• Journal of the Korean Geotechnical Society
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• v.24 no.7
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• pp.51-60
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• 2008

In this paper, the behaviour of shell foundation was studied. In the theoretical program, the general shallow foundation theories and failure mechanism developed by Terzaghi, Mayerhof and others were reviewed and compared. In the numerical study, the 2 and 3 dimensional FEM simulations were carried out using an uncoupled-analysis approach. The results obtained from the model test show that the bearing capacity of shell foundation was about 25% to 30% larger than that of general foundation. Due to the cases of shell angle, the maximum bearing capacity of shell foundation shows when the shell angle of foundation was $60^{\circ}$. In addition, even if the shell foundation has various advantages compared with the general foundations as described above, the practical verifications in full scale size will be necessary to use in the field and will be helpful in the technical development of other special foundations.

• 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.

• Journal of the Korea Society of Computer and Information
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• v.18 no.5
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• pp.113-120
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• 2013

This paper proposes an algorithm that proves an NP-complete 4-color theorem by employing a linear time complexity where $O(n)$. The proposed algorithm accurately halves the vertex set V of the graph $G=(V_1,E_1)$ into the Maximum Independent Set (MIS) $\bar{C_1}$ and the Minimum Vertex Cover Set $C_1$. It then assigns the first color to $\bar{C_1}$ and the second to $\bar{C_2}$, which, along with $C_2$, is halved from the connected graph $G=(V_2,E_2)$, a reduced set of the remaining vertices. Subsequently, the third color is assigned to $\bar{C_3}$, which, along with $C_3$, is halved from the connected graph $G=(V_3,E_3)$, a further reduced set of the remaining vertices. Lastly, denoting $C_3$ as $\bar{C_4}$, the algorithm assigns the forth color to $\bar{C_4}$. The algorithm has successfully obtained the chromatic number ${\chi}(G)=4$ with 100% probability, when applied to two actual map and two planar graphs. The proposed "four color algorithm", therefore, could be employed as a general algorithm to determine four-color for planar graphs.

• Journal of Educational Research in Mathematics
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• v.20 no.1
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• pp.85-102
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• 2010

Linear programming(LP) is useful for finding the best way in a given condition for some list of requirements represented as linear equations. This study analysed LP in mathematics contexts and LP in school mathematics contexts, considered learning process of LP from an epistemological point of view, and explored a hypothetical learning trajectory of LP. The differences between mathematics contexts and school mathematics contexts are whether they considered that the convex polytope $\Omega$ is feasible/infeasible or bounded/unbounded or not, and whether they prove the theorem that the optimum is always attained at a vertex of the polyhedronor not. And there is a possibility that students could not understand what is maximum and minimum of a linear function when the domain of the function is limited. By considering these three aspects, we constructed hypothetical learning trajectory consisted of 4 steps. The first step is to see a given linear expression as linear function, the second step is to partition a given domain by straight lines, the third step is to construct the conception of y-intercept by relating lines and the range of k, and the forth step is to identify whether there exists the optimum in a given domain or not.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.4 no.3
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• pp.75-83
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• 1984

The probability of failure is used to analyze the reliability of three dimensional slope failure, instead of conventional factor of safety. The strength parameters are assumed to be normal variated and beta variated. These are interval estimated under the specified confidence level and maximum likelihood estimation. The pseudonormal and beta random variables are generated using the uniform probability transformation method according to central limit theorem and rejection method. By means of a Monte-Carlo Simulation, the probability of failure is defined as; $P_f=M/N$ N: Total number of trials M: Total number of failures Some of the conclusions derived. from the case study include; 1. Three dimensional factors of safety are generally much higher than 2-D factors of safety. However situations appear to exist where the 3-D factor of safety can be lower than the 2-D factor of safety. 2. The $F_3/F_2$ ratio appears to be quite sensitive to c and ${\phi}$ and to the shape of the 3-D shear surface and the slope but not to be to the unit weight of soil. 3. From the two models (normal, beta) considered for the distribution of the factor of safety, the beta distribution generally provides lager than normal distribution. 4. Results obtained using the beta and normal models are presented in a nomgraph relating slope height and slop angle to probability of failure.

• Journal of KSNVE
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• v.6 no.1
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• pp.107-114
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• 1996

The damping characteristics of a cylindrical structure containing oil and bearing balls is investigated for external bending forces. The experimental data obtained through the use of bearing balls with viscous oil in a column is given and analyzed. The viscous action of the oil and inertia effects of the balls on the inside of column create a drag force. The drag force dampens the vibration of the column. This study aims to search for an optimum combination of oil and balls which would produce maximum damping. Machining oils of various viscosities along with ball bearings of various sizes place inside cantilevered aluminium tubes of various diameters to create a rig on which the damping properties of the oil and balls can be studied. The contileved tubes are studied in both horizontal and vertical positions in order to gauge the effect of gravity on the system. The actions of the ball in the column and damping characteristics are investigated according to the dimensionless terms. The Buckingham theorem is used to reduce the variables and to predict the damping of an oil ball column. Though the damping ratio remains fairly constant in the horizontal position of column, the damping ratio begins to increase as the ratio of the number of balls and column length rise above 0.28 in the vertical position of oil ball column. The ratio of the ball diameter to column diameter influences the damping ratio with an optimum diameter ratio. Slenderness ratio and gravity effects on the damping ratio ane investigated.

• Journal of the Korean Society of Propulsion Engineers
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• v.4 no.4
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• pp.50-58
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• 2000

Burning rate of the matrix propellant($r_{sb}$) and burning rate along the metal wire($r_w$) were measured and analyzed for the HTPB/AP/Al propellant embedded with Ag wire($\phi$0.15mm) according to weight % of RDX(0~20%). Variation of burning rate increment ratio($r_w$/$r_{sb}$) and pressure exponent(n) was studied for the nitramine propellant having 10% RDX embedded with three kinds of metal(Ag, Cu, and Ni-Cr) of which diameter range is between 0.1~0.6mm. Maximum burning rate increment ratio of the nitramine propellant embedded with Ag wire($\phi$0.1mm) was 5.94 at $20^{\cire}C$, 1000 psia, 16.4% faster than that of HTPB/AP propellant, it is because that autoignition temperature of the nitramine propellant was higher than that of HTPB/AP propellant. Standard deviation of absolute ($r_{wc}$/$r_{we}$)/$r_{we}$ calculated by using new empiracal equation composed of four dimensionless groups, is 6.11% less than that calculated by using original empirical equation composed of three dimensionless group. The new empiracal equation is derived from Buckingham pi theorem using the parameters such as thermal diffusivity, melting temperature. wire diameter, propellant sample diameter, frame temperature, autoignition temperature and matrix burning rate which influence on $r_w$.