• Communications of Mathematical Education
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• v.29 no.1
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• pp.91-110
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• 2015

The purpose of this study is to investigate the understanding of pi of elementary gifted students and explore improvement direction of teaching pi. The results of this study are as follows. First, students understood insufficiently the property of approximation, constancy and infinity of pi from the fixation on 'pi = 3.14'. They mixed pi up with the approximation of pi as well. Second, they had a inclination to understand pi as algebraic formula, circumference by diameter. Third, few students understood the property of constancy and infinity of pi deeply. Lastly, the discussion activity provided the chance of finding the idea of the property of approximation of pi. In conclusion, we proposed several methods which improve the teaching of pi at elementary school.

• Journal for History of Mathematics
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• v.24 no.3
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• pp.13-21
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• 2011

This mathematico-theological study addresses the Cantor's mathematics and theology of the infinite. From the scientific perspective, Cantor's landmark works opened the definition and logic of infinity in concreto, in abstracto, and in Deo. According to Cantor, the absolute infinite ${\Omega}$ could imply God's property beyond the actual infinite in physical and mathematical worlds.

• Journal of the Korean Mathematical Society
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• v.54 no.5
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• pp.1573-1594
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• 2017

This paper deals with the existence and energy estimates of solutions for a class of degenerate nonlocal problems involving sub-linear nonlinearities, while the nonlinear part of the problem admits some hypotheses on the behavior at origin or perturbation property. In particular, for a precise localization of the parameter, the existence of a non-zero solution is established requiring the sublinearity of nonlinear part at origin and infinity. We also consider the existence of solutions for our problem under algebraic conditions with the classical Ambrosetti-Rabinowitz. In what follows, by combining two algebraic conditions on the nonlinear term which guarantees the existence of two solutions as well as applying the mountain pass theorem given by Pucci and Serrin, we establish the existence of the third solution for our problem. Moreover, concrete examples of applications are provided.

• Journal of the Korea Institute of Military Science and Technology
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• v.13 no.3
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• pp.503-510
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• 2010

The quick variation of the canister wall temperature causes the modification of the shape of canister wall. This paper is the possibility of adoption and the error analysis about the transient heat flux method. The commercial code(Fluent Ver6.2.16) was employed for the calculation of surface temperature in the case of steady and unsteady heat flux condition. Based the surface temperature variation and surface material property, transient heat flux method can calculate the surface heat flux. In the case of steady heat flux condition, the error is about 2%, and in the case of unsteady heat flux condition, the error is about 3.6%. With the unsteady heat flux condition, the time which reach the maximum surface heat flux is almost same between the numerical analysis and transient heat flux method.

• Journal of Mechanical Science and Technology
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• v.17 no.8
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• pp.1120-1132
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• 2003

A problem of a circular elastic inhomogeneity interacting with a crack under uniform loadings (mechanical tension and heat flux at infinity) is solved. The singular. integral equations for edge and temperature dislocation distribution functions are constructed and solved numeric-ally, to obtain the stress intensity factors. The effects of the material property ratio on the stress intensity factor (SIF) are investigated. The computed SIFs are used to predict the kink angle of the crack when the crack grows.

• Communications for Statistical Applications and Methods
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• v.25 no.5
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• pp.453-470
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• 2018

We study how to distinguish the parameters of the sparse autoregressive (AR) process from zero using a non-convex penalized estimation. A class of non-convex penalties are considered that include the smoothly clipped absolute deviation and minimax concave penalties as special examples. We prove that the penalized estimators achieve some standard theoretical properties such as weak and strong oracle properties which have been proved in sparse linear regression framework. The results hold when the maximal order of the AR process increases to infinity and the minimal size of true non-zero parameters decreases toward zero as the sample size increases. Further, we construct a practical method to select tuning parameters using generalized information criterion, of which the minimizer asymptotically recovers the best theoretical non-penalized estimator of the sparse AR process. Simulation studies are given to confirm the theoretical results.

