• Kyungpook Mathematical Journal
• /
• 제61권4호
• /
• pp.679-710
• /
• 2021

We study the tensor product algebra P_k(x₁) ⊗ P_k(x₂) ⊗ ⋯ ⊗ P_k(x_m), where P_k(x) is the partition algebra defined by Jones and Martin. We discuss the centralizer of this algebra and corresponding Schur-Weyl dualities and also index the inequivalent irreducible representations of the algebra P_k(x₁) ⊗ P_k(x₂) ⊗ ⋯ ⊗ P_k(x_m) and compute their dimensions in the semisimple case. In addition, we describe the Bratteli diagrams and branching rules. Along with that, we have also constructed the RS correspondence for the tensor product of m-partition algebras which gives the bijection between the set of tensor product of m-partition diagram of P_k(n₁) ⊗ P_k(n₂) ⊗ ⋯ ⊗ P_k(n_m) and the pairs of m-vacillating tableaux of shape [λ] ∈ Γ_k^m, Γ_k^m = {[λ] = (λ₁, λ₂, …, λ_m)|λ_i ∈ Γ_k, i ∈ {1, 2, …, m}} where Γ_k = {λ_i ⊢ t|0 ≤ t ≤ k}. Also, we provide proof of the identity $(n_1n_2{\cdots}n_m)^k={\sum}_{[{\lambda}]{\in}{\Lambda}^k_{{n_1},{n_2},{\ldots},{n_m}}}$ f^[λ]m_k^[λ] where m_k^[λ] is the multiplicity of the irreducible representation of $S{_{n_1}}{\times}S{_{n_2}}{\times}....{\times}S{_{n_m}}$ module indexed by ${[{\lambda}]{\in}{\Lambda}^k_{{n_1},{n_2},{\ldots},{n_m}}}$, where f^[λ] is the degree of the corresponding representation indexed by ${[{\lambda}]{\in}{\Lambda}^k_{{n_1},{n_2},{\ldots},{n_m}}}$ and ${[{\lambda}]{\in}{\Lambda}^k_{{n_1},{n_2},{\ldots},{n_m}}}=\{[{\lambda}]=({\lambda}_1,{\lambda}_2,{\ldots},{\lambda}_m){\mid}{\lambda}_i{\in}{\Lambda}^k_{n_i},i{\in}\{1,2,{\ldots},m\}\}$ where ${\Lambda}^k_{n_i}=\{{\mu}=({\mu}_1,{\mu}_2,{\ldots},{\mu}_t){\vdash}n_i{\mid}n_i-{\mu}_1{\leq}k\}$.

• International Journal of Naval Architecture and Ocean Engineering
• /
• 제11권1호
• /
• pp.344-352
• /
• 2019

Marine production strings are continuously affected by unstable internal fluid during operation. In this paper, the structural governing equation for marine production string self-induced vibration is constructed. A finite element analysis model is established based on Euler-Bernoulli theory and solved by the Newmark method. Furthermore, based on reliability theory, a self-design procedure is developed to determine the operability envelope for marine production string self-induced vibration. Case studies show: the response frequency of the production strings is consistent with the excitation frequency under harmonic fluctuation and mainly determined by the first-order natural frequency under stochastic fluctuation. The operability envelope for marine production string self-induced vibration is a near symmetrical trapezium. With the increasing of natural gas output, the permissible fluctuation coefficient dramatically decreases. A reasonable centralizer spacing, increasing top tension, and controlling natural gas output are of great significance to the risk control in marine production string operation.

• Kyungpook Mathematical Journal
• /
• 제62권1호
• /
• pp.1-28
• /
• 2022

In this paper, we define the G-Brauer algebras $D^G_f(x)$, where G is a cyclic group, called cyclic G-Brauer algebras, as the linear span of r-signed 1-factors and the generalized m, k signed partial 1-factors is to analyse the multiplication of basis elements in the quotient $^{\rightarrow}_{I_f}^G(x,2k)$. Also, we define certain symmetric matrices $^{\rightarrow}_T_{m,k}^{[\lambda]}(x)$ whose entries are indexed by generalized m, k signed partial 1-factor. We analyse the irreducible representations of $D^G_f(x)$ by determining the quotient $^{\rightarrow}_{I_f}^G(x,2k)$ of $D^G_f(x)$ by its radical. We also find the eigenvalues and eigenspaces of $^{\rightarrow}_T_{m,k}^{[\lambda]}(x)$ for some values of m and k using the representation theory of the generalised symmetric group. The matrices $T_{m,k}^{[\lambda]}(x)$ whose entries are indexed by generalised m, k signed partial 1-factors, which helps in determining the non semisimplicity of these cyclic G-Brauer algebras $D^G_f(x)$, where G = ℤ_r.

• 비파괴검사학회지
• /
• 제21권5호
• /
• pp.556-560
• /
• 2001

배관의 관벽투과 특성을 지닌 원격장 와전류 비파괴 검사법은 열교환기 세관 검사에서부터 천연가스 수송관에 이르기까지 다양한 형태의 배관과 결함을 대상으로 적용 연구가 진행되고 있다. 공칭 외경 100mm의 주철관은 주로 상수도 관로의 배수관으로 활용되고 있는데, 차량 진동과 부식에 의한 결함의 생성으로 정수의 누수 문제를 일으킨다. 그러나, 탐상 경제성 및 효용성 문제로 관내 검사장치 투입과 같은 직접적인 검사 방법의 수행이 제한되어 왔다. 원격장 와전류 방법은 시스템 구성이 용이하고 내 외부 부식 결함에 대한 정량적인 평가가 가능하기 때문에 경제성 있는 장치 개발이 가능하다. 본 연구에서는 원격장 와전류 기술을 이용하여 상수도 관망의 특성을 고려한 매설 배관 검사시스템 개발을 수행하였다. 세부적으로는 관내 투입 원격장 와전류 검사의 기구부 설계 및 제작, 원격장 와전류 신호의 획득 및 처리 프로그램 개발, 그리고 개발 장치의 운용 방법 및 절차 검토 등으로 되어 있다.

• 한국환경과학회지
• /
• 제16권6호
• /
• pp.735-743
• /
• 2007

A grouting method is the way to effectively prevent pollutants from spreading into the ground during the digging process of groundwater. This study, based on the comparative study of grouting methods being generally accepted, suggests various construction methods which are suitable for geological structure as follows: In Jeju Island, it is very likely that rocks may fall in shuttered zones such as cracks, joints, scoria layers, and clinker layers. For this reason, it is recommended that materials be injected from the bottom toward the top, not from the top to the bottom. In the case where the amount of injected materials become too large in the areas of cracks or joints because of high level of permeability coefficient, grouting materials which smeared into surrounding areas may cause unwanted cut in the aquifer of the bottom level. To avoid this, the amount of water should be reduced from the typical water-cement ratio of 1:2, and grouting materials with larger grading should be used. If the deep excavation of ground is made in Jeju Island, it is likely to have lots of voids because of geological characteristics. Based on the results of this research, it is found that to construct interior casing, the centralizer should be attached to the casing to prevent the casing from being in contact with the counter fort. The grouting in Jeju Island should be thicker than usual. To avoid over-use of grouting materials, to prevent grouting in more than necessary zone, and to facilitate grouting of void areas, the flexible selection of materials is required. And, to exactly figure out the interior of dug well, an examination through CCTV should necessarily be performed when grouting work is in progress.