• Journal of Korea Multimedia Society
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• v.22 no.9
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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.

• IEMEK Journal of Embedded Systems and Applications
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• v.13 no.1
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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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• v.20 no.2
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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.

• Transactions of the Korean Society of Mechanical Engineers
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• v.18 no.5
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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.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.4 no.1
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• pp.105-113
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• 2000

This paper proposes the optimal design method of PSF(pulse shaping filter) with fixed-point coefficients, often used in digital communication system. Though RCF (Raised Cosine Filter) and Root-Squared RCF have less attenuation in stopband and are designed with floating point coefficients, those are selected by the reason that the design is simple. In this paper, 1 introduce the optimal design method for fixed point PSF including Root Squared type by using mixed integer linear programming. Through some design examples, it is shown that the proposed method better performs in ISI and requires less complexity. The complexity of the proposed filter is reduced to 20% as compared to conventional RCF and Root Squared RCF. For IS-95, that is the standard of CDMA system, the proposed filter reduces ISI up to 75% compared to the standard transmission filter.

• International Journal of Computer Science & Network Security
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• v.23 no.6
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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.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.13 no.8
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• pp.1593-1600
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• 2009

There are two major algorithms to find a square root of floating point number, one is the Newton_Raphson algorithm and GoldSchmidt algorithm which calculate it approximately by iterating multiplications and the other is SRT algorithm which calculates it exactly by iterating subtractions. This paper proposes an exact floating point square root algorithm using only multiplication. At first an approximate inverse square root is calculated by Newton_Raphson algorithm, and then an exact square root algorithm by reducing an error in it and a compensation algorithm of it are proposed. The proposed algorithm is verified to calculate all of numbers in a single precision floating point number and 1 billion random numbers in a double precision floating point number. The proposed algorithm requires only the multipliers without another hardware, so it can be widely used in an embedded system and mobile production which requires an efact square root of floating point number.

• Journal of the Korean Institute of Landscape Architecture
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• v.49 no.5
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• pp.59-70
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• 2021

This study was to investigate the measurement point of root collar diameter of landscape trees in Korea. It may contribute to avoiding disputes caused by the difference in measurement criteria of root collar diameter of landscape trees between tree growers and constructors. The difference between landscape trees' root collar diameter measurement point was 3.59cm from 6cm underground to the surface and 1.35cm from 0cm to 6cm above ground. The source root collar diameter measurement point difference was larger in the basement than in the ground. The standard deviation of the root collar diameter of the landscape tree was 0.64 from 6cm underground to the surface, and the difference in standard deviation from 0cm to 6cm above ground was 0.16. The difference by measurement point of the root collar diameter was larger in the basement than in the ground. It has been proposed to set the reasonable measurement point of the landscaping tree root collar diameter at the inflection point where the standard deviation of the tree trunk diameter is the smallest in line with the size change of the standard for each root collar diameter measurement point. By tree species, Cornus officinalis Siebold & Zucc. 18cm above the ground, Chionanthus retusus Lindl. & Paxton. 12cm above the ground, Zelkova serrata (Thunb.) Makino. 12cm above the ground, Celtis sinensis Pers. 12cm above the ground, Styrax japonicus Siebold & Zucc. 10 cm above the ground, Cornus officinalis Siebold & Zucc. 10cm above the ground, Acer palmatum Thunb. ex Murray. 6cm above the ground, Ilex rotunda Thunb. 6cm above the ground, Quercus myrsmaefolia Blume. 4cm above the ground, Lagerstroemia indica L. 2cm above the ground The above heights were shown as reasonable measurement points. The difference by landscape tree root collar diameter measurement site showed that the standard deviation was small throughout the tree species, and the reasonable average measurement point with a stable slope of the deviation was 12cm or more on average. It can be said that the reasonable measurement point of the root collar diameter of a landscape tree is set at an average of 12cm above the ground. However, recognizing 30cm, which is a familiar ruler(尺) in traditional practices, is quick, It was recommended to measure at the height of 30cm from the surface for a reasonable measurement point of the root collar diameter of a landscape tree, for the uniformity of measurement standards.

• Restorative Dentistry and Endodontics
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• v.18 no.1
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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.

• Journal of the Korean Mathematical Society
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• v.57 no.5
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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.