• Journal for History of Mathematics
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• v.28 no.2
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• pp.85-102
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• 2015

Elliptic curves are a common theme among various fields of mathematics, such as number theory, algebraic geometry, complex analysis, cryptography, and mathematical physics. In the history of elliptic curves, we can find number theoretic problems on the one hand, and complex function theoretic ones on the other. The elliptic curve theory is a synthesis of those two indeed. As an overview of the history of elliptic curves, we survey the Diophantine equations of 3rd degree and the congruent number problem as some of number theoretic trails of elliptic curves. We discuss elliptic integrals and elliptic functions, from which we get a glimpse of idea where the name 'elliptic curve' came from. We explain how the solution of Diophantine equations of 3rd degree and elliptic functions are related. Finally we outline the BSD conjecture, one of the 7 millennium problems proposed by the Clay Math Institute, as an important problem concerning elliptic curves.

• Proceedings of the Korean Society of Machine Tool Engineers Conference
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• 2004.10a
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• pp.170-174
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• 2004

Despite the widespread use in the various manufacturing industries, the full automation of the robotic CO$_2$ welding has not yet been achieved partly because the mathematical model for the process parameters of a given welding task is not fully understood and quantified. Several mathematical models to control welding quality, productivity, microstructure and weld properties in arc welding processes have been studied. However, it is not an easy task to apply them to the various practical situations because the relationship between the process parameters and the bead geometry is non-linear and also they are usually dependent on the specific experimental results. Practically, it is difficult, but important to know how to establish a mathematical model that can predict the result of the actual welding process and how to select the optimum welding condition under a certain constraint. In this paper, an attempt has been made to develop an Radial basis function network model to predict the weld top-bead width as a function of key process parameters in the robotic CO$_2$ welding. and to compare the developed model and a simple neural network model using two different training algorithms in order to verify performance. of the developed model.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.38 no.9
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• pp.773-779
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• 2014

A qualitative and quantitative analysis on flame dynamics is required to model combustion instability characteristics in gas turbine lean premixed combustors. The current paper shows the flame transfer function modeling results using CFD(Computational Fluid Dynamics) techniques for the flame dynamics study. It is generally known that flame shapes determine the basic characteristics of the flame transfer function. The comparisons of the modeled flame shapes with the measured ones were made using the optimized heat transfer conditions. Modeling results of the flame transfer function show the close behaviors to the measured data with a reasonable accuracy if the flame geometry can be exactly captured.

• Journal of Mechanical Science and Technology
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• v.14 no.6
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• pp.622-632
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• 2000

In a high precision vertical machining center, the estimation of cutting forces is important for many reasons such as prediction of chatter vibration, surface roughness and so on. The cutting forces are difficult to predict because they are very complex and time variant. In order to predict the cutting forces of end-milling processes for various cutting conditions, their mathematical model is important and the model is based on chip load, cutting geometry, and the relationship between cutting forces and chip loads. Specific cutting force coefficients of the model have been obtained as interpolation function types by averaging forces of cutting tests. In this paper the coefficients are obtained by neural network and the results of the conventional method and those of the proposed method are compared. The results show that the neural network method gives more correct values than the function type and that in the learning stage as the omitted number of experimental data increase the average errors increase as well.

• Journal of the Korean Mathematical Society
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• v.31 no.4
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• pp.569-608
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• 1994

The subject matter of this survey has to do with holomorphic maps from a compact Riemann surface to projective space, which are also called algebrac curves; the theory we survey lies at the crossroads of function theory, projective geometry, and commutative algebra (although we should mention that the present survey de-emphasizes the algebraic aspect). Algebraic curves have been vigorously and continuously investigated since the time of Riemann. The reasons for the preoccupation with algebraic curves amongst mathematicians perhaps have to do with-other than the usual usual reason, namely, the herd mentality prompting us to follow the leads of a few great pioneering methematicians in the field-the fact that algebraic curves possess a certain simple unity together with a rich and complex structure. From a differential-topological standpoint algebraic curves are quite simple as they are neatly parameterized by a single discrete invariant, the genus. Even the possible complex structures of a fixed genus curve afford a fairly complete description. Yet there are a multitude of diverse perspectives (algebraic, function theoretic, and geometric) often coalescing to yield a spectacular result.

