• Honam Mathematical Journal
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• v.6 no.1
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• pp.1-12
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• 1984

Let(X, $\Im$) be a probabilistic metric space with a t-norm. Common fixed point theorems and convergence theorems generalizing the results of Ćirić, Fisher, Sehgal, Istrătescu-Săcuiu and others are proved for three mappings P,S,T on X satisfying $F_{Pu, Pv}(qx){\geq}min\left{F_{Su,Tv}(x),F_{Pu,Su}(x),F_{Pv,Tv}(x),F_{Pu,Tv}(2x),F_{Pv,Su}(2x)\right}$ for every $u, v {\in}X$, all x>0 and some $q{\in}(0, 1)$. One of the main results is extended to uniform spaces. Mathematics Subject Classification (1980): 54H25.

• Journal of applied mathematics & informatics
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• v.37 no.5_6
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• pp.329-339
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• 2019

The Banach spaces $m^p(\phi)$ and $n^p(\phi)$ are very important sequence spaces related to $l_p$, which were defined to fill the gaps between $l_p(1{\leq}p{\leq}{\infty})$. In this paper, we investigated the solubility of the infinite system of differential equations in $m^p(\phi)$ and $n^p(\phi)$ by proving related theorems. Moreover, one example has been included for the justification of the claim of this paper.

• Journal of Acupuncture Research
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• v.19 no.6
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• pp.125-133
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• 2002

Objective : This study was designed to analyze the of correlation between narrowing disc space of lumbar X-ray and HIVD of L-spine CT in lumbosacral strain patients. Methods : 63 cases of lumbosacral strain patients who visited Bul-kyooh Oriental Hospital from June 13, 2000 to August 9, 2001 were selected. We performed the radiography by lumbar X-ray and L-spine CT for all cases. Results : 28 of 63 cases revealed narrowing disc space in Lumbar X-ray and these 28 cases were diagnosed as HIVD in L-spine CT at all. 35 of 63 cases revealed normal in Lumbar X-ray and 13 of these 35 cases were diagnosed as HIVD in L-spine CT. Conclusions : We found that narrowing disc space in lumbar X-ray has significant relevance to HIVD in L-spine CT(P-value = 0.001). For accurate diagnosis and treatment of lumbosacral strain patients. combination of clinical symptoms, physical examination and radiography of X-ray and HIVD is needed.

• Honam Mathematical Journal
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• v.31 no.2
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• pp.259-265
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• 2009

Let $\mathcal{L}$ be a subspace lattice on a Hilbert space $\mathcal{H}$. Let x and y be vectors in $\mathcal{H}$ and let $P_x$ be the projection onto sp(x). If $P_xE$ = $EP_x$ for each E ${\in}\;\mathcal{L}$, then the following are equivalent. (1) There exists an operator A in Alg$\mathcal{L}$ such that Ax = y, Af = 0 for all f in $sp(x)^{\perp}$ and A ${\geq}$ 0. (2) sup ${\frac{{\parallel}E^{\perp}y{\parallel}}{{\parallel}E^{\perp}x{\parallel}}:E{\in}\mathcal{L}}$ < ${\infty}$ < x, y > ${\geq}$ 0. Let X and Y be operators in $\mathcal{B}(\mathcal{H})$. Let P be the projection onto $\overline{rangeX}$. If PE = EP for each E ${\in}\;\mathcal{L}$, then the following are equivalent: (1) sup ${\frac{{\parallel}E^{\perp}Yf{\parallel}}{{\parallel}E^{\perp}Xf{\parallel}}:f{\in}\mathcal{H},E{\in}\mathcal{L}}$ < ${\infty}$ and < Xf, Yf > ${\geq}$ 0 for all f in H. (2) There exists a positive operator A in Alg$\mathcal{L}$ such that AX = Y.

• Journal of applied mathematics & informatics
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• v.34 no.3_4
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• pp.309-317
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• 2016

Let V be a Euclidean Jordan algebra with a symmetric cone K. We show that for a Z-transformation L with the additional property L(K) ⊆ K (which we will call ’cone-preserving’), GUS ⇔ strictly copositive on K ⇔ monotone + P. Specializing the result to the Stein transformation S_A(X) := X - AXA^T on the space of real symmetric matrices with the property $S_A(S^n_+){\subseteq}S^n_+$, we deduce that S_A GUS ⇔ I ± A positive definite.

