• Communications of the Korean Mathematical Society
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• v.37 no.1
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• pp.303-326
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• 2022

Our aim is to construct Hermite-type exponentially fitted interpolation formulas that use not only the pointwise values of an 𝜔-dependent function f but also the values of its first derivative at three unequally spaced nodes. The function f is of the form, f(x) = g₁(x) cos(𝜔x) + g₂(x) sin(𝜔x), x ∈ [a, b], where g₁ and g₂ are smooth enough to be well approximated by polynomials. To achieve such an aim, we first present Hermite-type exponentially fitted interpolation formulas I_N built on the foundation using N unequally spaced nodes. Then the coefficients of I_N are determined by solving a linear system, and some of the properties of these coefficients are obtained. When N is 2 or 3, some results are obtained with respect to the determinant of the coefficient matrix of the linear system which is associated with I_N. For N = 3, the errors for I_N are approached theoretically and they are compared numerically with the errors for other interpolation formulas.

• Journal of Korean Medical classics
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• v.36 no.2
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• pp.23-34
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• 2023

Objectives : We propose a method to disassemble Traditional East Asian Medicine herbal formulas using machine learning. Methods : After creating a model using Byte Pair Encoding(BPE) and G-Score, the model was trained with training data. Afterwards, the learned model was applied to the test data, of which the results were compared with expert opinion. Results : The results acquired through the model were not significantly different from those of modern expert opinions. However, there were cases where the meaning was partially unclear, while there were cases where new knowledge could be obtained through the disassembling process. Conclusions : It is expected that disassembling herbal formulas through the proposed method in this study will help save resources required to understand complex ones.

• Journal of Electrical Engineering and information Science
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• v.1 no.1
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• pp.160-163
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• 1996

New formulas for McClellan transform parameters for the design of 2-D zero-phase FIR fan filters are optimally derived under the integral squared error(ISE) criterion. By imposing the constraint that F(0, 0)=\ulcorner, where F($.$) is the McClellan transform and $\omega$\ulcorner is the cutoff frequency of the 1-D prototype filter, the ISE is directly minimized without modifying it and, as a consequence, closed-form formulas for the McClellan transform parameters are obtained. It is shown that these formulas lead to a very efficient design for 2-D zero-phase FIR fan filters.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.3 no.1
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• pp.127-135
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• 1999

An inequality of Ostrowski's type for monotonous nondecreasing mappings is given. Applications for quadrature formulas are pointed out.

• Honam Mathematical Journal
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• v.35 no.1
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• pp.17-27
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• 2013

We survey and study several volume formulas of a Euclidean tetrahedron.

• Communications of the Korean Mathematical Society
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• v.31 no.3
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• pp.567-573
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• 2016

We obtain solution formulas for some nonlocal heat equations. As a simple application, we prove finite time blow-up of the solution.

• The Korea Journal of Herbology
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• v.27 no.1
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• pp.17-25
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• 2012

Objectives : The objectives of this study lie in theoretical establishment of formulas for purging five viscera for curing the sthenic syndrome of five viscera through analyzing the component medicines and combination principles of Hyeongok's formulas for purging five viscera, and furthermore, maximizing the clinical use of them. Methods : This study analyzed the component medicines and combination principles of Hyeongok's formulas for purging five viscera based on the theory for properties and tastes of herbal medicines from the "Yellow Emperor's Canon of Internal Medicine", the theory for principal herbal medicine, assistant herbal medicine, adjuvant herbal medicine, dispatcher herbal medicine, and the five elements doctrine. Hyeongok's formulas for purging five viscera are Sagantang, Saseemtang, Sabeetang, Sapyeotang, and Pyeongshintang. Results : There are three methods for curing the sthenic syndrome of five viscera according to the five elements doctrine : in case of Sagantang purging the liver, purging the heart and invigorating the lung ; Saseemtang, purging the heart, purging the spleen and invigorating the kidney ; Sabeetang, purging the spleen, purging the lung and invigorating the liver ; Sapyeotang, purging the lung, purging the kidney and invigorating the heart ; Pyeongshintang, purging the kidney, purging the spleen and invigorating the spleen. Conclusions : First, to cure the sthenic syndrome of five viscera, the methods of purging five viscera, and invigorating five viscera should be used according to the five elements doctrine. Secondly, herbal medicines appropriate for those treatment methods should be chosen according to the theory for properties and tastes of herbal medicine and thirdly, the combination of those herbal medicines should be carried out according to the theory for principal herbal medicine, assistant herbal medicine, adjuvant herbal medicine, dispatcher herbal medicine. As a good example, Hyeongok's formulas for purging five viscera are combined according to the above theories. In conclusion, this formula was created by applying to the theory for properties and tastes of herbal medicines.

