• Journal of applied mathematics & informatics
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• v.32 no.1_2
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• pp.55-60
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• 2014

In this paper, we will obtain Marcinkiewicz's type limit laws for fuzzy random sets as follows : Let {$X_n{\mid}n{\geq}1$} be a sequence of independent identically distributed fuzzy random sets and $E{\parallel}X_i{\parallel}^r_{{\rho_p}}$ < ${\infty}$ with $1{\leq}r{\leq}2$. Then the following are equivalent: $S_n/n^{\frac{1}{r}}{\rightarrow}{\tilde{0}}$ a.s. in the metric ${\rho}_p$ if and only if $S_n/n^{\frac{1}{r}}{\rightarrow}{\tilde{0}}$ in probability in the metric ${\rho}_p$ if and only if $S_n/n^{\frac{1}{r}}{\rightarrow}{\tilde{0}}$ in $L_1$ if and only if $S_n/n^{\frac{1}{r}}{\rightarrow}{\tilde{0}}$ in $L_r$ where $S_n={\Sigma}^n_{i=1}\;X_i$.

• East Asian mathematical journal
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• v.19 no.2
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• pp.221-232
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• 2003

An identity for n-time differentiable functions of a real variable in terms of multiple integrals and applications for Ostrowski type inequalities are given.

• Communications of the Korean Mathematical Society
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• v.19 no.2
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• pp.293-305
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• 2004

Trotter-Kato type approximations of the convoluted solution operator families for the Volterra integral equations (V $E_n$): v(t)=$A_{n} \int_0^t v(t-s) d\mu_n(s) + f_n(t), t \geq 0$ and the convergence of the solutions to the equations (V $E_n$) are studied.

• Journal of Biosystems Engineering
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• v.40 no.4
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• pp.305-313
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• 2015

Purpose: This study was performed to predict the fatigue life of a crank-type rotavator operated in domestic soil conditions using Recurdyn$^{(R)}$, a dynamic analysis program. Methods: Torque on the PTO shaft was measured using experiments conducted on the uplands and paddy fields in Korea. On the basis of the experimental and analytical results, the fatigue life of the crank-type rotavator was predicted by constructing an S-N curve according to the GL (Germanischer Lloyd Wind Energie GmbH) guideline. Results: The torques experienced by the PTO shaft in the paddy soil and the uplands were in the range of 472~797 N m and 313~430 N m, respectively, for every condition. In case of load condition, the peak torques (846 N m, 770 N m) were applied for severe conditions, resulting in a maximum (von Mises) stress of 75 MPa at the crank arm. The fatigue life of the crank-type rotavator was predicted to be 1,167 h that satisfies the target value of 1,110 h, by substituting the analysis results into an S-N curve of crank arm. Conclusions: The fatigue life of the crank-type rotavator was within the target life for the studied soil conditions; however, further field experiments for various soil conditions would be required to verify the prediction results.

• Korean Journal of Mathematics
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• v.8 no.1
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• pp.73-86
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• 2000

We study the Sobolev spaces to the generalized Sobolev spaces $H^s_{\mathcal{G}}$ of exponential type based on the Silva space $\mathcal{G}$ and investigate its properties such as imbedding theorem and structure theorem. In fact, the imbedding theorem says that for $s$ > 0 $u{\in}H^s_{\mathcal{G}}$ can be analytically continued to the set {$z{\in}\mathbb{C}^n{\mid}{\mid}Im\;z{\mid}$ < $s$}. Also, the structure theorem means that for $s$ > 0 $u{\in}H^{-s}_{\mathcal{G}}$ is of the form $$u={\sum_{\alpha}\frac{s^{{|\alpha|}}}{{\alpha}!}D^{\alpha}g{\alpha}$$ where $g{\alpha}$'s are square integrable functions for ${\alpha}{\in}\mathbb{N}^n_0$. Moreover, we introduce a classes of symbols of exponential type and its associated pseudo-differential operators of exponential type, which naturally act on the generalized Sobolev spaces of exponential type. Finally, a generalized Bessel potential is defined and its properties are investigated.

• Journal of applied mathematics & informatics
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• v.16 no.1_2
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• pp.79-90
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• 2004

In this paper the authors present sufficient conditions for all bounded solutions of the second order neutral difference equation ${\Delta}^2(y_n\;-\;py_{n-{\kappa}})\;-\;q_nf(y_{n-e})\;=\;0,\;n\;{\in}\;N$ to be oscillatory. Examples are provided to illustrate the results.

