• Journal of Korea Society of Digital Industry and Information Management
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• v.4 no.3
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• pp.33-43
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• 2008

As internet is spreaded widely, the number of cyber terror using hacking and virus is increased. Also the hacking to the internet shopping mall go on increasing. If the large shopping mall is attacked by the hacker, a number of user's information are exposed to the hacker. The private information as like a resident registration number, user's real name, the date of user's birth, the mobile phone number, the office phone number / address, the home phone number / address and so on include the information. These information are used in the phishing e-mails / call and spam. And them are selling and buying maliciously. The large internet shopping mall 'auction' was hacked in April, 2008. After the incident, this paper suggested a countermeasures on the hacking for the internet shopping mall. The technical item and political item are included among the countermeasures. The countermeasures can protect the hacking not only the internet shopping mall but also the web sites basically.

• Journal for History of Mathematics
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• v.30 no.2
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• pp.71-86
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• 2017

When looking for solutions of Jisuguimundo with magic number 88~92 and 94~98, alternating method is applied to each possible partitions of each magic number. But this method does not apply in case of finding solutions of Jisuguimundo with magic number 87, 93, and 99. In this study, it is shown that solutions of Jisuguimundo with magic number 87, 93, and 99 can be found by applying alternating method to two partitions. These two partitions are derived partitions obtained by each partitions of magic number 87, 93, and 99. If every number from 1 to 30 which satisfy every unit path of Jisuguimundo can be found in all components of these two derived partitions, that arrangement is just a solution of Jisuguimundo. The method suggested in this study is more developed one than the method which is applied to just one partition.

• Bulletin of the Korean Mathematical Society
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• v.56 no.4
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• pp.1059-1075
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• 2019

Let G be a graph with no isolated vertex. A total dominating set, abbreviated TDS of G is a subset S of vertices of G such that every vertex of G is adjacent to a vertex in S. The total domination number of G is the minimum cardinality of a TDS of G. In this paper, we study the total domination number of central graphs. Indeed, we obtain some tight bounds for the total domination number of a central graph C(G) in terms of some invariants of the graph G. Also we characterize the total domination number of the central graph of some families of graphs such as path graphs, cycle graphs, wheel graphs, complete graphs and complete multipartite graphs, explicitly. Moreover, some Nordhaus-Gaddum-like relations are presented for the total domination number of central graphs.

• Bulletin of the Korean Mathematical Society
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• v.60 no.4
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• pp.1017-1024
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• 2023

A celebrated result in the study of integer partitions is the identity due to Lehmer whereby the number of partitions of n with an even number of even parts minus the number of partitions of n with an odd number of even parts equals the number of partitions of n into distinct odd parts. Inspired by Lehmer's identity, we prove explicit formulas for evaluating generating functions for sequences that enumerate integer partitions of fixed width with an even/odd number of even parts. We introduce a technique for decomposing the even entries of a partition in such a way so as to evaluate, using a finite sum over q-binomial coefficients, the generating function for the sequence of partitions with an even number of even parts of fixed, odd width, and similarly for the other families of fixed-width partitions that we introduce.

• Journal of applied mathematics & informatics
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• v.41 no.6
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• pp.1193-1207
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• 2023

In this paper, we introduce an iP₂ extension of a star graph S_n for n ≥ 2 and 1 ≤ i ≤ n - 1. Certain general properties satisfied by order, size, domination (or Roman) numbers γ (or γ_R) of an iP₂ extended star graph are studied. Finally, we study how the parameters such as chromatic number and harmonious chromatic number are affected when an iP₂ extension process acts on the star graphs.

• Journal of Animal Science and Technology
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• v.45 no.6
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• pp.917-922
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• 2003

This study was conducted to investigate effects of farm, type of sow Landrace${\times}$Yorkshire, LY; Yorkshire${\times}$ Landrace, YL; Yorkshire${\times}$Yorkshire, YY and multi-cross bred sow, MBS), parity, farrowing year, farrowing season and mating method on reproductive traits such as total number born per litter, number of born alive per litter, number of weaned per litter, number of mummified per litter, number of stillbirth. The Reproductive Records of 3,387 litters from January, 1999 to September, 2002 were obtained from four pig farms managed by Electronic Data Processing(EDP) system. Reproductive performances for two types of F1 Sows(YL and LY) were estimated as 11.34${\pm}$0.266 and 11.57${\pm}$0.263 heads for total number of born per litter, 10.56${\pm}$0.216 and 11.81${\pm}$0.251 heads for number of born alive per litter, and 10.05${\pm}$0.131 and 9.96${\pm}$0.153 heads for number of weaned per litter, respectively. These records are significantly higher(P〈0.05) than those of YY and MBS. However, number of mummified per litter, number of stillborn per litter, number of dead by diarrhea per litter, number of dead by other reasons during lactating period per litter and estrus interval did not show significant difference between types of sows. There were more total number of born per litter and number of weaned per litter in year 2001 than other year. As year passed, number of dead by crush per litter, number of dead by diarrhea per litter and number of dead by other reasons during lactating period per litter reduced from 0.18${\pm}$0.023 to 0.07${\pm}$0.022 head, 0.12${\pm}$0.21 to 0.02${\pm}$0.020 head and 0.43${\pm}$0.041 to 0.22${\pm}$0.040 head, respectively and weaning rate increased from 0.94${\pm}$0.005% to 0.97${\pm}$0.005%. The total number of born per litter and number of born alive per litter were higher(P〈0.05) in the case of mating twice than mating once. The number of weaned per litter, number of mummified per litter and number of stillborn per litter were not significant(P〈0.05) between mating methods. Estrus interval was shorter on the occasion of twice artificial insemination(5.24${\pm}$0.153days) than twice natural mating(6.51${\pm}$0.466days).

• Journal of the Chungcheong Mathematical Society
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• v.19 no.4
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• pp.403-408
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• 2006

A pebbling move on a connected graph G is taking two pebbles off of one vertex and placing one of them on an adjacent vertex. The domination cover pebbling number ${\psi}(G)$ is the minimum number of pebbles required so that any initial configuration of pebbles can be transformed by a sequence of pebbling moves so that the set of vertices that contain pebbles forms a domination set of G. We determine the domination cover pebbling number for fans, fuses, and pseudo-star.

• Journal of the Korean Mathematical Society
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• v.41 no.5
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• pp.921-931
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• 2004

We derive a formula for the expected value $\mu$(n) of the independent domination number of a random directed rooted tree with n labeled vertices and determine the asymptotic behavior of $\mu$(n) as n goes to infinity.

• Journal of the Korean Mathematical Society
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• v.33 no.4
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• pp.709-716
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• 1996

Nielsen coincidence theory is concerned with the determinatin of a lower bound of the minimal number MC[f,g] of coincidence points for all maps in the homotopy class of a given map (f,g) : X $\to$ Y. The Nielsen Nielsen number $N_R(f,g)$ (similar to [9]) is introduced in [3], which is a lower bound for the number of coincidence points in the relative homotopy class of (f,g) and $N_R(f,g) \geq N(f,g)$.

• Communications of the Korean Mathematical Society
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• v.28 no.2
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• pp.361-369
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• 2013

We introduce a Nielsen type number of a fibre preserving map, and show that it is a lower bound for the number of $n$-orbits in the homotopy class. Under suitable conditions we show that it is equal to the Nielsen type relative essential $n$-orbit number. We also give necessary and sufficient conditions for it and the essential $n$-orbit number to coincide.