• Communications of the Korean Mathematical Society
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• v.38 no.2
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• pp.331-340
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• 2023

In this paper, the concept of a maximal chain of ideals is introduced. Some properties of such chains are studied. We introduce some other concepts related to a maximal chain of ideals such as the n-maximal ideal, the maximal dimension of a ring S (M. dim(S)), the maximal depth of an ideal K of S (M.d(K)) and maximal height of an ideal K(M.d(K)).

• Journal of applied mathematics & informatics
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• v.41 no.5
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• pp.1145-1153
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• 2023

The notion of maximal product of two fuzzy graphs was introduced by Radha and Arumugam in 2015 and the notion of balanced fuzzy graph was introduced by Al-Hawary in 2011. In this paper, we give a modification of the maximal product definition, which we call maximal strong product. We also introduce the relatively new notion of maximal-balanced fuzzy graphs. We give necessary and sufficient conditions for the maximal strong product of two balanced (resp., maximal-balanced) fuzzy graphs to be balanced (resp., maximal-balanced) and we prove that these two independent notions are preserved under isomorphism.

• Bulletin of the Korean Mathematical Society
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• v.50 no.2
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• pp.627-637
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• 2013

Let [$n$] = {1, 2, ${\ldots}$, $n$} be ordered in the standard way. The order-preserving full transformation semigroup ${\mathcal{O}}_n$ is the set of all order-preserving singular full transformations on [$n$] under composition. For this semigroup we describe maximal subsemibands, maximal regular subsemibands, locally maximal regular subsemibands, and completely obtain their classification.

• The Korean Journal of Physiology
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• v.2 no.2
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• pp.11-20
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• 1968

Maximal oxygen uptake was measured in thirty-three secondary school girls by means of the treadmill test. Eighteen middle school girls aged 14.0 (range: $13.0{\sim}15.9$) years and fifteen high school girls aged 16.9 (range: $16.0{\sim}18.0$) years served as subjects. Maximal treadmill run lasted for 2 minutes and 20 seconds and the expired air was collected in a Douglas bag through a J-valve during the last one minute period. In general, absolute values of various measurements in the high school girls were greater than those of the middle school girls. When values were expressed on the body weight or lean body weight basis, however, work capacity of middle school girls was superior to that of the high school girls. The detailed results are as follows: 1. In middle school girls maximal oxygen uptake was 1.78 l/min., 47.4 ml/kg body weight, 12.3 ml/cm body height, and 61.7ml/kg lean body mass. In high school girls maximal oxygen uptake was 1.93 l/min., 39.7ml/kg body weight, 12.3 ml/cm body height, and 51.2 ml/kg LBM. Although the absolute value of maximal oxygen uptake was greater in high school girls than in middle school girls, values expressed on the body weight basis showed the reverse trend, namely, values of the middle school girls was greater than those of the high school girls. 2. The ratio of maximal to resting oxygen uptake was 8.8 in the middle school girls and was 10.2 in the high school girls. 3. Maximal pulmonary ventilation in the middle school girls was 55.3 l/min. and 66.1 l/min. in the high school girls. The ratio of maximal to resting pulmonary ventilation was 10.2 in the middle school girls and 10.1 in the high school girls. 4. The correlation between body weight and maximal oxygen uptake was relatively high, namely, r=0.79 both in middle and high school girls. The correlation coefficient between body weight and maximal pulmonary ventilation was a little less that of between maximal oxygen uptake and showed a value of r=0.60 both in middle and high school girls. The lean body mass was a poor reference of maximal oxygen uptake or maximal pulmonary ventilation as compared to body weight. The correlation between maximal oxygen uptake and maximal pulmonary ventilation was high and the coefficient of correlation in middle school girls was 0.927 and in high school girls it was 0.856. 5. Maximal ventilation equivalent was 30.9 liters in middle school girls and 33.9 liters in high school girls. This indicated that no hyperventilation was induced during the maximal of oxygen uptake exercise period as related to the maximal oxygen uptake. 6. Heart rate reached to the peak value within 1.5 minutes after beginning of maximal oxygen uptake run and remained at the same peak plateau level throughout the entire running period. Heart rate decreased steeply on cessation of running and subsided slowly thereafter. The maximal heart rate was 184 beat/min. in middle school girls and 189 beat/min. in high school girls. 7. Maximal oxygen pulse was 9.4 in middle school girls and 9.9 ml/beat in high school girls.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.13 no.3
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• pp.231-238
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• 1988

A new approach to the reachability analysis of communication protocols is presented using a modified maximal progress state exploation for two communicating finite state machines. The task of generating all reachable states is divided into two independent subtasks. In each subtask, only the states which are reachable by forcing modified maximal progress sequence for one machine are generated. Modified maximal progress state exploration saves space and time over maximal progress state exploration.

• Journal of the Korean Mathematical Society
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• v.34 no.1
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• pp.213-225
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• 1997

Let A be a real $m \times n$ matrix. The column rank of A is the dimension of the column space of A and the maximal column rank of A is defined as the maximal number of linearly independent columns of A. It is wekk known that the column rank is the maximal column rank in this situation.

• Communications of the Korean Mathematical Society
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• v.30 no.3
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• pp.277-282
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• 2015

We obtain some conditions for disconnectedness of a topological space in terms of maximal and minimal open sets, and some similar results in terms of maximal and minimal closed sets along with interrelations between them. In particular, we show that if a space has a set which is both maximal and minimal open, then either this set is the only nontrivial open set in the space or the space is disconnected. We also obtain a result concerning a minimal open set on a subspace.

• Communications of the Korean Mathematical Society
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• v.32 no.1
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• pp.175-181
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• 2017

In this paper, we introduce a notion of cleanly covered topological spaces along with two strong separation axioms. Some properties of cleanly covered topological spaces are obtained in term of maximal open sets including some similar properties of a topological space in term of maximal closed sets. Two strong separation axioms are also investigated in terms of minimal open and maximal closed sets.

• Journal of the Korean Mathematical Society
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• v.40 no.6
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• pp.943-950
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• 2003

The maximal column rank of an m by n matrix A over max algebra is the maximal number of the columns of A which are linearly independent. We compare the maximal column rank with rank of matrices over max algebra. We also characterize the linear operators which preserve the maximal column rank of matrices over max algebra.

• Communications of the Korean Mathematical Society
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• v.25 no.4
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• pp.623-628
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• 2010

Nakaoka and Oda ([1] and [2]) introduced the notion of maximal open sets and minimal closed sets in topological spaces. In this paper, we introduce new classes of sets called maximal $\theta$-open sets, minimal $\theta$-closed sets, $\theta$-semi maximal open and $\theta$-semi minimal closed and investigate some of their fundamental properties.