• Korean Journal of Mathematics
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• v.23 no.1
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• pp.47-64
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• 2015

We express generalized Fourier-Feynman transform and convolution product of functionals in a Banach algebra $\mathcal{S}(L^2_{a,b}[0,T])$ as limits of function space integrals on $C_{a,b}[0,T]$. Moreover we obtain change of scale formulas for function space integrals related with generalized Fourier-Feynman transform and convolution product of these functionals.

• Honam Mathematical Journal
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• v.40 no.1
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• pp.61-73
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• 2018

The main aim of this research paper is to evaluate the general integral of the form $${\int_{0}^{1}}x^{c-1}(1-x)^{c+{\ell}}[1+{\alpha}x+{\beta}(1-x)]^{-2c-{\ell}-1}\atop {\times}_3F_2\left\[ {a,\;b,\;2c+{\ell}+1} \\ {\frac{1}{2}(a+b+i+1),\;2c+j\;;\frac{(1+{\alpha})x}{1+{\alpha}x+{\beta}(1-x)} }\right]dx$$ in the most general form for any ${\ell}{\in}\mathbb{Z}$; and $i, j=0,{\pm}1,{\pm}2$. The results are established with the help of generalized Watson's summation theorem due to Lavoie, et al. Fifty interesting general integrals have also been obtained as special cases of our main findings.

• East Asian mathematical journal
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• v.28 no.5
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• pp.553-559
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• 2012

The noncommutative extension of the complex numbers for the four dimensional real space is a quaternion. R. Fueter, C. A. Deavours and A. Subdery have developed a theory of quaternion analysis. M. Naser and K. N$\hat{o}$no have given several results for integral formulas of hyperholomorphic functions in Clifford analysis. We research the properties of hyperholomorphic functions on $\mathbb{C}^2{\times}\mathbb{C}^2$.

• Journal of the Korean Mathematical Society
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• v.53 no.1
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• pp.147-159
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• 2016

In this paper, subordination results of analytic function $f{\in}{\mathcal{A}}_p$ involving linear operator ${\mathcal{K}}^{{\delta},{\lambda}}_{c,p}$ are obtained. By applying the differential subordination method, results are derived under some sufficient subordination conditions. On using some hypergeometric identities, corollaries of the main results are derived. Furthermore, convolution preserving properties for a class of multivalent analytic function associated with the operator ${\mathcal{K}}^{{\delta},{\lambda}}_{c,p}$ are investigated.

• Journal of the Korean Society of Safety
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• v.20 no.3 s.71
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• pp.98-104
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• 2005

This study experimentally and theoretically examines the fire characteristics of 100- by 100- by 50-mm samples of flame retardant treated Douglas fir. Samples were exposed to a range of incident heat fluxes 10 to $50kW/m^2$. The time to ignition measurements obtained from the cone heater were used to derive characteristic properties of the materials. A one-dimensional integral model has been used to predict the, time to ignition, critical heat flux and ignition temperature of samples. Ignition data and best-fit curves confirm ${{\dot{q}}_i}^{'}{\rightarrow}{{\dot{q}}_{cr}^{'}\;then\;t_{ig}{\rightarrow}{\infty}$ and when ${{\dot{q}}_i}^'{\gg}{{\dot{q}}_{cr}^'\;then\;t_{ig}{\rightarrow}0$. And Ignition of flame retardant treated samples occurred not at incident heat flux of bellow $10kW/m^2.$. By a one-dimensional integral model, the critical heat flux of each samples was predicted $10.21kW/m^2,\;11.82kW/m^2,\;and\;14.16kW/m^2$ for the D-N, D-F2, and D-F4, respectively. In ignition temperature of each samples, flame retardant treated samples were measured high about $50^{\circ}C$ than non-treated samples. Water-soluble flame retardant used in this study finds out more effect in delay of time to ignition when incident heat flux is low than high.

