• Advances in nano research
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• v.11 no.6
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• pp.581-593
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• 2021

This model is proposed to describe the buckling behavior of Carbon Nanotubes (CNTs) embedded in an elastic medium taking into account the combined effects of the magnetic field, the temperature, the nonlocal parameter, the number of walls. Using Eringen's nonlocal elasticity theory, thin cylindrical shell theory and Van der Waal force (VdW) interactions, we develop a system of partial differential equations governing the buckling response of CNTs embedded on Winkler, Pasternak, and Kerr foundations in a thermal-magnetic environment. The pre-buckling stresses are obtained by applying airy's stress function and an adjacent equilibrium criterion. To estimate the nonlocal critical buckling load of CNTs under the simultaneous effects of the magnetic field, the temperature change, and the number of walls, an optimization technique is proposed. Furthermore, analytical formulas are developed to obtain the buckling behavior of SWCNTs embedded in an elastic medium without taking into account the effects of the nonlocal parameter. These formulas take into account VdW interactions between adjacent tubes and the effect of terms involving differences in tube radii generally neglected in the derived expressions of the critical buckling load published in the literature. Most scientific research on modeling the effects of magnetic fields is based on beam theories, this motivation pushes me to develop a cylindrical shell model for studying the effect of the magnetic field on the static behavior of CNTs. The results show that the magnetic field has significant effects on the static behavior of CNTs and can lead to slow buckling. On the other hand, thermal effects reduce the critical buckling load. The findings in this work can help us design of CNTs for various applications (e.g. structural, electrical, mechanical and biological applications) in a thermal and magnetic environment.

• Communications of the Korean Mathematical Society
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• v.15 no.4
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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$S^2$.

• Communications of the Korean Mathematical Society
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• v.11 no.1
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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.

• Journal of the Daesoon Academy of Sciences
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• v.38
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• pp.183-208
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• 2021

In order to examine the origin of Image-Number Theory in Cho Hoik (曺好益)'s Yixiangshuo (易象說), it is necessary to review Hu Yigui (胡一桂)'s Zhouyi Benyi Fulu Zuanzhu (周易本義附録纂注). Hu Yigui based his work on Zhu Xi's Zhouyi Benyi, he took related contents such as the Zhu Xi's writings and phrases and organized them into a fulu (附録), and he collected commentaries that matched the meaning of Zhouyi Benyi among the theories of many Confucian scholars and produced a zuanzhu (纂注). In addition to these, there are 'Yuwei (愚謂)' and 'Yuan (愚案)' which allowed him to add his own opinion. The system of Hu Yigui's Zhouyi Benyi Fulu Zuanzhu almost coincides with Cho Hoik's Yi-ological writing system. In other words, Cho Hoik appears to have written Yizhuan Bianjie (易傳辨解) and Zhouyi Shijie (周易釋解) as a fulu and zuanzhu of Zhouyi Benyi Fulu Zuanzhu. And there is Yixiangshuo which corresponds to 'Yuwei' and 'Yuan' of Zhouyi Benyi Fulu Zuanzhu. Yixiangshuo was not originally an independent Yi-ological book, but was compiled by later generations from what was recorded in the form of the head notes of Zhouyi (周易). Thus, Yixiangshuo takes almost the same form as the 'Yuwei' and 'Yuan' of Zhouyi Benyi Fulu Zuanzhu. In addition, Cho Hoik's Yixiangshuo cites many contents from 'Yuwei' and 'Yuan' of Zhouyi Benyi Fulu Zuanzhu. On the other hand, in order to examine the origin of Image-Number Theory in Cho Hoik's Yixiangshuo, the Yi-ology of Zhu Zhen (朱震) cannot be overlooked. This is true not only due to the fact that Yixiangshuo is quoting Zhu Zhen. The more significant reason is Yixiangshuo is a fundamental aspect of Zhu Zhen's Yi-ology. As demonstrated in the main body of this article, the methodology of Image-Number Theory in Yixiangshuo and its counterpart in Hanshang Yizhuan (漢上易傳) are almost identical. In conclusion, the origin of Image-Number Theory in Cho Hoik's Yixiangshuo can be found in both the Hu Yigui's Zhouyi Benyi Fulu Zuanzhu and Zhu Zhen's Hanshang Yizhuan. In particular, it can be said that its origin can be found in both the 'Yuwei' and 'Yuan' of Zhouyi Benyi Fulu Zuanzhu and the methodlogy of Image-Number Theory in Hanshang Yizhuan.

• Herbal Formula Science
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• v.11 no.2
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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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• v.22 no.3
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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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• v.72 no.3
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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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• v.28 no.5
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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.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.27 no.4
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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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• v.8 no.2
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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.