• Korean Journal of Mathematics
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• v.32 no.1
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• pp.43-57
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• 2024

Given a domain X and a collection H of functions h : X → {0, 1}, the Vapnik-Chervonenkis (VC) dimension of H measures its complexity in an appropriate sense. In particular, the fundamental theorem of statistical learning says that a hypothesis class with finite VC-dimension is PAC learnable. Recent work by Fitzpatrick, Wyman, the fourth and seventh named authors studied the VC-dimension of a natural family of functions ℋ'²_t(E) : 𝔽²_q → {0, 1}, corresponding to indicator functions of circles centered at points in a subset E ⊆ 𝔽²_q. They showed that when |E| is large enough, the VC-dimension of ℋ'²_t(E) is the same as in the case that E = 𝔽²_q. We study a related hypothesis class, ℋ^d_t(E), corresponding to intersections of spheres in 𝔽^d_q, and ask how large E ⊆ 𝔽^d_q needs to be to ensure the maximum possible VC-dimension. We resolve this problem in all dimensions, proving that whenever |E| ≥ C_dq^d-1/(d-1) for d ≥ 3, the VC-dimension of ℋ^d_t(E) is as large as possible. We get a slightly stronger result if d = 3: this result holds as long as |E| ≥ C_3q^7/3. Furthermore, when d = 2 the result holds when |E| ≥ C_2q^7/4.

• The Bulletin of The Korean Astronomical Society
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• v.40 no.1
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• pp.66.1-66.1
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• 2015

We present the first observational detection of radial and azimuthal oscillations in full halo coronal mass ejections (HCMEs). We analyze nine HCMEs well-observed by LASCO from Feb 2011 to Jun 2011. Using the LASCO C3 running difference images, we estimated the instantaneous apparent speeds of the HCMEs in different radial directions from the solar disk center. We find that the development of all these HCMEs is accompanied with quasi-periodic variations of the instantaneous radial velocity with the periods ranging from 24 to 48 mins. The amplitudes of the instant speed variations reach about a half of the projected speeds. The amplitudes are found to anti-correlate with the periods and correlate with the HCME speed, indicating the nonlinear nature of the process. The oscillations have a clear azimuthal structure in the heliocentric polar coordinate system. The oscillations in seven events are found to be associated with distinct azimuthal wave modes with the azimuthal wave number m=1 for six events and m=2 for one event. The polarization of the oscillations in these seven HCMEs is broadly consistent with those of their position angles with the mean difference of $42.5^{\circ}$. The oscillations may be connected with natural oscillations of the plasmoids around a dynamical equilibrium, or self-oscillatory processes, e.g. the periodic shedding of Alfvenic vortices. Our results indicate the need for advanced theory of oscillatory processes in CMEs.

• Journal of Computational Design and Engineering
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• v.2 no.4
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• pp.233-247
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• 2015

In this paper, the cutting force calculation of ball-end mill processing was modeled mathematically. All derivations of cutting forces were directly based on the tangential, radial, and axial cutting force components. In the developed mathematical model of cutting forces, the relationship of average cutting force and the feed per flute was characterized as a linear function. The cutting force coefficient model was formulated by a function of average cutting force and other parameters such as cutter geometry, cutting conditions, and so on. An experimental method was proposed based on the stable milling condition to estimate the cutting force coefficients for ball-end mill. This method could be applied for each pair of tool and workpiece. The developed cutting force model has been successfully verified experimentally with very promising results.

• Journal of Institute of Control, Robotics and Systems
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• v.22 no.8
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• pp.615-618
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• 2016

This paper proposes a method to estimate vertical interaction force to the end of the surgical instrument by measuring reaction force at the part supporting the trocar. Relation between the force to the trocar and the interaction force is derived using the beam theory. The vertical interaction force is modeled as a function of the reaction force to the trocar and the distance between the drape plate and the trocar. Experimental results show that error is induced by the asymmetric shape of the trocar tip because contact position between the instrument and the trocar tip is changed depending on the direction of the interaction force. The theoretical relation, therefore, is compensated and reduced. Average $L_2$ relative error of the estimated force in the x-direction and the y-direction is 5.81 % and 5.99 %, respectively.

