• Journal of the Korean Institute of Intelligent Systems
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• v.10 no.6
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• pp.557-563
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• 2000

We introduce r-fuzzy $\delta$-cluster ($\theta$-cluster) points and r-fuzzy $\delta$-closure ($\theta$-closure) sets in smooth fuzzy topological spaces in a view of the definition of A.P. Sostak [13]. We study some properties of them.

• Communications of the Korean Mathematical Society
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• v.26 no.3
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• pp.339-348
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• 2011

A ring R is called symmetric, if abc = 0 implies acb = 0 for a, b, c ${\in}$ R. An ideal I of a ring R is called symmetric (resp. radically-symmetric) if R=I (resp. R/$\sqrt{I}$) is a symmetric ring. We first show that symmetric ideals and ideals which have the insertion of factors property are radically-symmetric. We next show that if R is a semicommutative ring, then $T_n$(R) and R[x]=($x^n$) are radically-symmetric, where ($x^n$) is the ideal of R[x] generated by $x^n$. Also we give some examples of radically-symmetric ideals which are not symmetric. Connections between symmetric ideals of R and related ideals of some ring extensions are also shown. In particular we show that if R is a symmetric (or semicommutative) (${\alpha}$, ${\delta}$)-compatible ring, then R[x; ${\alpha}$, ${\delta}$] is a radically-symmetric ring. As a corollary we obtain a generalization of [13].

• The Journal of Korean Academy of Prosthodontics
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• v.47 no.1
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• pp.82-90
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• 2009

Statement of problem: Recently, as patients' expectation and interest for esthetics are increasing, concerns of esthetic restoration for removable dentures as well as fixed prosthodontics are also increasing. And the color stability of artificial teeth will affect a long term success rate of the denture. But the stain or discoloration of these artificial teeth as well as denture resin has caused esthetic problem. Purpose: This study was designed to evaluate the influence on color stability of artificial teeth when soy sauce, red pepper paste and coffee which many Koreans have eaten were applied. Material and methods: For artificial teeth type(Endura $Anterio^{(R)}$, Physio $Duracross^{(R)}$, Trubyte $Biotone^{(R)}$) selected for the study, 10 specimens each were soaked into individual beakers of soy sauce, red pepper paste, coffee and distilled water. And $L^*$, $a^*$, $b^*$ value were measured for evaluation of the color difference (${\Delta}E^*$) with spectrophotometer on the 1 day, 1 week, 2 weeks, 4 weeks and 8 weeks after immersion. Results: 1. ${\Delta}E^*$ value of artificial teeth which were soaked in soy sauce and coffee was various according to soaking periods. However there was significant difference between Trubyte $Biotone^{(R)}$ and Physio $Duracross^{(R)}$ in red pepper paste regardless of soaking period(P<.05). 2. Except for 8 weeks of Endura $Anterio^{(R)}$, 4 weeks and 8 weeks of Physio $Duracross^{(R)}$, artificial teeth soaked in red pepper paste regardless of the type had significant difference of ${\Delta}E^*$ value compared with other groups (P<.05). 3. $a^*$, $b^*$ value of Endura $Anterio^{(R)}$ and Trubyte $Biotone^{(R)}$ which were soaked in red pepper paste had significant difference compared with the value of other group(P<.05). Conclusion: Red pepper paste had the greatest effect on color difference of artificial tooth. Physio $Duracross^{(R)}$ showed relatively less color difference than Trubyte $Biotone^{(R)}$ and Endura $Anterio^{(R)}$. But as ${\Delta}E^*$ difference were all less than 3.3, these artificial resin teeth seemed appropriate for clinical use.

