• Journal of Korean Society of Steel Construction
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• v.11 no.2 s.39
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• pp.153-165
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• 1999

In order to trace the lateral-torsional post-bucking behaviors of thin-walled space frames with non-symmetric cross sections, a geometrically non-linear finite element formulation is presented by applying incremental equilibrium equations based on the updated Lagrangian formulation and introducing Vlasov's assumption. The improved displacement field for non-symmetric thin-walled cross sections is introduced based on inclusion of second order terms of finite rotations, and the potential energy corresponding to the semitangential rotations and moments is consistently derived. For finite element analysis, tangent stiffness matrices of thin-walled space frame element are derived by using the Hermition polynomials as shape functions. A co-rotational formulation in order to evaluate the unbalanced loads is presented by separating the rigid body rotations and pure deformations from incremental displacements and evaluating the updated direction cosines and incremental member forces.

• Geomechanics and Engineering
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• v.30 no.4
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• pp.325-336
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• 2022

This paper analyzes the ground surface settlements induced by side-by-side twin shield tunnels bored in sedimentary soils, which primarily consist of sand with clay strata above the tunnel crown. The measurements were obtained during the construction of twin tunnels underneath the Incheon International Airport (IIA) located in Korea. The measured surface settlement troughs are approximated with Gaussian functions. The trough width parameters i and K of the settlement troughs produced by the first and second tunnel passings are determined, along with those for the total settlement trough. The surface settlement troughs produced by the first shield passing are reasonably represented by a symmetric Gaussian curve. The surface settlement troughs induced by the second shield tunnel display marginal asymmetric shapes at selected sections. The total settlement troughs are fitted both with a shifted symmetric Gaussian function and the superposition method utilizing an asymmetric function for the incremental trough produced by the second tunnel. It is revealed that the superposition method does not always produce better fits with the total settlement. Instead, the shifted symmetric Gaussian function is overall demonstrated to provide more favorable agreements with the recordings. Therefore, the shifted symmetric Gaussian function is recommended to be used in the design for the prediction of the settlement in clays caused by twin tunneling considering the simplicity of the procedure compared with the superposition method. The amount of increase in the width parameter K for the twin tunnel relative to that for the single tunnel is quantified, which can be used for a preliminary estimate of the surface settlement in clay induced by twin shield tunnels.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.15 no.3
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• pp.1724-1733
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• 2014

This paper presents a pattern recognition analysis of two spirals problem and optimization of Cascade Correlation learning algorithm using in combination with a non-monotone function as CosExp(cosine-modulated symmetric exponential function) and a monotone function as sigmoid function. In addition, the algorithm's optimization is attempted. By using genetic algorithms the optimization of the algorithm will attempt. In the first experiment, by using CosExp activation function for candidate neurons of the learning algorithm is analyzed the recognized pattern in input space of the two spirals problem. In the second experiment, CosExp function for output neurons is used. In the third experiment, the sigmoid activation functions with various parameters for candidate neurons in 8 pools and CosExp function for output neurons are used. In the fourth experiment, the parameters are composed of 8 pools and displacement of the sigmoid function to determine the value of the three parameters is obtained using genetic algorithms. The parameter values applied to the sigmoid activation functions for candidate neurons are used. To evaluate the performance of these algorithms, each step of the training input pattern classification shows the shape of the two spirals. In the optimizing process, the number of hidden neurons was reduced from 28 to15, and finally the learning algorithm with 12 hidden neurons was optimized.

• Journal of applied mathematics & informatics
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• v.38 no.1_2
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• pp.145-157
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• 2020

In this article, we define a generating function of the generalized (p, q)-poly-Bernoulli polynomials with variable a by using the polylogarithm function. From the definition, we derive some properties that is concerned with other numbers and polynomials. Furthermore, we construct a special functions and give some symmetric identities involving the generalized (p, q)-poly-Bernoulli polynomials and power sums of the first integers.

• Communications of the Korean Mathematical Society
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• v.30 no.3
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• pp.269-276
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• 2015

We investigate the Hopf algebra conjugation, ${\chi}$, of the mod 2 Steenrod algebra, $\mathcal{A}_2$, in terms of the Hopf algebra conjugation, ${\chi}^{\prime}$, of the mod 2 Leibniz-Hopf algebra. We also investigate the fixed points of $\mathcal{A}_2$ under ${\chi}$ and their relationship to the invariants under ${\chi}^{\prime}$.

• Journal of the Korean Data and Information Science Society
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• v.16 no.4
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• pp.1141-1145
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• 2005

In this note, we show that Theorem 2.1[Kybernetika, 28(1992) 45-49], a result of a functional relationship between the membership function of LR fuzzy numbers of T-sum and T-product, remains valid for convex additive generator and concave shape functions L and R with simple proof. We also consider the case for 0-symmetric R fuzzy numbers.

• Journal of applied mathematics & informatics
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• v.36 no.5_6
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• pp.475-489
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• 2018

In this paper, by using the polylogarithm function, we introduce a generalized poly-Bernoulli numbers and polynomials with variable a. We find several combinatorial identities and properties of the polynomials. We give some properties that is connected with the Stirling numbers of second kind. Symmetric properties can be proved by new configured special functions. We display the zeros of the generalized poly-Bernoulli polynomials with variable a and investigate their structure.

• Communications for Statistical Applications and Methods
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• v.9 no.2
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• pp.325-335
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• 2002

In this paper we introduce some adaptive M-estimators using selector statistics to estimate the center of symmetric and continuous underlying distributions. This selector statistics is based on the idea of Hogg(1983) and Hogg et. al. (1988) who used averages of some order statistics to discriminate underlying distributions. In this paper, we use the functions of sample quantiles as selector statistics and determine the suitable quantile points based on maximizing the distance index to discriminate distributions under consideration. In Monte Carlo study, this robust estimation method works pretty good in wide range of underlying distributions.

• Communications for Statistical Applications and Methods
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• v.10 no.1
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• pp.145-151
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• 2003

We shall propose several estimators for the scale parameter in the uniform distribution when the parameter is functions of a known exposure level, and obtain expectations and variances for their proposed estimators. And we shall compare numerically relative efficiencies for proposed estimators of the scale parameter in the small sample sizes.

• Honam Mathematical Journal
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• v.42 no.3
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• pp.477-499
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• 2020

In this paper, we introduce a new class of generalized Apostol-type Frobenius-Euler-Hermite polynomials and derive some explicit and implicit summation formulae and symmetric identities by using different analytical means and applying generating functions. These results extend some known summations and identities of generalized Frobenius-Euler type polynomials and Hermite-based Apostol-Euler and Apostol-Genocchi polynomials studied by Pathan and Khan, Kurt and Simsek.