• International Journal of Naval Architecture and Ocean Engineering
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• v.9 no.5
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• pp.525-536
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• 2017

Course keeping is hard to implement under the condition of the propeller stopping or reversing at slow speed for berthing due to the ship's dynamic motion becoming highly nonlinear. To solve this problem, a practical Maneuvering Modeling Group (MMG) ship mathematic model with propeller reversing transverse forces and low speed correction is first discussed to be applied for the right-handed single-screw ship. Secondly, a novel PID-based nonlinear feedback algorithm driven by bipolar sigmoid function is proposed. The PID parameters are determined by a closed-loop gain shaping algorithm directly, while the closed-loop gain shaping theory was employed for effects analysis of this algorithm. Finally, simulation experiments were carried out on an LPG ship. It is shown that the energy consumption and the smoothness performance of the nonlinear feedback control are reduced by 4.2% and 14.6% with satisfactory control effects; the proposed algorithm has the advantages of robustness, energy saving and safety in berthing practice.

• Korean Institute of Interior Design Journal
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• v.15 no.4 s.57
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• pp.97-105
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• 2006

Richard Meier has earned his recognition by developing his unique design approach and keeping consistency in design concept in museum architecture over the years of his practice. The purpose of this study is finding common characteristics of the exhibition space spatial organization based on actual site visit analysis. This study will mainly focus on the museums Richard Meier designed between 1979, which is the year he started, until 1997 which is the year Getty Museum opened. For the purpose of this study, Museum of Applied Art, Frankfurt(1979-85), High Museum of Art, Atlanta(1980-83), Museum of Contemporary Art, Barcelona(1987-95), and The J.Paul Getty Museum(1984-1997) have been selected for analysis. This study will reveal fundamental characteristics of Richard Meier's architectural philosophy through his early residential projects and give background information of the 'white architecture' Close analysis will continue by reviewing four museums selected specifically for this study and focus more from the point of issues such as; 1)applying various axis in space programming, 2)symbolic significance of exhibition space, 3)hierarchy of each space, 4)design elements and characteristics of the exhibition space. Furthermore, quantitative research on exhibition space organization will be done by Space Syntax theory method. The result of the study will be a significant data in designing a modern museum.

• Steel and Composite Structures
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• v.44 no.4
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• pp.587-602
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• 2022

In this study, the classical J₂ flow theory is explicitly proved to be inappropriate to describe the plastic behaviour of structural steels under different stress states according to the reported test results. A numerical framework of the characterization of the strain hardening and ductile fracture initiation involving the effect of stress states, i.e., stress triaxiality and Lode angle parameter, is proposed based on the mechanical response of structural steels under monotonic loading. Both effects on strain hardening are determined by correction functions, which are implemented as different modules in the numerical framework. Thus, other users can easily modify them according to their test results. Besides, the ductile fracture initiation is determined by a fracture locus in the space of stress triaxiality, Lode angle parameter, and fracture strain. The numerical implementation of the proposed model and the corresponding code are provided in this paper, which are also available on GitHub. The validity of the numerical procedure is examined through single element tests and the accuracy of the proposed model is verified by existing test results.

• Korean Journal of Community Nutrition
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• v.3 no.3
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• pp.358-367
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• 1998

