• 제목/요약/키워드: The Proving of Theorem

검색결과 53건 처리시간 0.022초

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

  • 김진상;신양규
    • Journal of the Korean Data and Information Science Society
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    • 제12권1호
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    • pp.61-69
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    • 2001
  • 본 논문은 논리문장으로 표현된 지식을 처리하는 정리증명 과정에서 증명이 완료되기 전에 잠정적 결론을 유도하는 확률추론 기법을 제시한다. 정리증명 과정 중에 베이지안 해석을 이용하여 지식을 갱신하는 방법을 제시하고, 의사결정 방법을 사용하여 시간에 민감한 사안에 대해 신속하게 대처할 것인지 아니면 고의로 미룰 것인지를 결정하는 방법을 밝힌다.

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On a New Selection Theorem

  • Kim, Won Kyu
    • 충청수학회지
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    • 제7권1호
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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.

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

  • 한인기
    • 한국수학교육학회지시리즈A:수학교육
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    • 제41권2호
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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.

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ANOTHER PROOF OF KUMMER'S SECOND THEOREM

  • Arjun K. Rathie;Choi, June-Sang
    • 대한수학회논문집
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    • 제13권4호
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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.

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

  • 박춘명
    • 한국정보통신학회논문지
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    • 제10권10호
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    • pp.1773-1778
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    • 2006
  • 본 논문에서는 개선된 자동정리증명 기법에 기초하여 유한체상의 디지털논리 시스템을 구성하는 방법을 제안하였다. 제안한 방법은 먼저 유한체상의 중요한 학적 성질을 논의하였고 자동정리증명기법의 개념과 기본 성질을 서술하였다. 그리고 개선된 자동정리증명기법을 적용하기 위해 몇 가지 정의를 하였으며 이를 근간으로 디지털논리 시스템의 Building Block을 제안하였다. 또한, 디지털논리 시스템을 구성하기 위한 중요한 관계를 정의하였으며 최종 유한체상의 디지털논리시스템을 개선된 자동정리 증명 기법에 의해 구성하였다.

모어-마스케로니의 정리에 대한 고찰

  • 한인기;강인주
    • 한국수학사학회지
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    • 제13권2호
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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.

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

  • Nam, Hyewon
    • 충청수학회지
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    • 제31권1호
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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.

ON EXISTENCE THEOREMS FOR NONLINEAR INTEGRAL EQUATIONS IN BANACH ALGEBRAS VIA FIXED POINT TECHNIQUES

  • Dhage, B.C.
    • East Asian mathematical journal
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    • 제17권1호
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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.

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