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ON A NEW CLASS OF DOUBLE INTEGRALS INVOLVING GENERALIZED HYPERGEOMETRIC FUNCTION 3F2

  • Kim, Insuk
    • Honam Mathematical Journal
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    • v.40 no.4
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    • pp.809-816
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    • 2018
  • The aim of this research paper is to evaluate fifty double integrals invoving generalized hypergeometric function (25 each) in the form of $${{\int}^1_0}{{\int}^1_0}\;x^{{\gamma}-1}y^{{\gamma}+c-1}(1-x)^{c-1}(1-y)^{c+{\ell}}(1-xy)^{{\delta}-2c-{\ell}-1}{\times}_3F_2\[{^{a,\;b,\;2c+{\ell}+1}_{\frac{1}{2}(a+b+i+1),\;2c+j}}\;;{\frac{(1-x)y}{1-xy}}\]dxdy$$ and $${{\int}^1_0}{{\int}^1_0}\;x^{{\gamma}-1}y^{{\gamma}+c+{\ell}}(1-x)^{c+{\ell}}(1-y)^{c-1}(1-xy)^{{\delta}-2c-{\ell}-1}{\times}_3F_2\[{^{a,\;b,\;2c+{\ell}+1}_{\frac{1}{2}(a+b+i+1),\;2c+j}}\;;{\frac{1-y}{1-xy}}\]dxdy$$ in the most general form for any ${\ell}{\in}{\mathbb{Z}}$ and i, j = 0, ${\pm}1$, ${\pm}2$. The results are derived with the help of generalization of Edwards's well known double integral due to Kim, et al. and generalized classical Watson's summation theorem obtained earlier by Lavoie, et al. More than one hundred ineteresting special cases have also been obtained.

ON STRONGLY QUASI J-IDEALS OF COMMUTATIVE RINGS

  • El Mehdi Bouba;Yassine EL-Khabchi;Mohammed Tamekkante
    • Communications of the Korean Mathematical Society
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    • v.39 no.1
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    • pp.93-104
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    • 2024
  • Let R be a commutative ring with identity. In this paper, we introduce a new class of ideals called the class of strongly quasi J-ideals lying properly between the class of J-ideals and the class of quasi J-ideals. A proper ideal I of R is called a strongly quasi J-ideal if, whenever a, b ∈ R and ab ∈ I, then a2 ∈ I or b ∈ Jac(R). Firstly, we investigate some basic properties of strongly quasi J-ideals. Hence, we give the necessary and sufficient conditions for a ring R to contain a strongly quasi J-ideals. Many other results are given to disclose the relations between this new concept and others that already exist. Namely, the primary ideals, the prime ideals and the maximal ideals. Finally, we give an idea about some strongly quasi J-ideals of the quotient rings, the localization of rings, the polynomial rings and the trivial rings extensions.

Effect of Organo Nanoclay and Catalyst on the Polyesterification between Adipic Acid and Diethylene Glycol (Adipic Acid와 Diethylene Glycol의 Polyesterification에 대한 유기나노점토와 촉매의 영향)

  • Park, Kyung-Kyu;Shin, Sung-Wook;Oh, Min-Ji;Lee, Sang-Ho
    • Elastomers and Composites
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    • v.46 no.1
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    • pp.37-44
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    • 2011
  • Effect of organo nanoclay (Cloisite 30B) on the polyesterification of adipic acid (AA) with diethylene glycol(DEG) was investigated with p-toluene sulfonic acid (p-TSA) (Br${\phi}$nsted acid) and butylchlorotin dihydroxide (Lewis acid) catalyst at 383 and 423 K. The initial [OH]/[COOH] molar ratio was two and the concentration of the catalysts in the reactants was 0.14 mol% based on the total reactants. The kinetics of the polyesterification was interpreted with the conversion data that was calculated from the acid values of the reactant-product mixture. The reaction rate of the polyesterification, which was catalyzed with p-TSA, exhibited the second-order dependency on AA concentration. When Butylchlorotin dihydroxide was used, the reaction rate revealed the first-order dependency on AA concentration. The activation energy of the reactions catalyzed with p-TSA and Butylchlorotin dihydroxide were calculated at 42.2 and 63.8 kJ/mol, respectively. Addition of 5 wt% Cloisite 30B to the reactant significantly diminished the activity of p-TSA, so the reaction rate decreased and the activation energy was calculated at 72.9 kJ/mol. Butylchlorotin dihydroxide catalyst maintained its activity regardless of the addition of Cloisite 30B to the reactant and the activation energy was calculated to 61.8 kJ/mol. Lewis acid catalyst, butylchlorotin dihydroxide, was more effective than Br${\phi}$nsted acid catalyst for the esterification of AA with DEG.

