• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.6 no.4
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• pp.325-336
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• 1994

A numerical simulation of velocity and temperature fields and Nusselt number distributions is performed by using the algebraic stress model (ASM) for the velocity profiles and low Reynolds number ${\kappa}-{\varepsilon}$ model and the algebraic heat flux model(AHFM) for turbulent heat transfer in a $180^{\circ}$ bend with a constant wall heat flux. In the low Reynolds number ${\kappa}-{\varepsilon}$ model, turbulent Prandtl number is modified by considering the streamline curvature effect and the non-equilibrium effect between turbulent kinetic energy production and dissipation rate. Every heat flux term presented in the transport equation of turbulent heat flux is reduced to algebraic expressions in a way similar to algebraic stress model. Also. in the wall region, low Reynods number algebraic heat flux model(AHFM) is applied.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.27 no.12
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• pp.1724-1733
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• 2003

This paper assesses the prediction performance of explicit algebraic stress and heat-flux models for reduction of heat transfer coefficient in a strongly-heated vertical tube. Two explicit algebraic stress models and four explicit algebraic heat-flux models are selected for assessment. Eight combinations of explicit algebraic stress and heat-flux models are used in predicting the turbulent gas flows with intense heating, which yields the significant property-variation. The results showed that the two combinations of GS-AKN and WJ-mAKN predicted the Nusselt number and the axial wall temperature variations well and that the predictions of Nusselt number with WJ-combinations spread in a wider range than those with Gs-combinations. WJ is the explicit algebraic stress model of Wallin and Johansson and GS is the model of Gatski and Speziale and that AKN is the explicit heat-flux model of Abe, Kondoh and Nagano and mAKN is the modified AKN.

• Transactions of the Korean Society of Mechanical Engineers
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• v.17 no.6
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• pp.1596-1608
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• 1993

Low Reynolds number second moment turbulence model which be applicable to the fine gird near the wall region was developed. In this model, turbulence model coefficients in the pressure strain model of the Reynolds stress equation was expressed as functions of turbulence Reynolds number $R_{t}\equivk^{2}/(\nu\varepsilon)).$ In the derivation procedure of the present low Reynolds number algebraic stress model, Laufer's near wall experimental data on Reynolds stresses were curve fitted as functions of R$_{t}$ and the resulting simultaneous equations of the model coefficients were solved by using the boundary conditions at wall and high Reynolds number limiting conditions. Predicted Reynolds stresses and dissipation rate of turbulent kinetic energy etc. in the 2 dimensional parallel, plane channel flow and pipe flow were compared with the preditions obtained by employing the Launder-Shima model, standard algebraic stress model and several experimental data. Results show that all the Reynolds stresses and dissipation rate of turbulent kinetic energy predicted by the present low Reynolds number algebraic stress model agree better with the experimental data than those predicted by other algebraic stress models.

• East Asian mathematical journal
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• v.29 no.4
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• pp.355-392
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• 2013

Generally school algebra is to start with introducing variables and algebraic expressions, which have major cognitive obstacles to students in the transfer from arithmetic to algebra. But the recent studies in the teaching school algebra argue the algebraic thinking from an early algebraic point of view. We compare the Korean elementary mathematics textbooks with Americans from this perspective. First, we discuss the history of school algebra in the school curriculum. And Second, we investigate the recent studies in relation to early algebra. We clarify the goals of this study(the importance of early algebra in the elementary school) through these discussions. Next we examine closely the number sense in the arithmetic and the symbol sense in the algebra. And we conclude that the operation sense can connect these senses within early algebra using the algebraic thinking. Finally, we compare the elementary mathematics books between Korean and American according to the components of the operation sense. In this comparative study, we identify a possibility of teaching algebraic thinking in the elementary mathematics and early algebra can be introduced to the elementary mathematics textbooks from aspects of the operation sense.

• Communications of the Korean Mathematical Society
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• v.22 no.3
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• pp.331-351
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• 2007

Let k be an imaginary quadratic field, h the complex upper half plane, and let $\tau{\in}h{\cap}k$, $q=e^{{\pi}i\tau}$. We find a lot of algebraic properties derived from theta functions, and by using this we explore some new algebraic numbers from Rogers-Ramanujan continued fractions.

