• Bulletin of the Korean Mathematical Society
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• v.61 no.1
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• pp.247-262
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• 2024

In this paper we introduce and study the notions of topological sensitivity and its stronger forms on semiflows and on product semiflows. We give a relationship between multi-topological sensitivity and thick topological sensitivity on semiflows. We prove that for a Urysohn space X, a syndetically transitive semiflow (T, X, 𝜋) having a point of proper compact orbit is syndetic topologically sensitive. Moreover, it is proved that for a T₃ space X, a transitive, nonminimal semiflow (T, X, 𝜋) having a dense set of almost periodic points is syndetic topologically sensitive. Also, wherever necessary examples/counterexamples are given.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.8 no.6
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• pp.15-20
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• 2008

Provable security has widely been used to prove a cryptosystem's security formally in crpytography. In this paper, we analyze the Cramer-Shoup public key cryptosystem that has been known to be provable secure against adaptive chosen ciphertext attack and argue that its security proof is not complete in the generic sense of adaptive chosen ciphertext attack. Future research should be directed toward two directions: one is to make the security proof complete even against generic sense of adaptive chosen ciphertext attack, and another is to try finding counterexamples of successful adaptive chosen ciphertext attack on the Cramer-Shoup cryptosystem.

• Research in Mathematical Education
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• v.12 no.4
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• pp.283-291
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• 2008

The extension to a wide population of secondary education in many advanced countries seems to have led to a weakening of the mathematics curriculum. In response, many students have been classified as "gifted" so that they can access a stronger program. Apart from the difficulties that might arise in actually determining which students are gifted (Is it always clear what the term means?), there are dangers inherent in programs that might be devised even for those that are truly talented. Sometimes students are moved ahead to more advanced mathematics. Elementary students might be taught algebra or even subjects like trigonometry and vectors, and secondary students might be taught calculus, differential equations and linear algebra. It is my experience over thirty-five years of contact with bright students that acceleration to higher level mathematics is often not a good idea. In this paper, I will articulate some of the factors that have led me to this opinion and suggest alternatives. First, I would like to emphasize that in matters of education, almost every statement that can be made to admit counterexamples; my opinion on acceleration is no exception. Occasionally, a young Gauss or Euler walks in the door, and one has no choice but to offer the maximum encouragement and allow the student to go to the limit of his capabilities. A young genius can demonstrate an incredible amount of mathematical insight, maturity and mastery of technique. A classical example is probably the teen-age Euler, who in the 1720s was allowed regular audiences with Jean Bernoulli, the foremost mathematician of his day.

• Bulletin of the Korean Mathematical Society
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• v.39 no.3
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• pp.411-422
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• 2002

In this note we are concerned with relationships between one-sided ideals and two-sided ideals, and study the properties of polynomial rings whose maximal one-sided ideals are two-sided, in the viewpoint of the Nullstellensatz on noncommutative rings. Let R be a ring and R[x] be the polynomial ring over R with x the indeterminate. We show that eRe is right quasi-duo for $0{\neq}e^2=e{\in}R$ if R is right quasi-duo; R/J(R) is commutative with J(R) the Jacobson radical of R if R[$\chi$] is right quasi-duo, from which we may characterize polynomial rings whose maximal one-sided ideals are two-sided; if R[x] is right quasi-duo then the Jacobson radical of R[x] is N(R)[x] and so the $K\ddot{o}the's$ conjecture (i.e., the upper nilradical contains every nil left ideal) holds, where N(R) is the set of all nilpotent elements in R. Next we prove that if the polynomial rins R[x], over a reduced ring R with $\mid$X$\mid$ $\geq$ 2, is right quasi-duo, then R is commutative. Several counterexamples are included for the situations that occur naturally in the process of this note.

