• East Asian mathematical journal
• /
• v.16 no.2
• /
• pp.233-237
• /
• 2000

Since the time of Euler, there have been many proofs giving the value of $\zeta(2n)$. We also give an evaluation of $\zeta(2n)$ by analyzing the generating function of Bernoulli numbers.

• East Asian mathematical journal
• /
• v.27 no.3
• /
• pp.339-348
• /
• 2011

B. C. Berndt [6] has evaluated the transformation formula for a large class of functions that includes and generalizes the classical Dedekind eta-function. In this paper, we consider a twisted version of his formula. Using this transformation formula, we derive modular trans-formation formulas for the generating functions for cranks which were central to deduce K. Mahlburg's results in [11].

• Korean Journal of Mathematics
• /
• v.28 no.4
• /
• pp.791-802
• /
• 2020

We obtain a two variable generating function for the number of triangular partitions. Using this generating function, we study arithmetic properties of a certain weighted count of triangular partitions. Finally, we introduce a rank-type function for triangular partitions, which gives a combinatorial explanation for a triangular partition congruence.

• Honam Mathematical Journal
• /
• v.43 no.4
• /
• pp.741-749
• /
• 2021

A variant of up-down posets described below and the number of their linear extensions were studied. We obtained the exponential generating functions which showed that how they are related to the Euler's up-down numbers.

• Journal of the Korean Chemical Society
• /
• v.55 no.3
• /
• pp.509-518
• /
• 2011

In this study, we investigated the effects of analogy-generating in small group in elementary science-gifted education upon the types and the mapping errors of student-generated analogies, and the perceptions of the instruction. Fifth graders (N=37) at two science-gifted classes in two elementary schools were selected and assigned to individualistic analogygenerating (IA, n=19) and pair analogy-generating (PA, n=18) groups. After the students of each group performed the experiment and were taught about 'saturated solution' concept in the first class, they administered the test on the self-generating analogies on the concept in the second class. The students in the PA group also administered the test on perceptions of analogy-generating in small group and some of them were interviewed deeply. The results revealed that the students in the PA group made more verbal/pictorial, structural/functional, enriched, and higher systematic analogies than those in the IA group. However, there were little difference between the two groups in the subcategories of artificiality (artificial and everyday) and abstraction (abstract and concrete). The students in the PA group fewer mapping errors than those in the IA group. Many students in PA group perceived the analogy-generating in small group positively upon various cognitive and motivational aspects. However, they also pointed a few disadvantages of the activity. Educational implications of these findings are discussed.

• Journal of Science Education
• /
• v.33 no.2
• /
• pp.173-183
• /
• 2009

We aimed to examine difference between the brain activation pattern based upon hypothesis-generating and hypothesis-understanding among the pre-service teachers not majoring in biology, the pre-service teachers majoring in biology and the biologists using fMRI. We have designed two sets of task paradigm on the biological phenomena: hypothesis-generating and hypothesis-understanding and thirty six healthy participants (twelve participants per group) performed the tasks. The result was showed that 1) there were significant differences of brain activation patterns in hypothesis-generating on the biological phenomena among three groups, 2) the left middle frontal gyrus in the part of DLPFC region was play an important roles of hypothesis-generating and make a significant differences among three groups. The superior ability of biologists were based upon the activation of middle frontal gyrus which has secondary integration of abstract information, and 3) there were no significant differences of brain activation patterns in hypothesis-understanding on the biological phenomena among three groups. These findings provided that scientist might be skillful in generating a new scientific knowledge.

• Journal of the Korean Solar Energy Society
• /
• v.32 no.spc3
• /
• pp.220-227
• /
• 2012

The maximum power point tracking(MPPT) is important part pf PV generating system, because of nonlinear characteristic of PV array. Many MPPT algorithms have been developed and proposed, but partially shaded in PV generating system, these algorithms can not track maximum power point. This paper explains the partially shaded conditions in the PV generating system and describes a novel new MPPT algorithm. To verify the proposed novel algorithm, PSIM simulation tool is used in this paper, and proper 3kW PV module modeling is made. As a result, the right maximum power point(11PP) of PV PCS can be tracked directly under shading effect for any mismatched condition in solar array.

• Journal of the Korean Ceramic Society
• /
• v.56 no.6
• /
• pp.583-588
• /
• 2019

Silicon carbide (SiC) fiber mats generate large amounts of heat through microwave interactions and are used as heating elements in rapid heat treatment furnaces. However, SiC fibers cool immediately when the microwave power is turned off. Therefore, ceramic layers are inserted between the SiC fiber layers to improve the heat conservation performance of SiC fiber mats. In this study, we fabricated SiC fiber mat composites (SMCs) with ceramic layers under various pressures. The SMC fabricated under 0.007 kPa showed the lowest heat-generating temperature and deviation because less necking was observed between the materials. On the other hand, the SMC fabricated under 0.375 kPa showed the highest heat-generating temperature of 1532.33℃. The SMCs prepared in this study using ceramic powder not only showed heat-generating temperatures comparable to those of conventional SiC fiber mats but also exhibited excellent heat-preserving ability.

• Journal of Environmental Science International
• /
• v.23 no.11
• /
• pp.1835-1842
• /
• 2014

The goal of this study was to evaluate micro-bubble concentration ($C_{air}$) in water by air/water ratio (A/W ratio) with a micro-bubble generating pump. The estimation of micro-bubble concentration is based on the balance of inlet/outlet air and water flow rate. On net A/W ratio to be generated micro-bubble, we found that the obtained the $C_{air}$ are shown as a function of discharge pressure ($P_g$) of the micro-bubble generating pump. The correlation of the $C_{air}$ and the $P_g$ ($C_{air}=3.261P_g-1.754$) was adequately described by the least square methods with a high correlation coefficient (r = 0.9459) and calculated values fit the experimental data quite well. The $C_{air}$ was lower than theoretical dissolved air concentration ($C_{aq}$) calculated by Henry's law. The $C_{air}$ for being operated the micro-bubble generating pump was 6.75 - 39.53 mL/L, however, we found that the optimum of the $C_{air}$ to generate micro-bubble was the range from 10 to 12 mL/L.

• Transactions of the Korean Society of Automotive Engineers
• /
• v.22 no.6
• /
• pp.14-22
• /
• 2014

An autonomous vehicle requires a technology of generating maps by recognizing surrounding environment. The recognition of the vehicle's environment can be achieved by using distance information from a 2D laser scanner and color information from a camera. Such sensor information is used to generate 2D or 3D maps. A 2D map is used mostly for generating routs, because it contains information only about a section. In contrast, a 3D map involves height values also, and therefore can be used not only for generating routs but also for finding out vehicle accessible space. Nevertheless, an autonomous vehicle using 3D maps has difficulty in recognizing environment in real time. Accordingly, this paper proposes the technology for generating 2D maps that guarantee real-time recognition. The proposed technology uses only the color information obtained by removing height values from 3D maps generated based on the fusion of 2D laser scanner and camera data.