• Bulletin of the Korean Mathematical Society
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• v.35 no.3
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• pp.397-408
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• 1998

We often use the Hausdorff dimension as a tool of measuring how complicate the fractal is. But it is usually very difficult to calculate that value. So there have been many tries to find the dimension of the given set and most of these are related to the density theorem of invariant measure. The aims of this paper are to introduce the k-irreducible subsimilar sets as a generalization of the set defined by V.Drobot and J.Turner in ([1]) and calculate their Hausdorff dimensions by using algebraic methods.

• Korean Institute of Interior Design Journal
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• no.11
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• pp.20-25
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• 1997

The purpose of this study is to find out the correlation between Truth(道) and dimension through the understanding of architectural point of value in the aspect of correlation between modern western thoughts and the thoughts of Truth and also through the reading of what kind of composite trend of the Truth can be seen in a Korea traditional house. This stduy takes the following procedure with reference books and traditional house that we have. 1) Making foundation for this study by finding out the fundamental meaning of the thoughts of Truth through the comparing and analyzing between modern western thoughts and the thoughts of Truth. 2) Reviewing the understanding of dimension in the thoughts of Truth. 3) Traslation of the organic correlation through the analysis of composition, placement and characteristics of dimension in a real present traditional Korea house. 4) Finding out the meaning of each dimension through the adaptation of the fundamental rules of nature of Jane(藏:store), Sang(生:life), Jang(長:long), Su(收obtain) to the dimension composite of a traditional house and concluding that the cyclical process in the oriental thoughts could be made.

• Journal of the Korean Wood Science and Technology
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• v.38 no.6
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• pp.470-479
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• 2010

In this study, the visual grading based on the visual characteristics and structural timber bending test were conducted for domestic yellow poplar dimension lumber. Structural performance of domestic yellow poplar dimension lumber was conducted through the evaluation of strength and stiffness. Visual grading rule of yellow poplar dimension lumber did not exist in Korea. Visual grading of yellow poplar dimension lumber was performed according to the NSLB (Northern Softwood Lumber Bureau) standard grading rules including several hardwood dimension lumber. The allowable bending stress was calculated from the results of a visual grading. Compared with NDS (National Design Specification), the yellow poplar dimension lumber showed enough strength for structural uses. In addition, the visual grading was performed according to the KFRI (Korea Forest Research Institute) grading rule to calculated allowable bending stress and to evaluated the feasibility. The yellow poplar was classified into the pine groups by the KFRI criteria regulated by specific gravity. Allowable bending stress based on weibull distribution had became highly than KFRI criteria, as No. 1 (10.0 MPa), No. 2 (7.4 MPa) and No. 3 (4.1 MPa). And the availability of yellow poplar dimension lumber for structural uses had been confirmed. The Modulus of Elasticity (MOE) of domestic yellow poplar dimension lumber had not met the NDS and KFRI criteria. However, for the use of domestic yellow poplar, average values of MOE which obtained through this test were suggested as design value for domestic yellow poplar. Design values were supposed No. 1, 2 (9,000 MPa) and No. 3 (8,000 MPa).

• Geomechanics and Engineering
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• v.4 no.3
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• pp.219-227
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• 2012

Pavement management systems require systematic monitoring of pavement surfaces to determine preventive and corrective maintenance. The process involves the accumulation of large amounts of visual data, typically obtained from site visitation. The pavement surface condition is then correlated to a pavement distress index that is based on a scoring system previously established by state or federal agencies. The scoring system determines if the pavement section requires maintenance, overlay or reconstruction. One of the surface distresses forming part of the overall pavement distress index is the Alligator Crack Index (AC Index). The AC Index involves the visual evaluation of the crack severity of a section of a pavement as being low, medium, or high. This evaluation is then integrated into a formula in order to obtain the AC Index. In this study a quantification of the visual evaluation of the severity of alligator cracking is carried out using photographs and the fractal dimension concept from fractal theory. Pavements with low levels of cracking were found to have a fractal dimension equal to 1.051. Pavements with moderate levels of cracking had a fractal dimension equal to 1.1754. Pavements with high degrees of cracking had a fractal dimension that varied between 1.5037 (high) and 1.7111 (very high). Pavements with a level of cracking equal to 1.8976 represented pavements that disintegrated and developed potholes. Thus, the visual evaluation of the state of cracking of a pavement (the AC Index) could be enhanced with the use of the fractal dimension concept from fractal theory.

