• Journal of the Korean Mathematical Society
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• v.57 no.2
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• pp.471-487
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• 2020

We find congruences modulo 32, 64 and 128 for the partition function ${\overline{PP}_o}(n)$, the number of overpartition pairs of n into odd parts, with the aid of Ramamnujan's theta function identities and some known identities of t_k(n), for k = 6, 7, where t_k(n) denotes the number of representations of n as a sum of k triangular numbers. We also find two Ramanujan-like congruences for ${\overline{PP}_o}(n)$ modulo 128.

• East Asian mathematical journal
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• v.35 no.1
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• pp.85-90
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• 2019

In this paper, we are interested in the evaluation of special values of the Dedekind zeta function of a totally real number field. In particular, we revisit Siegel method for values of the zeta function of a totally real number field at negative odd integers and explain how this method is applied to the case of non-normal totally real number field. As one of its applications, we give divisibility property for the values in the special case

• Kyungpook Mathematical Journal
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• v.55 no.2
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• pp.485-506
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• 2015

Every classical or virtual knot is equivalent to the unknot via a sequence of extended Reidemeister moves and the so-called forbidden moves. The minimum number of forbidden moves necessary to unknot a given knot is an invariant we call the forbidden number. We relate the forbidden number to several known invariants, and calculate bounds for some classes of virtual knots.

• Culinary science and hospitality research
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• v.13 no.2
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• pp.123-135
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• 2007

This study intended to determine how price-ending types used for menu products affected consumers' price evaluation and value perception and such behavioral intentions as purchase intention and search intention. The collected data went through statistical processing, including frequency analysis, factor analysis, T-test and ANOVA using an $SPSS/PC^+$ 12.0 statistical package. The results can be summarized as follows: First, as for differences in internal reference price by ending, internal reference price was lower if menu ending was an odd number than it was an even number, which indicates that consumers tend to consider the price of the menu products to be lower if the ending of menu products is an odd number. Second, menu price-ending was found to have significant differences on consumers' purchase intention, search intention, and value perception. But the results of two-way ANOVA showed that price ending by restaurant types had no effect on consumers' search intention and restaurant type. This study suggested a desirable external reference price-ending type for menu products as one of sales promotion strategies to menu products planners and drew up a concrete plan to determine which price-ending type is useful by consumers' personal properties.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.18 no.4
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• pp.177-182
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• 2018

The home-and-way round-robin sports leagues scheduling problem with minimum brake is very hard to solve in polynomial time. This problem is NP-hard, the complexity status is not yet determined. This paper suggests round-robin sports leagues scheduling algorithm not computer-aided program but by hand with O(n) time complexity for arbitrary number of teams n with always same pattern. The algorithm makes a list of mathes using $n{\times}n$ canonical latin square for n=even teams. Then trying to get home(H) and away(A) with n-2 minimum number of brakes. Also, we get the n=odd scheduling with none brakes delete a team own maximum number of brakes from n=even scheduling.

• Journal of the Korean Solar Energy Society
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• v.37 no.4
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• pp.1-11
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• 2017

Most PV modules are fabricated by 6 cell-strings with solar cells connected in series. Moreover, bypass diodes are generally installed every 2 cell-strings to prevent PV modules from a damage induced by current mismatch or partial shading. But, in the case of special purpose PV module, like as BIPV (Building Integrated Photovoltaic), the number of cell-strings per module varies according to its size. Differ from a module employing even cell-strings, the configuration of bypass diode should be optimized in the PV module with odd strings because of oppositely facing electrodes. Hence, in this study, electrical characteristics of special purposed PV module with odd string was empirically and theoretically studied depending on arrangement of bypass diode. Here, we assumed that PV module has 3 strings and the number of bypass diodes in the system varies from 2 to 6. In case of 2 bypass diodes, shading on a center string increases short circuit current of the module, because of a parallel circuit induced by 2 bypass diodes connected to center string. Also, the loss is larger, as the shading area in the center string is enlarged. Thus, maximum power of the PV module with 2 bypass diode decreases by up to 59 (%) when shading area varies from 50 to 90 (%). On the other hand, In case of 3 and 6 bypass diodes, the maximum power reduction was within about 3 (W), even the shading area changes from 50 to 90 (%). As a result, It is an alternative to arrange the bypass diode by each string or one bypass diode in the PV module in order to completely bypass current in case of shading, when PV module with odd string are fabricated.

