• Journal of applied mathematics & informatics
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• v.34 no.3_4
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• pp.309-317
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• 2016

Let V be a Euclidean Jordan algebra with a symmetric cone K. We show that for a Z-transformation L with the additional property L(K) ⊆ K (which we will call ’cone-preserving’), GUS ⇔ strictly copositive on K ⇔ monotone + P. Specializing the result to the Stein transformation S_A(X) := X - AXA^T on the space of real symmetric matrices with the property $S_A(S^n_+){\subseteq}S^n_+$, we deduce that S_A GUS ⇔ I ± A positive definite.

• Journal of applied mathematics & informatics
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• v.39 no.3_4
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• pp.487-496
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• 2021

In this paper we show that if A ∈ L(X) and B ∈ L(Y), X and Y complex Banach spaces, then A ⊕ B ∈ L(X ⊕ Y) is subscalar if and only if both A and B are subscalar. We also prove that if A, Q ∈ L(X) satisfies AQ = QA and Q^p = 0 for some nonnegative integer p, then A has property (C) (resp. property (𝛽)) if and only if so does A + Q (resp. property (𝛽)). Finally, we show that A ∈ L(X, Y) and B, C ∈ L(Y, X) satisfying operator equation ABA = ACA and BA ∈ L(X) is subscalar with property (𝛿) then both Lat(BA) and Lat(AC) are non-trivial.

• Journal of the Chungcheong Mathematical Society
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• v.30 no.4
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• pp.381-385
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• 2017

Let (X, d) be a compact metric space with metric d and let f : $X{\rightarrow}X$ be a continuous map. In this paper, we consider that for a subset ${\Lambda}$, a map f has the eventual shadowing property if and only if f has the eventual shadowing property on ${\Lambda}$. Moreover, a map f has the eventual shadowing property if and only if f has the eventual shadowing property in ${\Lambda}$.

• Journal of the Korean Mathematical Society
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• v.54 no.4
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• pp.1345-1356
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• 2017

For a given number field K, we show that the ranks of elliptic curves over K are uniformly finitely bounded if and only if the weak Mordell-Weil property holds in all (some) ultrapowers $^*K$ of K. We introduce the nonstandard weak Mordell-Weil property for $^*K$ considering each Mordell-Weil group as $^*{\mathbb{Z}}$-module, where $^*{\mathbb{Z}}$ is an ultrapower of ${\mathbb{Z}}$, and we show that the nonstandard weak Mordell-Weil property is equivalent to the weak Mordell-Weil property in $^*K$. In a saturated nonstandard number field, there is a nonstandard ring of integers $^*{\mathbb{Z}}$, which is definable. We can consider definable abelian groups as $^*{\mathbb{Z}}$-modules so that the nonstandard weak Mordell-Weil property is well-defined, and we conclude that the nonstandard weak Mordell-Weil property and the weak Mordell-Weil property are equivalent. We have valuations induced from prime numbers in nonstandard rational number fields, and using these valuations, we identify two nonstandard rational numbers.

• Communications of the Korean Mathematical Society
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• v.12 no.4
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• pp.865-868
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• 1997

Let R be a ring with a unity and let M be a unitary left R-module. In this paper, we establish [5, Proposition 2.8] by showing the proof of it. Moreover, from the above result, we obtain some properties of direct projective modules which have the summand sum property.

• Journal of the Chungcheong Mathematical Society
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• v.6 no.1
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• pp.53-57
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• 1993

Let E and F be Banach spaces with $X{\subset}E$ and $Y{\subset}F$. Suppose that X is weakly compact, convex and has the fixed point property for a nonexpansive mapping, and Y has the fixed point property for a multivalued nonexpansive mapping. Then $(X{\oplus}Y)_p$, $1{\leq}$ P < ${\infty}$ has the fixed point property for a multi valued nonexpansive mapping. Furthermore, if X has the generic fixed point property for a nonexpansive mapping, then $(X{\oplus}Y)_{\infty}$ has the fixed point property for a multi valued nonexpansive mapping.

• Toxicological Research
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• v.23 no.2
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• pp.115-121
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• 2007

Biotechnology is often described as the 'exploitation of biological processes for industrial purposes'. The last twenty years have seen phenomenal growth in this industry. The 21 century promises to see further advances in the field. However, since the cost of research is high, and the potential returns are linked to exclusivity, intellectual property protection is critical to this burgeoning industry. Without protection such investments in R&D would not be made and, the benefit that BT-related development are expected to bring, would not occur. BT industry are eager for high technology, and the technology must be transferred to a corporation from a research organization. In order to be successful, it is important that scientist must be directed toward R&D outcome beyond performance assessment. The process to gain a outcome involves multiple steps to turn the idea into the profit, and intellectual property issues are considered into the critical factors to affect the quality of R&D. The management of Intellectual property is very important in R&D. However, According to the survey conducted by KIIP (Korea Institute of Intellectual Property) and KOSEF (Korea Science and Engineering Foundation) in 2006, it is estimated the ability to treat Intellectual property is not sufficient because 82.5% of the respondents have not received an education. Governmental Support is needed to prompt systematically the ability of intellectual property management through education and consulting.

• International Journal of Contents
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• v.7 no.4
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• pp.30-34
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• 2011

A Leader is a Coordinator that supports a set of processes to cooperate a given task. This concept is used in several domains such as distributed systems, parallelism and cooperative support for cooperative work. In completely asynchronous systems, there is no solution for the election problem satisfying both of safety and liveness properties in asynchronous distributed systems. Therefore, to solve the election problem in those systems, one property should be weaker than the other property. If an election algorithm strengthens the safety property in sacrifice of liveness property, it would not nearly progress. But on the contrary, an election algorithm strengthening the liveness property in sacrifice of the safety property would have the high probability of violating the safety property. In this paper, we presents a safety strengthened Leader Election protocol with an unreliable failure detector and analyses it in terms of safety and liveness properties in asynchronous distributed systems.

• Communications of the Korean Mathematical Society
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• v.21 no.2
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• pp.355-361
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• 2006

We prove that if a continuous surjective map f on a compact metric space X has the average shadowing property, then every point x is chain recurrent. We also show that if a homeomorphism f has more than two fixed points on $S^1$, then f does not satisfy the average shadowing property. Moreover, we construct a homeomorphism on a circle which satisfies the shadowing property but not the average shadowing property. This shows that the converse of the theorem 1.1 in [6] is not true.

• International Commerce and Information Review
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• v.6 no.1
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• pp.249-265
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• 2004

In the current digital age, most of the countries in the world recognize the electronic business to be a very prospective area in the future and plan to activate for the preoccupation of the business. As a result, this led a rapid increase of the electronic business volume. Electronic business takes place in the cyber space, using internet. However, the intellectual property rights have a high degree of possibility of being infringed as the digitalized intellectual property is easy to receive, copy and transmit in the cyber space. The language structure on the web, represented by HTML, makes easier to copy the intellectual property. And, as the internet has no national boundary, the infringement of the intellectual property rights is easier regardless of country, which could lead to the commercial disputes between the concerned countries. There are in fact many legal disputes nowadays on the infringement of the intellectual property rights in such field as computer programming, infringement of the copyright, business model patent and infringement of the trademark right on the registered name of the domain. It is, therefore, time now to prepare a new theory or legal system to protect the intellectual property rights on copyright, patent and trademark right so as to comply with the digital environment together with such a splendid growth of "electronic business." USA and Germany are nowadays making a significant movement on the legislation of the electronic business, and this study will focus on the legislative contents, judicial precedents and interpretation of law in the above countries.