• Korean Journal of Logic
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• v.18 no.2
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• pp.265-289
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• 2015

The idea that an effect counterfactually depends on its cause is simple and intuitive. However, this simple idea runs into various difficulties. The active route account, in order to avoid the difficulties, analyzes causation in terms of counterfactual dependence under certain control. In her recent article, Seahwa Kim criticizes Sungsu Kim's earlier attempt to defend the active route account from its counterexamples. Her criticisms are convincing, and defenders of the active route account or counterfactual analysis of causation in general need another defense. In response, a two-step defense is proposed. First, the scope of the active route account is restricted to 'proximate' causal relation. Second, a control over factors that are in proximate causal relation is offered to figure out 'distant' causal relation. The result is that with proper control, an effect indeed counterfactually depends on its cause.

• The KIPS Transactions:PartD
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• v.12D no.1 s.97
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• pp.81-90
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• 2005

Given a model and a property, model checking determines whether the model satisfies the property. In case the model does not satisfy the property model checking gives a counterexample which explains where the violation occurs. Since counterexamples are useful for model debugging as well as model understanding, counterexample generation is one of the indispensable components in the model checking tool. This paper presents efficient counterexample generation techniques when a safety property is falsified. These techniques are used to solve Push Push games which consist of 50 games. As a result, all the games are solved with the proposed techniques. However, with the original NuSMV, 42 games are solved but 8 failed. In addition, we obtain $86{\%}$ time improvement and $62{\%}$ space improvement compared to the original NuSMV in solving the game.

• Journal of Educational Research in Mathematics
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• v.23 no.4
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• pp.553-565
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• 2013

The purpose of this study was to examine how the Lakatos method works in the elementary teacher education program. Elementary preservice teachers were given a task in which they examined the Pick's theorem. The finding revealed that Lakatos method was usable in the elementary teacher education. They produced initial conjecture and found counterexamples, and finally made improved conjectures. These experience encourage them to change their belief of teaching and learning mathematics and to find alternative ways of teaching mathematics.

• Korean Journal of Logic
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• v.18 no.3
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• pp.337-358
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• 2015

Vann Mcgee produced "counterexamples" to Modus Ponens in "A Counterexample to Modus Ponens". Discussions about the examples tended to focus on a probabilistic reading of conditional statements. This article attempts to establish both (1) Modus Ponens is a deductively valid rule of inference, and (2) the counterexample-like appearance of Mcgee's example can be (and should be) explained without making a reference to the notion of conditional probability. The reason why his examples seem to counter Modus Ponens is found rather within the ambiguity a conditional statement exhibits. That is, Mcgee's examples are cases of equivocation on the conditional statements involved.

• Korean Journal of Logic
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• v.21 no.2
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• pp.175-207
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• 2018

Since Kit Fine's influential paper, Essence and Modality (1994), many philosophers have doubted the prospects of modalism, according to which we can analyze the concept of essence with that of de re modality. However, some philosophers have tried to save modalism against Fine's counterexamples seriously. In this paper, we examine two such attempts which appeal to some kind of 'impossible possibilities.' We argue that such attempts have strong tendency to end in either a metaphysical picture which is very similar to Fine's or a concept of essence which is quite different from Fine's. For this reason, we claim that Fine has no reason to worry about such attempts.

• Bulletin of the Korean Mathematical Society
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• v.58 no.1
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• pp.31-46
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• 2021

Let a and b be positive integers, and let V (G), ��(G), and ��2(G) be the vertex set of a graph G, the minimum degree of G, and the minimum degree sum of two non-adjacent vertices in V (G), respectively. An even [a, b]-factor of a graph G is a spanning subgraph H such that for every vertex v ∈ V (G), dH(v) is even and a ≤ dH(v) ≤ b, where dH(v) is the degree of v in H. Matsuda conjectured that if G is an n-vertex 2-edge-connected graph such that $n{\geq}2a+b+{\frac{a^2-3a}{b}}-2$, ��(G) ≥ a, and ${\sigma}_2(G){\geq}{\frac{2an}{a+b}}$, then G has an even [a, b]-factor. In this paper, we provide counterexamples, which are highly connected. Furthermore, we give sharp sufficient conditions for a graph to have an even [a, b]-factor. For even an, we conjecture a lower bound for the largest eigenvalue in an n-vertex graph to have an [a, b]-factor.