• Bulletin of the Korean Mathematical Society
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• v.31 no.1
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• pp.93-97
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• 1994

Previously T.Porter [3] has given a relative Chinese Remainder Theorem under the hypothesis that given ring R has at least one .tau.-closed maximal ideal (by his notation Ma $x_{\tau}$(R).neq..phi.). In this short paper we drop his overall hypothesis that Ma $x_{\tau}$(R).neq..phi. and give the proof and some related results with this Theorem. In this paper R will always denote a commutative ring with identity element and all modules will be unitary left R-modules unless otherwise specified. Let .tau. be a given hereditarty torsion theory for left R-module category R-Mod. The class of all .tau.-torsion left R-modules, dented by J is closed under homomorphic images, submodules, direct sums and extensions. And the class of all .tau.-torsionfree left R-modules, denoted by F, is closed under taking submodules, injective hulls, direct products, and isomorphic copies ([2], Proposition 1.7 and 1.10).

• Communications of the Korean Mathematical Society
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• v.20 no.3
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• pp.427-436
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• 2005

Let (R, m) be a 2-dimensional regular local ring with algebraically closed residue field R/m. Let K be the quotient field of R and v be a prime divisor of R, i.e., a valuation of K which is birationally dominating R and residually transcendental over R. Zariski showed that there are finitely many simple v-ideals $m=P_0\;{\supset}\;P_1\;{\supset}\;{\cdotS}\;{\supset}\;P_t=P$ and all the other v-ideals are uniquely factored into a product of those simple ones. It then was also shown by Lipman that the predecessor of the smallest simple v-ideal P is either simple (P is free) or the product of two simple v-ideals (P is satellite), that the sequence of v-ideals between the maximal ideal and the smallest simple v-ideal P is saturated, and that the v-value of the maximal ideal is the m-adic order of P. Let m = (x, y) and denote the v-value difference |v(x) - v(y)| by $n_v$. In this paper, if the m-adic order of P is 2, we show that $O(P_i)\;=\;1\;for\;1\;{\leq}\;i\; {\leq}\;{\lceil}\;{\frac{b+1}{2}}{\rceil}\;and\;O(P_i)\;=2\;for\;{\lceil}\;\frac{b+3}{2}\rceil\;{\leq}\;i\;\leq\;t,\;where\;b=n_v$. We also show that $n_w\;=\;n_v$ when w is the prime divisor associated to a simple v-ideal $Q\;{\supset}\;P$ of order 2 and that w(R) = v(R) as well.

• Journal of the Korean Mathematical Society
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• v.31 no.3
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• pp.467-475
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• 1994

In 1983 Harmand and Lima [5] proved that if X is a Banach space for which K(X), the space of compact linear operators on X, is an M-ideal in L(X), the space of bounded linear operators on X, then it has the metric compact approximation property. A strong converse of the above result holds if X is a closed subspace of either $\elll_p(1 < p < \infty) or c_0 [2,15]$. In 1979 J. Johnson [7] actually proved that if X is a Banach space with the metric compact approximation property, then the annihilator K(X)^\bot$ of K(X) in $L(X)^*$ is the kernel of a norm-one projection in $L(X)^*$, which is the case if K(X) is an M-ideal in L(X).

• Kyungpook Mathematical Journal
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• v.45 no.4
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• pp.455-470
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• 2005

This paper introduces compactness notions for frames which are expressed in terms of the convergence of suitably specified general filters. It establishes several preservation properties for them as well as their coreflectiveness in the setting of regular frames. Further, it shows that supercompact, compact, and $Lindel{\ddot{o}}f$ frames can be described by compactness conditions of the present form so that various familiar facts become consequences of these general results. In addition, the Prime Ideal Theorem and the Axiom of Countable Choice are proved to be equivalent to certain conditions connected with the kind of compactness considered here.

