• 대한수학회논문집
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• 제15권4호
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• pp.675-681
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• 2000

Let f : M longrightarrow M be a homotopically periodic self-map of a closed surface M. Except for M = $S^2$, the Nielsen number N(f) and the Lefschetz number L(f) of the self-map f are the same. This is a generalization of Kwasik and Lee's result to 2-dimensional case. On the 2-sphere $S^2$, N(f) = 1 and L(f) = deg(f) + 1 for any self-map f : $S^2$longrightarrow$S^2$.

• 대한수학회논문집
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• 제11권1호
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• pp.245-252
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• 1996

The relative Nielsen number N(f;X,A) was introduced in 1986. It gives us a better, and ideally sharp, lower bound for the minimum number MF[f;X,A] of fixed points in the homotopy class of the map $f;(X,A) \to (X,A)$. Similarly, we also can think about the Nielsen map $f:(X,A) \to (X,A)$. Similarly, we also can be think about the Nielsen root theory. In this paper, we introduce a relative root Nielsen number N(f;X,A,c) of $f:(X,A) \to (Y,B)$ and show some basic properties.

• 대순사상논총
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• 제38집
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• pp.183-208
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• 2021

조호익(曺好益) 『역상설(易象說)』의 상수학적 연원을 검토하기 위해서는 호일계의 『주역본의부록찬주(周易本義附録纂注)』를 검토할 필요가 있다. 호일계는 주자의 『주역본의』를 기본으로 하고, 주자의 문집과 어록 등의 관련 내용을 찾아 부록이라 하였고, 그리고 제유의 역설 중 『주역본의』의 뜻에 부합하는 주석을 모아서 찬주로 하였다. 여기에다 호일계 자신의 의견을 덧붙이는 형식의 '우위(愚謂)'나 '우안(愚案)' 등이 있다. 이러한 호일계의 『주역본의부록찬주』 체제는 사실상 조호익의 역학 저서 체제와 거의 일치한다. 즉 조호익은 호일계의 『주역본의부록찬주』의 부록, 찬주의 내용에 해당하는 저서로 『역전변해(易傳辨解)』, 『주역석해(周易釋解)』를 지은 듯하다. 이러한 저서는 주자의 『주역본의』의 단상을 정밀하게 밝힌 것이라고 이미 밝힌 바 있다. 그리고 『주역본의부록찬주』 '우위'나 '우안'에 해당하는 저서로 『역상설』이 있다. 『역상설』은 원래 독립적인 역학 저서가 아니라 『주역』의 두주 형태로 기록된 것을 후인들이 모아 편찬한 것이다. 따라서 『역상설』은 『주역본의부록찬주』의 '우위'나 '우안'과 거의 같은 형식이다. 그리고 조호익의 『역상설』은 내용적인 측면에서도 『주역본의부록찬주』의 '우위'나 '우안'의 역설을 많이 인용하고 있다. 한편, 조호익 『역상설』의 상수학적 연원을 검토하기 위해서 주진의 역학을 간과할 수 없다. 『역상설』이 주진을 인용하고 있는 점 때문만이 아니다. 보다 큰 이유는 『역상설』과 주진 역학의 골간적 측면 때문이다. 본론에서도 증명했지만, 『역상설』의 상수학적 『주역』 해석 방법론과 『한상역전(漢上易傳)』의 상수학적 『주역』 해석 방법론이 거의 일치한다. 결론적으로, 조호익 『역상설』의 상수학적 연원은 호일계의 『주역본의부록찬주』와 주진의 『한상역전』에서 모두 찾을 수 있을 것 같다. 특히 『주역본의부록찬주』의 '우위'나 '우안' 부분, 그리고 『한상역전』의 한대(漢代) 상수학적 체례에 그 연원이 있다고 할 수 있다.

• 대한한의학방제학회지
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• 제11권2호
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• pp.1-18
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• 2003

