• Honam Mathematical Journal
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• v.21 no.1
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• pp.49-56
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• 1999

The object of this note is to provide various methods for proving two results contiguous to Kummer's second theorem by using the classical Gauss's summation theorem and contiguous relations.

• Journal of the Korean Data and Information Science Society
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• v.12 no.1
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• pp.61-69
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• 2001

We present a probabilistic reasoning method for inferring knowledge about mathematical truth before an automated theorem prover completes a proof. We use a Bayesian analysis to update beleif in truth, given theorem-proving progress, and show how decision-theoretic methods can be used to determine the value of continuing to deliberate versus taking immediate action in time-critical situations.

• Journal of the Chungcheong Mathematical Society
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• v.7 no.1
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• pp.47-51
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• 1994

The purpose of this note is to give a new selection theorem which is an essential tool for proving the new kind of existence theorem of the equilibrium price comparable to the Debreu-Gale-Nikaido theorem.

• The Mathematical Education
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• v.41 no.2
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• pp.215-225
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• 2002

In this paper we consider some properties of. bisector of interior angle(theorem 1) and exterior angle(theorem 2) in triangle by using analogy. As a result of analyzing various mathematics textbooks we have known that they focused not on relation between two theorems, but on describing two theorems. We have seen that theorem 2 is able to be inferred from theorem 1 by using analogy. After proving theorem 1 by some methods we analyze proof process, extract proof ideas, and analogize some ideas for proving theorem 2. From this we are able to find relationships between theorem 1 and 2.

• Communications of the Korean Mathematical Society
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• v.13 no.4
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• pp.933-936
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• 1998

We aim at giving another method of proving the well-known and useful Kummer's second theorem without changing its original form.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.10 no.10
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• pp.1773-1778
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• 2006

This paper propose the method of constructing the Digital Logic Systems based on the Improved Automatic Theorem Proving Techniques(IATP) over Finite Fields. The proposed method is as following. First, we discuss the background and the important mathematical properties for Finite Fields. Also, we discuss the concepts of the Automatic Theorem Proving Techniques(ATP) including the syntactic method and semantic method, and discuss the basic properties for the Alf. In this step, we define several definitions of the IAIP, Table Pseudo Function Tab and Equal. Next, we propose the T-gate as Building Block(BB) and describe the mathematical representation for the notation of T-gate. Then we discuss the important properties for the T-gate. Also, we propose the several relationships that are Identity relationship, Constant relationship, Tautology relationship and Mod R cyclic relationship. Then we propose Mod R negation gate and the manipulation of the don't care conditions. Finally, we propose the algorithm for the constructing the method of the digital logic systems over finite fields. The proposed method is more efficiency and regularity than my other earlier methods. Thet we prospect the future research and prospects.

• Kyungpook Mathematical Journal
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• v.30 no.1
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• pp.65-73
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• 1990

• Journal for History of Mathematics
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• v.13 no.2
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• pp.133-144
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• 2000

We study on a Mohr-Mascheroni theorem, which is the followings: If a construction problem is solved by euclidean tools(compass and ruler), then it can be solved using only compass. Though it is known that Mohr-Mascheroni theorem was proved by Mascheroni, but we have not any materials concerned with Mascheroni's work. In order to investigate Mohr-Mascheroni theorem, we analyze Euclid's Elements, and we draw some construction problems, which are essential for proving Mohr-Mascheroni theorem. We solve these problems using only compass. Though we don't solve all construction problems of Euclid's Elements, we can regard that Mohr-Mascheroni theorem is proved.

• Journal of the Chungcheong Mathematical Society
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• v.31 no.1
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• pp.53-64
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• 2018

This paper deals with the study of solutions for the elliptic system with jumping nonlineartity and growth nonlinearity and Dirichlet boundary condition. We apply the two critical point theorem when proving the existence of nontrivial solutions for the elliptic system. We define the energy functional associated to the elliptic system and prove that the functional has two critical values.

• East Asian mathematical journal
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• v.17 no.1
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• pp.33-45
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• 2001

In this paper an improved version of a fixed point theorem of the present author [3] in Banach algebras is obtained under the weaker conditions with a different method and using measure of non-compactness. The newly developed fixed point theorem is further-applied to certain nonlinear integral equations of mixed type for proving the existence theorems and stability of the solution in Banach algebras.