• 한국멀티미디어학회논문지
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• 제22권9호
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• pp.1029-1035
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• 2019

In this paper, a tentative Kth order Goldschmidt floating point number Nth root algorithm for K order convergence rate in one iteration is proposed by applying Taylor series to the Goldschmidt square root algorithm. Using the proposed algorithm, Nth root and Nth inverse root can be computed from iterative multiplications without division. It also predicts the error of the algorithm iteration. It iterates until the predicted error becomes smaller than the specified value. Since the proposed algorithm only performs the multiplications until the error gets smaller than a given value, it can be used to improve the performance of a floating point number Nth root unit.

• 대한임베디드공학회논문지
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• 제13권1호
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• pp.45-51
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• 2018

In this paper, a tentative Kth order Newton-Raphson's floating point number Nth root algorithm for K order convergence rate in one iteration is proposed by applying Taylor series to the Newton-Raphson root algorithm. Using the proposed algorithm, $F^{-1/N}$ and $F^{-(N-1)/N}$ can be computed from iterative multiplications without division. It also predicts the error of the algorithm iteration and iterates only until the predicted error becomes smaller than the specified value. Since the proposed algorithm only performs the multiplications until the error gets smaller than a given value, it can be used to improve the performance of a floating point number Nth root unit.

• Restorative Dentistry and Endodontics
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• 제20권2호
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• pp.768-779
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• 1995

This study was performed to investigate the effect of root canal shaping techniques on the change of the shape of prepared root canal. 40 mesiobuccal canals of recently extracted mandibular 1st and 2nd molars were divided into 4 groups and shaped by step-down/balanced force technique, step-down/step-back technique, step-back technique and conventional technique respectively. The change of the shape of root canal was traced by superimposing the radiographs obtained before and after shaping of each root canal. The results were as follows. 1. By the experimented techniques except conventional technique, the root canals were more shaped in convex side of apical area and in concave side of most curved and coronal area than in the other sides(P<0.05). By conventional technique, the root canals were more shaped in convex side than in convave side from apex to orifice(P<0.05). 2. By step-down/balanced force technique, the cancave sides at C and D points of proximal view and C point of clinical view were more shaped than the convex side(P<0.05). Through the entire canal, the concave side was more shaped than the convex side in proximal view(P<0.01). But there was no statistical difference between both sides in clinical view. 3. By step-down/step-back technique, the change of root canal shape was not statistically different in concave and convex sides at each point of both views(P>0.05). And through the entire canal in proximal view, there was no statistical difference in shaping percentage between both sides. But through the entire canal in clinical view, the concave side was more shaped than the convex side(P<0.1). 4. By step-back technique, the convex side at B point of clinical more shaped than the other sides(P<0.05). Through the entire canal in proximal and clinical views, there was no statistical difference in shaping percentage between both sides. 5. Comparing the total shaping percentage among techniques, that in conventional technique was the greatest numerically, and followed by the percentages in step-down/step-back, step-down/balanced force and step-back technique. But, in proximal view, shaping percentages were not statistically different among techniques(P>0.05, ANOVA test). In clinical view, shaping percentages in step-back and conventional techniques were statistically different(P<0.01, ANOVA test). * Proximal view: radiograph taken in mesiodistal direction. * Clincal view: radiograph taken in faciolingual direction. A point : 1mm point from radiographic apex B point : center point between A and C points C point : most curved point of root canal D point : center point between C point and canal oriffice.

• 대한기계학회논문집
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• 제18권5호
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• pp.1126-1133
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• 1994

When designing an internal gear. the bending strength around pitch point as well as that at tooth root fillet should be considered because the bending stress around pitch point may occur as high as that at tooth root fillet. In this study, including stress state around pitch point, the bending strength (tensile side and compressive side) of internal gear tooth is investigated by the use of the finite element method(FEM) with regarding many influencing factors of cutter and gear geometries. Then, the critical sections around pitch point and at tooth root fillet are determined, and the simple formulae based on nominal stresses(bending, compressive, and shear) are derived for the calculations of actual stresses as the functions of tooth thicknesses and radii of curvatures of involute and fillet curve at those critical sections. The stresses calculated by the formulae agree well with those by the FEM. And the bending stresses around pitch point and at tooth root are easily estimated by the use of those formulae, therefore, those formulae are useful for the purpose of the design or the bending strength estimation of internal gear.