The Theory for Monarch, Minister, Adjuvant and Dispatcher (or the Theory of Principal, Assistant, Adjuvant and Guiding Korean Oriental Herbal Medicines) has served as a standard principle for newly developed prescription formulas as well as established ones. Despite its significance, however, this theory hasn't been thoroughly studied and covered in the academic journals of Korean Oriental Herbal Medicines (KOHM) yet. This paper inquires into the origin of the theory while presenting the definitions and functions of Principal, Assistant, Adjuvant, and Guiding KOHM. In the end, the recommended doses and number of the KOHM comprising each of Principal, Assistant, Adjuvant, and Guiding KOHM are suggested. The compatibility theory of Principal, Assistant, Adjuvant, and Guiding KOHM can be traced back to the Warring States Period during which it was recorded in the treatise of the various schools of thoughts and their exponents. The theory was firmly established as a full system in ${\ulcorner}Shinnong's\;Pharmacopoeia{\lrcorner}\;and\;{\ulcorner}Yellow\;Emperor's\;Cannon\;of\;Internal\;Medicine{\lrcorner}$. While ${\ulcorner}Shinnong's\;Pharmacopoeia{\lrcorner}$ focuses on the classification of the properties of KOHM, ${\ulcorner}Yellow\;Emperor's\;Cannon\;of\;Internal\;Medicine{\lrcorner}$ mainly deals with the principles for writing prescriptions. In this regard, it is ${\ulcorner}Yellow\;Emperor's\;Cannon\;of\;Internal\;Medicine{\lrcorner}$ that systemized the Theory of Principal, Assistant, Adjuvant, and Guiding KOHM in a real sense. Principal KOHM aims at the causes of diseases and treat main symptoms. The doses are greater than Assistant, Adjuvant and Guiding KOHM. With their comprehensive effects, Principal KOHM is a leading ingredient of any prescription formula. Assistant KOHM are similar to Principal KOHM in its natures and flavors. Although its natures, flavors as well as efficacies may slightly differ from those of Principal KOHM, Assistant KOHM strengthens the therapeutic effects, jointly working with Principal KOHM. They mainly treat accompanying diseases and symptoms. Adjuvant KOHM is divided into two types: facilitator and inhibitor. Facilitators with the similar properties to those of Principal and Assistant KOHM help strengthen the therapeutic effects. Since they usually treat accompanying symptoms or secondary accompanying symptoms (minor accompanying symptoms), there are two kinds of facilitators. (1) The first kind of facilitators assists Principal KOHM, targeting accompanying symptoms. (2) The second ones supporting Assistant KOHM are for accompanying or secondary accompanying symptoms (or minor accompanying symptoms). Inhibitors counteract and thereby complement Principal and Assistant KOHM. Some of them inhibit the side effects or toxicity of Principal KOHM for the sake of the safety of the whole prescription formula while the others generate induced interactions. Guiding KOHM can be used for two purposes: guiding and mediating. The Guiding KOHM for the former purpose leads the other KOHM in a prescription formula to the lesion. But, the Guiding KOHM for mediating coodinate and harmonize all the ingredients in a prescription formula. The number of KOHM for those Principal, Assistant, Adjuvant and Guiding KOHM and their doses are different, depending on the types of prescriptions: classical prescriptions, prescriptions after ${\ulcorner}$Treatise of Cold-Induced Diseases${\lrcorner}$ and prescriptions of Sasang Constitutions Medicines. In the case of the prescriptions after ${\ulcorner}$Treatise of Cold-Induced Diseases${\lrcorner}$, it is highly recommended to follow the view of ${\ulcorner}$Thesaurus of Korean Oriental Medicine Doctors in Chosun Dynasty${\lrcorner}$ for the number of KOHM to be used. For the doses, however, ${\ulcorner}$Elementary Course for Medicine${\lrcorner}$, is found to be more accurate. The most appropriate number of KOHM per prescription is 11-13. To be more specific, for one prescription formula, it is recommended to administer one kind of KOHM for Principal KOHM, 2-3 for Assistant KOHM, 3-4 for Adjuvant KOHM and 5 for Guiding KOHM. As for the proportion of the doses, when 10 units are to be administered for Principal KOHM in a formula, the doses for the other three should be 7-8 units for Assistant KOHM, 5-6 for Adjuvant KOHM and 3-4 for Guiding KOHM. The doses of the KOHM added to or taken out of the prescription correspond to those of Adjuvant and Guiding KOHM.

• Smart Structures and Systems
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• 제22권3호
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• pp.303-314
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• 2018

An original quasi-3D hyperbolic shear deformation theory for simply supported functionally graded plates is proposed in this work. The theory considers both shear deformation and thickness-stretching influences by a hyperbolic distribution of all displacements within the thickness, and respects the stress-free boundary conditions on the upper and lower surfaces of the plate without using any shear correction coefficient. By expressing the shear parts of the in-plane displacements with the integral term, the number of unknowns and equations of motion of the proposed theory is reduced to four as against five in the first shear deformation theory (FSDT) and common quasi-3D theories. Equations of motion are obtained from the Hamilton principle. Analytical solutions for dynamic problems are determined for simply supported plates. Numerical results are presented to check the accuracy of the proposed theory.

