• Structural Engineering and Mechanics
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• v.35 no.4
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• pp.431-457
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• 2010

This article provides a discussion of the mathematic modeling of connections for designing and qualifying structures, systems, and components subject to monotonic or cyclic loading. To characterize the force-deformation behavior of connections under monotonic loading, a review of the Ramberg-Osgood, Richard-Abbott, and Menegotto-Pinto models is conducted, and it is shown that these nonlinear functions can be mathematically derived by scaling up or down a linear force-deformation function. A generalized four-parameter model for simulating connection behavior is investigated to facilitate nonlinear regression analysis. In order to perform seismic analysis of frameworks, a hysteretic model accounting for loading, unloading, and reloading is described using the established monotonic model. For preliminary analysis, a method is provided to quickly determine the model parameters that fit approximately with the observed data. To reach more accurate values of the parameters, the methods of nonlinear regression analysis are investigated and the modified Levenberg-Marquardt and separable nonlinear least-square algorithms are applied in determining the model parameters. Example case studies illustrate the procedure for the computation through the use of experimental/analytical data taken form the literature. Transformation of connection curves from the three-parameter model to the four-parameter model for structural analysis is conducted based on the modeling of connections subject to fire.

• Journal of the Korean Operations Research and Management Science Society
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• v.12 no.1
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• pp.10-18
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• 1987

This paper discusses algorithmic properties of a class of complementarity programs involving strictly diagonally isotone and off-diagonally isotone functions, i. e., functions whose Jacobian matrices have positive diagonal elements and nonnegative off-diagonal elements, A typical traffic equilibrium under elastic demands is cast into this class. Algorithmic properties of these complementarity problems, when a Jacobi-type iteration is applied, are investigated. It is shown that with a properly chosen starting point the generated sequence are decomposed into two converging monotonic subsequences. This and related will be useful in developing solution procedures for this class of complementarity problems.

• Journal of Korea Society of Industrial Information Systems
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• v.15 no.5
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• pp.179-185
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• 2010

In a sensitivity analysis, an uncertainty importance measure is often used to assess how much uncertainty of an output is attributable to the uncertainty of an input, and thus, to identify those inputs whose uncertainties need to be reduced to effectively reduce the uncertainty of output. A function is called monotonic if the output is either increasing or decreasing with respect to any of the inputs. In this paper, for a monotonic function, we propose a method for evaluating the measure which assesses the expected percentage reduction in the variance of output due to ascertaining the value of input. The proposed method can be applied to the case that the output is expressed as linear and nonlinear monotonic functions of inputs, and that the input follows symmetric and asymmetric distributions. In addition, the proposed method provides a stable uncertainty importance of each input by discretizing the distribution of input to the discrete distribution. However, the proposed method is computationally demanding since it is based on Monte Carlo simulation.

• Communications of the Korean Mathematical Society
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• v.31 no.2
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• pp.355-363
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• 2016

By employing a refined version of the $P{\acute{o}}lya$ type integral inequality and other techniques, the authors establish some inequalities and absolute monotonicity for modified Bessel functions of the first kind with nonnegative integer order.

• International Journal of CAD/CAM
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• v.6 no.1
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• pp.59-64
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• 2006

A new method to obtain explicit re-parameterization that preserves the curve degree and parametric domain is presented in this paper. The re-parameterization brings a curve very close to the arc length parameterization under $L_2$ norm but with less segmentation. The re-parameterization functions we used are $C^1$ continuous piecewise rational linear functions, which provide more flexibility and can be easily identified by solving a quadratic equation. Based on the outstanding performance of Mobius transformation on modifying pieces with monotonic parametric speed, we first create a partition of the original curve, in which the parametric speed of each segment is of monotonic variation. The values of new parameters corresponding to the subdivision points are specified a priori as the ratio of its cumulative arc length and its total arc length. $C^1$ continuity conditions are imposed to each segment, thus, with respect to the new parameters, the objective function is linear and admits a closed-form optimization. Illustrative examples are also given to assess the performance of our new method.

• Bulletin of the Korean Mathematical Society
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• v.50 no.1
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• pp.263-273
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• 2013

A mean-value result, saying that the difference quotient of a differentiable function in a real interval is a mean value of its derivatives at the endpoints of the interval, leads to the functional equation $$\frac{f(x)-F(y)}{x-y}=M(g(x),\;G(y)),\;x{\neq}y$$, where M is a given mean and $f$, F, $g$, G are the unknown functions. Solving this equation for the arithmetic, geometric and harmonic means, we obtain, respectively, characterizations of square polynomials, homographic and square-root functions. A new criterion of the monotonicity of a real function is presented.

• Journal of the Earthquake Engineering Society of Korea
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• v.23 no.2
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• pp.131-140
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• 2019

Diagonally reinforced concrete coupling beams (DRCBs) have been widely adopted in reinforced concrete (RC) bearing wall systems. DRCBs are known to act as a fuse element dissipating most of seismic energies imparted to the bearing wall systems during earthquakes. Despite such importance of DRCBs, the damage estimation of such components and the corresponding consequences within the knowledge of performance based seismic design framework is not well understood. In this paper, drift-based fragility functions are developed for in-plane loaded DRCBs. Fragility functions are developed to predict the damage and to decide the repair method required for DRCBs subjected to earthquake loading. Thirty-seven experimental results are collected from seventeen published literatures for this effort. Drift-based fragility functions are developed for four damage states of DRCBs subjected to cyclic and monotonic loading associated with minor cracking, severe cracking, onset of strength loss, and significant strength loss. Damage states are defined in a consistent manner. Cumulative distribution functions are fit to the empirical data and evaluated using standard statistical methods.

• The Pure and Applied Mathematics
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• v.17 no.2
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• pp.175-183
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• 2010

Using Darbo's fixed point theorem, we establish the existence of monotone solutions for a nonlinear quadratic integral equation of Volterra type in the Banach space of real functions defined and continuous on a bounded and closed interval.

• Journal of the Korean Data and Information Science Society
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• v.23 no.6
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• pp.1223-1229
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• 2012

In this paper, we propose a generalized Kullback-Leibler (KL) information for measuring the distance between two distribution functions where the extension to the censored case is immediate. The generalized KL information has the nonnegativity and characterization properties, and its censored version has the additional property of monotonic increase. We also extend the discussion to the discrete case and propose a generalized censored measure which is comparable to Pearson's chi-square statistic.

• The Pure and Applied Mathematics
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• v.21 no.2
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• pp.141-145
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• 2014

In the paper, by directly verifying an inequality which gives a lower bound for the first order modified Bessel function of the first kind, the authors supply a new proof for the complete monotonicity of a difference between the exponential function $e^{1/t}$ and the trigamma function ${\psi}^{\prime}(t)$ on (0, ${\infty}$).