• Journal of Educational Research in Mathematics
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• v.19 no.4
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• pp.479-491
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• 2009

This paper researches the possibility of introducing Descartes' theorem to mathematically gifted students. Not only is Descartes' theorem logically equivalent to Euler's theorem but is hierarchically connected with Gauss-Bonnet theorem which is the core concept on differential geometry. It is possible to teach mathematically gifted students Descartes' theorem by generalizing mathematical property in solid geometry through analogical reasoning, that is, so in a polyhedrons the sum of the deficient angles is $720^\circ$ as in an polygon the sum of the exterior angles is $360^\circ$. This study introduces an alternative method of instruction that we enable mathematically gifted students to reinvent Descartes' theorem through analogical reasoning instead of deductive reasoning.

• Proceedings of the IEEK Conference
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• 1999.06a
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• pp.1013-1016
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• 1999

Simple Genetic Algorithm(SGA) proposed by J. H. Holland is a population-based optimization method based on the principle of the Darwinian natural selection. The theoretical foundations of GA are the Schema Theorem and the Building Block Hypothesis. Although GA does well in many applications as an optimization method, still it does not guarantee the convergence to a global optimum in GA-hard problems and deceptive problems. Therefore as an alternative scheme, there is a growing interest in a co-evolutionary system, where two populations constantly interact and co-evolve. In this paper we propose an extended schema theorem associated with a schema co-evolutionary algorithm(SCEA), which explains why the co-evolutionary algorithm works better than SGA. The experimental results show that the SCEA works well in optimization problems including deceptive functions.

• Kyungpook Mathematical Journal
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• v.49 no.4
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• pp.691-700
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• 2009

We use the fixed alternative theorem to establish Hyers-Ulam-Rassias stability of the quadratic functional equation where functions map a linear space into a complete quasi p-normed space. Moreover, we will show that the continuity behavior of an approximately quadratic mapping, which is controlled by a suitable continuous function, implies the continuity of a unique quadratic function, which is a good approximation to the mapping. We also give a few applications of our results in some special cases.

• Korean Journal of Logic
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• v.20 no.2
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• pp.241-271
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• 2017

Dialetheism is the view that there exists a true contradiction. This paper ventures to suggest that Priest's argument for Dialetheism from $G{\ddot{o}}del^{\prime}s$ theorem is unconvincing as the lesson of $G{\ddot{o}}del^{\prime}s$ proof (or Rosser's proof) is that any sufficiently strong theories of arithmetic cannot be both complete and consistent. In addition, a contradiction is derivable in Priest's inconsistent and complete arithmetic. An alternative argument for Dialetheism is given by applying $G{\ddot{o}}del$ sentence to the inconsistent and complete theory of arithmetic. We argue, however, that the alternative argument raises a circularity problem. In sum, $G{\ddot{o}}del^{\prime}s$ and its related theorem merely show the relation between a complete and a consistent theory. A contradiction derived by the application of $G{\ddot{o}}del$ sentence has the value of true sentences, i.e. the both-value, only under the inconsistent models for arithmetic. Without having the assumption of inconsistency or completeness, a true contradiction is not derivable from the application of $G{\ddot{o}}del$ sentence. Hence, $G{\ddot{o}}del^{\prime}s$ and its related theorem never can be a ground for Dialetheism.

• Honam Mathematical Journal
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• v.30 no.2
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• pp.363-368
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• 2008

In this paper, we find some properties of multiplication modules and give an alternative proof of a Theorem of P.F. Smith.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.2 no.1
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• pp.95-110
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• 1998

Evolutionary Algorithms (EAs) are population-based optimization methods based on the principle of Darwinian natural selection. The representative methodology in EAs is genetic algorithm (GA) proposed by J. H. Holland, and the theoretical foundations of GA are the Schema Theorem and the Building Block Hypothesis. In the meaning of these foundational concepts, simple genetic algorithm (SGA) allocate more trials to the schemata whose average fitness remains above average. Although SGA does well in many applications as an optimization method, still it does not guarantee the convergence of a global optimum in GA-hard problems and deceptive problems. Therefore as an alternative scheme, there is a growing interest in a co-evolutionary system, where two populations constantly interact and co-evolve in contrast with traditional single population evolutionary algorithm. In this paper we show why the co-evolutionary algorithm works better than SGA in terms of an extended schema theorem. And predator-prey co-evolution and symbiotic co-evolution, typical approaching methods to co-evolution, are reviewed, and dynamic fitness landscape associated with co-evolution is explained. And the experimental results show a co-evolutionary algorithm works well in optimization problems even though in deceptive functions.

• The Journal of the Korean dental association
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• v.48 no.7
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• pp.514-521
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• 2010

The relationship between dental occlusion to temporomandibular Joint (TMJ), systemic symptoms and health has been discussed and theoretical reasons have been the foundation for treatments performed by various areas of alternative treatments. It has been noted that there have been increase in the available methods and treatments for the general public regarding these areas of treatment modality. Korean Academy of Stomatognathic function and Occlusion have carried out literature review of five of those treatment theories available; they are Craniosacral mechanism, Osteopathy, Myodontics, Chirodontics, Dental distress syndrome and Quadrant theorem. Each of these modalities will be introduced and brief summary of their efficacy and efficiency will be discussed.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.3 no.1
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• pp.115-125
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• 1999

Simple Genetic Algorithm(SGA) proposed by J. H. Holland is a population-based optimization method based on the principle of the Darwinian natural selection. The theoretical foundations of GA are the Schema Theorem and the Building Block Hypothesis. Although GA does well in many applications as an optimization method, still it does not guarantee the convergence to a global optimum in some problems. In designing intelligent systems, specially, since there is no deterministic solution, a heuristic trial-and error procedure is usually used to determine the systems' parameters. As an alternative scheme, therefore, there is a growing interest in a co-evolutionary system, where two populations constantly interact and co-evolve. In this paper we review the existing co-evolutionary algorithms and propose co-evolutionary schemes designing intelligent systems according to the relation between the system's components.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1998.03a
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• pp.77-80
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• 1998

The theoretical foundations of simple genetic algorithm(SGA) are the Schema Theorem and the Building Block Hypothesis. Although SGA does well in many applications as an optimization method, still it does not guarantee the convergence of a global optimum in GA-hard problems and deceptive problems. Therefore as an alternative scheme, there is a growing interest in a co-evolutionary system, where two populations constantly interact and cooperate each other. In this paper we show why the co-evolutionary algorithm works better than SGA in terms of an extended schema theorem. Also the experimental results show a co-evolutionary algorithm works well in optimization problems.

• Nonlinear Functional Analysis and Applications
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• v.26 no.1
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• pp.197-223
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• 2021

In this paper, we investigate existence, uniqueness and four different types of Ulam's stability, that is, Ulam-Hyers stability, generalized Ulam-Hyers stability, Ulam-Hyers-Rassias stability and generalized Ulam-Hyers-Rassias stability of the solution for a class of nonlinear fractional Pantograph differential equation in term of a proportional Caputo fractional derivative with mixed nonlocal conditions. We construct sufficient conditions for the existence and uniqueness of solutions by utilizing well-known classical fixed point theorems such as Banach contraction principle, Leray-Schauder nonlinear alternative and $Krasnosel^{\prime}ski{\breve{i}}{^{\prime}}s$ fixed point theorem. Finally, two examples are also given to point out the applicability of our main results.