• Title, Summary, Keyword: The Proving of Theorem

### CERTAIN METHODS FOR PROVING TWO RESULTS CONTIGUOUS TO KUMMER'S SECOND THEOREMS

• KIM, YONGSUP;RATHIE, ARJUN K.;CHOI, JUNESANG
• 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.

### An Investigation of Bisector of Interior and Exterior Angles in Triangle by Using Analogy (유추를 이용한 삼각형의 각의 이등분선 성질 탐구)

• 한인기
• 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.

### A Probabilistic Reasoning in Incomplete Knowledge for Theorem Proving (불완전한 지식에서 정리증명을 위한 확률추론)

• Kim, Jin-Sang;Shin, Yang-Kyu
• 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.

### On a New Selection Theorem

• Kim, Won Kyu
• 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.

### ANOTHER PROOF OF KUMMER'S SECOND THEOREM

• Arjun K. Rathie;Choi, June-Sang
• 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.

### Construction of the Digital Logic Systems based on the Improved Automatic Theorem Proving Techniques over Finite Fields (개선된 자동정리증명 기법에 기초한 유한체상의 디지털논리시스템 구성)

• Park, Chun-Myoung
• 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.

### 모어-마스케로니의 정리에 대한 고찰

• 한인기;강인주
• 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.

### ON PROVING THE TYCHONOFF PRODUCT THEOREM

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

### THE EXISTENCE OF THE SOLUTION OF ELLIPTIC SYSTEM APPLYING TWO CRITICAL POINT THEOREM

• Nam, Hyewon
• 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.

### A CHARACTERIZATION OF DIRICHLET SETS

• Lee, Hung-Hwan
• Bulletin of the Korean Mathematical Society
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• v.27 no.2
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• pp.183-188
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• 1990
• The notion of a Dirichlet set has been studied for several decades. Such sets are named in honour of Dirichlet's Theorem [4, pp.235] which, in modern terminology, simply says that every finite set in R is a dirichlet set. In this paper, we present a structure theorem which characterizes all D-sets on the real line. We also use our structure theorem to give a new proof of a known criterion for proving that a set fails to be a D-set.