Using Image J program, compared of focusing distance and grid rate (Image J 프로그램을 이용한 격자집속거리와 격자비에 따른 영상비교평가)

  • Seo, Won-Joo;Seo, Jeong-Beom;Lee, Jong-Woong
    • Korean Journal of Digital Imaging in Medicine
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    • v.14 no.1
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    • pp.37-42
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    • 2012
  • Pediatric head and neck phantom, using the rate by focusing distance and grid images, Image J using the Quality Assessment and Dose Area Product compared. X-ray laboratory equipment due to the Philips Digital DIAGNOST a 110 cm FFD set and using ACE Non-grid, focusing distance 110 cm (12 : 1), 140 cm (12 : 1), 180 cm (8 : 1) Focused grid, Acryl Phantom (Fluke Model 76-2 Series Phantom) 15.24 cm, by resolution chart image acquisition, image evaluation program (Image J Ver. 1.4.3.67, USA) imaging experiments were analyzed using. Dose Area Product in the Non Grid 0.028 $mGy{\cdot}cm^2$, focusing distance 110 cm (12 : 1), the 0.129 $mGy{\cdot}cm^2$, 140 cm (12 : 1), the 0.135 $mGy{\cdot}cm^2$, 180 cm (8 : 1) was measured with a 0.110 $mGy{\cdot}cm^2$ Non Grid, focusing distance 110 cm (12 : 1), 140 cm (12 : 1), 180 cm (8 : 1) Image obtained when grid using the image J program focusing distance 110 cm with grid based on the measured SNR and PSNR Non Grid if the SNR the 17.307 dB, PSNR of the 20.002 dB, if the SNR 28.755 dB, PSNR was measured by the 31.451 dB. Image J image analysis through the streets, rather than focusing on grid by the rate that could see an increase in dose. Select the grid by a small dose rate reduction is possible.

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Molecular Theory of Plastic Deformation (Ⅲ)$^*$

  • Kim, Jae-Hyun;Ree, Tai-Kyue;Kim, Chang-Hong
    • Bulletin of the Korean Chemical Society
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    • v.2 no.3
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    • pp.96-104
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    • 1981
  • (1) The flow data of f (stress) and ${\dot{s}$ (strain rate) for Fe and Ti alloys were plotted in the form of f vs. -ln ${\dot{s}$ by using the literature values. (2) The plot showed two distinct patterns A and B; Pattern A is a straight line with a negative slope, and Pattern B is a curve of concave upward. (3) According to Kim and Ree's generalized theory of plastic deformation, pattern A & B belong to Case 1 and 2, respectively; in Case 1, only one kind of flow units acts in the deformation, and in Case 2, two kinds flow units act, and stress is expressed by $f={X_1f_1}+{X_2f_2}$where $f_1\;and\;f_2$ are the stresses acting on the flow units of kind 1 and 2, respectively, and $X_1,\;X_2$ are the fractions of the surface area occupied by the two kinds of flow units; $f_j=(1/{\alpha}_j) sinh^{-1}\;{\beta}_j{{\dot{s}}\;(j=1\;or\;2)$, where $1/{\alpha}_j\;and\;{\beta}_j$ are proportional to the shear modulus and relaxation time, respectively. (4) We found that grain-boundary flow units only act in the deformation of Fe and Ti alloys whereas dislocation flow units do not show any appreciable contribution. (5) The deformations of Fe and Ti alloys belong generally to pattern A (Case 1) and B (Case 2), respectively. (6) By applying the equations, f=$(1/{\alpha}_{g1}) sinh^-1({\beta}_{g1}{\dot{s}}$) and $f=(X_{g1}/{\alpha}_{g1})sinh^{-1}({\beta}_{g1}{\dot{s}})+ (X_{g2}/{\alpha}_{g2})\;shih^{-1}({\beta}_{g2}{\dot{s}})$ to the flow data of Fe and Ti alloys, the parametric values of $x_{gj}/{\alpha}_{gj}\;and\;{\beta}_{gs}(j=1\;or\;2)$ were determined, here the subscript g signifies a grain-boundary flow unit. (7) From the values of ($({\beta}_gj)^{-1}$) at different temperatures, the activation enthalpy ${\Delta}H_{gj}^{\neq}$ of deformation due to flow unit gj was determined, ($({\beta}_gj)^{-1}$) being proportional to , the jumping frequency (the rate constant) of flow unit gj. The ${\Delta}H_{gj}\;^{\neq}$ agreed very well with ${\Delta}H_{gj}\;^{\neq}$ (self-diff) of the element j whose diffusion in the sample is a critical step for the deformation as proposed by Kim-Ree's theory (Refer to Tables 3 and 4). (8) The fact, ${\Delta}H_{gj}\;^{\neq}={\Delta}H_{j}\;^{\neq}$ (self-diff), justifies the Kim-Ree theory and their method for determining activation enthalpies for deformation. (9) A linear relation between ${\beta}^{-1}$ and carbon content [C] in hot-rolled steel was observed, i.e., In ${\beta}^{-1}$ = -50.2 [C] - 40.3. This equation explains very well the experimental facts observed with regard to the deformation of hot-rolled steel..