• 한국정보통신학회논문지
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• 제4권1호
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• pp.105-113
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• 2000

디지털 통신시스템에 사용되는 파형 성형 필터를 고정소수점으로 설계하는 방법에 대하여 제시한다. 기존에는 설계가 간단한 RCF(Raised Cosine Filter) 또는 Root Squared RCF를 많이 사용했으나 대역제한 특성이 나쁘고 부동소수점 계수로 설계되는 단점이 있다. 본 논문에서는 혼합 선형계획법을 이용하여 고정소수점 파형 성형 필터를 설계하는 방법을 제시하구 정합 필터로 사용하기 위한 Root Squared 형태에 대해서도 소개한다. 몇 개의 설계 예제를 통하여 제안된 설계 방식이 기존의 RCF나 Root Squared RCF와 비교하여 동일한 성능에서 20%이상 간단히 설계가 가능함을 보이고 있다. 특히 급격한 대역제한이 요구되는 IS-95와 같은 무선 통신시스템에서 표준 필터보다 ISI가 75%이상 개선된 결과를 제시하고 있다.

• International Journal of Computer Science & Network Security
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• 제23권6호
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• pp.84-90
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• 2023

In this article the problem of computing floating-point reciprocal cube root functions is considered. Our new algorithms for this task decrease the number of arithmetic operations used for computing $1/{\sqrt[3]{x}}$. A new approach for selection of magic constants is presented in order to minimize the computation time for reciprocal cube roots of arguments with movable decimal point. The underlying theory enables partitioning of the base argument range x∈[1,8) into 3 segments, what in turn increases accuracy of initial function approximation and decreases the number of iterations to one. Three best algorithms were implemented and carefully tested on 32-bit microcontroller with ARM core. Their custom C implementations were favourable compared with the algorithm based on cbrtf(x) function taken from C ＜math.h＞ library on three different hardware platforms. As a result, the new fast approximation algorithm for the function $1/{\sqrt[3]{x}}$ was determined that outperforms all other algorithms in terms of computation time and cycle count.

• 한국정보통신학회논문지
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• 제13권8호
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• pp.1593-1600
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• 2009

부동소수점 제곱근 연산은 곱셈을 반복하여 근사값을 계산하는 뉴턴-랍손 알고리즘 및 골드스미트 알고리즘과 뺄셈을 반복하여 정확한 간을 계산하는 SRT 알고리즘이 있다. 본 논문에서는 곱셈기를 사용하여 정확한 값을 계산하는 제곱근 알고리즘을 제안한다. 본 논문에서는 뉴턴-랍손 알고리즘을 이용하여 근사 역제곱근을 구하고, 이의 오차를 줄이면서 제곱근을 구하는 알고리즘과 계산된 제곱근을 보정하는 알고리즘을 제안한다. 제안한 알고리즘은 단정도 실수에서는 전수 조사를 통해서, 배정도 실수에서는 10억 개의 무작위 수를 계산하여 모두 정확한 값을 얻었다. 본 논문에서 제안한 알고리즘은 곱셈기만을 사용하므로 별도의 하드웨어가 필요하지 않다. 따라서 실장제어용기기, 휴대용기기 등 정확한 제곱근 연산을 요구하는 분야에서 사용될 수 있다.

