• Research in Mathematical Education
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• v.12 no.2
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• pp.127-142
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• 2008

The most important aim of mathematics education is to promote mathematical thinking. In the Hong Kong primary school, mathematical thinking is usually conducted through the use of formula and working on "application problem" or "word problems". However, there are many other ways that can promote mathematical thinking, and investigation on mathematical structure by using counting is one important source for promoting mathematical thinking for primary school children, as every children can count and hence a well designed question that can be solved by counting can enable children of different abilities to work together and obtain different results.

• Journal of Korean Elementary Science Education
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• v.35 no.2
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• pp.137-149
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• 2016

The purpose of this study is to develop a descriptive paper test item which can evaluate elementary school students' HGA (scientific Hypothesis Generating Ability) and to propose a counting formula that can easily assess student's HGA objectively and quantitatively. To make the test item can possibly evaluate all the students from 6th graders to 3rd graders, the 'rabbit's ear' item is developed. Developed test item was distributed to four different elementary schools in Seoul. Total 280 students who were in the 6th grade solved the item. All the students' reponses to the item were analyzed. Based on the analyzed data evaluation factors and evaluation criteria are extracted to design a Hypothesis Generating ability Quotient (HGQ). As the result 'Explican's Degree of Likeness' and 'Hypothesis' Degree of Explanation' are chosen as evaluation factors. Also precedent evaluation criteria were renewed. At first, Explican's Degree of Likeness evaluation criterion was turned four levels into three levels and each content of evaluation criterion is also modified. Secondly, new evaluation factor 'Hypothesis' Degree of Explanation' was developed as combined three different evaluation criteria, 'level of explican', 'number of explican' and 'structure of explican'. This evaluation factor was designed to assess how the suggested hypothesis can elaborately explain the cause of one phenomenon. Newly designed evaluation factors and evaluation criteria can assess HGA more in detail and reduce the scoring discordant through the markers. Lastly, Developed counting formula is much more simple than precedent Kwon's equation for evaluating the Hypothesis Explanation Quotient. So it could help easily distinguish one student's scientific hypothesis generating ability.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2004.10a
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• pp.166-169
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• 2004

A fatigue test was used to evaluate the fatigue life of an actual structure. The loaded state and the constraint condition of an actual structure must be same as the specimen in order to apply the test results to an actual structure by the specimen. The loaded state and constraint conditions can't be same as the specimen in the actual structure which is complicated. In order to reduce these differences, an actual structure test with a lot of frequencies is need to get a fatigue life curve. Therefore, ten sets of accelerated test units which attached unbalanced mass were composed in this study. Acceleration history about the vibration of an actual structure was acquired. Rainflow counting was used on acceleration history, and the life curve return formula was assumed. The return formula that damage satisfied `1' was acquired in a feedback process by the Miner's rule, which was the linear cumulative damage theory. A conservative fatigue life curve was determined with a return formula to have been presumed by each set. The fatigue life of regular rpm condition was calculated by these conservative fatigue life curves.

• East Asian mathematical journal
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• v.39 no.3
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• pp.331-347
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• 2023

We present an identity on moments of a compound random variable by using an auxiliary counting random variable. Based on this identity, we develop a new recurrence formula for obtaining the raw and central moments of any order for a given compound random variable.

• The Korean Journal of Nuclear Medicine Technology
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• v.22 no.2
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• pp.105-111
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• 2018

Purpose Quality control of instrument takes up a large part in the Radioimmunoassays. The gamma-ray instrument, which is one of the important instruments in the laboratory, observes the condition and performance of instrument and performs quality control of the instrument by measuring the Normalization, Calibration, Background and etc. However, there are some automation instruments which can't measure the counting efficiency of gamma-ray meters, resulting in insufficient management in terms of performance evaluation of gamma-ray meters. Therefore, the purpose of this paper is to manage the quality control continuously and regularly by suggesting how to measure the counting efficiency of gamma-ray instruments. Materials and Methods In case of a comparative measurement method to a gamma-ray instrument dedicated to nuclear medical examination, the CPM and counting efficiency can be obtained after the measurement of normalization by inserting the I-125 $200{\mu}L$(CPM 50,000~500,000) into the test tube. With this CPM and counting efficiency values, it's possible to calculate the measurement of the DPM value and count the CPM from the automation instrument from the same source, and enter the DPM to calculate the counting efficiency using a comparative measurement method. Another method is to calculate the counting efficiency by estimating the half life using the radiation source information of the tracer in B test reagents of company A. Results According to the calculation formula using the DPM obtained by counting the normalization of gamma-ray meters, the detection efficiency was 75.16% for Detector 1, 76.88% for Detector 2, 77.13% for Detector 3, 75.36% for Detector 4 and 73.2% for Detector 5 respectively. Using another calculation formula estimated from the shelf life, the data of the detection efficiency from Detector 1 to Detector 5 were 74.9%, 75.1%, 76.5%, 74.9% and 73.2% respectively. Conclusion Although the accuracy of counting efficiencies of both methods are insufficient, this is considered to be useful for ongoing management of quality control if counting efficiency is managed after setting the acceptable ranges. For example, if the measurement efficiency is set to 70% or higher, the allowed %difference between measurements is within 3% and the %difference with the detector wall is set within 5%.

