• Journal of the Korean Mathematical Society
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• v.60 no.2
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• pp.395-406
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• 2023

As an analogy of the Rogers-Ramanujan continued fraction, we define a Ramanujan continued fraction of order eighteen. There are essentially three Ramanujan continued fractions of order eighteen, and we study them using the theory of modular functions. First, we prove that they are modular functions and find the relations with the Ramanujan cubic continued fraction C(𝜏). We can then obtain that their values are algebraic numbers. Finally, we evaluate them at some imaginary quadratic quantities.

• Kyungpook Mathematical Journal
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• v.58 no.2
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• pp.319-332
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• 2018

In the present paper, we establish relationship between continued fraction U(-q) of order 12 and Ramanujan's cubic continued fraction G(-q) and $G(q^n)$ for n = 1, 2, 3, 5 and 7. Also we evaluate U(q) and U(-q) by using two parameters for Ramanujan's theta-functions and their explicit values.

• The Korean Journal of Food And Nutrition
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• v.7 no.4
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• pp.332-337
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• 1994

The antioxidant activity of solvent extracts isolated from barley leaves was investigated by measuring peroxide value. The fractions of methanol extract obtained from preparative TLC was also studies, with UV-Visible spectrum, total phenol contents and hydrogen donating ability(HDA) The antioxidant activity of various solvent extracts was, in decreasing order, methanol> ethyl ether> methylene chloride $\geq$ ethyl acetate $\geq$acetone> hexane. The antioxidant activity of the fractions of methanol extract was, in decreasing order, fraction 2> fraction 3> fraction 1 and their activity was all superior to that of tocopherol at 500 ppm level. All fraction(1, 2 and 3) exhibited a strong UV absorption at 280 m which would be specifically produced by phenolic compound. UV absorption at 280 m of fraction 2 was greater than those of fraction 1 and 3. In the visible spectrum of these fractions, the maximum .absorption wavelengths of fraction 1, 2 and 3 were 660, 460 and 460 m, respectively. Antioxidant activity of barley leaves seemed to be due to the flavonoids containing phenolic group by UV spectrum and total phenol content.

• Steel and Composite Structures
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• v.30 no.6
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• pp.603-615
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• 2019

In the present work, free vibration of beams made of imperfect functionally graded materials (FGMs) including porosities is investigated. Because of faults during process of manufacture, micro voids or porosities may arise in the FGMs, and this situation causes imperfection in the structure. Therefore, material properties of the beams are assumed to vary continuously through the thickness direction according to the volume fraction of constituents described with the modified rule of mixture including porosity volume fraction which covers two types of porosity distribution over the cross section, i.e., even and uneven distributions. The governing equations of power law FGM (P-FGM) and sigmoid law FGM (S-FGM) beams are derived within the frame works of classical beam theory (CBT) and first order shear deformation beam theory (FSDBT). The resulting equations are solved using separation of variables technique and assuming FG beams are simply supported at both ends. To validate the results numerous comparisons are carried out with available results of open literature. The effects of types of volume fraction function, beam theory and porosity volume fraction, as well as the variations of volume fraction index, span to depth ratio and porosity volume fraction, on the first three non-dimensional frequencies are examined in detail.

• Korean Journal of Soil Science and Fertilizer
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• v.32 no.4
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• pp.375-382
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• 1999

In order to investigate the contamination characteristics of the heavy metals in the mine tailings of abandoned gold mine and its surrounding agricultural soils, a sequential extraction procedure of increasing reactivity in the dissolution processes of the heavy metals(Cd, Cu, and Pb) which were associated with solid and/or solution phase in soils was attempted to partition into six particulate fractions : exchangeable, bound to carbonate, bound to Fe-Mn oxides, bound to organic matter, residual, and soluble. Among indigenous heavy metals in the mine tailings, Pb was the most abundant and Cu and Cd were followed by. Fractionation result of Pb obtained from the triplicate samples of the mine tailings were in the order of Fe-Mn oxide> Carbonate> Residual> Organic> Exchangeable> Soluble, while Wolgok series were Exchangeable > Fe-Mn oxide > Carbonate> Organic> Residual> Soluable. However the other heavy metals studied were not followed this trend. The fractionation results of mine tailing and agricultural soils demonstrated that different geochemical fractions were operationally defined by an extraction sequence that generally followed the order of decreasing solubility. Therefore potential mobility and bioavailability of heavy metals as toxic pollution sources can be evaluated when studying the pollution levels of heavy metals in soils.

