• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.8 no.2
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• pp.1-5
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• 2004

A multiplicative plane partition is a two-dimensional array of positive integers larger than 1 that are nonincreasing both from left to right and top to bottom and whose multiple is a given number n. For a natural number n, let $f_2(n)$ be the number of multiplicative plane partitions of n. In this paper, we prove $f_2(n)\;{\leq}\;n^2$ and a table of them up to $10^5$ is provided.

• East Asian mathematical journal
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• v.37 no.1
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• pp.9-17
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• 2021

For a positive integer n, let μd(n) be the number of multiplicative d-dimensional partitions of ${\prod\limits_{i=1}^{n}}p_i$, where pi denotes the ith prime. The number of multiplicative partitions of a square free number with n prime factors is the Bell number μ1(n) = ��n. By the definition of the function μd(n), it can be seen that for all positive integers n, μ1(n) = Tn(1) = ��n, where Tn(x) is the nth Touchard (or exponential ) polynomial. We show that, for a positive n, μ2(n) = 2nTn(1/2). We also conjecture that for all m, μ3(m) ≤ 3mTm(1/3).

• Earthquakes and Structures
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• v.6 no.5
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• pp.515-537
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• 2014

Current seismic codes (e.g. the NTC08 Italian code and the EC8 European code) adopt a performance-based approach for both the design of new buildings and the assessment of existing ones. Different limit states are considered by verifying structural members as well as non structural elements and facilities which have generally been neglected in practice. The key role of non structural elements on building performance has been shown by recent earthquakes (e.g. L'Aquila 2009) where, due to the extensive damage suffered by infills, partitions and ceilings, a lot of private and public buildings became unusable with consequent significant socio-economic effects. Furthermore, the collapse of infill panels, particularly in the case of out-of-plane failure, represented a serious source of risk to life safety. This paper puts forward an infill model capable of accounting for the effects arising from prior in-plane damage on the out-of-plane capacity of infill panels. It permits an assessment of the seismic performance of existing RC buildings with reference to both structural and non structural elements, as well as of their mutual interaction. The model is applied to a building type with RC framed structure designed only to vertical loads and representative of typical Italian buildings. The influence of infill on building performance and the role of the out-of-plane response on structural response are also discussed.

• Structural Engineering and Mechanics
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• v.68 no.1
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• pp.17-38
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• 2018

In this paper, we compare and assess the performance of the standard 3- and 6-node MITC shell elements (Lee and Bathe 2004) with the recently developed MITC triangular elements (Lee et al. 2014, Jeon et al. 2014, Jun et al. 2018) which were based on the partitions of unity approximation, bubble node, or both. The convergence behavior of the shell elements are measured in well-known benchmark tests; four plane stress tests (mesh distortion test, cantilever beam, Cook's skew beam, and MacNeal beam), two plate tests (Morley's skew plate and circular plate), and six shell tests (curved beam, twisted beam, pinched cylinder, hemispherical shells with or without hole, and Scordelis-Lo roof). To precisely compare and evaluate the solution accuracy of the shell elements, different triangular mesh patterns and distorted element mesh are adopted in the benchmark problems. All shell finite elements considered pass the basic tests; namely, the isotropy, the patch, and the zero energy mode tests.

• Journal of the Korean Institute of Telematics and Electronics D
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• v.34D no.12
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• pp.22-30
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• 1997

The design procedure for direct coupled combline filter with tapped line in/out was summarized on Ku-band satellite frequency downconverter for stellite application. We calculated the resonator dimensions, spacing between successive resonators, ground plane spacing and tapping position of in/output lines in accordance with the given procedure. Partitions wer eemployed between adjacent resonators by inserting irises to improve filter response characteristis. The designed filter was manufactued with aluminum alloy package to reduce mass, and resonators wer machined from the filter body and in/output lines wer fixed on resonators with epoxy to survive in vibration conditon during launch.

• The Journal of the Korea Contents Association
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• v.14 no.3
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• pp.11-21
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• 2014

Multi-scale image segmentation is important in many applications such as image stylization and medical diagnosis. This paper proposes a novel segmentation algorithm based on MSER(maximally stable extremal region) which captures multi-scale structure and is stable and efficient. The algorithm collects MSERs and then partitions the image plane by redrawing MSERs in specific order. To denoise and smooth the region boundaries, hierarchical morphological operations are developed. To illustrate effectiveness of the algorithm's multi-scale structure, effects of various types of LOD control are shown for image stylization. The proposed technique achieves this without time-consuming multi-level Gaussian smoothing. The comparisons of segmentation quality and timing efficiency with mean shift-based Edison system are presented.