• Journal of the Korean Institute of Electrical and Electronic Material Engineers
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• v.24 no.3
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• pp.234-239
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• 2011

In this study, the heat transfer capability have been improved by using via-holes in FR4 PCB, when the LED lighting is designed to solve the thermal problem. The thermal resistance and junction temperature were measured by changing the dimension of FR4 PCB and size of via hole. As a result, when the dimension was increased initially, the thermal resistance and junction temperature was decreased rapidly, the ones was stabilized after the dimension of 200 $[mm^2]$. Also, the light output was improved up to maximum 17% by formation of via-hole and expansion of dimension in FR4 PCB. Therefore, the thermal resistance and junction temperature could be improved by expansion of PCB dimension and configuration of via-hole ability.

• Journal of Magnetics
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• v.15 no.3
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• pp.99-102
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• 2010

We present the fractal properties of the magnetic domain walls in $(5-{\AA}\;Co_{90}Fe_{10}/10-{\AA}\;Pt)_n$ multilayer films with perpendicular magnetic anisotropy for the number of repeats n (1 to 5). In these films, the magnetization reversed due to the domain wall propagation throughout the films with rare nucleations. As n increased, it was observed that the jaggedness of the domain walls increased noticeably, which is possibly due to the accumulation of irregularities at the layer interfaces. The jaggedness of the domain walls was analyzed in terms of the fractal dimension by use of the ruler method, and it was revealed that the fractal dimension significantly changed from $1.0{\pm}0.002$ to $1.3{\pm}0.05$ as n increased from 1 to 5.

• Communications of the Korean Mathematical Society
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• v.38 no.3
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• pp.733-740
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• 2023

Let R be a commutative ring and M be an R-module. The dimension graph of M, denoted by DG(M), is a simple undirected graph whose vertex set is Z(M) ⧵ Ann(M) and two distinct vertices x and y are adjacent if and only if dim M/(x, y)M = min{dim M/xM, dim M/yM}. It is shown that DG(M) is a disconnected graph if and only if (i) Ass(M) = {𝖕, 𝖖}, Z(M) = 𝖕 ∪ 𝖖 and Ann(M) = 𝖕 ∩ 𝖖. (ii) dim M = dim R/𝖕 = dim R/𝖖. (iii) dim M/xM = dim M for all x ∈ Z(M) ⧵ Ann(M). Furthermore, it is shown that diam(DG(M)) ≤ 2 and gr(DG(M)) = 3, whenever M is Noetherian with |Z(M) ⧵ Ann(M)| ≥ 3 and DG(M) is a connected graph.

• Communications for Statistical Applications and Methods
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• v.13 no.3
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• pp.567-576
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• 2006

In this paper, we applied the multiblock dimension reduction methods to the classification of tumor based on microarray gene expressions data. This procedure involves clustering selected genes, multiblock dimension reduction and classification using linear discrimination analysis and quadratic discrimination analysis.

• Communications of the Korean Mathematical Society
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• v.17 no.3
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• pp.519-529
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• 2002

In this paper. We Study (n + 1)-dimensional Contact CR-submanifolds of (n - 1) contact CR-dimension immersed in a Sasakian space form M$\^$2m+1/(c) (2m=n+p, p>0), and especially determine such submanifolds under additional condition concerning with shape operator.

• Journal of the Korean Mathematical Society
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• v.36 no.3
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• pp.633-648
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• 1999

In this paper, for any two bipartite ordered sets P and Q, we define the convolution P * Q of P and Q. For dim(P)=s and dim(Q)=t, we prove that s+t-(U+V)-2 dim(P*Q) s+t-(U+V)+2, where U+V is the max-mn integer of the certain realizers. In particular, we also prove that dim(P)=n+k- {{{{ { n+k} over {3 } }}}} for 2 k n<2k and dim(Pn ,k)=n for n 2k, where Pn,k=Sn*Sk is the convolution of two standard ordered sets Sn and Sk.