• Biomolecules & Therapeutics
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• v.6 no.3
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• pp.242-246
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• 1998

The inhibitory activities of Amberlite active fraction, which was obtained from methanol soluble fraction of freeze dried slikworm urine, on the rat intestinal glycosidase-catalyzed enzymatic reaction were examined in in viro and in vivo experiments. Amberlite active fraction showed significant inhibitory effects on the hydrolysis of o-glycosidic bond, especially $\alpha$-1,4 bond. On the other hand, the inhibition on the hydrolysis of $\beta$-glycosidic bond was very weak. Oral administration of Amberlite active fraction resulted in a dose-dependent decrease in the blood glucose after an oral maltose load, and postprandial hyperglycemia in carbohydrate-loaded mice was suppressed by Amberlite active fraction at 60 mgHg in decreasing order of maltose, starch, sucrose and lactose. 60 mg/kg of Amberlite active fraction lowered the blood glucose level markedly after 18, 35, and 60 min after an oral maltose load and the antihyperglycemic activity was maintained upto 90 min. In alloxan-induced hyperglycemic mice, Amberlite active fraction at a dose of 100 mg/kg also significantly lowered blood glucose after an oral maltose load, and its efficacy was almost equivalent to that of acarbowe.

• Solar Energy
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• v.4 no.2
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• pp.37-42
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• 1984

A computer code for an optimum design of solar space and domestic hot water heating system has been developed. The f-chart method developed by S.A. Klein et al. has been incorporated in the present computer code. The main conclusions obtained from the present work may be summarized as follows: (1) In Seoul area, about 46% of the total heating load can be obtained from the solar collectors whose total surface area is about one-third of the total heating floor area. (2) In Pusan area, total area of solar collectors should be about half of the total heating floor area in order to obtain an equivalent solar fraction of Seoul. (3) In cheju area, on the other hand, only about 42% of the total heating floor area of solar collectors is needed to get the same solar fraction as in Seoul and Pusan. (4) In order to get the first 50% solar fraction, only about 10-14 collectors ($4'{\times}8'$ collectors) are required, whereas about 48 collectors are needed to obtain the solar fraction of 100%. That is, roughly 3.5-4.5 times greater number of collectors are required to increase the solar fraction from 50% to 100%. Therefore, it can be concluded that it is relatively inefficient and less economical to build a solar system whose solar fraction exceeds more than 50%.

• Korean Journal of Pharmacognosy
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• v.48 no.3
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• pp.208-212
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• 2017

In this study, analysis of active compounds that are believed to be highly relevant to antioxidant activity was carried out on the methanol extract and its solvent fractions of Corni fructus. The DPPH radical scavenging activity for the comparison of antioxidant activity was higher in order of aqueous fraction > methanol extract > ethyl acetate fraction > n-hexane fraction. It is similar to the order of total polyphenol contents in the samples. As a result of LC-MS analysis, phenolic acid compounds such as caffeic acid, gallic acid and chlorogenic acid and lognin, which is known as a representative active ingredient of Corni fructus, were identified as active compounds. And the antioxidative activity and the total polyphenol content of the extracts and solvent fractions were found to be related to the contents of the compounds. Particularly, it was confirmed that phenolic acid such as caffeic acid contributes to the antioxidative activity of the aqueous fraction of Corni fructus methanol extract.

• Research in Mathematical Education
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• v.16 no.4
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• pp.217-232
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• 2012

While many studies on early algebra have been conducted, there have been only a few studies on the operation sense as the fundamental element of algebraic thinking, especially the fraction operation sense. This study explored the dimensions of fraction operation sense and then investigated students' fraction operation sense. A total of 183 of sixth graders were surveyed and 5 students who showed high operation sense were clinically interviewed in order to analyze their algebraic thinking in detail. The results showed that students had a tendency to use direct calculation or employ inappropriate operation sense rather than to use the structure of operation or the relation between operations on the basis of algebraic thinking. This study implies that explicit instruction on early algebra is necessary from the elementary school years.

• Journal of Food Hygiene and Safety
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• v.11 no.1
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• pp.41-50
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• 1996

The yields of solvent fraction of irradiated red ginseng powder were increased in the order of petroleum ether(PE)