• Journal of Intelligence and Information Systems
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• v.28 no.2
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• pp.19-31
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• 2022

In Machine learning, we usually divide the entire data into training data and test data, train the model using training data, and use test data to determine the accuracy and generalization performance of the model. In the case of models with low generalization performance, the prediction accuracy of newly data is significantly reduced, and the model is said to be overfit. This study is about a method of generating training data based on central limit theorem and combining it with existed training data to increase normality and using this data to train models and increase generalization performance. To this, data were generated using sample mean and standard deviation for each feature of the data by utilizing the characteristic of central limit theorem, and new training data was constructed by combining them with existed training data. To determine the degree of increase in normality, the Kolmogorov-Smirnov normality test was conducted, and it was confirmed that the new training data showed increased normality compared to the existed data. Generalization performance was measured through differences in prediction accuracy for training data and test data. As a result of measuring the degree of increase in generalization performance by applying this to K-Nearest Neighbors (KNN), Logistic Regression, and Linear Discriminant Analysis (LDA), it was confirmed that generalization performance was improved for KNN, a non-parametric technique, and LDA, which assumes normality between model building.

• Bulletin of the Korean Mathematical Society
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• v.52 no.4
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• pp.1149-1167
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• 2015

We get a theorem which shows the existence of at least four $2{\pi}$-periodic weak solutions for the bifurcation problem of the Hamiltonian system with the superquadratic nonlinearity. We obtain this result by using the variational method, the critical point theory induced from the limit relative category theory.

• Journal of the Korean Mathematical Society
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• v.33 no.4
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• pp.983-992
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• 1996

Let p(x, dy) be a transition probability function on $(S, \rho)$, where S is a complete separable metric space. Then a Markov process $X_n$ which has p(x, dy) as its transition probability may be generated by random iterations of the form $X_{n+1} = f(X_n, \varepsilon_{n+1})$, where $\varepsilon_n$ is a sequence of independent and identically distributed random variables (See, e.g., Kifer(1986), Bhattacharya and Waymire(1990)).

• Communications of the Korean Mathematical Society
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• v.18 no.3
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• pp.541-550
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• 2003

We consider the generalized autoregressive model with conditional heteroscedasticity process(GARCH). It is proved that if (equation omitted) β/sub i/ < 1, then there exists a unique invariant initial distribution for the Markov process emdedding the given GARCH process. Geometric ergodicity, functional central limit theorems, and a law of large numbers are also studied.

• Journal of the Korean Mathematical Society
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• v.36 no.6
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• pp.1115-1132
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• 1999

We consider a supercritical multitype age dependent branching process. We define a stochastic process Zf(t) which is a functional of the empirical age distribution. When the limit of the expectation of this functional vanishes we4 find some sufficient conditions for the asymptotic normality of the mean of f with respect to the empirical age distribution at time t.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.12 no.4
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• pp.296-299
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• 2012

In this paper, we give definitions for common limit in the range property of mappings and obtain common fixed point theorem for a pair of weakly compatible functions in intuitionistic fuzzy metric space using the joint common limit in the range property of mappings(shortly, (JCLR) property). Our results improve and generalize results of Chauhan et al[1].

• Proceedings of the Korean Geotechical Society Conference
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• 2002.03a
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• pp.93-100
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• 2002

Vertical reinforcement of soft soils using the deep mixing method has received increasing applications. In this study, the theory of elasticity and plasticity including the upper bound theorem of limit analysis were used to derive the equations for obtaining composite elastic properties and shear strength parameters. The developed equations were validated using the finite element computer program SAGE CRISP. The analysis involved 4 different cases-two different type of soil and replacement ratios. Tile results of the analysis show that the proposed equations could determine the properties of composite material for practical applications.

• The Pure and Applied Mathematics
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• v.28 no.1
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• pp.1-13
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• 2021

In this note we use a generalization of coincidence point(a property which was defined by [1] in symmetric spaces) to prove common fixed point theorem on S-metric spaces for weakly compatible maps. Also the results are used to achieve the solution of an integral equation and the bounded solution of a functional equation in dynamic programming.

• Structural Engineering and Mechanics
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• v.42 no.2
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• pp.247-267
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• 2012

Calculating the displacements of retaining walls under seismic loads is a crucial part in optimum design of these structures and unfortunately the techniques based on active seismic pressure are not sufficient alone for an appropriate design of the wall. Using limit analysis concepts, the seismic displacements of retaining walls are studied in present research. In this regard, applying limit analysis method and upper bound theorem, a new procedure is proposed for calculating the yield acceleration, critical angle of failure wedge, and permanent displacements of retaining walls in seismic conditions for two failure mechanisms, namely sliding and sliding-rotational modes. Also, the effect of internal friction angle of soil, the friction angle between wall and soil, maximum acceleration of the earthquake and height of the wall all in the magnitude of seismic displacements has been investigated by the suggested method. Two sets of ground acceleration records related to near-field and far-field domains are employed in analyses and eventually the results obtained from the suggested method are compared with those from other techniques.

• Geomechanics and Engineering
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• v.6 no.5
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• pp.503-515
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• 2014

On the basis of Hoek-Brown failure criterion, a numerical solution for the shape of collapsing block in the rectangular cavity subjected to seepage forces is obtained by upper bound theorem of limit analysis. The seepage forces obtained from the gradient of excess pore pressure distribution are taken as external loadings in the limit analysis, and the pore pressure is easily calculated with pore pressure coefficient. Thus the seepage force is incorporated into the upper bound analysis as a work rate of external force. The upper solution of the shape of collapsing block is derived by virtue of variational calculation. In order to verify the validity of the method proposed in the paper, the result when the pore pressure coefficient equals zero, and only hydrostatic pressure is taken into consideration, is compared with that of previous work. The results show good effectiveness in calculating the collapsing block shape subjected to seepage forces. The influence of parameters on the failure mechanisms is investigated.