• JSTS:Journal of Semiconductor Technology and Science
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• v.12 no.4
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• pp.418-425
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• 2012

In this paper, efficient implementation of error correction code (ECC) processing circuits based on single error correction and double error detection (SEC-DED) code with check bit pre-computation is proposed for memories. During the write operation of memory, check bit pre-computation eliminates the overall bits computation required to detect a double error, thereby reducing the complexity of the ECC processing circuits. In order to implement the ECC processing circuits using the check bit pre-computation more efficiently, the proper SEC-DED codes are proposed. The H-matrix of the proposed SEC-DED code is the same as that of the odd-weight-column code during the write operation and is designed by replacing 0's with 1's at the last row of the H-matrix of the odd-weight-column code during the read operation. When compared with a conventional implementation utilizing the odd-weight- column code, the implementation based on the proposed SEC-DED code with check bit pre-computation achieves reductions in the number of gates, latency, and power consumption of the ECC processing circuits by up to 9.3%, 18.4%, and 14.1% for 64 data bits in a word.

• Journal of the Institute of Electronics Engineers of Korea SD
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• v.47 no.7
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• pp.61-69
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• 2010

In this paper, an 1.2V 8b 800MSPS A/D Converter(ADC) with an odd number of folding block to overcome the asymmetrical boundary-condition error is described. The architecture of the proposed ADC is based on a cascaded folding architecture using resistive interpolation technique for low power consumption and high input frequency. The ADC employs a novel odd folding block to improve the distortion of signal linearity and to reduce the offset errors. In the digital block, furthermore, we use a ROM encoder to convert a none-$2^n$-period code into the binary code. The chip has been fabricated with an $0.13{\mu}m$ 1P6M CMOS technology. The effective chip area is $870{\mu}m\times980{\mu}m$. SNDR is 44.84dB (ENOB 7.15bit) and SFDR is 52.17dBc, when the input frequency is 10MHz at sampling frequency of 800MHz.

• Journal of the Korean School Mathematics Society
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• v.18 no.1
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• pp.1-14
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• 2015

In this paper, in order to improve the teaching contents on even and odd number, composition and decomposition of numbers, and (1 digit)+(1 digit) with carrying, (10 and 1 digit)-(1 digit) with borrowing, the corresponding teaching contents in ${\ll}$Math 1-1${\gg}$, ${\ll}$Math 1-2${\gg}$ are critically reviewed. Implications obtained through this review can be summarized as follows. First, the current incomplete definition of even and odd numbers would need to be reconsidered, and the appropriateness of dealing with even and odd numbers in first grade would need to be reconsidered. Second, it is necessary to deal with composition and decomposition of numbers less than 20. That is, it need to be considered to compose (10 and 1 digit) with 10 and (1 digit) and to decompose (10 and 1 digit) into 10 and (1 digit) on the basis of the 10. And the sequence dealing with composition and decomposition of 10 before dealing with composition and decomposition of (10 and 1 digit) need to be considered. And it need to be considered that composing (10 and 1 digit) with (1 digit) and (1 digit) and decomposing (10 and 1 digit) into (1 digit) and (1 digit) are substantially useless. Third, it is necessary to eliminate the logical leap in the calculation process. That is, it need to be considered to use the composing (10 and 1 digit) with 10 and (1 digit) and decomposing (10 and 1 digit) into 10 and (1 digit) on the basis of the 10 to eliminate the leap which can be seen in the explanation of calculating (1 digit)+(1 digit) with carrying, (10 and 1 digit)-(1 digit) with borrowing. And it need to be considered to deal with the vertical format for calculation of (1 digit)+(1 digit) with carrying and (10 and 1 digit)-(1 digit) with borrowing in ${\ll}$Math 1-2${\gg}$, or it need to be considered not to deal with the vertical format for calculation of (1 digit)+(1 digit) with carrying and (10 and 1 digit)-(1 digit) with borrowing in ${\ll}$Math 1-2 workbook${\gg}$ for the consistency.

• Parasites, Hosts and Diseases
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• v.45 no.3
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• pp.191-198
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• 2007

A total of 205 larval gnathostomes were collected from 18 (22.5%) of 80 red banded odd-tooth snakes, Dinodon rufozonatum rufozonatum, which had been smuggled from China and confiscated at Customs in Susan, Republic of Korea. In order to identify the species, some of the larvae were observed by a light microscope and a scanning electron microscope (SEM). The larvae were $2.18{\times}0.29mm$ in average size, and had a pair of lips at the anterior end, a muscular esophagus, 2 pairs of cervical sacs, and brownish intestines. The head bulb was characteristically equipped with 4 rows of hooklets; the average number of hooklets in each respective row was 38.6, 40.5, 41.5, and 43.7. In SEM views, the mouth evidenced a pair of lateral lips of equal size in a half-moon shape. Each lip featured a couple of labial papillae and a small amphid located between the 2 papillae. The hooklets on the head bulb had single-pointed, posteriorly-curved tips. The cuticular spines were larger and more densely distributed on the anterior part of the body, and decreased gradually in size and number toward the posterior body. On the basis of these morphological characteristics, the larvae were identified as the third stage larvae of Gnathostoma hispidum.