• Structural Engineering and Mechanics
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• 제72권3호
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• pp.329-338
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• 2019

In this paper, the magnetic field influence on the wave propagation characteristics of graphene nanosheets is examined within the frame work of a two-variable plate theory. The small-scale effect is taken into consideration based on the nonlocal strain gradient theory. For more accurate analysis of graphene sheets, the proposed theory contains two scale parameters related to the nonlocal and strain gradient effects. A derivation of the differential equation is conducted, employing extended principle of Hamilton and solved my means of analytical solution. A refined trigonometric two-variable plate theory is employed in Kinematic relations. The scattering relation of wave propagation in solid bodies which captures the relation of wave number and the resultant frequency is also investigated. According to the numerical results, it is revealed that the proposed modeling can provide accurate wave dispersion results of the graphene nanosheets as compared to some cases in the literature. It is shown that the wave dispersion characteristics of graphene sheets are influenced by magnetic field, elastic foundation and nonlocal parameters. Numerical results are presented to serve as benchmarks for future analyses of graphene nanosheets.

• Structural Engineering and Mechanics
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• 제28권5호
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• pp.495-514
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• 2008

In this paper, experimental and theoretical investigations of the effect of the mean moment on the response and collapse of circular thin-walled tubes subjected to cyclic bending are discussed. To highlight the influence of the mean moment effect, three different moment ratios r (minimum moment/ maximum moment) of -1, -0.5 and 0, respectively, were experimentally investigated. It has been found that the moment-curvature loop gradually shrinks with the number of cycles, and becomes stable after a few cycles for symmetric cyclic bending (r = -1). However, the moment-curvature loop exhibits ratcheting and increases with the number of cycles for unsymmetric cyclic bending (r = -0.5 or 0). In addition, although the three groups of tested specimens had three different moment ratios, when plotted in a log-log scale, three parallel straight lines describe the relationship between the controlled moment range and the number of cycles necessary to produce buckling. Finally, the endochronic theory combined with the principle of virtual work was used to simulate the relationship among the moment, curvature and ovalization of thin-walled tubes under cyclic bending. An empirical formulation was proposed for simulating the relationship between the moment range and the number of cycles necessary to produce buckling for thin-walled tubes subjected to cyclic bending with different moment ratios. The results of the experimental investigation and the simulation are in good agreement with each other.

• 대한기계학회논문집B
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• 제27권4호
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• pp.415-423
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• 2003

The hydrodynamic instability of the three-dimensional boundary-layer over a rotating disk has been numerically investigated for these flows; Ro = -1, -0.5, and 0, using linear stability theory. Detailed numerical values of the disturbance wave number. wave frequency. azimuth angle. radius (Reynolds number, Re) and other characteristics have been calculated for the pre-swirl flows. On the basis of Ekman and Karman boundary layer theory, the instability of the pre-swirl flows have been investigated for the unstable criteria. The disturbance will be relatively fast amplified at small fe and within wide bands of wave number compared with previously known Karman boundary-layer results. The flow (Ro =-0.5) is found to be always stable for a disturbance whose dimensionless wave number is greater than 0.9. It has a larger range of unstable interval than Karman boundary layer and can be unstable at smaller Re.

• Ocean Systems Engineering
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• 제8권2호
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• pp.167-182
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• 2018

RTI (Rayleigh-Taylor instability) is investigated by a multi-liquid MPS (Moving Particle Semi-implicit) method for both viscous and inviscid flows for various density differences, initial-disturbance amplitudes, viscosities, and surface tensions. The MPS simulation can be continued up to the late stage of high nonlinearity with complicated patterns and its initial developments agree well with the linear theoretical results. According to the relevant linear theory, the difference between inviscid and viscous fluids is the rising velocity at which upward-mushroom-like RTI flow with vortex formation is generated. However, with the developed MPS program, significant differences in both growing patters and developing speeds are observed. Also, more dispersion can be observed in the inviscid case. With larger Atwood (AT) number, stronger RTI flows are developed earlier, as expected, with higher potential-energy differences. With larger initial disturbances, quite different patterns of RTI-development are observed compared to the small-initial-disturbance case. If AT number is small, the surface tension tends to delay and suppress the RTI development when it is sufficiently large. Interestingly, at high AT number, the RTI-suppressions by increased surface tension become less effective.

• 한국수학사학회지
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• 제28권2호
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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.