Carbon-coated boron using low-cost naphthalene for substantial enhancement of Jc in MgB2 superconductor

  • Ranot, Mahipal;Shinde, K.P.;Oh, Y.S.;Kang, S.H.;Jang, S.H.;Hwang, D.Y.;Chung, K.C.
    • Progress in Superconductivity and Cryogenics
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    • v.19 no.3
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    • pp.40-43
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    • 2017
  • Carbon coating approach is used to prepare carbon-doped $MgB_2$ bulk samples using low-cost naphthalene ($C_{10}H_8$) as a carbon source. The coating of carbon (C) on boron (B) powders was achieved by direct pyrolysis of naphthalene at $120^{\circ}C$ and then the C-coated B powders were mixed well with appropriate amount of Mg by solid state reaction method. X-ray diffraction analysis revealed that there is a noticeable shift in (100) and (110) Bragg reflections towards higher angles, while no shift was observed in (002) reflections for $MgB_2$ doped with carbon. As compared to un-doped $MgB_2$, a systematic enhancement in $J_c(H)$ properties with increasing carbon doping level was observed for naphthalene-derived C-doped $MgB_2$ samples. The substantial enhancement in $J_c$ is most likely due to the incorporation of C into $MgB_2$ lattice and the reduction in crystallite size, as evidenced by the increase in the FWHM values for doped samples.

Post-harvest LED and UV-B Irradiation Enhance Antioxidant Properties of Asparagus Spears (수확 후 LED와 UV-B 조사에 의한 아스파라거스 순의 항산화 기능 향상)

  • Yoo, Nam-Hee;Jung, Sun-Kyun;Lee, Chong Ae;Choi, Dong-Geun;Yun, Song Joong
    • Horticultural Science & Technology
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    • v.35 no.2
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    • pp.188-198
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    • 2017
  • Asparagus (Asparagus officinalis L.) spears were treated with white (color temperature 4,500 k), blue (peak 450 nm), and red (peak 660 nm) light-emitting diodes (LEDs) at a photosynthetic photon flux density (PPFD) of $200{\mu}mol{\cdot}m^{-2}{\cdot}s^{-1}$ for 12 h, and UV-B (280 nm) at 0.5 kJ or 1.0 kJ to determine the effect on agronomic characteristics, antioxidant phytochemicals, and antioxidant activity. The fresh weight, length, and width of spears were not affected by light quality treatments. The free sugars and chlorophyll contents were increased by 9 and 41%, respectively in the UV-0.5 kJ treatments. Among the antioxidant phytochemicals (vitamin C, total phenol, rutin, and total flavonoid), vitamin C was most greatly affected by the light treatments. Vitamin C content was significantly increased in asparagus spears subjected to the white (114%), red (137%), and UV-0.5 kJ(127%) treatments compared to the control. By contrast, rutin, total phenol, and total flavonoid content were increased only in samples subjected to the red and UV-0.5 kJ treatment. Furthermore, antioxidant activity, as measured by DPPH (2,2-diphenyl-1-picrylhydrazyl) radical scavenging activity, increased in white, red, and UV-0.5 kJ treatments by about 43, 41, and 43%, respectively, compared to the control. These results suggest that postharvest treatment of asparagus spears with red light at $200{\mu}mol{\cdot}m^{-2}{\cdot}s^{-1}$ for 12 h or with UV-B (280 nm) at 0.5 kJ could enhance the functional quality of the asparagus spears by increasing the content of phytochemicals like vitamin C, rutin, total phenolics, and total flavonoids.

Progress in $MgB_2$ Superconductor Wires and Tapes

  • Kim, Jung-Ho;Kumakura, Hiroaki;Rindflesich, Matthew;Dou, Shi Xue;Hwang, Soo-Min;Joo, Jin-Ho
    • Progress in Superconductivity
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    • v.12 no.2
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    • pp.75-81
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    • 2011
  • We report on the progress that has been made in developing $MgB_2$ superconducting wires and tapes for commercialization and research efforts. A number of techniques have been developed to overcome the obstacle posed by the poor critical current density ($J_c$) of pristine $MgB_2$. Chemical doping has proved to be the effective way to modify and enhance the superconducting properties, such as the $J_c$ and the irreversibility field ($B_{irr}$). More than 100 different types of dopants have been investigated over the past 8 years. Among these, the most effective dopants have been identified to be SiC and malic acid ($C_4H_6O_5$). The best results, viz. a $B_{irr}$ of 22 T and $J_c$ of $30,000\;A{\cdot}cm^{-2}$ at 4.2 K and 10 T, were reported for malic acid doped $MgB_2$ wires, which matched the benchmark performance of commercial low temperature superconductor wires. In this work, we discuss the progress made in $MgB_2$ conductors over the past few years at the University of Wollongong, Hyper Tech Research, Inc., and Ohio State University.