• Journal of the Korean Society of Safety
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• v.6 no.4
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• pp.81-87
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• 1991

We propose the crack growth rate equation which will model fatigue crack growth rate behavior such that constant stress amplitude fatigue crack growth behavior can be predicted. Constant stress amplitude fatigue tests are conducted for four materials under three stress ratios of R＝0.2, R＝0.4 and R＝0.6. Materials which have different mechanical properties i.e. stainless steel, low carbon steel, medium carbon steel and aluminum alloy are used. Through constant stress amplitude fatigue test by using unloading elastic compliance method, it is confirmed that crack closure is a close relationship with fatigue crack propagation. We describe simply fatigue crack propagation behavior as a function of the effective stress intensity factor range ($\Delta$ $K_{eff}$＝U .$\Delta$K) for all three regions (threshold region, stable region). The fatigue crack growth rate equation is given by da / dN＝A($\Delta$ $K_{eff}$­$\Delta$ $K_{o}$ )$^{m}$ / ($\Delta$ $K_{eff}$­$\Delta$K) Where, A and m are material constants, and $\Delta$ $K_{o}$ is stress intensity factor range at low $\Delta$K region. $K_{cf}$ is critical fatigue stress intensity factor.actor.

• The Journal of Korean Academy of Prosthodontics
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• v.39 no.5
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• pp.477-491
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• 2001

The purpose of this study is to compare and analyze the shade changes(${\Delta}E^*$) about $In-Ceram^{(R)}$, $IPS-Empress^{(R)}$, $OPC^{(R)}$ by using of the spectrophotometer arising from inital status and before and after cementation of the resin cement mounted on the metal core. We used a couple of statistics such as 'One- Way ANOVA' and 'Multiple Range Test.' We could be able to verify significantly what is being discussed here up to 95%. The results drawn from our research are as follows : 1. At the time of our experiments regarding the initial shapes of all-ceramic and mounting status of all-ceramic on the metal crown(${\Delta}E^*1$), and a comparison of mounting of all ceramic on the metal crown with all-ceramic cemented on the metal core(${\Delta}E^*2$), at the time of shade change of initial shapes and after we cemented on the metal core. (1) no significant difference among all-ceramics was found. (2) no particular difference was found regarding the $In-Ceram^{(R)}$. (3) a significant difference between the ${\Delta}E^*1$ and ${\Delta}E^*2$ regarding the $IPS-Empress^{(R)}$ was found(P<0.05). (4) a significant difference between the ${\Delta}E^*1$ and ${\Delta}E^*2$ regarding the $OPC^{(R)}$ was found(P<0.05). 2. When we compared the shade changes(${\Delta}E^*$) resulted from before and after the cementation on each of the parts involved of some all-ceramic, we could be able to find shade change increase form incisal third, middle third. and cervical third in that order in $In-Ceram^{(R)}$(spinell), IPS $Empress^{(R)}$, and $OPC^{(R)}$ all. In addition. we could be able to find a significant difference between cervical third and incisal third, middle third. (P<0.05) From what we have just seen, we might conclude that there is a significant shade change difference before and after the cementation with respect to $IPS-Empress^{(R)}$ and $OPC^{(R)}$. In addition, we could also be able to find more shade change difference at the cervical third rather than incisal third and middle third depending on the parts involved.

• Transactions of the Korean Society of Mechanical Engineers
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• v.12 no.1
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• pp.53-63
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• 1988

Using COD-R curves, instability of crack growth in ductile material is studied here. Tearing modulus $T_{\delta}$, based on the COA concept is defined and the instability criterion $T_{{\delta}{\app}}$> $T_{{\delta}{\mat}}$ is compared with experiments. Variations of the COD-R curve and the location of rotation center are experimentally investigated as the initial crack ratio varies. Three-point bend specimens of alloy steel SCM4 are used here and two clip-on gauges are installed in order to obtain the COD-R curve. The results show that the tearing modulus $T_{\delta}$ is a good measure to characterize the instability of crack growth. Also it is found that the location of rotation center is almost constant regardless of the initial crack ratio and the amount of the crack growth.

