• Kyungpook Mathematical Journal
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• v.61 no.4
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• pp.679-710
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• 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
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• v.11 no.1
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• pp.344-352
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• 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
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• v.62 no.1
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• pp.1-28
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• 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.

• Journal of the Korean Society for Nondestructive Testing
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• v.21 no.5
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• pp.556-560
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• 2001

Remote field eddy current testing (RFECT) with through-wall transmission characteristic is being applied to pipes ranging from small tubes of heat exchanger to natural gas supply pipelines. Cast iron pipes with nominal diameter of 100mm are used primarily as the waterline pipes. The leakage of water occurs due to defects in the pipes caused by vibration of automobiles and corrosion. But, the use of direct inspection methods such as insertion of inspection equipment inside the pipelines has been limited due to its lack of economical efficiency. Economical development of inspection equipments is possible since RFECT method can be easily employed for system integration and quantitative evaluation of both inside and outside defects. In this study, the development of underground pipeline inspection system was tarried out by using RFECT method in consideration of the characteristics of waterline network. This paper specifically describes the design and production of RFECT pipeline inspection pig using centralizer mechanism, development of remote field eddy current signal acquisition and processing software, and review of RFECT system operation procedures.

• Journal of Environmental Science International
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• v.16 no.6
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• pp.735-743
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• 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.