• East Asian mathematical journal
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• v.33 no.2
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• pp.177-197
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• 2017

The purpose of this study is to investigate and analyze the understandings of elementary pre-service teachers about 'estimation' in the elementary mathematics. Together with this analysis, we identify elementary pre-service teacher's Mathematical Pedagogical Contents Knowledge(MPCK), especially focusing to Subject Matter Knowledge(SMK). In order to this goals, we investigate contents relating to 'estimation' from $1^{st}$ curriculum to 2009 revised curriculum and compare 'rounding up', 'rounding off', 'rounding' in the elementary mathematics textbooks. As results of investigations, 'estimation' has been teaching at the 'Measurement' domain from $3^{rd}$ curriculum, but contexts of measuring weaken from $7^{th}$ curriculum. 'Rounding up(off)' is defined three types in the textbooks from $1^{st}$ to 2009 revised curriculum. And we examine elementary pre-service teachers through the questions on these 'estimation' contents. On the analysis of pre-service teacher's understanding relating MPCK, four themes is summarized as followings; the understanding of '0' in the 'rounding up', the cognitive gap between 'rounding up' and 'rounding off', the difference of percentage of correct answers according to types of question in the 'rounding up', and the difference between the definition of 'rounding up' and the definition of 'rounding'.

• Journal of the Korean Institute of Telematics and Electronics B
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• v.32B no.3
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• pp.24-30
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• 1995

The process of conventional floating-point additio $n_traction operation consists of alignment, additio $n_traction, normalization, and rounding stage. Because rounding stage needs an incrementor or adder, it occupies much time and chip area. In addition, it needs additional time and hardware for renormalization which occurs in overflow due to rounding In this paper, floating-point adde $r_tractor performing rounding and additio $n_traction in parallel is presented by using the feature of additio $n_traction and carry select adder used in additio $n_tracting stage. Proposed floating point adde $r_tractor doesn't need time and incrementor nor adder for rounding. Also, renormalization doesn't occur since rounding is performed prior to normalization.to normalization.

• Proceedings of the IEEK Conference
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• 1998.10a
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• pp.1017-1020
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• 1998

We propose an algorithm which processes the floating-point $n_{addition}$traction and rounding in parallel. It also processes multiplication and rounding in the same way. The hardware model is presented that minimizes the delay time to get results for all the rounding modes defined in the IEEE Standards. An unified method to get the three bits(L, G, S)for the rounding is described. We also propose an unified guide line to determine the 1-bit shift for the post-normalization in the Floating-point $n_{addition}$traction and multiplication.

• Korean Journal of Computational Design and Engineering
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• v.6 no.2
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• pp.111-124
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• 2001

In this paper, we propose rounding operations on shell meshes, which give a constant or variable radius of rounding directly to sharp edges on a shell mesh. The rolling-ball methods for freeform surface rounding are introduced to devise the algorithms for these operations. Our algorithms consists of three steps as follows: detecting sharp edges, generating a rolling-ball surface contacting with two face groups adjacent to the sharp edges, and then replacing the rounding area of the original mesh with the mesh generated on the rolling-ball surface. In addition, this paper shows their application to the area of stamping die design. These operations enable CAE engineers to directly change the meshes of stamping tools without modification of CAD models for dies and regeneration of their meshes.

• The Journal of Korean Academy of Prosthodontics
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• v.33 no.2
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• pp.198-209
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• 1995

