• Journal of the Korean Data and Information Science Society
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• 제15권3호
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• pp.617-624
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• 2004

In this article the fuzzy number rank and the fuzzy rank transformation method are introduced in order to analyse the non-parametric fuzzy regression model which cannot be described as a specific functional form such as the crisp data and fuzzy data as a independent and dependent variables respectively. The effectiveness of fuzzy rank transformation methods is compared with other methods through the numerical examples.

• Nonlinear Functional Analysis and Applications
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• 제29권1호
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• pp.99-111
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• 2024

In this paper, a new seven-parameter Mittag-Leffler function of a single complex variable is proposed as a generalization of the standard Mittag-Leffler function, certain generalizations of Mittag-Leffler function, hypergeometric function and confluent hypergeometric function. Certain essential analytic properties are mainly discussed, such as radius of convergence, order, type, differentiation, Mellin-Barnes integral representation and Euler transform in the complex plane. Its relation to Fox-Wright function and H-function is also developed.

• 대한수학회지
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• 제34권3호
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• pp.569-579
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• 1997

We investigate the existence of the operator-valued Feynman integral when a Wiener functional is given by a Fourier transform of complex Borel measure.

• 한국자원식물학회지
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• 제29권5호
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• pp.588-597
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• 2016

Little attention has been paid to the functional aspect of the flower petal of Paeonia lactiflora, compared to that of its root. To determine the components of flower petal of Paeonia lactiflora, we conducted the Fourier transform ion cyclotron resonance (FT-ICR) MASS spectrophotometric analysis. We detected the 24 different types of ingredients from the 70% ethanol extracts of flower petal of peonia lactiflora cv. ‘Red Charm’. The main compounds were quercetin glucopyranosides, methyl gallate, paonioflolol and kaemperol glucopyranosides. We further tested its functional activity. The 2,2-diphenyl-1-picrylhydrazyl (DPPH) radical scavenging activity of the extracts was 87.9-90.4% at 0.1mg/ml. This result showed that these flower extracts have approximately 5-fold stronger antioxidant potential than a previous report with root extracts (Bang et al. 1999). The result of tyrosinase inhibition assay of Paeonia lactflora extract was almost similar to that of arbutin except significantly higher effect in the coral sunset extract at 0.1% concentration. Hyaluronidase inhibition assay showed 76.5% inhibition at 5% concentration of this flower extract, indicating that Peaonia lactiflora flower extracts have the major anti-inflammatory, anti-oxidant and brightening effects. Taken together, these results suggest these three Paeonia lactiflora species extracts might provide the basis to develop a new natural brightening agent.

• Bulletin of the Korean Chemical Society
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• 제35권3호
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• pp.871-874
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• 2014

Monodispersed carbon nanospheres (CNSs) were fabricated by a novel method and their structural properties were investigated. CNSs were prepared by the pyrolysis of nanospherical polystyrenes (PS). With the coating of $SiO_2$ shell, PS particles were effectively separated during pyrolysis process which resulted to CNSs with an average diameter of 40 nm. Moreover, CNSs could be crosslinked with each other through the bondings between the functional groups on their surfaces. Morphology of the fabricated carbon spheres and their crosslinked form were characterized by X-ray diffraction (XRD), field-emission scanning electron microscopy (FESEM), transmission electron microscopy (TEM), and fourier transform infrared spectroscopy (FT-IR).

• International Journal of Reliability and Applications
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• 제1권1호
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• pp.49-64
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• 2000

We consider a system whose inherent life follows an Erlang distribution, which is subject to two heterogeneous random shocks. Minor shocks arrive according to a renewal process and each causes the system to fail independently with a certain probability. A major shock whose interarrival times follow an Erlang distribution causes the system to fail with probability one. The Laplace transform of the distribution of the time to system failure is derived in a functional form of the Laplace transform of the interarrival time distribution of minor shocks. An algorithm is given for the computation of the moments of the time to system failure.

• 대한수학회지
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• 제57권3호
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• pp.655-668
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• 2020

In this paper, we establish the generalized Cameron-Storvick type theorem on function space. We then give relationships involving the generalized Cameron-Storvick type theorem, modified generalized integral transform and modified convolution product. A motivation of studying the generalized Cameron-Storvick type theorem is to generalize formulas and results with respect to the modified generalized integral transform on function space. From the some theories and formulas in the functional analysis, we can obtain some formulas with respect to the translation theorem of exponential functionals.

• 대한수학회보
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• 제35권1호
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• pp.99-117
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• 1998

Let $(B, H, p_1)$ be an abstract Wiener space and $F(B)$ the Fresnel class on $(B, H, p_1)$ which consists of functionals F of the form : $$ F(x) = \int_{H} exp{i(h,x)^\sim} df(h), x \in B, $$ where $(\cdot, \cdot)^\sim$ is a stochastic inner product between H and B, and f is in $M(H)$, the space of complex Borel measures on H. We introduce an $L_1$ analytic Fourier-Feynman transforms for functionls in $F(B)$. Furthermore, we introduce a convolution on $F(B)$, and then verify the existence of the $L_1$ analytic Fourier-Feynman transform for the convolution product of two functionals in $F(B)$, and we establish the relationships between the $L_1$ analytic Fourier-Feynman tranform of the convolution product for two functionals in $F(B)$ and the $L_1$ analytic Fourier-Feynman transforms for each functional. Finally, we show that most results in [7] follows from our results in Section 3.

• Nonlinear Functional Analysis and Applications
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• 제28권2호
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• pp.439-448
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• 2023

In this article, we are interested in studying the fractional Sadik Transform and a combination of the method of steps that will be applied together to find accurate solutions or approximations to homogeneous and non-homogeneous delayed fractional differential equations with constant-coefficient and possible extension to time-dependent delays. The results show that the process is correct, exact, and easy to do for solving delayed fractional differential equations near the origin. Finally, we provide several examples to illustrate the applicability of this method.

• 대한수학회논문집
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• 제17권1호
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• pp.21-29
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• 2002

The existence of the operator-valued Feynman integral was established when a Wiener functional is given by a Fourier transform of complex Borel measures. In this paper, we investigate the stability of the Feynman integral with respect to the measures.