• Journal of Korean Society of Water and Wastewater
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• v.23 no.1
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• pp.107-112
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• 2009

This study was conducted for verification and systematization of estimation method about the headloss using CFD(Computational Fluid Dynamics). Head loss which happens between the inlet and outlet of in-line mixer can be a major factor for the design and construction. Also, this Case studies about the sensitivity related to the velocity in the piping system. As result, program's default calculation function was used to get each side's total pressure and the differential of each total pressure could be defined as head loss from in-line mixer. In the case of adopting pipe surface friction factor and geometry loss, Calculation residual can be much more reduced. It was found that residual of value between CFD method and field test ranged about 3 through 18 precent.

• Journal of ILASS-Korea
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• v.8 no.1
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• pp.1-8
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• 2003

The flow analysis of the axial fan of rotary burner was performed by SIMPLE(Semi Implicit Method for Pressure Linked Equations) algorithm and finite volume mothod performed in the case of 3-D, incompressible, turbulent flow. In this study, the coordinate transformation was adapted for the complex geometry of axial fan, and the standard $k-{\varepsilon}$ model and wall function method were used for analysis of turbulent flow. Multi-block grid system was used for flow field and divided into four domains such as the inlet, outlet, flow field of rotating vane, and tip clearance. Fan rotation was simulated by rotational motion using MRF(Multiple Rotating Reference Frame) in steady, incompressible state flow.

• Fibers and Polymers
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• v.5 no.3
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• pp.209-212
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• 2004

A nonsteady axi-symmetric ideal flow solution is obtained here. It is based on the rigid perfect-plastic constitutive law with the Tresca yield condition and its associated flow rule. The process is to deform a circular solid disk into a spherical shell of prescribed geometry. It is assumed that there are no rigid zones and friction stresses. The solution obtained provides the distribution of kinematic variables and involves one undetermined function of the time. This function can be in general found by superimposing an optimality criterion.

• Journal of ILASS-Korea
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• v.11 no.2
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• pp.105-112
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• 2006

A unique feature of fluidic atomizers is that the nozzle geometry produces a thin capillary Jet which is forced to oscillate on a 2-dimensional plane through the use of a passive feedback mechanism. The objective of the current work is to characterize the influence of the stagnation pressure at the nozzle exit, jet oscillation and stretching on the breakup properties of the capillary ligament. To achieve this, shadow graph technique is used to measure size, shape, velocity and the number density of the droplets as a function of the position within the spray fan. The breakup length, defined as the radial distance from the breakup point, is analyzed as a function of the non-dimensional parameters. Finally, a kinematic model is developed to simulate the breakup of the oscillating jets at low stagnation pressures. Using the existing jet breakup theories, the model is used to predict the size and diameter distribution of the droplets after primary atomization.

• Transactions of the Korean Society of Mechanical Engineers
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• v.18 no.9
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• pp.2211-2224
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• 1994

On face milling operation a new optimal cutter, which can minimize the resultant cutting forces, was designed from the cutting force model. Cutting experiments were carried out and the cutting forces of the new and conventional cutters were analyed in time and frequency domains. The resultant cutting forces were used as the objective function and cutter angles as the variables. A new optimal cutter design model which can minimize the resultant cutting forces under the constraints of variables was developed and its usefulness was proven. The cutting forces in feed direction of the newly designed cutter are reduced in comparison with those from the conventional cutter. The magnitudes of an insert frequency component of cutting force from the newly designed cutter are reduced than those from conventional cutter and the fluctuations of cutting force are also reduced.