• Journal of Biosystems Engineering
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• v.34 no.5
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• pp.371-376
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• 2009

Microwave digestion is a preferred pretreatment method for agricultural samples because of its quick chemical reaction and minimum loss of analytes. In this research, a feedback temperature controller was developed to control the temperature inside a vessel for the microwave-assisted digestion system. An existing industrial microwave oven was fitted with the temperature controller for controlling inside temperature of the vessel. Four control methods, On/Off, proportional (P), proportional integral (PI), and proportional integral derivative (PID) were used and compared. Experimental results showed that PID control produced best temperature control performance. The PID controller could maintain the temperature of water sample and rice sample in the digestion system with error range of $-2.5{\sim}3.3^{\circ}C$ and $-1.9{\sim}0.5^{\circ}C$ at set temperature of $170^{\circ}C$, respectively.

• Journal of the Korean Society of Food Science and Nutrition
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• v.37 no.11
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• pp.1491-1496
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• 2008

Twenty natural plants from Jeju were extracted by pressurized organic solvent (100% methanol, $40^{\circ}C$, 13.6 MPa, 10 min). Extraction yield, total phenolic content (TPC) and integral antioxidant capacity were measured, and each component was identified by GC/MS. Extraction yields were high as 21.8%, 21.5, 21.1, 20.7 and 20.1% in Rhus javanica, Euscaphis japonica, Alnus firma, Sapium japonicum and Sorbus alnifolia, respectively. The extracts containing high TPC (mg GAE/g of dry sample) were obtained from Malus sieboldii (68.3), Sapium japonicum (57.6), Pyrrosia lingua (56.6) and Euscaphis japonica (55.1). Integral antioxidant capacities of water-soluble substances were 598, 394, 293 and $270\;{\mu}mol$ ascorbic acid equivalent/g in Geranium thunbergii, Sapium japonicum, Cornus kousa and Rhus javanica, respectively. Integral antioxidant capacities of lipidsoluble substances were 611, 314, 296 and $242\;{\mu}mol$ trolox equivalent/g in Ardisia crenata, Ostrya japonica, Geranium thunbergii and Quercus acuta, respectively. Fifteen major peaks were identified by GC/MS from the extract of pressurized organic solvent from Sapium japonicum. Two polyphenols (gallic acid (retention time (RT) 19.7 min)) and quercetin (33.5 min)), ascorbic acid (RT 35.3 min), and several fatty acids (retention time 18.6, 21.0, 21.8, 21.9 and 23.6 min) were identified, and gallic acid was the major polyphenol component due to high peak area.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.28 no.5
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• pp.524-531
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• 2004

To investigate relevance of the definition of the reference stress to estimate J and $C^{*}$ for surface crack problems, this paper compares FE J and $C^{*}$ results for surface cracked pipes with those estimated according to the reference stress approach using various definitions of the reference stress. Pipes with part circumferential inner surface crack and finite internal axial crack are considered, subject to internal pressure and global bending. The crack depth and aspect ratio are systematically varied. The reference stress is defined in four different ways using (i) the local limit load, (ii) the global limit load, (iii) the global limit load determined from the FE limit analysis, and (iv) the optimized reference load. It is found that the reference stress based on the local limit load gives overall excessively conservative estimates of J and $^{*}$. Use of the global limit load clearly reduces the conservatism, compared to that of the local limit load, although it can provide sometimes non-conservative estimates of J and $^{*}$. The use of the FE global limit load gives overall non-conservative estimates of J and $^{*}$. The reference stress based on the optimised reference load gives overall accurate estimates of J and $^{*}$, compared to other definitions of the reference stress. Based on the present finding, general guidance on the choice of the reference stress for surface crack problems is given.

• East Asian mathematical journal
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• v.34 no.5
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• pp.577-585
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• 2018

For the purpose of characterizing subharmonic or ${\mathcal{M}}$-subharmonic Hardy classes in the unit ball of ${\mathbb{C}}^n$, we establish fundamental identities between integral means in terms of volume integrals and Green's functions.

• Communications of the Korean Mathematical Society
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• v.33 no.2
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• pp.515-525
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• 2018

In this paper, we investigate a modified $G^2$ transform on a class of Boehmians. We prove the axioms which are necessary for establishing the $G^2$ class of Boehmians. Addition, scalar multiplication, convolution, differentiation and convergence in the derived spaces have been defined. The extended $G^2$ transform of a Boehmian is given as a one-to-one onto mapping that is continuous with respect to certain convergence in the defined spaces. The inverse problem is also discussed.