• Bulletin of the Korean Mathematical Society
• /
• v.51 no.4
• /
• pp.1055-1062
• /
• 2014

Let $O_n$ and $PO_n$ denote the order-preserving transformation and the partial order-preserving transformation semigroups on the set $X_n=\{1,{\ldots},n\}$, respectively. Then the strictly partial order-preserving transformation semigroup $SPO_n$ on the set $X_n$, under its natural order, is defined by $SPO_n=PO_n{\setminus}O_n$. In this paper we find necessary and sufficient conditions for any subset of SPO(n, r) to be a (minimal) generating set of SPO(n, r) for $2{\leq}r{\leq}n-1$.

• Communications of the Korean Mathematical Society
• /
• v.37 no.3
• /
• pp.669-679
• /
• 2022

We provide a characterization of the positive monoids (i.e., additive submonoids of the nonnegative real numbers) that satisfy the finite factorization property. As a result, we establish that positive monoids with well-ordered generating sets satisfy the finite factorization property, while positive monoids with co-well-ordered generating sets satisfy this property if and only if they satisfy the bounded factorization property.

• Korean Management Science Review
• /
• v.25 no.2
• /
• pp.81-88
• /
• 2008

This paper presents a new algorithm for the K shortest paths problem in a network. After a shortest path is produced with Dijkstra algorithm. detouring paths through inward arcs to every vertex of the shortest path are generated. A length of a detouring path is the sum of both the length of the inward arc and the difference between the shortest distance from the origin to the head vertex and that to the tail vertex. K-1 shorter paths are selected among the detouring paths and put into the set of K paths. Then detouring paths through inward arcs to every vertex of the second shortest path are generated. If there is a shorter path than the current Kth path in the set. this path is placed in the set and the Kth path is removed from the set, and the paths in the set is rearranged in the ascending order of lengths. This procedure of generating the detouring paths and rearranging the set is repeated until the $K^{th}-1$ path of the set is obtained. The computational results for networks with about 1,000,000 nodes and 2,700,000 arcs show that this algorithm can be applied to a problem of generating the detouring paths in the metropolitan traffic networks.

• Proceedings of the Korean Operations and Management Science Society Conference
• /
• 2006.11a
• /
• pp.60-66
• /
• 2006

This paper presents a new algorithm for the K shortest path problem in a directed network. After a shortest path is produced with Dijkstra algorithm, detouring paths through inward arcs to every vertex of the shortest path are generated. A length of a detouring path is the sum of both the length of the inward arc and the difference between the shortest distance from the origin to the head vertex and that to the tail vertex. K-1 shorter paths are selected among the detouring paths and put into the set of K paths. Then detouring paths through inward arcs to every vertex of the second shortest path are generated. If there is a shorter path than the current Kth path in the set, this path is placed in the set and the Kth path is removed from the set, and the paths in the set is rearranged in the ascending order of lengths. This procedure of generating the detouring paths and rearranging the set is repeated for the K-1 st path of the set. This algorithm can be applied to a problem of generating the detouring paths in the navigation system for ITS and also for vehicle routing problems.

• Kyungpook Mathematical Journal
• /
• v.54 no.4
• /
• pp.607-617
• /
• 2014

Let S = C(r,m), the finite cyclic semigroup with index r and period m. Each subsemigroup of S is cyclic if and only if either r = 1; r = 2; or r = 3 with m odd. For $r{\neq}1$, the maximum value of the minimum number of elements in a (minimal) generating set of a subsemigroup of S is 1 if r = 3 and m is odd; 2 if r = 3 and m is even; (r-1)/2 if r is odd and unequal to 3; and r/2 if r is even. The number of cyclic subsemigroups of S is $r-1+{\tau}(m)$. Formulas are also given for the number of 2-generated subsemigroups of S and the total number of subsemigroups of S. The minimal generating sets of subsemigroups of S are characterized, and the problem of counting them is analyzed.

