• 대한수학회보
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• 제53권5호
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• pp.1385-1394
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• 2016

Let (R, m) be a Noetherian local ring, I, J two ideals of R, and A an Artinian R-module. Let $k{\geq}0$ be an integer and $r=Width_{>k}(I,A)$ the supremum of lengths of A-cosequences in dimension > k in I defined by Nhan-Hoang [9]. It is first shown that for each $t{\leq}r$ and each sequence $x_1,{\cdots},x_t$ which is an A-cosequence in dimension > k, the set $$\Large(\bigcup^{t}_{i=0}Att_R(0:_A(x_1^{n_1},{\ldots},x_i^{n_i})))_{{\geq}k}$$ is independent of the choice of $n_1,{\ldots},n_t$. Let r be the eventual value of $Width_{>k}(0:_AJ^n)$. Then our second result says that for each $t{\leq}r$ the set $\large(\bigcup\limits_{i=0}^{t}Att_R(Tor_i^R(R/I,\;(0:_AJ^n))))_{{\geq}k}$ is stable for large n.

• Journal of Preventive Medicine and Public Health
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• 제31권3호
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• pp.440-448
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• 1998

In many developed countries, for example, USA, respirator fit testing is required before entering specific work environment to ensure that the respirator worn satisfies a minimum of fit and that the user knows when the respirator fits properly. Unfortunately because we have not fit test regulation in Korea, a lot of workers wearing respirators may be potentially exposed to hazards. This study was conducted to evaluate the fitting performance for respirators and correlation fit factors with facial dimensions of wearers. 110 subjects (70 males, 40 females) were fit tested for three quarter masks, i.e., two domestic-made Mask 2, and Y and one foreign-made Mask T using PortaCount 8020. A facial dimension survey of the same subjects was conducted to develop a facial dimension grids fer correlation fit factors with facial dimension parameters. A facial dimension grid was developed on the basis of face length and lip length for quarter masks. The results obtained were as follows : 1 Fit factors of Mask T were much higher than those of Masks Z, and Y. 2. Males were fitted more properly than females. 3. Male in box 'f' of grid would be adequately fitted Mask Y and male in box 'b', 'e', 'f', 'h' of grid would be sufficiently fitted Mask T. Female in box 'h' of grid may have a good fitting performance for both Mask Y, and T. But subjects in all boxes of grid would be inadequately fitted Mask Z.

• 대한치과교정학회지
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• 제45권2호
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• pp.59-65
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• 2015

Objective: To investigate skeletal and dental changes after application of a mandibular setback surgery-first orthodontic treatment approach in cases of skeletal Class III malocclusion. Methods: A retrospective study of 34 patients (23 men, 11 women; mean age, $26.2{\pm}6.6years$) with skeletal Class III deformities, who underwent surgery-first orthodontic treatment, was conducted. Skeletal landmarks in the maxilla and mandible at three time points, pre-treatment (T0), immediate-postoperative (T1), and post-treatment (T2), were analyzed using cone-beam computed tomography (CBCT)-generated half-cephalograms. Results: The significant T0 to T1 mandibular changes occurred $-9.24{\pm}3.97mm$ horizontally. From T1 to T2, the mandible tended to move forward $1.22{\pm}2.02mm$, while the condylar position (Cd to Po-perpendicular plane) shifted backward, and the coronoid process (Cp to FH plane) moved vertically. Between T1 and T2, the vertical dimension changed significantly (p < 0.05). Changes in the vertical dimension were significantly correlated to T1 to T2 changes in the Cd to Po-perpendicular plane (r = -0.671, p = 0.034), and in the Cp to FH plane (r = 0.733, p = 0.016), as well as to T0 to T1 changes in the Cp to Po-perpendicular plane (r = 0.758, p = 0.011). Conclusions: Greater alterations in the vertical dimension caused larger post-treatment (T2) stage skeletal changes. Studying the mandibular position in relation to the post-surgical vertical dimension emphasized the integral importance of vertical dimension control and proximal segment management to the success of surgery-first orthodontic treatment.

• 대한환경공학회지
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• 제32권3호
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• pp.234-240
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• 2010

SBR시스템을 이용한 비염분 폐수와 염분 폐수의 생물학적 처리 시 starvation이전 제올라이트 및 입상활성탄 주입이 starvation 이후 시스템의 재가동시 시스템의 성능회복에 대해 조사하였다. Starvation 이후 시스템의 재가동시, SVI, floc의 크기, fractal dimension, 유기물 지표인 $COD_{Mn}$과 T-N, T-P의 처리효율에 미치는 영향을 알아보고 회복 기간을 도출하고자 하였다. 5일 동안 starvation 후 재가동하였을 때에 초기의 SVI는 증가하였으나 시간이 경과함에 따라 감소하였다. 또한 floc 크기 및 fractal dimension이 클수록, 유기물, T-N 및 T-P 처리효율도 증가하였다. 시스템의 성능회복은 floc 크기 및 fractal dimension에 상관성을 가지고 있었다. Starvation 이후 재가동시 오염물질($COD_{Mn}$, T-N, T-P) 처리효율이 정상상태로 회복하는데 필요한 시간은 담체 주입이 미주입보다 더 짧은 시간이 소요되었다.

