• Bulletin of the Korean Mathematical Society
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• v.48 no.2
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• pp.223-245
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• 2011

In this paper, we de ne an $L_p$ analytic generalized Fourier Feynman transform and a convolution product of functionals in a Ba-nach algebra $\cal{F}$($C_{a,b}$[0, T]) which is called the Fresnel type class, and in more general class $\cal{F}_{A_1;A_2}$ of functionals de ned on general functio space $C_{a,b}$[0, T] rather than on classical Wiener space. Also we obtain some relationships between the $L_p$ analytic generalized Fourier-Feynman transform and convolution product for functionals in $\cal{F}$($C_{a,b}$[0, T]) and in $\cal{F}_{A_1,A_2}$.

• Journal of Fashion Business
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• v.11 no.1
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• pp.125-135
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• 2007

Each cotton fiber is a unicellular hair collected from the seed of cotton plant. The fiber contains many convolutions along its length. Mercer was the first to suggest caustic soda treatment of cotton in commercial application. Mercerization has been commercially used since Lowe's suggestion to endow cotton with increased strength and affinity for dyes with additional properties such as fabric touch or luster. In this study, cotton fabric specimens were mercerized to investigate the changes in physical and mechanical properties pertaining to the hand or touch of fabrics. Physical properties were measured using the KES(Kawabata Evaluation System).

• Journal of the Korean Mathematical Society
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• v.50 no.2
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• pp.259-274
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• 2013

In this paper, we consider the Fourier-type functionals on Wiener space. We then establish the analytic Feynman integrals involving the ${\diamond}$-convolutions. Further, we give an approach to solution of the Schr$\ddot{o}$dinger equation via Fourier-type functionals. Finally, we use this approach to obtain solutions of the Schr$\ddot{o}$dinger equations for harmonic oscillator and double-well potential. The Schr$\ddot{o}$dinger equations for harmonic oscillator and double-well potential are meaningful subjects in quantum mechanics.

• Honam Mathematical Journal
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• v.35 no.1
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• pp.51-71
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• 2013

In the present paper, we evaluate the analytic conditional Fourier-Feynman transforms and convolution products of unbounded function which is the product of the cylinder function and the function in a Banach algebra which is defined on an analogue o Wiener space and useful in the Feynman integration theories and quantum mechanics. We then investigate the inverse transforms of the function with their relationships and finally prove that th analytic conditional Fourier-Feynman transforms of the conditional convolution products for the functions, can be expressed in terms of the product of the conditional Fourier-Feynman transforms of each function.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.17 no.29
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• pp.30-36
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• 1994

This paper has provided a systematic technique, the evaluation of the distribution with the NPV ana the derivation of the IRR in the investment alternatives, for the cost estimating analysts. The proposals of investment alternatives are included the venture capital under risk and probabilities at each events, within the cash inflows are occuring at random timing. Therefore. we have considered the followings : 1) the first cash outflow is deterministic. 2) the cash inflows are random variables with known distributions. 3) the lengths of the time intervals between the cash inflows are independently distributed and independent of the cash inflows. In this paper. the first two moments of the distribution, the Laplace Transforms and the convolutions are computed for both independent cash inflows and mutually exclusive alternatives as in the case of quite correlated cash inflows.

• Bulletin of the Korean Mathematical Society
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• v.52 no.6
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• pp.1925-1935
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• 2015

In this paper, we study right half-plane harmonic mappings $f_0$ and f, where $f_0$ is fIxed and f is such that its dilatation of a conformal automorphism of the unit disk. We obtain a sufficient condition for the convolution of such mappings to be convex in the direction of the real axis. The result of the paper is a generalization of the result of by Li and Ponnusamy [11], which itself originates from a problem posed by Dorff et al. in [7].

• The Korean Journal of Applied Statistics
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• v.25 no.5
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• pp.813-820
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• 2012

A surplus process with two types of claims is considered, where Type I claims occur more frequently, however, their sizes are smaller stochastically than Type II claims. The ruin probabilities of the surplus caused by each type of claim are obtained by establishing integro-differential equations for the ruin probabilities. The formulas of the ruin probabilities contain an infinite sum and convolutions that make the formulas hard to be applicable in practice; subsequently, we obtain explicit formulas for the ruin probabilities when the sizes of both types of claims are exponentially distributed. Finally, we show through a numerical example, that Type II claims have more impact on the ruin probability of the surplus than Type I claims.

• Proceedings of the Korean Society for Agricultural Machinery Conference
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• 1996.06c
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• pp.812-819
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• 1996

This study was performed to quantify microscopically morphological characteristics of cotton fiber to identify parameters for quality evaluation using image analysis . The image of each fiber was captured by a Pc-based color imaging system using a conventional microscope. Ends of individual cotton fibers were glued on a microscope slide without any tension or straightening. A modified watershed technique was implemented to identify individual convolution segments, which were defined as sections of the fiber bordered by two neighboring convolutions. Length, area and perimeter of each convolution segment were measured directly from the image . Average width, shape factor and number of convolution segments in mm were calculated from the measured parameters. The performance of the image analysis algorithm was compared with visual varieties of cotton . The image analysis results agreed with visual inspection in 89.6% of the tested images.

• Journal of Korean Society for Quality Management
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• v.17 no.1
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• pp.82-88
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• 1989

This paper has provided a systematic technique, the evaluation of the distribution with the NPV and the derivation of the IRR in the investment alternatives, for the cost estimating analysts, The proposals of investment alternatives are included the venture capital under risk and probabilities at each events, within the cash inflows are occuring at random timing. Therefore, we have considered the followings ; 1) the first cash outflow is deterministic, 2) the cash inflows are random variables with known distributions, 3) the lengths of the time intervals between the cash inflows are independently distributed and independent of the cash inflows. In this paper, the first two moments of the distribution, the Laplace Transforms and the convolutions are computed for both independent cash inflows and mutually exclusive alternatives as in the case of quite correlated cash inflows.

• Kyungpook Mathematical Journal
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• v.57 no.3
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• pp.493-502
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• 2017

We propose an accurate approximation method via discrete Krawtchouk orthogonal polynomials to the distribution of a sum of independent but non-identically distributed binomial random variables. This approximation is a weighted binomial distribution with no need for continuity correction unlike commonly used density approximation methods such as saddlepoint, Gram-Charlier A type(GC), and Gaussian approximation methods. The accuracy obtained from the proposed approximation is compared with saddlepoint approximations applied by Eisinga et al. [4], which are the most accurate method among higher order asymptotic approximation methods. The numerical results show that the proposed approximation in general provide more accurate estimates over the entire range for the target probability mass function including the right-tail probabilities. In addition, the method is mathematically tractable and computationally easy to program.