• Journal of the Chungcheong Mathematical Society
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• v.30 no.1
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• pp.41-51
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• 2017

In this note, we deal with some characterizations of relative compactness on the $L_p$ metric space of fuzzy sets. And then, we point out that a characterization of relative compact subsets of fuzzy numbers with sendograph metric can be improved.

• Journal of the Korean Mathematical Society
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• v.36 no.5
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• pp.855-890
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• 1999

Necessary and sufficient conditions on the weight functions u(.) and $\upsilon$(.) are derived in order that the fractional maximal operator $M\alpha,\;0\;\leq\;\alpha\;<\;1$, is bounded from the weighted amalgam space $\ell^s(L^p(\mathbb{R},\upsilon(x)dx)$ into $\ell^r(L^q(\mathbb{R},u(x)dx)$ whenever $1\leq s\leq r<\infty\;and\;1. The boundedness problem for the fractional intergral operator $I_{\alpha},0<\alpha\leq1$, is also studied.

• The Pure and Applied Mathematics
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• v.28 no.2
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• pp.119-142
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• 2021

In this paper, we first introduce a new L_p analytic Fourier-Feynman transform with respect to subordinate Brownian motion (AFFTSB), which extends the Fourier-Feynman transform in the Wiener space. We next examine several relationships involving the L_p-AFFTSB, the convolution product, and the gradient operator for several types of functionals.

• Journal of Microbiology and Biotechnology
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• v.26 no.8
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• pp.1348-1357
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• 2016

An enzymatic reaction system was developed and optimized for bioconversion of resveratrol from glucose. Liquid enzyme extracts were prepared from Alternaria sp. MG1, an endophytic fungus from grape, and used directly or after immobilization with sodium alginate. When the enzyme solution was used, efficient production of resveratrol was found within 120 min in a manner that was pH-, reaction time-, enzyme amount-, substrate type-, and substrate concentration-dependent. After the optimization experiments using the response surface methodology, the highest value of resveratrol production (224.40 μg/l) was found under the conditions of pH 6.84, 0.35 g/l glucose, 0.02 mg/l coenzyme A, and 0.02 mg/l ATP. Immobilized enzyme extracts could keep high production of resveratrol during recycling use for two to five times. The developed system indicated a potential approach to resveratrol biosynthesis independent of plants and fungal cell growth, and provided a possible way to produce resveratrol within 2 h, the shortest period needed for biosynthesis of resveratrol so far.

• Bulletin of the Korean Chemical Society
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• v.20 no.3
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• pp.314-320
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• 1999

Several bisphosphine- and bisphosphite-substituted Re-imido complexes have been prepared from Re(NPh)(PPh3)2Cl3, 1, and Re(N-C6H3-i-Pr2)2Cl3(py), 4. Compound 1 reacted with trimethyl phosphate (P(OMe)3) to give a mixture of two isomers,mer,trans-Re(NPh)(P(OMe)3)2Cl3, 2, and fac,cis-Re(NPh)(P(OMe)3)2Cl3, 2a. In this reaction, the mer,trans-isomer is a major product. Complex 1 also reacted with triethylphosphine (PEt3) to exclusively give mertrans-Re(NPh)(PEt3)2Cl3, 3. Compound 4 reacted with trimethylphosphine (PMe3) to give mer,trans-Re(N-C6H3-i-Pr2)(PMe3)2Cl3, 5, which was converted to mer-Re(N-C6H3-i-Pr2)(PMe)(OPMe3)Cl3, 6, on exposure to air. Crystallographic data for 2: monoclinic space group P21/n, a = 8.870(2) Å, b = 14.393(3) Å, c = 17.114(4) Å, β = 101.43(2)°, Z = 4, R(wR2) = 0.0521(0.1293). Crystallographic data for 5: orthorhombic space group P212121, a = 11.307(l) Å, b = 11.802(l) Å, c = 19.193(2) Å, Z = 4, R(wR2) = 0.0250(0.0593). Crystallographic data for 6: orthorhombic space group P212121, a = 14.036(4) Å, b = 16.486(5) Å, c = 11.397(3) Å, Z = 4, R(wR2) = 0.0261(0.0630).