• Honam Mathematical Journal
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• v.36 no.3
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• pp.659-668
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• 2014

In this paper, we express the Green function in terms of the classical kernel functions in potential theory. In particular, we obtain a formula relating the Green function and the Szegő kernel function which consists of only the Szegő kernel function in a $C^{\infty}$ smoothly bounded finitely connected domain in the complex plane.

• 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 the Korean Society for Precision Engineering
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• v.18 no.2
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• pp.186-191
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• 2001

A crack with electrically impermeable surfaces in an electrostrictive material subjected to uniform electric loading is analysed. The effect of electric yielding on stress intensity factor is investigated by using a small scale yielding model and a strip yield zone model. Complete forms of electric fields and elastic fields are derived by using complex function theory. The electrical yield zone shapes for two models are different each other. The two models, however, predict similar yield zone sizes under the small scale yielding conditions. It is found that the influence of electric yielding on the stress intensity factor is insensitive to the modeling of the electrical yield zone shape.

• Korean System Dynamics Review
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• v.14 no.4
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• pp.5-35
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• 2013

The study examines the play theory based internet rumor process by using simulating tools, Vensim, which offer a new theoretical basis from which to explore complex adaptive social system. Internet rumor is not a simple linear diffusion process, but a complex interaction behavior between the actors of production and diffusion. Rumor actors consist of two type of diffusion, which is rumor mongers and playful mongers. These two type of mongers make the internet rumor as collective system. Playful mongers play strategically to maximize playfulness. Internet rumor as play is consequence of collective framing constituted by dynamic interaction and playfulness. The networking space spreading internet rumor function as a playground which mobilize play rule, ignoring fact based framing. Rumor as paly, even though it turns out to be a false and loses the public attentions rumor sustains the game play function which makes the rumor without natural extinction. The study proves that playful mongers is a main actors in rumor play ground.

• Fire Science and Engineering
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• v.25 no.4
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• pp.42-47
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• 2011

This study carried out the design and analysis of complex damper as basis study for development of complex damper for ventilation and fire protection. This study established design and analysis theory of complex damper based on process, kinematics mechanism and mechanism modelling of complex damper. And this study established engineering data construction and a source technology that can design each element of complex damper through motion analysis simulation based on design and analysis theory. Therefore, it got result that can apply comprehensively in development of complex damper for ventilation and fire protection from this study. Also, it sees that can ready control means and technological countermeasure of smoke to developed of complex damper with this study.

• 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.

• Korean Journal of Mathematics
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• v.30 no.2
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• pp.249-261
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• 2022

Let f be a non-constant meromorphic function in the open complex plane ℂ. In this paper we prove under certain essential conditions that R(f) and P[f], rational function and differential polynomial of f respectively, share a small function of f and obtain a conclusion related to Brück conjecture. We give some examples in support to our result.

• Advances in aircraft and spacecraft science
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• v.3 no.3
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• pp.317-330
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• 2016

Nowadays, the interest of aerospace and automotive industries on virtual testing of medium-frequency vibrational behavior of shallow shell structures is growing. The development of software capable of predicting the vibrational response in such frequency range is still an open question because classical methods (i.e., FEM, SEA) are not fully suitable for the medium-frequency bandwidth. In this context the Variational Theory of Complex Rays (VTCR) is taking place as an ad-hoc technique to address medium-frequency problems. It is a Trefftz method based on a weak variational formulation. It allows great flexibility because any shape function that satisfies the governing equations can be used. This work further develops such theory. In particular, orthotropic materials are introduced in the VTCR formulation for shallow shell structures. A significant numerical example is proposed to show the strategy.

• Proceedings of the Korean Society For Composite Materials Conference
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• 2004.04a
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• pp.155-160
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• 2004

This paper presents a study on the permittivities of the carbon black/epoxy composite at microwave frequency. The measurements were performed at the frequency band of $1 GHz\~18GHz$. The results show that the complex permittivities of composites depend strongly on the natures and concentrations of the carbon black dispersion. The frequency spectrums of dielectric constants and ac conductivities of composites show the good conformities with descriptions of the percolation theory. The carbon black concentration dependencies do not have conformities with the descriptions of percolation theory and there is no peculiar concentration like percolation threshold, on that concentration, the conductivity of composite jumps up. A new scheme, that is a branch of Lichtenecker-Rother formula, is proposed to obtain a mixing law to describe the complex permittivities of the composites as function frequency and concentration of carbon black.

• International Journal of Control, Automation, and Systems
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• v.1 no.3
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• pp.289-300
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• 2003

In this paper, we introduce an identification method in Fuzzy Relation-based Fuzzy Neural Networks (FRFNN) through a hybrid identification algorithm. The proposed FRFNN modeling implement system structure and parameter identification in the efficient form of "If...., then... " statements, and exploit the theory of system optimization and fuzzy rules. The FRFNN modeling and identification environment realizes parameter identification through a synergistic usage of genetic optimization and complex search method. The hybrid identification algorithm is carried out by combining both genetic optimization and the improved complex method in order to guarantee both global optimization and local convergence. An aggregate objective function with a weighting factor is introduced to achieve a sound balance between approximation and generalization of the model. The proposed model is experimented with using two nonlinear data. The obtained experimental results reveal that the proposed networks exhibit high accuracy and generalization capabilities in comparison to other models.er models.