• Bulletin of the Korean Mathematical Society
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• v.56 no.5
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• pp.1117-1127
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• 2019

Let ${\mathcal{L}}_2=(-{\Delta})^2+V^2$ be the $Schr{\ddot{o}}dinger$ type operator, where nonnegative potential V belongs to the reverse $H{\ddot{o}}lder$ class $RH_s$, s > n/2. In this paper, we consider the operator $T_{{\alpha},{\beta}}=V^{2{\alpha}}{\mathcal{L}}^{-{\beta}}_2$ and its conjugate $T^*_{{\alpha},{\beta}}$, where $0<{\alpha}{\leq}{\beta}{\leq}1$. We establish the $(L^p,\;L^q)$-boundedness of operator $T_{{\alpha},{\beta}}$ and $T^*_{{\alpha},{\beta}}$, respectively, we also show that $T_{{\alpha},{\beta}}$ is bounded from Hardy type space $H^1_{L_2}({\mathbb{R}}^n)$ into $L^{p_2}({\mathbb{R}}^n)$ and $T^*_{{\alpha},{\beta}}$ is bounded from $L^{p_1}({\mathbb{R}}^n)$ into BMO type space $BMO_{{\mathcal{L}}1}({\mathbb{R}}^n)$, where $p_1={\frac{n}{4({\beta}-{\alpha})}}$, $p_2={\frac{n}{n-4({\beta}-{\alpha})}}$.

• Analytical Science and Technology
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• v.13 no.2
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• pp.194-199
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• 2000

The study on the adsorption, the surface properties and the antibacterial effects of the Ni-treated PAN based activated carbon fibers was carried out. In the adsorption study on the Ni-treated PAN based ACFs, Type I isotherms for N1-N3 and Type II-Type III isotherms for N4-N6 were obtained, respectively. Futhermore, their adsorbed volumes slowly were decreased with the increase in the mole concentration of Ni on the treated PAN based ACFs. From the BET equation, the specific surface areas of the Ni-treated PAN based ACFs were in the range of $692.58-895.24m^2/g$. The micropore volumes obtained from ${\alpha}_s$-method using common-t value were $0.19-0.56cm^3/g$. The surfaces of PAN based ACFs partially blocked by metal after the treatment were observed from the SEM micrographs. Finally, from the antibacterial effects using Shake flask method against E. coli, the percentage of the effects was 92.5-100% and the antibacterial effect was increased with the increase in mole concentration of Ni treated.

• Journal of Magnetics
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• v.3 no.2
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• pp.39-40
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• 1998

Normal state EPR signals have been studied for the n-type$ high-T_c$ superconductors $Nd_{1.85}Ce_{0.15}CuO_{4-x} and Nd_2CuO_{3.6-x}F_{0.4-y}.$ Since EPR signals were observed only in quenched non-superconducting samples and were absent in furnace-cooled samples, our results suggest that no normal state EPR signals come from pure phase n-type hihg-Tc superconductors. Our observation is consistent with previously reported absence of nomal state EPR signals in the p-type high-Tc superconductors.

• Bulletin of the Korean Chemical Society
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• v.23 no.6
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• pp.851-856
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• 2002

The Reaction of S-methyl-S-cysteine(L-Smc) with racemic $s-cis-[Co(demba)Cl_2]-1$ (Hydmedba = $NN'-dimethylethylenediamine-NN'-di-\alpha-butyric$, acid) yields ${\Delta}$-s-cis-[Co(dmedba)(L-Smc)] 2 with N, O-chelation. Oxidation of sulfur of 2 with $H_2O_2$ in a 1 : 1 mole ratio gives ${\Delta}$-s-cis[Co(dmedba)(L-S(O)mc)] 3 having an uncoordinated sulfenate group. Oxidation of sulfur of L-Sm with $H_2O_2in$ a 1: 1 mole ratio produces S-methyl-L-cysteinesulfenate (L-S(O)me) 5. Direct reaction of 1 with 5 in basic medium gives an N.O-chelated ${\Delta}$s-cis[Co(dmedba)(L-S(O)mc)-N.O], which turmed out be same as obtained by oxidation of 2, while an N, S-chelated ${\Delta}$-s-cis-[Co(dmedba)(S-S(O)mc)-N,O] complex 4 is obtained in acidic medium from the reaction of 1 with 5. This is one of the rare $[$Co^{III}$(N_2O_2-type$ ligand)(amino acid)] type complex preparations, where the reaction conditions determine which mode of N, O and N, S caelation modes is favored.