• Journal of the Korean Mathematical Society
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• v.51 no.2
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• pp.239-250
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• 2014

Let R be a commutative Noetherian (not necessarily local) ring, I an ideal of R and M a finitely generated R-module. In this paper, by computing the local cohomology modules and Ext-modules via the injective resolution of M, we proved that, if for an integer t > 0, dim$_RH_I^i(M){\leq}k$ for ${\forall}i$ < t, then $$\displaystyle\bigcup_{i=0}^{j}(Ass_RH_I^i(M))_{{\geq}k}=\displaystyle\bigcup_{i=0}^{j}(Ass_RExt_R^i(R/I^n,M))_{{\geq}k}$$ for ${\forall}j{\leq}t$ and ${\forall}n$ >0. This shows that${\bigcup}_{n>0}(Ass_RExt_R^i(R/I^n,M))_{{\geq}k}$ is a finite set for ${\forall}i{\leq}t$. Also, we prove that $\displaystyle\bigcup_{i=1}^{r}(Ass_RM/(x_1^{n_1},x_2^{n_2},{\ldots},x_i^{n_i})M)_{{\geq}k}=\displaystyle\bigcup_{i=1}^{r}(Ass_RM/(x_1,x_2,{\ldots},x_i)M)_{{\geq}k}$ if $x_1,x_2,{\ldots},x_r$ is M-sequences in dimension > k and $n_1,n_2,{\ldots},n_r$ are some positive integers. Here, for a subset T of Spec(R), set $T_{{\geq}i}=\{{p{\in}T{\mid}dimR/p{\geq}i}\}$.

• Tribology and Lubricants
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• v.22 no.5
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• pp.276-281
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• 2006

The fractal dimension is quantitatively to define the irregular characteristic of the shape in natural. It can be useful in describing morphological characteristics of various wear particles. This paper was undertaken to diagnose failure condition for sliding members in lubrication by fractal dimension. It will be possible to diagnose wear mechanism, friction and damage state of machines through analysis of shape characteristics for wear particle on driving condition by fractal parameters. In this study, the calculating and analyzing methods of fractal dimensions were constructed for the condition monitoring and wear particle analysis in lubricant condition. So, we carried out the Friction and wear test with the ball on disk type tester, and the fractal parameters of wear particle in lubricated conditions were calculated. Fractal parameters were defined as texture fractal dimension ($D_{t}$), structure fractal dimension ($D_{s}$) and total fractal dimension (D).

• Elastomers and Composites
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• v.54 no.2
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• pp.156-160
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• 2019

The changes in the dispersion of carbon black in liquid polyisoprene under shear flow with time have been investigated by time-resolved ultra small-angle X-ray scattering (USAXS) method. The analyses of USAXS profile immediately after the start of shear flow clarified that the aggregates of carbon black with a mean radius of gyration of 14 nm and surface fractal dimension of 2.5 form the fractal network structure with mass-fractal dimension of 2.9. After the application of the shear flow, the scattering intensity increases with time at the observed whole entire q region, and then the a shoulder appears at $q=0.005nm^{-1}$, indicating that the agglomerate is broken and becomes smaller by shear flow. The analysis by the Unified Guinier/Power-law approach yielded several characteristic parameters, such as the sizes of aggregate and agglomerate, mass-fractal dimension of agglomerate, and surface fractal dimension of the primary particle. While the mean radius of gyration of the agglomerate decreases with time, the mean radius of gyration of the aggregate, mass fractal dimension, and surface fractal dimension don't change with time, indicating that the aggregates peel off the surface of the agglomerate.

• Transactions of the Korean Society of Machine Tool Engineers
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• v.10 no.4
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• pp.14-21
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• 2001

To estimate crack growth rate and cycle ratio uniquely, many investigators have developed various kinds of mechanical parameters and theories. But, thes have produced local solution space through single parameter. Neural Networks can perform patten classification using several input and output parameters. Fatigue damage model by neural networks was used to recognize the relation between da/dN/N/N(sub)f, and half-value breadth ratio B/Bo, fractal dimension D(sub)f, and fracture mechanical parameters in 2024-T3 aluminium alloy. Learned neural networks has ability to predict both crack growth rate da/dN and cycly ratio /N/N(sub)f within engineering estimated mean error(5%).

• Bulletin of the Korean Mathematical Society
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• v.58 no.6
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• pp.1483-1494
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• 2021

Let A and B be rings and U be a (B, A)-bimodule. If _BU has finite flat dimension, U_A has finite flat dimension and U ⊗_A C is a cotorsion left B-module for any cotorsion left A-module C, then the Gorenstein flat-cotorsion modules over the formal triangular matrix ring $T=\(\array{A&0\\U&B}\)$ are explicitly described. As an application, it is proven that each Gorenstein flat-cotorsion left T-module is flat-cotorsion if and only if every Gorenstein flat-cotorsion left A-module and B-module is flat-cotorsion. In addition, Gorenstein flat-cotorsion dimensions over the formal triangular matrix ring T are studied.

