• Journal of applied mathematics & informatics
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• v.39 no.3_4
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• pp.437-442
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• 2021

In this paper, we study the characterizations of two-sided best simultaneous approximations for ℓ-tuple subset from a closed convex subset of ℝ^m with ℓ^m₁(w)-norm. Main fact is, k^* is a two-sided best simultaneous approximation to F from K if and only if there exist f₁, …, f_p in F, for any k ∈ K $${\mid}{\sum\limits_{i=1}^{m}}sgn(f_{ji}-k^*_i)k_iw_i{\mid}{\leq}\;{\sum\limits_{i{\in}Z(f_j-k^*)}}\;{\mid}k_i{\mid}w_i$$ for each j = 1, …, p and 𝐰 ∈ W.

• Structural Engineering and Mechanics
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• v.82 no.2
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• pp.205-224
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• 2022

This paper presents a refined finite element formulation for nonlinear static and dynamic analysis of sliding cable structures, overcoming the limitation of the existing approaches that neglect or approximate the friction, pulley dimension, temperature and geometric nonlinearity. A new family of elements with the same framework is proposed, consisting of the cable-pulley (CP) elements considering sliding friction, and the non-sliding cable-pulley (NSCP) elements considering static friction. Thereafter, the complete procedure of static and dynamic analysis using the proposed elements is developed, with the capability of accurately dealing with the friction at each pulley. Several examples are utilized to verify the validity and accuracy of the proposed elements and analysis strategy, and investigate the frictional, thermal and pulley-dimension effects as well. The numerical examples show that the results obtained in this work are in good accordance with the existing works when using the same approximations of friction, pulley dimension and temperature. By avoiding the approximations, the proposed formulation can be effectively adopted in predicting the more precise nonlinear responses of sliding cable structures.

• Communications of the Korean Mathematical Society
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• v.6 no.1
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• pp.47-54
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• 1991

• Kyungpook Mathematical Journal
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• v.27 no.1
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• pp.55-60
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• 1987

A linear system $\dot{x}= A(t)x$, with A(t+w)=A(t) is considered. A step function approximation of a periodic matrix is constructed. The stability criteria is discussed.

• The Korean Journal of Applied Statistics
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• v.6 no.1
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• pp.125-143
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• 1993

The primary objective of the paper is to review the development of approximations of the null distribution of a scan statistic and to show how these approximations were improved. Let $X_1, \cdots, X_N$ be a sequence of independent uniform random variables on an interval (0, t]. A can statistic is defined to be the maximum number of observations in a subinterval of length t $\leq$ T, when we continuously (or discretely) move the subinterval from 0 to T. A scan statistic is used to test whether certain events occur in a cluster aganist a null hypothesis of the uniformity. It is difficult to calculate the exact null distribution of a scan statistic. Several authors have suggested approximations of the null distribution of a scan statistic since Naus(1966). We conceive that a scan statistic can be used for detecting a "hot region" is defined to be a region at which the frequencies of mutations are relatively high. A "hot region" may be regarded as a generalized version of a hot spot. We leave it for a further study the concrete formulation of deteciton a "hot region" in a mutational spectrum.uot; in a mutational spectrum.

• Journal of the Korean Data and Information Science Society
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• v.27 no.4
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• pp.959-967
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• 2016

Distributional assumptions on equity returns play a key role in valuation theories for derivative securities. Elberlein and Keller (1995) investigated the distributional form of compound returns and found that some of standard assumptions can not be justified. Instead, Generalized Hyperbolic (GH) distribution fit the empirical returns with high accuracy. Hu and Kercheval (2007) also show that the normal distribution leads to VaR (Value at Risk) estimate that significantly underestimate the realized empirical values, while the GH distributions do not. We consider saddlepoint approximations to estimate the VaR and the ES (Expected Shortfall) which frequently encountered in finance and insurance as measures of risk management. We supposed GH distributions instead of normal ones, as underlying distribution of linear portfolios. Simulation results show the saddlepoint approximations are very accurate than normal ones.

• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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• pp.759-769
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• 2005

We first discuss jump discontinuity in higher dimension, and then prove a local convergence theorem for wavelet approximations in higher dimension. We also redefine the concept of Gibbs phenomenon in higher dimension and show that wavelet expansion exhibits Gibbs phenomenon.

• Communications for Statistical Applications and Methods
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• v.14 no.1
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• pp.23-32
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• 2007

We consider penalized likelihood regression with data from the negative binomial distribution with unknown shape parameter. Smoothing parameter selection and asymptotically efficient low dimensional approximations are employed for negative binomial data along with shape parameter estimation through several different algorithms.

• 대한예방의학회:학술대회논문집
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• 2002.10a
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• pp.192-193
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• 2002

• Korean Journal of Mathematics
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• v.20 no.1
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• pp.61-75
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• 2012

We investigate the properties of various frames and connections on partially ordered sets. In particular, we study the relations between various connections and various frames.