• East Asian mathematical journal
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• v.35 no.3
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• pp.297-303
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• 2019

In this paper, the author introduces the class $L^p$-BV of functions which are of bounded variation in the sense of $L^p$-norm and investigates the degree of convergence for Fourier series of functions belonging to this class.

• Bulletin of the Korean Mathematical Society
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• v.57 no.6
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• pp.1451-1473
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• 2020

Widely orthant dependence (WOD, in short) is a special dependence structure. In this paper, by using the probability inequalities and moment inequalities for WOD random variables, we study the L_p convergence and complete convergence for the partial sums respectively under the conditions of RCI(α), SRCI(α) and R-h-integrability. We also give an application to nonparametric regression models based on WOD errors by using the L_p convergence that we obtained. Finally we carry out some simulations to verify the validity of our theoretical results.

• Journal for History of Mathematics
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• v.28 no.6
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• pp.321-332
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• 2015

This paper is concerned with the convergence of double trigonometric series and Fourier series. Since the beginning of the 20th century, many authors have studied on those series. Also, Ferenc $M{\acute{o}}ricz$ has studied the convergence of double trigonometric series and double Fourier series so far. We consider $L^p(T^2)$-convergence results focused on the Ferenc $M{\acute{o}}ricz^{\prime}s$ studies from the second half of the 20th century up to now. In section 2, we reintroduce some of Ferenc $M{\acute{o}}ricz^{\prime}s$ remarkable theorems. Also we investigate his several important results. In conclusion, we investigate his research trends and the simple minor genealogy from J. B. Joseph Fourier to Ferenc $M{\acute{o}}ricz$. In addition, we present the research minor lineage of his study on $L^p(T^2)$-convergence.

• The Mathematical Education
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• v.22 no.3
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• pp.25-26
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• 1984

This note treats the inclusive relation of L$_{p}$($\mu$) for 0$_{p}$($\mu$).X>).

• 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 $S_n={\Sigma}^n_{i=1}\;X_i$.

• Communications of the Korean Mathematical Society
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• v.11 no.1
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• pp.57-62
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• 1996

For $1 < p \leq 2$ it is shown that a certain sequence of functions converges to -1 in $L^{p-\varepsilon}(0, 1)$ for any small $\varepsilon > 0$ if and only if the Riemann zeta function satisfies $\zeta(s) \neq 0$ for $\sigma = Re s > 1/p$.

• Journal of the Korea Convergence Society
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• v.12 no.1
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• pp.317-326
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• 2021

This study was investigated to identify the factors influencing health related quality of life in older women with low muscle strength in Korea. The study design was a cross sectional study based on 7th Korea National Health and Nutrition Examination Survey data and the data were analyzed using the SPSS 26.0 program. The level of Health related Quality of Life(HRQoL) in older women with low muscle strength was 0.84. There were significant differences on HRQoL according to age, education level, perceived health, aerobic exercise, perceived stress, arthritis, osteoporosis and depression. The risk factors of HRQoL in older women with low muscle strength were age, education level, perceived health, perceived stress, aerobic exercise and arthritis. Based on this results to improve HRQoL, physical activity intervention should be developed to improve muscle strength and to manage arthritis in older women.

• Journal of Korean Ophthalmic Optics Society
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• v.12 no.3
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• pp.39-48
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• 2007

The stimulus of accommodation A, the stimulus of convergence C and the prism diopter ${\Delta}$ are reviewed and redefined more obviously. How the A and C are managed in the practice are reviewed and summarized. As a result, the common practical process of the binocular vision findings is most suitable in the case of the $l_c=26.67mm$, where the near distance is measured from the test lens to the near target and its value is 40 cm and the average of the P.D equal to 64 mm. The $l_c$ is the distance between the test lens and the center of rotation. Those values were used at calculating the various values in this paper. The error of the stimulus of accommodation values which are evaluated by the practically used formula (5) are calculated. Where the distance between lens and the principle point of eye is 15.07 mm ($=l_H$). The incremental stimulus of convergence values P' caused by the addition prism $P_m$ are evaluated by the recursion computation method. The P' are varied with the $P_m$, the distance $p_c$ between the prism and the center of rotation, the initial convergence value (or inverse target distance) $C_o$ and the refractive index n of the prism material. The recursion computation method and the other formulas are described in detail. In this paper n=1.7 is used. The two factors by which the P' is increased are exist. The one which is major is the property by which the values of convergence whose unit is ${\Delta}$ are not added in the generally way. The other is the that the actual power of the prism is varied with the angle of incidence light. And the P' is decreased remarkably by an increase in the $p_c$ and $C_o$. The $P^{\prime}/P_m$ are calculated and graphed which are varied with the $p_c$ and $C_o$, where the $P_m=20{\Delta}$, P.D=64 mm and n=1.7. The index n dependence of the $P^{\prime}/P_m$ is negligible (refer to fig. 6). The $p_c$ are evaluated at which the P' equal to the $P_m$ for various $P_m$ (refer to table 1). The actual values of the stimulus of convergence and accommodation which are manipulated simply in the practice are calculated. Two graphical forms are suggested. The one is like as the commonly used one. But the stimulus of convergence and of accommodation values in the practice are positioned at the exact positions when the graphic is made (refer to fig. 9). The other is the form that the incremental stimulus of convergence values caused by the addition prisms are represented at actual positions (refer to fig. 11).

• Journal of the Chungcheong Mathematical Society
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• v.28 no.3
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• pp.409-417
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• 2015

In this paper, some $L_p$-convergences and complete convergences of the maximum of the partial sum for negatively superadditive dependent random variables are obtained. The proofs of the results are based on a new Rosenthal type inequality concerning negatively superadditive dependent random variables.

• Journal of Microbiology and Biotechnology
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• v.27 no.3
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• pp.598-609
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• 2017

Pediococcus pentosaceus ID-7 was isolated from kimchi, a Korean fermented food, and it showed high activity for lactose hydrolysis. The ${\beta}$-galactosidase of P. pentosaceus ID-7 belongs to the GH2 group, which is composed of two distinct proteins. The heterodimeric LacLM type of ${\beta}$-galactosidase found in P. pentosaceus ID-7 consists of two genes partially overlapped, lacL and lacM encoding LacL (72.2 kDa) and LacM (35.4 kDa). In this study, Escherichia coli MM294 was used for the production of LacL, LacM, and LacLM. These three types of recombinant proteins were expressed, purified, and characterized. The specific activities of LacLM and LacL were 339 and 31 U/mg, respectively. However, activity was not detected with LacM alone. The optimal pH of LacLM and LacL was pH 7.5 and pH 7.0, and the optimal temperature of LacLM and LacL was $40^{\circ}C$ and $50^{\circ}C$, respectively. The optimal temperature changes indicate that LacLM is able to achieve higher activity at a relatively lower temperature. LacLM was strongly activated by $Mg^{2+}$, $Mn^{2+}$, and $Zn^{2+}$, which was not true for LacL. Consistent with this, EDTA strongly inactivated LacLM and LacL, but the presence of reducing agents did not dramatically alter the activity. Taken together, multiple alignment of amino acid sequences and phylogenetic analysis results of LacL and LacM of P. pentosaceus ID-7 suggest the evolution of LacL into LacLM and that the use of divalent metal ions results in higher activity.