• Journal of Sasang Constitutional Medicine
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• v.24 no.4
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• pp.40-50
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• 2012

Objectives : This study was performed to find out the correlation between the use of herbal extracts and the Sasang constitution of patients in Japan. Methods : We recruited 315 subjects who had been visiting the Center for Kampo Medicine for the treatment, Keio University in Tokyo, Japan. They answered SSCQ-P(Sasang Constitution Questionaire for Patients) questionnaire, a sasang constitution specialist interviewed them and diagnosed the sasang constitution. And the 80 herbal extracts subject's having taken were classified into four type Sasang constitutional herbal formulas according to "Donguisusebowon", the ingredients in a formula that have different role(sovereign, minister, assistant and courie) and effect and indication of formula. Results : 1. Among the total 315 subjects, the number of Taeyangin, Soyangin, Taeeumin, and Soeumin was 3(1.0%), 85(27.0%), 90(28.6%), and 137(43.5%). 2. Among the 80 herbal extracts subject's having taken, the number of each Soyangin, Taeeumin, and Soeumin herbal formulas was 30, 7 and 43. 3. 1 Soyangin and 2 Soeumin herbal formulas were prescribed in 3 Taeyangin subjects group. 29 Soyangin, 4 Taeeumin, 52 Soeumin herbal formulas were prescribed in 85 Soyangin subjects group. 39 Soyangin, 6 Taeeumin, 45 Soeumin herbal formulas were prescribed in 90 Taeeumin subjects group. 51 Soyangin, 6 Taeeumin, 80 Soeumin herbal formulas were prescribed in 137 Soeumin subjects group. Conclusions : The Soeumin rate in Japan was significantly higher than that in Korea. There was no significant correlation between the use of herbal extracts and the Sasang constitution in Japan.

• Journal of Physiology & Pathology in Korean Medicine
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• v.27 no.5
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• pp.637-643
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• 2013

Daesiho-tang (DST), Yijin-tang (YJT), Gyeoneumjisil-hwan (GJH), Ukdam-hwan (UDH), and Sojojung-tang (SJT) have been used to treat hypertension. The aim of this study was to investigate whether five formulas were effective for improving obesity in high fat diet (HFD) induced obese mice. The mice were divided into seven groups: (1) a normal diet (ND), (2) a high fat diet (HFD) (3) a HFD plus DST (HFD + DST), (4) a HFD plus YJT (HFD + YJT), (5) a HFD plus GJH (HFD + GJH), (6) a HFD plus UDH (HFD + UDH), or (7) HFD plus SJT (HFD + SJT) at 150 mg/kg/day for 7 weeks. All five formulas treatments significantly lowered blood pressure, final liver weights, and serum total triglyceride levels. The four formulas (HFD+DST, HFD+YJT, HFD+UDH, and HFD+SJT) decreased body weights. Also, HFD+DST, HFD+YJT, and HFD+UDH groups reduced abdominal and epididymal fat weights. The serum LDL-cholesterol levels were decreased in HFD+YJT, HFD+UDH, and HFD+SJT groups compared to the HFD group. These results demonstrate that five formulas ameliorated obesity.

• School Mathematics
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• v.9 no.1
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• pp.141-160
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• 2007

The purpose of this paper was to evaluate how students apply prior knowledge or experience in solving algebra word problems from the chain of signification-based perspective. Three middle school students were evaluated in this case study. The results showed that the subjects formed similarities in the process of applying knowledge needed for solving a problem. The student A and C used semi-open-end formulas and closed formulas as solutions. They then formed concrete shape for each solution using the chain of signification that was applied for solution by forming procedural similarity. At this time, the chain of signification could be the combination of numbers, words, and pictures (such as diagrams or graphs) or just numbers or words. On the other hand, the student C who recognized closed formulas and her own rule as a solution method could not formulate completely procedural similarity due to many errors arising from number information. Nonetheless, all of the subjects showed something in common in the process of coming up with a algorithm that was semi-open-end formula or closed formula.