• Women's Health Nursing
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• v.1 no.2
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• pp.244-259
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• 1995

This study was designed and carried out to describe the stress of the infertile women and identify its predictors. The subjects of this study, 131 infertile women, were in primary or secondary infertility. the were conveniently sampled out from the infertility clinics of K University Medical Center and C Hospital in Seoul. The data were collected by using the Infertility Stress Scale which consisted of 35 items with four dimensions(cognitive, affective, marital and social stress) from August to November 1994. The data were analyzed by using the pc-SAS program. The information was obtained of Mean, Standard Deviation, Frequencies, Percentile, t-test, ANOVA, Duncan's multiple comparison test and Multiple Regression. The results are as follows; 1. The Mean of the stress of the infertile women is 2.78. The Means of the stress in 4 dimensions are 3.81 in the cognitive dimension, 3.05 in the affective dimension, 2.06 in the marital adjustment dimension and 2.41 in the social adjustment dimension. 2. The predictors of the stress of the infertile women are their educational levels and subjective economic status. They explain 14.08% of total variance.

• Journal of Korean Academy of Oral and Maxillofacial Radiology
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• v.28 no.2
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• pp.339-353
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• 1998

The purpose of this study was to investigate whether a radiographic estimate of osseous fractal dimension and power spectrum of 2D discrete Fourier transform is useful in the characterization of structural changes in bone. Ten specimens of bone were decalcified in fresh 50 ml solutions of 0.1 N hydrochloric acid solution at cummulative timed periods of 0 and 90 minutes. and radiographed from 0 degree projection angle controlled by intraoral parelleling device. I performed one-dimensional variance. fractal analysis of bony profiles and 2D discrete Fourier transform. The results of this study indicate that variance and fractal dimension of scan line pixel intensities decreased significantly in decalcified groups but Fourier spectral analysis didn't discriminate well between control and decalcified specimens.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 2009.05a
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• pp.129-134
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• 2009

The dimension of forged part is different from that of die. Therefore, a more precise die dimension is necessarys to produce the precise part, considering the dimensional changes from forging die to final part. In this paper, both experimental and FEM analysis are performed to investigate the effect of several features including die dimension at each forging step and heat-treatment on final part accuracy in the closed-die upsetting. The dimension of forged part is checked at each stage as machined die, cold forged, and post-heat-treatment steps. The elastic characteristics and thermal influences on forging stage are analyzed numerically by the DEFORM-$2D^{TM}$. The effect of residual stress after heat-treatment on forged part could be considered successfully by using DEFOAM-$HT^{TM}$.

• Journal of information and communication convergence engineering
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• v.2 no.3
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• pp.187-192
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• 2004

A method using two dimension Haar functions approximation for solving the problem of a partial differential equation and estimating the parameters of a non-linear distributed parameter system (DPS) is presented. The applications of orthogonal functions, including Haar functions, and their transforms have been given much attention in system control and communication engineering field since 1970's. The Haar functions set forms a complete set of orthogonal rectangular functions similar in several respects to the Walsh functions. The algorithm adopted in this paper is that of estimating the parameters of non-linear DPS by converting and transforming a partial differential equation into a simple algebraic equation. Two dimension Haar functions approximation method is introduced newly to represent and solve a partial differential equation. The proposed method is supported by numerical examples for demonstration the fast, convenient capabilities of the method.

• Journal of the Korean Mathematical Society
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• v.52 no.6
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• pp.1253-1270
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• 2015

Let (R, m) be a commutative Noetherian local domain, M a non-zero finitely generated R-module of dimension n > 0 and I be an ideal of R. In this paper it is shown that if $x_1,{\ldots },x_t$ ($1{\leq}t{\leq}n$) be a sub-set of a system of parameters for M, then the R-module $H^t_{(x_1,{\ldots },x_t)}$(R) is faithful, i.e., Ann $H^t_{(x_1,{\ldots },x_t)}$(R) = 0. Also, it is shown that, if $H^i_I$ (R) = 0 for all i > dim R - dim R/I, then the R-module $H^{dimR-dimR/I}_I(R)$ is faithful. These results provide some partially affirmative answers to the Lynch's conjecture in [10]. Moreover, for an ideal I of an arbitrary Noetherian ring R, we calculate the annihilator of the top local cohomology module $H^1_I(M)$, when $H^i_I(M)=0$ for all integers i > 1. Also, for such ideals we show that the finitely generated R-algebra $D_I(R)$ is a flat R-algebra.