• Bulletin of the Korean Mathematical Society
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• v.56 no.4
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• pp.815-827
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• 2019

It is well known that the denominator of the Dedekind sum s(c, d) divides 2 gcd(d, 3)d and that no smaller denominator independent of c can be expected. In contrast, here we prove that we usually get a smaller denominator in S(H, d), the sum of the s(c, d)'s over all the c's in a subgroup H of order n > 1 in the multiplicative group $(\mathbb{Z}/d\mathbb{Z})^*$. First, we prove that for p > 3 a prime, the sum 2S(H, p) is a rational integer of the same parity as (p-1)/2. We give an application of this result to upper bounds on relative class numbers of imaginary abelian number fields of prime conductor. Finally, we give a general result on the denominator of S(H, d) for non necessarily prime d's. We show that its denominator is a divisor of some explicit divisor of 2d gcd(d, 3).

• Journal of Trauma and Injury
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• v.30 no.4
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• pp.126-130
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• 2017

Purpose: Preventable Trauma Death Rate (PTDR) using Trauma and Injury Severity Score (TRISS) has been most widely used as a quality indicator in South Korea. However, this method has a small number of deaths corresponding to the denominator. Therefore, it is difficult to check the change of quality improvement for annual mortality, and there is a disadvantage that variation is severe. Therefore, we attempted to improve the quality of the mortality evaluation by reducing the variation by applying the PARK Index (preventable major trauma death rate, PMTDR) which can increase the number of denominator significantly. And the Save score (S-score) was also examined as another quality indicator. Methods: In the PARK Index, the denominator is number of all patients who have survival probability (Ps) larger than 0.25. Numerator is the number of deaths among these. The PARK Index includes only patients with ISS >15. The S-score is calculated in the same way as the W-score, but the S-score includes only patients with ISS >15, which is a difference from the W-score. Results: PARK Index decreased annually and was 12.9 (37/287) in 2014, 9.6 (33/343) in 2015, and 7.3 (52/709) in 2016. S-score increased annually and was -0.29 in 2014, 4.21 in 2015, and 8.75 in 2016. Conclusions: PARK Index and S-score improved annually. This shows that both quality indicators are improving year by year. PARK Index (PMTDR) has 9.5-fold increase in denominator overall compared to PTDR by TRISS. The S-score used only ISS >15 patients as a denominator. Therefore, there is an advantage that the numerical value change is larger than the W-score. In addition, S-score is not affected by the ratio of major trauma patients to minor trauma patients.

• Journal of Trauma and Injury
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• v.28 no.3
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• pp.115-122
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• 2015

Purpose: To calculate Preventable Trauma Death Rate (PTDR), Trauma and Injury Severity Score (TRISS) is the most utilized evaluation index of the trauma centers in South Korea. However, this method may have greater variation due to the small number of the denominator in each trauma center. Therefore, we would like to develop new indicators that can be used easily on quality improvement activities by increasing the denominator. Methods: The medical records of 1005 major trauma (ISS >15) patients who visited 2 regional trauma center (A center and B center) in 2014 were analyzed retrospectively. PTDR and PARK Index (Preventable Major Trauma Death Rate, PMTDR) were calculated in 731 patients with inclusion criteria. We invented PARK Index to minimize the variation of preventability of trauma death. In PTDR the denominator is all number of deaths, and in PARK Index the denominator is number of all patients who have survival probability (Ps) larger than 0.25. Numerator is the number of deaths from patients who have Ps larger than 0.25. Results: The size of denominator was 40 in A center, 49 in B center, and overall 89 in PTDR. The size of denominator was significantly increased, and 287 (7.2-fold) in A center, 422 (8.6-fold) in B center, and overall 709 (8.0-fold) in PARK Index. PARK Index was 12.9% in A center, 8.3% in B center, and overall 10.2%. Conclusion: PARK Index is calculated as a rate of mortality from all major trauma patients who have Ps larger than 0.25. PARK Index obtain an effect that denominator is increased 8.0-fold than PTDR. Therefore PARK Index is able to compensate for greater disadvantage of PTDR. PARK Index is expected to be helpful in implementing evaluation of mortality outcome and to be a new index that can be applied to a trauma center quality improvement activity.

