered were 204, 243, 285, 360 rpm, and the forwarding speeds of the rotary system considered were 29.40cm/sec, 46.93em/sec. The power requirements of rotary blade were measured by a dynamic strain gage systems at the soil bin which was filled with artificial soil. The results of the study were summarized as follows: 1. The response surface analysis showed that the revolution and forwarding speed of the rotary shaft had an interacting influence on the torque requirement of the rotary blade. The mathematical model developed by the above was repersented as follow. $$T=a_0+a_1V+a_2R +a_3VR+a_4VR^2$$ where, $a_0=constant$ $a_1,\;a_2,\;a_3,\;a_4=coefficients$ V=forwarding speed of the rotary system. (em/sec) R=revolution of the rotary shaft. (rpm) T=tilling torque requirement. (kg-m) 2. When the maximum tilling torque requirement was analyzed, ${\partial}T/{\partial}R$ was decreased with the increasing revolution of rotary shaft, while ${\partial}T/{\partial}V$ was increased, which was minimum at 200~220 rpm. When the forwarding speeds were increased, ${\partial}T/{\partial}R$ was decreased with increasing rate. 3. When the mean tilling torque requirement was analyzed, ${\partial}T/{\partial}V$ was constant at 320~360 rpm and ${\partial}T/{\partial}R$ was decreased with increasing rate along with the increasing revolution of rotary shaft. 4. When the mean tilling torgue requirement per unit volume of soil was analyzed, ${\partial}T/{\partial}V$ was minimum at 270~300 rpm. ${\partial}T/{\partial}R$ for the forwarding speeds of 29.40cm/sec and 46.93cm/sec was same as that for 280~290 rpm. 5. Increasing the edge curves of the rotary blades, the tilling torque requirement was increased. But other studies showed that the smaller the edge curve, the more straw could be wrapped on blades which resulted in increasing torque requirements. Therefore, the edge curve of rotary blade should be considered for the future study.