• Journal of the Korean Mathematical Society
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• v.45 no.6
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• pp.1635-1646
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• 2008

Schanuel's formula describes the distribution of rational points on projective space. In this paper we will extend it to algebraic points of bounded degree in the case of ${\mathbb{P}}^1$. The estimate formula will also give an explicit error term which is quite small relative to the leading term. It will also lead to a quasi-asymptotic formula for the number of points of bounded degree on ${\mathbb{P}}^1$ according as the height bound goes to $\infty$.

• Journal of The Korean Astronomical Society
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• v.41 no.4
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• pp.99-107
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• 2008

When a new counting experiment is proposed, it is crucial to predict whether the desired source signal will be detected, or how much observation time is required in order to detect the signal at a certain significance level. The concept of the a priori prediction of the detection limit in a newly proposed experiment should be distinguished from the a posteriori claim or decision whether a source signal was detected in an experiment already performed, and the calculation of statistical significance of a measured source signal. We formulate precise definitions of these concepts based on the statistical theory of hypothesis testing, and derive an approximate formula to estimate quickly the a priori detection limit of expected Poissonian source signals. A more accurate algorithm for calculating the detection limits in a counting experiment is also proposed. The formula and the proposed algorithm may be used for the estimation of required integration or observation time in proposals of new experiments. Applications include the calculation of integration time required for the detection of faint emission lines in a newly proposed spectroscopic observation, and the detection of faint sources in a new imaging observation. We apply the results to the calculation of observation time required to claim the detection of the surface thermal emission from neutron stars with two virtual instruments.

• Pediatric Gastroenterology, Hepatology & Nutrition
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• v.12 no.sup1
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• pp.27-36
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• 2009

Some pediatric patients who can not eat orally depend on enteral tube feedings, and some patients require more nutrients and calories to achieve the catch-up growth. If a patient is counting on the parenteral nutrition, early initiation of enteral feeding, orally or enterally, is a very good for the intestinal mucosal maturity and motility. There are numerous kinds of formulas and supplements for the enteral feeding for neonates, infants, and children. Depending on the intestinal symptoms, allergic symptoms, requirement of special nutrients, we can choose regular infant formula (milk-based, soy-based), protein hydrolysate formula, amino acid hydrolysate formula, elemental formula. Proper use of these formulas would help for the pediatric patients to recover from their diseases, to facilitate the intestinal mucosal maturity and to achieve their goal of growth.

• East Asian mathematical journal
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• v.37 no.1
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• pp.79-85
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• 2021

In this paper, we investigate the valuation of vulnerable exchange option that has credit risk of option issuer. The reduced-form model is used to model credit risk. We assume that credit event is determined by the jump of the counting process with stochastic intensity, which follows the mean reverting process. We propose a simple approach to derive the closed-form pricing formula of vulnerable exchange option under the reduced-form model and provide the pricing formula as the standard normal cumulative function.

• Nuclear Engineering and Technology
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• v.3 no.1
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• pp.3-7
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• 1971

A method for determining dead times of a G.M. detector as a function of the count rate has been investigated using the Mn$^{56}$ radioactive sample. The formula, (equation omitted), seems to be useful for determining a relation between the dead time and the count rate. Here (equation omitted)(N$_1$) is the dead time for the count rate N$_1$, N$_1$is the count rate at time zero, Nt is the count rate at time t, λ is the radioactive decay constant of the sample used, and t is the time between the first and second runs. When all the counting data were corrected for the dead times evaluated with this formula and then a variation of these corrected counting data with rime was observed, the results showed quite a good agreement with the published data for the radioactive decay of Mn$^{56}$ . Besides, it appears that the dead time decreases as the count rate increases in a dead time-to-count rate relation obtained by the same formula.