• Journal of the Korean Institute of Telematics and Electronics
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• v.27 no.12
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• pp.1940-1946
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• 1990

In this paper, we are proposed a 2-D zero-phase IIR second-order filter which have separable denominators. The filter combines the advantages of the separable denominator and the simplicity of the McClellan transform. Generally, the McClellan transformation is not suitable for IIR filter because the 1-D to 2-D substibution can not be achieved easily in most of denominators. So we have designed the second order denominator using a separable condition via a first order McClellan transformation. The implementation of a higher order filter can be achieved by cascading such second order parts with different coefficients in denominator. As a result, we have suppressed the ripples in stopband and obtained the narrow transition band.

• Journal of the Korean Institute of Telematics and Electronics
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• v.24 no.6
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• pp.948-955
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• 1987

The model reduction method of the high order linear time invariant systems is proposed. The continuous fraction expansion of Auxiliary denominator polynomial is used to obtain denominator polynomial of the reduced order model, and the numerator polynomial of the reduced order model is obtained by equating the first some moments of the original and the reduced order model, using simplified moment function. This methiod does not require the calculation of the reciprocal transformation which should be calculated in Routh approximation, furthemore the stability of the reduced order model is guaranted if original system is stable. Responses of this method showed us good characteristics.

• Journal of the Korean Institute of Telematics and Electronics
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• v.24 no.4
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• pp.583-589
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• 1987

A new approximation method is proposed for the linear model reduction of high order dynamic systems. This mehtod is based upon the denominator table(D-table) and time moment-matching technique. The denominator table(D-table) is used to obtain the denominator polynomial of reduced-order model, and the numerator polynomial is obtained by time moment-matching method. This proposed method does not require the calculation of the alpha-beta expansion and reciprocal transformation which should be calculadted by Routh approximation method. The advantages of the proposed method are that it is computationally every attractive better than Routh approximation method and the reduced model is stable Il the original system is stable.

• Journal of the Korean Statistical Society
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• v.24 no.1
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• pp.111-125
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• 1995

Let $F_1$ and $F_2$ be two F ratios with independent numerators and a common denominator. They are known to be positively dependent. The probabilities of simultaneous rejection and conditional rejection are numerically computed for both null and nonnull cases. The probabilities are presented in tables and graphics to show the influence of the seven parameters, the degrees of freedom of the numerators and the denominator, the non-centralities of the numerators, and the two levels of significance of the tests. The values of the correlation coefficient between $F_1$ and $F_2$ are also presented. Finally, a conjecture on the dependence order of the family of distributions of $(F_1, F_2)$ is given.

• International Journal of Control, Automation, and Systems
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• v.5 no.2
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• pp.208-211
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• 2007

In a recently proposed method of model reduction for discrete interval systems, the denominator polynomial of a reduced model is computed by applying interval arithmetic to dominant poles of the original system. However, the denominator polynomial obtained via interval arithmetic usually has poles with larger intervals than desired ones. Hence an unstable polynomial can be derived from the stable polynomial. In this paper a simple technique is presented to partially overcome such a stability problem by accurately preserving desired real dominant poles.

• Proceedings of the KSMRM Conference
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• 2003.10a
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• pp.72-72
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• 2003

In SENSE, division process is used in order to get a raw sensitivity map. This process requires denominator which is estimated by "sum-of-squres". However, this image does not have uniformbrightness because of the non-symmetrical property of RF coil arrays. Thus, this study is focused on better estimation of the denominator image.

• Proceedings of the IEEK Conference
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• 2000.07b
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• pp.633-636
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• 2000

The decoupling of the systems is to let the inputs and outputs correspond one to one, by performing the state feedback or the output feedback on the given systems. In this paper, we propose a method for decoupling the separable-denominator two-dimensional systems. And, we study about the realization dimension of the dynamical feedback and the dynamical feedforward performed for decoupling.