• 한국조경학회지
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• 제49권5호
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• pp.59-70
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• 2021

본 연구는 한국 조경수목의 근원직경 측정의 모호성으로 생산자와 시공자 간의 검측 기준이 달라서 발생되는 분쟁을 줄일 수 있는 합리적인 근원직경 측정 위치 설정 방안에 대하여 실증 조사·분석하였다. 조경수목의 근원직경 측정 부위별 차이는 지하부 -6cm에서 표토부인 0cm까지는 3.59cm이었고, 지상부의 표토 0cm에서부터 6cm까지는 1.35cm로 근원직경의 측정위치별 차이는 지상부보다는 지하부에서 더 크게 나타났다. 조경수목 근원직경의 표준편차의 크기는 지하부 -6cm에서 표토부인 0cm까지는 0.64이었고, 지상부의 표토 0cm에서부터 6cm까지의 표준편차 차이는 0.16으로 근원직경의 측정위치별 차이는 지상부보다는 지하부에서 더 크게 나타났다. 조경수목 근원직경의 합리적 측정 위치 설정은 근원직경 측정 위치별 규격의 크기 변화 추세선에서 수간직경의 표준편차가 가장 적어지는 변곡점으로 설정하는 것이 제안되었다. 수종별 합리적인 측정 위치는 산딸나무 지상 18cm, 이팝나무 지상 12cm·느티나무 지상 12cm·팽나무 지상 12cm, 때죽나무 지상 10cm·산수유 지상 10cm, 단풍나무 지상 6cm·먼나무 지상 6cm, 가시나무 지상 4cm, 배롱나무 지상 2cm 이상으로 나타났다. 조경수목 근원직경 측정 부위별 차이가 공시수종 전체에서 표준편차가 작고, 편차의 기울기가 안정적인 합리적인 평균 측정위치는 지상부 평균 12cm 이상으로 나타났다. 조경수목 근원직경의 합리적인 측정위치 설정은 지상부 평균 12cm 이상에서부터라고 할 수 있으나 전통적인 관행상으로 익숙한 1자(尺) 30cm 인식이 빠르며, 측정자의 측정 위치의 편리성, 외국의 조경수목 측정기준에 대한 통일성 등 조경수목 근원직경의 합리적인 측정위치는 지표면 30cm 높이에서 측정하는 것이 좋을 것으로 추천되었다.

• Restorative Dentistry and Endodontics
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• 제18권1호
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• pp.133-143
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• 1993

The aim of this study was to establish reproducible method for measurements of radiopacity and to investigate the level of radiopacity of root canal sealers. The experiments were performed in two parts. In the first part, densitometric readings were performed using an aluminum step wedge as a reference at variable voltages and exposure times. Then standard curves for the aluminum step wedge were compared to comprehend the effect of voltage and exposure time. In the second part, on the basis of these results, appropriate conditions for exposure were adopted for standardized measurements of radiopacity. Under standardized set of conditions, densitometric measurements of ten root canal sealers and one gutta-percha point were performed and the levels of radiopacity referable to an equivalent thickness of aluminum were compared. The following results were obtained : 1. At 50 and 60 kVp, increasing the exposure time caused a decrease in the slope of the standard curve for the aluminum step wedge. However, at 70 kVp increasing the exposure time causing a parallel shift of the standard curve to the right. 2. At constant exposure time, increasing the voltage caused a decrease in the slope of the standard curve. 3. The radiopacity of root canal sealers and a gutta-percha point varied between 2.43 mm Al and 9.20 mm Al equivalent. 4. All the root canal sealers had radiopacities more than dentin, and the radiopacity of the gutta-percha point was approximately 5 times as much as that of dentin in terms of equivalent thickness of aluminum. 5. The AH26 had radiopacity more than the gutta-percha point, and the radiopacities of ZOE, Vitapex, Canals, Kerr PCS, Nogenol were similar to that of the gutta-percha point, and Tubliseal, Apatite II, Apatite III, Silapex were less radiopaque than the gutta-percha point.

• 대한수학회지
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• 제57권5호
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• pp.1119-1133
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• 2020

In this paper, we derive an upper bound for the distance from a point in the immediate basin of a root of a complex polynomial to the root itself. We establish that if z is a point in the immediate basin of a root α of a polynomial p of degree d ≥ 12, then ${\mid}z-{\alpha}{\mid}{\leq}{\frac{3}{\sqrt{d}}\(6{\sqrt{310}}/35\)^d{\mid}N_p(z)-z{\mid}$, where N_p is the Newton map induced by p. This bound leads to a new bound of the expected total number of iterations of Newton's method required to reach all roots of every polynomial p within a given precision, where p is normalized so that its roots are in the unit disk.