• East Asian mathematical journal
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• v.18 no.1
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• pp.111-125
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• 2002

Many different families of infinite series were recently observed to be summable in closed forms by means of certain operators of fractional calculus(that is, calculus of integrals and derivatives of any arbitrary real or complex order). In this sequel to some of these recent investigations, the authors present yet another instance of applications of certain fractional calculus operators. Alternative derivations without using these fractional calculus operators are shown to lead naturally a family of analogous infinite sums involving hypergeometric functions.

• International Journal of Reliability and Applications
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• v.18 no.2
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• pp.65-82
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• 2017

Abstract. Camilo Dagum proposed several variants of a new model for the size distribution of personal income in a series of papers in the 1970s. He traced the genesis of the Dagum distributions in applied economics and points out parallel developments in several branches of the applied statistics literature. The main aim of this paper is to define a bivariate Dagum distribution so that the marginals have Dagum distributions. It is observed that the joint probability density function and the joint cumulative distribution function can be expressed in closed forms. Several properties of this distribution such as marginals, conditional distributions and product moments have been discussed. The maximum likelihood estimates for the unknown parameters of this distribution and their approximate variance-covariance matrix have been obtained. Some simulations have been performed to see the performances of the MLEs. One data analysis has been performed for illustrative purpose.

• 전기의세계
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• v.31 no.3
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• pp.209-217
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• 1982

This paper considers a finite spectrum assignment Problem for a functional retarded linear differential system with delays in control only. In this problem, by generalizing from an abstract linear system characterized by Semigroups on a Hilbert space to a finite dimensional linear system, we unify the relationship between a control-delayed system and its non-delayed system, and then by using the spectrum of the generator-decomposition of Semigroup, we try to get a feedback law which yields a finite spectrum of the closed-loop system, located at an arbitrarily preassigned sets of n points in the complex plane. The comparative examinations between the standard spectrum assignment method and the method of spectral projection for the feedback law which consists of proportional and finite interval terms over present and past values of control variables are also considered. The analysis is carry down to the elementary spectral projection level because, in spite of all the research efforts, so far there has been no significant attempt to obtain the feedback implementation directly from the abstract representation forms in the case of multivariables.

• Journal of Ocean Engineering and Technology
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• v.28 no.3
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• pp.193-198
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• 2014

An elastic cable with piecewise constant properties under the action of concentrated static loads is studied analytically. Analytic solutions for catenary cables are combined at the discontinuous points caused by the discontinuous elastic properties or concentrated loads. The application of the boundary conditions at both ends of the multi-component cable results in three algebraic non-linear equations for three unknown parameters, which are determined numerically. The solutions for the shape, tension, elongation, and cross-sectional contraction of the cable are expressed in closed forms. Some examples are given for cases of two- and three-dimensional loads.

• Proceedings of the Korean Powder Metallurgy Institute Conference
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• 2006.09a
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• pp.264-265
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• 2006

The directions of further developments in the modeling of sintering are pointed out, including multi-scale modeling of sintering, on-line sintering damage criteria, particle agglomeration, sintering with phase transformations. A true multi-scale approach is applied for the development of a new meso-macro methodology for modeling of sintering. The developed macroscopic level computational framework envelopes the mesoscopic simulators. No closed forms of constitutive relationships are assumed for the parameters of the material. The model framework is able to predict the final dimensions of the sintered specimen on a global scale and identify the granular structure in any localized area for prediction of the material properties.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.22 no.5
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• pp.915-927
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• 1997

In this paper, we propose an error concealment technique using directional interpolation in block-based image compression. In the proposed method the edge direction is determined by finding the maximum correlation coefficients of boundary pixels of blocks neighboring the errored block in spatial domain. Then the errored block is interpolated linearly or bilinearly along the determined edge direction. The proposed method can conceal the block error, the macro block error, and the slice error adaptively. Also, the parameters for the directional interpolation are represented by closed forms. When applied to compressed images, the proposed method shows superior subjective and objective quality to conventional error concealment methods.

• Communications for Statistical Applications and Methods
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• v.17 no.2
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• pp.255-261
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• 2010

A class of threshold-asymmetric GRACH(TGARCH, hereafter) models has been useful for explaining asymmetric volatilities in the field of financial time series. The cumulative impulse response function of a conditionally heteroscedastic time series often measures a degree of unstability in volatilities. In this article, a general form of the cumulative impulse response function of the TGARCH model is discussed. In particular, We present formula in their closed forms for the first two lower order models, viz., TGARCH(1, 1) and TGARCH(2, 2).

• Journal of Mechanical Science and Technology
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• v.20 no.6
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• pp.828-839
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• 2006

In this paper, a 2-DOF planar parallel manipulator with two revolute actuators and one passive constraining leg. The kinematic analysis of the mechanism is analytically performed : the inverse and forward kinematics problems are solved in closed forms, the workspace is derived systematically, and the three kinds of singular configurations are round. The optimal design to determine the geometric parameters and the operating limits of the actuated legs is performed considering the kinematic manipulability and workspace size. These results of the paper show the effectiveness of the presented manipulator.

• Communications of the Korean Mathematical Society
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• v.15 no.2
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• pp.285-308
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• 2000

We generalize bi-orthogonal (non-orthogona) MRA to frame MRA in which the family of integer translates of a scaling func-tion forms a frame for the initial ladder space V0. We investigate the internal structure of frame MRA and establish the existence of a dual scaling function, and show that, unlike bi-orthogonal MRA, there ex-ists a frame MRA that has no (frame) 'wavelet'. Then we prove the existence of a dual wavelet under the assumption of the existence of a wavelet and present easy sufficient conditions for the existence of a wavelet. Finally we give a new proof of an equivalent condition for the translates of a function in L2(R) to be a frame of its closed linear span.

• Bulletin of the Korean Chemical Society
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• v.10 no.6
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• pp.529-535
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• 1989

A general perturbation series solution of the Smoluchowski equation is applied to investigate the rate of recombination and the remaining probability of a pair of particles in liquids. The radiative boundary condition is employed and the convergence of the perturbation series is analyzed in terms of a convergene factor in time domain. The upper bound to the error introduced by the n-th order perturbation scheme is also evaluated. The long time behaviors of the rate of recombination and the remaining probability are found to be expressed in closed forms if the perturbation series is convergent. A new and efficient method of purely numerical integration of the Smoluchowski equation is proposed and its results are compared with those obtained by the perturbation method. For the two cases where the interaction between the particles is given by (i) the Coulomb potential and (ii) the shielded Coulomb potential, the agreement between the two results is found to be excellent.