• 대한수학회지
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• 제36권3호
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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.

• Korean Journal of Mathematics
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• 제32권1호
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• pp.43-57
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• 2024

Given a domain X and a collection H of functions h : X → {0, 1}, the Vapnik-Chervonenkis (VC) dimension of H measures its complexity in an appropriate sense. In particular, the fundamental theorem of statistical learning says that a hypothesis class with finite VC-dimension is PAC learnable. Recent work by Fitzpatrick, Wyman, the fourth and seventh named authors studied the VC-dimension of a natural family of functions ℋ'²_t(E) : 𝔽²_q → {0, 1}, corresponding to indicator functions of circles centered at points in a subset E ⊆ 𝔽²_q. They showed that when |E| is large enough, the VC-dimension of ℋ'²_t(E) is the same as in the case that E = 𝔽²_q. We study a related hypothesis class, ℋ^d_t(E), corresponding to intersections of spheres in 𝔽^d_q, and ask how large E ⊆ 𝔽^d_q needs to be to ensure the maximum possible VC-dimension. We resolve this problem in all dimensions, proving that whenever |E| ≥ C_dq^d-1/(d-1) for d ≥ 3, the VC-dimension of ℋ^d_t(E) is as large as possible. We get a slightly stronger result if d = 3: this result holds as long as |E| ≥ C_3q^7/3. Furthermore, when d = 2 the result holds when |E| ≥ C_2q^7/4.

• 대한수학회논문집
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• 제17권2호
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• pp.221-227
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• 2002

In this paper we will show that the followings ; (1) Let R be a regular local ring of dimension n. Then $A_{n-2}$(R) = 0. (2) Let R be a regular local ring of dimension n and I be an ideal in R of height 3 such that R/I is a Gorenstein ring. Then [I] = 0 in $A_{n-3}$(R). (3) Let R = V[[ $X_1$, $X_2$, …, $X_{5}$ ]]/(p+ $X_1$$^{t1}$ + $X_2$$^{t2}$ + $X_3$$^{t3}$ + $X_4$$^2$+ $X_{5}$ $^2$/), where p $\neq$2, $t_1$, $t_2$, $t_3$ are arbitrary positive integers and V is a complete discrete valuation ring with (p) = mv. Assume that R/m is algebraically closed. Then all the Chow group for R is 0 except the last Chow group.group.oup.

• 한국농공학회논문집
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• 제53권6호
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• pp.43-50
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• 2011

The fractal method has recently been applied to a model for determining soil grain size distribution. The objective of this study is to review the applicability of the fractal method for a analysis of submarine sedimentary environments by comparing fractal constants with grain size statistical analysis for the soil samples of Pohang (PH) and Namhae (NH). The y-interception of log (grain size)-log (passing) equation was also used because grain size distribution couldn't be expressed with fractal dimension only. The result of comparison between fractal constants (dimension, y-interception) and grain size statistical indices, the fractal dimension was directly proportional to the mean and the sorting. And the y-interception showed high correlation with the mean. The fractal dimension and y-interception didn't show significant correlation with the skewness and the kurtosis. Thus regression equations between fractal constants and two statistical indices (mean, sorting) were derived. All classifications of the mean and the sorting could be determined using the regression equation based on the fractal dimension and y-interception. Therefore, fractal constants could be used as an alternative index representing the sedimentary environments instead of the mean and sorting.

• 대한수학회보
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• 제54권4호
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• pp.1331-1336
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• 2017

Assume that R is a commutative Noetherian ring with non-zero identity, a is an ideal of R, X is an R-module, and t is a non-negative integer. In this paper, we present upper bounds for the injective dimension of X in terms of the injective dimensions of its local cohomology modules and an upper bound for the injective dimension of $H^t_{\alpha}(X)$ in terms of the injective dimensions of the modules $H^i_{\alpha}(X)$, $i{\neq}t$, and that of X. As a consequence, we observe that R is Gorenstein whenever $H^t_{\alpha}(R)$ is of finite injective dimension for all i.

• 한국해양공학회지
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• 제14권1호
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• pp.29-36
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• 2000

Surface micro-crack grows along intergranular or transgranular region of crystal grains. But if it meets the barrier such as sessile dislocation and precipitates it loses straightness and deflects. Investigators had many difficulties in estimating fatigue life of smooth specimen because of the random distribution growth and coalescence of surface micro-cracks. The path of surface micro-crack has irregularity due to nonhomogeneous microstructure. Euclidian geometry can't quantify the shape of surface micro-crack but fractal geometry can. Therefore in this paper fractal dimension is measured at various stage of cycle ratio and estimated cycle ratio in 2024-T3 aluminium, alloy.