• Korean Journal of Digital Imaging in Medicine
• /
• v.12 no.2
• /
• pp.97-101
• /
• 2010

This experimental study is carried out one of the General Hospital in Kyungbok providence. Abdomen Phantom being located Anterior-posterior(AP) position on portable bed, and the portable X-ray generating device was placed the phantom at $-90^{\circ}$ direction. The experiment were set 65 kVp, 10 mAs, $10{\times}10\;cm^2$, 100 cm(FOD) for the measurement. Digital proportional counting tube survey meter was used for measuring the space scatter dose. Measurement points of horizontal distribution was set up at $30^{\circ}$ interval by increasing 50 cm radius of upside, downside, left and right. Vertical distribution of measurement points were set up for the vertical plane with a radius of at $30^{\circ}$ intervals with 50cm increments. It is concluded that longer distance from the soure of X-ray significantly decrease radiation dose to the patient and use of the radiation protection device should be applied in clinical practice to reduce dose to the patient.

• Bulletin of the Korean Mathematical Society
• /
• v.51 no.6
• /
• pp.1841-1850
• /
• 2014

It is known that the ranks of the semigroups $\mathcal{SOP}_n$, $\mathcal{SPOP}_n$ and $\mathcal{SSPOP}_n$ (the semigroups of orientation preserving singular self-maps, partial and strictly partial transformations on $X_n={1,2,{\ldots},n}$, respectively) are n, 2n and n + 1, respectively. The idempotent rank, defined as the smallest number of idempotent generating set, of $\mathcal{SOP}_n$ and $\mathcal{SSPOP}_n$ are the same value as the rank, respectively. Idempotent can be seen as a special case (with m = 1) of m-potent. In this paper, we investigate the m-potent ranks, defined as the smallest number of m-potent generating set, of the semigroups $\mathcal{SOP}_n$, $\mathcal{SPOP}_n$ and $\mathcal{SSPOP}_n$. Firstly, we characterize the structure of the minimal generating sets of $\mathcal{SOP}_n$. As applications, we obtain that the number of distinct minimal generating sets is $(n-1)^nn!$. Secondly, we show that, for $1{\leq}m{\leq}n-1$, the m-potent ranks of the semigroups $\mathcal{SOP}_n$ and $\mathcal{SPOP}_n$ are also n and 2n, respectively. Finally, we find that the 2-potent rank of $\mathcal{SSPOP}_n$ is n + 1.

• Bulletin of the Korean Mathematical Society
• /
• v.46 no.5
• /
• pp.867-871
• /
• 2009

A module M over a ring R is said to satisfy (P) if every generating set of M contains an independent generating set. The following results are proved; (1) Let $\tau$ = ($\mathbb{T}_\tau,\;\mathbb{F}_\tau$) be a hereditary torsion theory such that $\mathbb{T}_\tau$ $\neq$ Mod-R. Then every $\tau$-torsionfree R-module satisfies (P) if and only if S = R/$\tau$(R) is a division ring. (2) Let $\mathcal{K}$ be a hereditary pre-torsion class of modules. Then every module in $\mathcal{K}$ satisfies (P) if and only if either $\mathcal{K}$ = {0} or S = R/$Soc_\mathcal{K}$(R) is a division ring, where $Soc_\mathcal{K}$(R) = $\cap${I 4\leq$ $R_R$ : R/I$\in\mathcal{K}$}.

• Journal of Digital Convergence
• /
• v.12 no.6
• /
• pp.223-229
• /
• 2014

In an attempt to retrieve useful information for an efficient decision in the large knowledge system, it is generally necessary and important for a refined feature selection. Rough set has difficulty in generating optimal reducts and classifying boundary objects. In this paper, we propose quick reduction algorithm generating optimal features by rough entropy analysis for condition and decision attributes to improve these restrictions. We define a new conditional information entropy for efficient feature extraction and describe procedure of feature selection to classify the significance of features. Through the simulation of 5 datasets from UCI storage, we compare our feature selection approach based on rough set theory with the other selection theories. As the result, our modeling method is more efficient than the previous theories in classification accuracy for feature selection.

• Journal of the Korean Institute of Telematics and Electronics
• /
• v.12 no.4
• /
• pp.21-27
• /
• 1975

In this paper, a procedure for deriving of multiple fault detection test sets is presented for fan-out reconvergent combinational logic networks. A fan-out network is decomposed into a set of fan-out free subnetworks by breaking the internal fan-out points, and the minimal detecting test sets for each subnetwork are found separately. And then, the compatible tests amonng each test set are combined maximally into composite tests to generate primary input binary vectors. The technique for generating minimal test experiments which cover all the possible faults is illustrated in detail by examples.