• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• 제8권2호
• /
• pp.1-5
• /
• 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
• /
• 제37권1호
• /
• pp.9-17
• /
• 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
• /
• 제6권5호
• /
• pp.515-537
• /
• 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
• /
• 제68권1호
• /
• pp.17-38
• /
• 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.

• 전자공학회논문지D
• /
• 제34D권12호
• /
• pp.22-30
• /
• 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.

• 한국콘텐츠학회논문지
• /
• 제14권3호
• /
• pp.11-21
• /
• 2014

다중 스케일 영상 분할은 영상 스타일링과 의료진단과 같은 여러 응용에서 매우 중요하다. 이 논문은 다중 스케일 구조를 확보하며 안정적이고 효율적인 MSER에 기반을 둔 새로운 알고리즘을 제안한다. 이 알고리즘은 영상에서 MSER를 수집한 후, 이것들을 특정한 순서대로 영상에 다시 그려 넣음으로써 영상을 분할한다. 영상 경계를 평활화하고 잡음을 제거하기 위한 계층적 모폴로지 연산을 제안한다. 알고리즘의 다중 스케일 특성을 보이기 위해, 여러 종류의 상세 단계 제어의 효과를 영상 스타일링에 적용한다. 제안한 기법은 이러한 효과를 시간이 많이 걸리는 다중 가우시언 평활화없이 수행한다. 분할 품질과 계산 시간 측면에서 민쉬프트-기반 Edison 시스템과 비교 결과를 제시한다.