• The Pure and Applied Mathematics
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• v.17 no.1
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• pp.87-92
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• 2010

Let R be a 2-torsion free $\sigma$-prime ring with an involution $\sigma$, U a nonzero square closed $\sigma$-Lie ideal, Z(R) the center of Rand d a derivation of R. In this paper, it is proved that d = 0 or $U\;{\subseteq}\;Z(R)$ if one of the following conditions holds: (1) $d(xy)\;-\;xy\;{\in}\;Z(R)$ or $d(xy)\;-\;yx\;{\in}Z(R)$ for all x, $y\;{\in}\;U$. (2) $d(x)\;{\circ}\;d(y)\;=\;0$ or $d(x)\;{\circ}\;d(y)\;=\;x\;{\circ}\;y$ for all x, $y\;{\in}\;U$ and d commutes with $\sigma$.

• Kyungpook Mathematical Journal
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• v.45 no.2
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• pp.199-209
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• 2005

An ideal space is ${\cal{I}}-resolvable$ if it has two disjoint ${\cal{I}}-dense$ subsets. We answer the question: If X is ${\cal{I}}-resolvable$, then is X (${\cal{I}}\;{\cup}\;{\cal{N}$)-resolvable?, posed by Dontchev, Ganster and Rose. We give three generalizations of the well known Banach Category Theorem and deduce the Banach category Theorem as a corollary. Characterizations of completely codense ideals and ${\cal{I}-locally$ closed sets are given and their properties are discussed.

• Fire Science and Engineering
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• v.17 no.2
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• pp.50-55
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• 2003

The lower flash points for the binary system, n-butanol+n-decane, were measured by Pensky-Martens closed cup tester. The experimental results showed the minimum in the flash point versus composition curve. The experimental data were compared with the values calculated by the reduced model under an ideal solution assumption and the flash point-prediction models based on the Van Laar and Wilson equations. The predictive curve based upon the reduced model deviated form the experimental data for this system. The experimental results were in good agreement with the predictive curves, which use the Van Laar and Wilson equations to estimate activity coefficients. However, the predictive curve of the flash point prediction model based on the Willson equation described the experimentally-derived data more effectively than that of the flash point prediction model based on the Van Laar equation.

• International Journal of Precision Engineering and Manufacturing
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• v.2 no.2
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• pp.73-80
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• 2001

The objective of this research is to develop a measurement error model for sculptured surface in On-Machine Measurement(OMM) process based on a closed-loop configuration. The geometric error model of each axis of a vertical CNC machining center is derived using a 4$\times$4 homogeneous transformation matrix. The ideal locations of a touch-type probe for the sculptured surface measurement are calculated from the parametric surface representation and X-, Y- directional geometric errors of the machine. Also the actual coordinates of the probe are calculated by considering the pre-travel variation of a probe and Z-directional geometric errors. Then, the step-by-sep measurement error analysis method is suggested based on a closed-loop configuration of the machining center including workpiece and probe errors. The simulation study shows the simplicity and effectiveness of the proposed error modeling strategy.

• Honam Mathematical Journal
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• v.41 no.4
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• pp.725-744
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• 2019

In this paper we introduce some new types of double difference sequence spaces defined by a new definition of convergence of double sequences and a double series with the help of sequence of Orlicz functions and a four dimensional bounded regular matrices A = (a_rtkl). We also make an effort to study some topological properties and inclusion relations between these sequence spaces. Finally, we compute the closed ideals in the space 𝑙²_∞.

• Journal of the Korean Society for Precision Engineering
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• v.16 no.10
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• pp.172-181
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• 1999

The objective of this research is to develop a measurement error model for sculptured surfaces in On-Machine Measurement (OMM) process based on a closed-loop configuration. The geometric error model of each axis of a vertical CNC Machining center is derived using a 4${\times}$4 homogeneous transformation matrix. The ideal locations of a touch-type probe for the scupltured surface measurement are calculated from the parametric surface representation and X-, Y- directional geometric errors of the machine. Also, the actual coordinates of the probe are calculated by considering the pre-travel variation of a probe and Z-directional geometric errors. Then, the step-by-step measurement error analysis method is suggested based on a closed-loop configuration of the machining center including workpiece and probe errors. The simulation study shows the simplicity and effectiveness of the proposed error modeling strategy.