• 전기의세계
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• v.29 no.7
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• pp.471-477
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• 1980

This paper deals with a modified Kalman filter. An approaching horizon with a suitable initial condition will be considered, which is a little different from the classical Kalman filter. It will be shown in this paper that the new filter with approaching horizons is not only easy to computer but also possesses asymptotic stability properties. Thus this new estimatoris an excellent compromise between the ease of computation and the strict sense of optimality. When this estimator is used for the standard problem, the error covariance bound has been obtained. It is shown that the new estimator can be used as a suboptimal estimator which has a stability property. It is also demonstrated that the steady state Kalman filter can be obtained from the moving horizon estimator by taking the horizon parameter as infinity.

• Journal of the Chungcheong Mathematical Society
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• v.37 no.1
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• pp.27-40
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• 2024

In this paper, we consider the higher-order HartreeFock equations. The higher-order linear Schrödinger equation was introduced in [5] as the formal finite Taylor expansion of the pseudorelativistic linear Schrödinger equation. In [13], the authors established global-in-time Strichartz estimates for the linear higher-order equations which hold uniformly in the speed of light c ≥ 1 and as their applications they proved the convergence of higher-order Hartree-Fock equations to the corresponding pseudo-relativistic equation on arbitrary time interval as c goes to infinity when the Taylor expansion order is odd. To achieve this, they not only showed the existence of solutions in L² space but also proved that the solutions stay bounded uniformly in c. We address the remaining question on the convergence of higherorder Hartree-Fock equations when the Taylor expansion order is even. The distinguished feature from the odd case is that the group velocity of phase function would be vanishing when the size of frequency is comparable to c. Owing to this property, the kinetic energy of solutions is not coercive and only weaker Strichartz estimates compared to the odd case were obtained in [13]. Thus, we only manage to establish the existence of local solutions in H^s space for s > $\frac{1}{3}$ on a finite time interval [-T, T], however, the time interval does not depend on c and the solutions are bounded uniformly in c. In addition, we provide the convergence result of higher-order Hartree-Fock equations to the pseudo-relativistic equation with the same convergence rate as the odd case, which holds on [-T, T].

• Journal of the Korean institute of surface engineering
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• v.50 no.2
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• pp.98-107
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• 2017

Pd-based membranes have been widely used in hydrogen purification and separation due to their high hydrogen diffusivity and infinite selectivity. However, it has been difficult to fabricate thin and dense Pd-based membranes on a porous stainless steel(PSS) support. In case of a conventional PSS support having the large size of surface pores, it was required to use complex surface treatment and thick Pd coating more than $6{\mu}m$ on the PSS was required in order to form pore free surface. In this study, we could fabricate thin and dense Pd membrane with only $3{\mu}m$ Pd layer on a new PSS support manufactured by metal injection molding(MIM). The PSS support had low surface roughness and mean pore size of $5{\mu}m$. Pd membrane were prepared by advanced Pd sputter deposition on the modified PSS support using fine polishing and YSZ vacuum filling surface treatment. At temperature $400^{\circ}C$ and transmembrane pressure difference of 1 bar, hydrogen flux and selectivity of $H_2/N_2$ were $11.22ml\;cm^{-2}min^{-1}$ and infinity, respectively. Comparing with $6{\mu}m$ Pd membrane, $3{\mu}m$ Pd membrane showed 2.5 times higher hydrogen flux which could be due to the decreased Pd layer thickness from $6{\mu}m$ to $3{\mu}m$ and an increased porosity. It was also found that pressure exponent was changed from 0.5 on $6{\mu}m$ Pd membrane to 0.8 on $3{\mu}m$ Pd membrane.

• The Journal of the Korea Contents Association
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• v.11 no.1
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• pp.56-64
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• 2011

It is difficult to discover frequent itemsets based on whole data from data stream since data stream has the characteristics of infinity and continuity. Therefore, a specialized data mining method, which reflects the properties of data and the requirement of users, is required. In this paper, we propose the method of FIMWB discovering the frequent itemsets which are reflecting the property that the recent events are more important than old events. Data stream is splitted into batches according to the given time interval. Our method gives a weighted value to each batch. It reflects user's interestedness for recent events. FP-Digraph discovers the frequent itemsets by using the result of FIMWB. Experimental result shows that FIMWB can reduce the generation of useless items and FP-Digraph method shows that it is suitable for real-time environment in comparison to a method based on a tree(FP-Tree).