The study purpose was to investigate psychosocial factors related to smoking among adolescent boys. The Theory of Planned Behavior provide the basis for the study. Twenty-five attitudinal beliefs, 9 normative beliefs and 20control beliefs were identified through questionnaire development. The data were analyzed using t-test and χ2-test. Thirty-three percent of 300 students were smokers. Most of the beliefs examined were significantly different between smokers(n=92) and nonsmokers(n=92). With respect to attitudinal beliefs, smokers responded less negatively on the items of bad health effects of smoking such as sore throat, headache, chest pain, risk of cancer and bad blood circulation(p<0.001), and decreased physical strength(p<0.05). Smokers believed less negatively on the items that smoking leads to bothering others, bad breath, yellow teeth and making them spend money(p<0.001). In contrast, smokers felt more positively on smoking as a means of stress management, relaxing, helping digestion(P<0.001). Smokers felt less pressure for not smoking from significant others. Especially mother, siblings, friends, girl friends, seniors of school were important sources of influence regarding subject's smoking. Smokers felt less confident in controlling the urge to smoke in several situations including; when they were with friends or asked to smoke by friends; after the meal, or drinking; when they were bored or stressed, upset, and when they felt unstable(p<0.001). Smokers also scored lower on specific skills to quit or control the urge to smoke as well as overall perceived control, compared to nonsmokers(p<0.001). These results suggest that interventions for adolescents incorporate diverse strategies to increase the perceived control over smoking in specific situations as well as overall perceived control, to help them realize and modify attitudinal beliefs, and to elicit support from significant others for not smoking. (Korean J Community Nutrition 3(3) : 358∼367,1998)

• Nuclear Engineering and Technology
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• v.51 no.5
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• pp.1373-1380
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• 2019

Besides promising implications as fertile nuclear materials, thorium carbonitrides are of great interest owing to their peculiar physical and chemical properties, such as high density, high melting point, good thermal conductivity. This paper reports first-principles simulation results on the structural, electronic and magnetic properties of cubic thorium carbonitrides $ThC_xN_{(1-x)}$ (X = 0.03125, 0.0625, 0.09375, 0.125, 0.15625) employing formalism of density-functional-theory. For the simulation of physical properties, we incorporated full-potential linearized augmented plane-wave (FPLAPW) method while the exchange-correlation potential terms in Kohn-Sham Equation (KSE) are treated within Generalized-Gradient-Approximation (GGA) in conjunction with Perdew-Bruke-Ernzerhof (PBE) correction. The structural parameters were calculated by fitting total energy into the Murnaghan's equation of state. The lattice constants, bulk moduli, total energy, electronic band structure and spin magnetic moments of the compounds show dependence on the C/N concentration ratio. The electronic and magnetic properties have revealed non-magnetic but metallic character of the compounds. The main contribution to density of states at the Fermi level stems from the comparable spectral intensity of Th (6d+5f) and (C+N) 2p states. In comparison with spin magnetic moments of ThSb and ThBi calculated earlier with LDA+U approach, we observed an enhancement in the spin magnetic moments after carbon-doping into ThN monopnictide.

• Bulletin of the Korean Chemical Society
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• v.31 no.6
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• pp.1704-1710
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• 2010

The structure of a 2D grid-like copper(II) complex [Cu$(NCO)_2$(pyz)](pyz=pyrazine) (1) consists of 1D chains of Cu-pyz units connected by double end-on (EO) cyanato bridges. Each Cu(II) ion has a distorted octahedral coordination, completed by the four EO cyanato and two pyrazine ligands. Magnetic interactions through EO cyanato and pyrazine bridges in 1 are discussed on the basis of DFT broken-symmetry calculations at the B3LYP level. For model dicopper(II) complexes I (bridged by cyanato) and II (bridged by pyrazine), electronic structure calculations reproduce very well the experimental couplings for the S = 1/2 ferromagnetic and antiferromagnetic exchange-coupled 2D system: the calculated exchange parameters J are +1.25 $cm^{-1}$ and -3.07 $cm^{-1}$ for I and II, respectively. The $\sigma$ orbital interactions between the Cu $x^2-y^2$ magnetic orbitals and the nitrogen lone-pair orbitals of pyrazine are analyzed from the viewpoint of through-bond interaction. The energy splitting of 0.106 eV between two SOMOs indicates that the superexchange interaction should be antiferromagnetic in II. On the other hand, there are no bridging orbitals that efficiently connect the two copper(II) magnetic orbitals in I because the HOMOs of the basal-apical NCO bridge do not play a role in the formation of overlap interaction pathway. The energy separation in the pair of SOMOs of I is calculated to be very small (0.054 eV). This result is consistent with the occurrence of weakly ferromagnetic properties in I.