• Journal of the Korean Mathematical Society
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• v.57 no.4
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• pp.973-986
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• 2020

In this paper, we compute the Hankel matrix representation of the Hankel operator on the Hardy space of a general bounded domain with respect to special orthonormal bases for the Hardy space and its orthogonal complement. Moreover we obtain the compact form of the Hankel matrix for the unit disc case with respect to these bases. One can see that the Hankel matrix generated by this computation turns out to be a generalization of the case of the unit disc from the single simply connected domain to multiply connected domains with much diversities of bases.

• Korean Journal of Crystallography
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• v.11 no.2
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• pp.89-94
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• 2000

A crystallographic unit cell can be transformed into another one by a 3×3 transformantion matrix. If the determinant of the transformation matrix has a negative value, the newly transformed unit cell becomes a left-handed cell. The best way of transforming the left-handed cell to the right-handed one is to multiply each element of the transformation matrix by-1, and its corresponding transformation matrix must be applied tot he atomic coordinates of a noncentrosymmetric crystal so as to maintain the absolute configuration unchanged. The behaviour of absolute configuration caused by transforming the crystallographic unit cell was examined theoretically and experimentally on the compound (S)-(+)-4-phenyl-1-[4-aminobenzoyl) indoline-5-sulfonyl]-4,5-dihydro-2-imidazolone hydrochloride.

• IEMEK Journal of Embedded Systems and Applications
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• v.4 no.1
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• pp.1-8
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• 2009

This paper proposes a 24-bit floating point multiply and accumulate(MAC) unit that can be used in geometry transformation process in 3D graphics. The MAC unit is composed of floating point multiplier and floating point accumulator. When separate multiplier and accumulator are used, matrix calculation, used in the transformation process, can't use continuous accumulation values. In the proposed MAC unit the accumulator can get continuous input from the multiplier and the calculation time is reduced. The MAC unit uses about 4,300 gates and can be operated at 150 MHz frequency.

• Journal of Satellite, Information and Communications
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• v.10 no.2
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• pp.115-120
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• 2015

Until now, AOCS SW has used FPU which is one of CPU resources for satellite attitude control. And most of the SW Throughput was consumed to calculate Matrix Multiply. As SW throughput margin is decreasing seriously with shorter control period and more computational burden at next satellite programs, a dedicated HW matrix multiplier is absolutely required. This paper represents results of HW implementation & performance measurement and mentions several techniques for performance improvement, further works.

• Journal of the Institute of Electronics Engineers of Korea SD
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• v.48 no.10
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• pp.82-90
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• 2011

Because of the development of Smart phone devices, the demands of high performance FPU(Floating-point Unit) becomes increasing. Therefore, we propose the high-speed single-/double-precision FPU design that includes an elementary add/sub unit and improved multiplier and compare and convert units. The most commonly used add/sub unit is optimized by the parallel rounding unit. The matrix operation is used in complex calculation something like a graphic calculation. We designed the Multiply-Add Fused(MAF) instead of multiplier to calculate the matrix more quickly. The branch instruction that is decided by the compare operation is very frequently used in various programs. We bypassed the result of the compare operation before all the pipeline processes ended to decrease the total execution time. And we included additional convert operations that are added in IEEE754-2008 standard. To verify our RTL designs, we chose four hundred thousand test vectors by weighted random method and simulated each unit. The FPU that was synthesized by Samsung's 45-nm low-power process satisfied the 600-MHz operation frequency. And we confirm a reduction in area by comparing the improved FPU with the existing FPU.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.19 no.3
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• pp.165-171
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• 2019

The study of the computer architecture has shown that major improvements in price-to-energy performance stems from domain-specific hardware development. This paper analyzes the tensor processing unit (TPU) ASIC which can accelerate the reasoning of the artificial neural network (NN). The core device of the TPU is a MAC matrix multiplier capable of high-speed operation and software-managed on-chip memory. The execution model of the TPU can meet the reaction time requirements of the artificial neural network better than the existing CPU and the GPU execution models, with the small area and the low power consumption even though it has many MAC and large memory. Utilizing the TPU for the tensor flow benchmark framework, it can achieve higher performance and better power efficiency than the CPU or CPU. In this paper, we analyze TPU, simulate the Python modeled OpenTPU, and synthesize the matrix multiplication unit, which is the key hardware.

• Coupled systems mechanics
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• v.11 no.1
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• pp.33-41
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• 2022

Quite often we have a lot of measurement data and would like to find some relation between them. One common task is to see whether some measured data or a curve of known shape fit into the cumulative measured data. The problem can be visualized since data could generally be presented as curves or planes in Cartesian coordinates where each curve could be represented as a vector. In most cases we have measured the cumulative 'curve', we know shapes of other 'curves' and would like to determine unknown coefficients that multiply the known shapes in order to match the measured cumulative 'curve'. This problem could be presented in more complex variants, e.g., a constant could be added, some missing (unknown) data vector could be added to the measured summary vector, and instead of constant factors we could have polynomials, etc. All of them could be solved with slightly extended version of the procedure presented in the sequel. Solution procedure could be devised by reformulating the problem as a measurement problem and applying the generalized inverse of the measurement matrix. Measurement problem often has some errors involved in the measurement data but the least squares method that is comprised in the formulation quite successfully addresses the problem. Numerical examples illustrate the solution procedure.