• Journal of the Korean Society for Precision Engineering
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• v.8 no.2
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• pp.27-35
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• 1991

We propose the crack growth rate equation which applied over three regions (threshold region, stable region, unstable region) of fatigue crack propagation. Constant stress amplitude fatigue tests are conducted for four materials under three stress ratios of R=0.05, R=0.2 and R=0.4. Materials which have different mechanical properties i.e. stainless steel, low carbon steel, medium carbon steel and aluminum alloy are used. The fatigue crack growth rate equation is given by $da/dN={\beta} (1-R)^{\delta}\({\DELTA}K-{\DELTA}K_t)^{\alpha} / (K_{cf}-K_{max})$${\alpha}, {\beta}$ , and ${\delta}$ are constants, and ${\Delta}K_t$ is stress intensity factor range at low ${\Delta}K$ region. The constants are obtained from nonlinear least square method. $K_{ef}$is critical fatigue stress intensity factor. The relation between half crack length and number of cycles obtained by integrating the crack growth rate equation is in agreement with the experimental data. It is also experimented with constant maximum stress and decreasing stress ratios, and the fatigue growth rate of each material is in accord with the proposed equation.

• Bulletin of the Korean Mathematical Society
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• v.20 no.1
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• pp.31-36
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• 1983

Let R be a commutative ring with 1, and A a unitary commutative R-algebra. By a derivation module of A, we mean a pair (M, d), where M is an A-module and d: A.rarw.M and R-derivation, i.e., d is an R-linear mapping such that d(ab)=a)db)+b(da). A derivation module homomorphism f:(M,d).rarw.(N, .delta.) is an A-homomorphism f:M.rarw.N such that f.d=.delta.. A derivation module of A, (U, d), there exists a unique derivation module homomorphism f:(U, d).rarw.(M,.delta.). In fact, a universal derivation module of A exists in the category of derivation modules of A, and is unique up to unique derivation module isomorphisms [2, pp. 101]. When (U,d) is a universal derivation module of R-algebra A, the A-module U is denoted by U(A/R). For out convenience, U(A/R) will also be called a universal derivation module of A, and d the R-derivation corresponding to U(A/R).

• Journal of applied mathematics & informatics
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• v.29 no.3_4
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• pp.921-936
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• 2011

In this paper, our main purpose is to establish the existence of weak solutions of a weak solutions of a class of p-q-Laplacian system involving concave-convex nonlinearities: $$\{\array{-{\Delta}_pu-{\Delta}_qu={\lambda}V(x)|u|^{r-2}u+\frac{2{\alpha}}{\alpha+\beta}|u|^{\alpha-2}u|v|^{\beta},\;x{\in}{\Omega}\\-{\Delta}p^v-{\Delta}q^v={\theta}V(x)|v|^{r-2}v+\frac{2\beta}{\alpha+\beta}|u|^{\alpha}|v|^{\beta-2}v,\;x{\in}{\Omega}\\u=v=0,\;x{\in}{\partial}{\Omega}}$$ where ${\Omega}$ is a bounded domain in $R^N$, ${\lambda}$, ${\theta}$ > 0, and 1 < ${\alpha}$, ${\beta}$, ${\alpha}+{\beta}=p^*=\frac{N_p}{N_{-p}}$ is the critical Sobolev exponent, ${\Delta}_su=div(|{\nabla}u|^{s-2}{\nabla}u)$ is the s-Laplacian of u. when 1 < r < q < p < N, we prove that there exist infinitely many weak solutions. We also obtain some results for the case 1 < q < p < r < $p^*$. The existence results of solutions are obtained by variational methods.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.24 no.3 s.174
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• pp.794-802
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• 2000

Since the examination of CTOD problem revealed that the discrepancy among CTOD's was a matte., of definition, the relationships among parameters based on different definitions have been studied Particularly, the relationship between $\sigma$BS R-curve based on BS 7448 and R-curve based on the recently introduced $\sigma$5 parameter was investigated in this research. For the comparison, compact tension specimens of used 1Cr-0.5Mo steel, heat treated 1Cr-0.5Mo steel to mimic the new one, A12024-T6, and A12024-T351 were prepared and tested. Consequently, the relationship between $\sigma$5 and $\sigma$BS R-curves for tested materials were established by shifting the rotational center which could determined by rotation factor and ligament size.