• Communications of Mathematical Education
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• v.25 no.2
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• pp.473-495
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• 2011

Across the secondary school, students deal with the algebraic conditions like as identity, inverse, commutative law, associative law and distributive law. The algebraic structures, group, ring and field, are determined by these algebraic conditions. But the conditioning of these algebraic structures are not mentioned at all, as well as the meaning of the algebraic structures. Thus, students is likely to be considered the algebraic conditions as productions from the number sets. In this study, we systematize didactically the meanings of algebraic conditions and algebraic structures, considering connections between the number systems and the solutions of the equation. Didactically systematizing is to construct the model for student's natural mental activity, that is, to construct the stream of experience through which students are considered mathematical concepts as productions from necessities and high probability. For this purpose, we develop the program for the gifted, which its objective is to teach the meanings of the number system and to grasp the algebraic structure conceptually that is guaranteed to solve equations. And we verify the effectiveness of this developed program using didactical experiment. Moreover, the program can be used in ordinary students by replacement the term 'algebraic structure' with the term such as identity, inverse, commutative law, associative law and distributive law, to teach their meaning.

• Proceedings of the IEEK Conference
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• 2005.11a
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• pp.849-852
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• 2005

A factorization is an extremely important part of multi-level logic synthesis. The number of literals in a factored from is a good estimate of the complexity of a logic function, and can be translated directly into the number of transistors required for implementation. Factored forms are described as either algebraic or Boolean, according to the trade-off between run-time and optimization. A Boolean factored form contains fewer number of literals than an algebraic factored form. In this paper, we present a new method for a Boolean factorization. The key idea is to identify two-cube Boolean subexpression pairs from given expression. Experimental results on various benchmark circuits show the improvements in literal counts over the algebraic factorization based on Brayton's co-kernel cube matrix.

• Journal of the Korean Society of Industry Convergence
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• v.3 no.1
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• pp.17-27
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• 2000

A factorization is an extremely important part of multi-level logic synthesis. The number of literals in a factored form is a good estimate of the complexity of a logic function. and can be translated directly into the number of transistors required for implementation. Factored forms are described as either algebraic or Boolean, according to the trade-off between run-time and optimization. A Boolean factored form contains fewer number of literals than an algebraic factored form. In this paper, we present a new method for a Boolean factorization. The key idea is to build an extended co-kernel cube matrix using co-kernel/kernel pairs and kernel/kernel pairs together. The extended co-kernel cube matrix makes it possible to yield a Boolean factored form. We also propose a heuristic method for covering of the extended co-kernel cube matrix. Experimental results on various benchmark circuits show the improvements in literal counts over the algebraic factorization based on Brayton's co-kernel cube matrix.

• Journal of the Korea Computer Industry Society
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• v.7 no.4
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• pp.293-298
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• 2006

A factorization is an extremely important part of multi-level logic synthesis. The number of literals in a factored form is a good estimate of the complexity of a logic function, and can be translated directly into the number of transistors required for implementation. Factored forms are described as either algebraic or Boolean, according to the trade-off between run-time and optimization. A Boolean factored form contains fewer number of literals than an algebraic factored form. In this paper, we present a new method for a Boolean factorization. The key idea is to identify two-cube Boolean subexpression pairs from given expression. Experimental results on various benchmark circuits show the improvements in literal counts over the algebraic factorization based on Bryton's co-kernel cube matrix.

• Journal of the Korean Society of Radiology
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• v.17 no.1
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• pp.141-148
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• 2023

The algebraic reconstruction technique is one of the reconstruction methods in CT and shows good image quality against noise-dominant conditions. The number of iteration is one of the key factors determining the execution time for the algebraic reconstruction technique. However, there are some rules for determining the number of iterations that result in more than a few hundred iterations. Thus, the rules are difficult to apply in practice. In this study, we proposed a method to determine the number of iterations for practical applications. The reconstructed image quality shows slow convergence as the number of iterations increases. Image quality 𝜖 < 0.001 was used to determine the optimal number of iteration. The Shepp-Logan head phantom was used to obtain noise-free projection and projections with noise for 360, 720, and 1440 views were obtained using Geant4 Monte Carlo simulation that has the same geometry dimension as a clinic CT system. Images reconstructed by around 10 iterations within the stop condition showed good quality. The method for determining the iteration number is an efficient way of replacing the best image-quality-based method, which brings over a few hundred iterations.