In order to evaluate the fitness and the degree of rounding of porcelain margins in collarless metal cermic restorations, collarless metal ceramic restorations were fabricated with shoulder margins of 90 and 120 degress, each consisting of ten specimens, on master dies through the direct lift technique. And ten metal ceramic restorations with a shoulder 90 degrees were fabricated. All specimens were embedded in resin and sectioned longitudinally. The sections were observed under a stereomicroscope and photographed(${\times}$200). The labial marginal gap between the die and the porcelain margin were measured with a scale. The space between the porcelain margin and the die, that is formed from marginal rounding and cementation were calculated with a computer coordinating area curvimeter. The following results were obtained. 1. There was no statistical difference between the fitness of porcelain margin of collarless metal ceramic restorations and marginal fitness of metal ceramic restoration. 2. There was no statistical difference between a shoulder of 90 and 120 degrees in the fitness of porcelain margin of collarless metal ceramic resorations. 3. Collarless metal ceramic restorations with a shoulder of 90 degrees and 120 degrees showed significantly more labial marginal rounding than metal ceramic restorations. 4. There was no statistical difference between a shoulder of 90 and 120 degrees in rounding of porcelain margin of collarless metal ceramic restorations. According to the results, rounding of porcelain margins can be observed in collarless metal ceramic restorations. Thus, there is a need for improvement in dental materials and techniques to minimize this problem, Furthermore, care should be exercised during the clinical procedure.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2000.11a
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• pp.624-627
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• 2000

This paper describes a local modification capability on shell meshes, which can change a 'constant or variable radius of rounding for the s h q edges of the stamping die shoulder in the mesh. The algorithm consists of the followin_e three main steps; (1) the rounding area for sharp edges of a die shoulder are detected from the given shell mesh, (2) a rolling-ball surface with a given constant or variable radius is generated, which is contacti% with two incident face groups of the sharp edges, (3) the rounding area of the mesh is cut off, and a new mesh for the rolling-ball surface is generated and implanted into the gap. Owing to this rounding modification capability, CAE engineers can examine various cases based on the existing dies by scanning them to form polyhedral models and then changing radii of die shoulders for stamping process simulation.

• Proceedings of the KSME Conference
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• 2001.11a
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• pp.389-395
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• 2001

To restrain contact failure, present study investigates the influence of edge machining of an indenter (punch). As for the edge machining, rounding, chamfering, and chamfering and rounding are considered. Contact mechanics is consulted to examine the traction profile and the size of the contact region which are directly influenced by the end profile of the indenter. The effect of rounding size (i.e., radius) in the case of the chamfering and rounding edge-indenter is studied. Shear traction is also evaluated within the regime of partial slip. Size of slip region and its expansion rate due to the increase of shear force are considered to investigate the shape effect of the indenter on contact failure.

• Proceedings of the IEEK Conference
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• 2000.07b
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• pp.657-660
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• 2000

This paper proposes a Data-Flow-Graph (DFG) restructuring to reduce calculating errors in loop folding scheduling. The prime cause of calculating error is rounding errors due to the restriction of the operation digit of functional units. This rounding error is increased more by using multipliers than adders, so reducing the number of multiplications and putting off them as much as possible reduce rounding errors. The proposed approach reduces the number of multiplications by restructuring DFG in loop folding.

• 한국정보통신설비학회:학술대회논문집
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• 2008.08a
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• pp.201-204
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• 2008

In this paper a new steganographic method is presented with minimum distortion. This paper focused on DCT rounding error and optimized that in a very easy way, resulting stego image has less distortion than other existing methods. The proposed method compared with F5 steganography algorithm, and the proposed method achieved better performance. This paper considered the DCT rounding error for lower distortion with possibly higher embedding capacity.

• ETRI Journal
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• v.26 no.6
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• pp.657-660
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• 2004

We propose a fine phase tuner and a rounding processor for a numerically controlled oscillator (NCO), yielding a reduced phase error in generating a digital sine waveform. By using the fine phase tuner presented in this paper, when the ratio of the desired sine wave frequency to the clock frequency is expressed as a fraction, an accurate adjustment in representing the fractional value can be achieved with simple hardware. In addition, the proposed rounding processor reduces the effects of phase truncation on the output spectrum. Logic simulation results of the NCO using these techniques show that the noise spectrum and mean square error (MSE) for eight output bits of a 3.125 MHz sine waveform are reduced by 8.68 dB and 5.5 dB, respectively, compared to those of the truncation method, and 2.38 dB and 0.83 dB, respectively, compared to those of Paul's scheme.