• 대한수학회지
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• 제36권2호
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• pp.267-298
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• 1999

A geometric construction of an exact algebraic formula for graded partition functions, of which a special one is the classical unrestricted partition function p(n), from a diophantine point of view is presented. Moreover, the involved process allows us to compute the value of a graded partition function in an inductive manner with a geometrically built-in self-error-checking ability at each step for correctness of the computed values of the partition function under consideration.

• 대한수학회논문집
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• 제26권4호
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• pp.551-555
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• 2011

In this note, we will give a short proof of an identity for cubic partition function.

• Korean Journal of Mathematics
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• 제28권4호
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• pp.791-802
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• 2020

We obtain a two variable generating function for the number of triangular partitions. Using this generating function, we study arithmetic properties of a certain weighted count of triangular partitions. Finally, we introduce a rank-type function for triangular partitions, which gives a combinatorial explanation for a triangular partition congruence.

• 대한수학회논문집
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• 제27권3호
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• pp.477-482
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• 2012

In this note, we investigate partition congruences for a certain type of partition function, which is named as the overcubic partition pairs in light of the literature. Let $\bar{cp}(n)$ be the number of overcubic partition pairs. Then we will prove the following congruences: $$\bar{cp}(8n+7){\equiv}0(mod\;64)\;and\;\bar{cp}(9m+3){\equiv}0(mod\;3)$$.

• 호남수학학술지
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• 제39권3호
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• pp.379-399
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• 2017

The objective of this research article is to establish two relationships between q-product identities, theta function identities and combinatorial partition identities, using elementary results.

• 한국정보통신학회논문지
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• 제19권9호
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• pp.2029-2036
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• 2015

하둡 MR(MapReduce)는 매퍼(Mapper)의 출력을 리듀서(Reducer)의 입력으로 전달하기 위해 파티션 함수(Partition Function)을 사용한다. 파티션 함수는 키에서 해쉬 값을 계산한 후 리듀서 개수로 나머지 연산을 수행하여 대상 리듀서를 결정한다. 기존 파티션 함수는 키의 편중도에 민감하여 잡이 균등하게 배분될 수 없었다. 잡이 균등하게 배분되지 못하면 특정 리듀서들의 처리 수행 시간이 길어져 전체 분산 처리 수행 성능에 영향을 주게 된다. 이에 본 논문은 VPT(Virtual Partition Table)을 제안하고 편중도가 심한 데이터에 VPT을 적용하여 실험을 수행 하였다. 적용된 VPT는 기존 파티션 함수와 대비하여 평균 3초 정도 성능향상이 발생하였으며, 데이터 처리량이 증가할수록 성능 향상 폭이 증가할 것으로 예상된다.

• 전기의세계
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• 제23권4호
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• pp.53-59
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• 1974

This paper investigates the theoretical properties of a logic element called the multithreshold threshold element, which is a generalization of the single-threshold threshold element. The primary partition os a systematic method of obtaining the multi-threshold realization of a switching function by the index numbers. The concept of comparable vertices of the same index numbers introduced in this paper is very promising for testing the multi-threshold partition by the initial condition to be defined by the minterms of the same index numbers.

• Nuclear Engineering and Technology
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• 제5권2호
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• pp.77-82
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• 1973

Fermi통계를 도입한 새로운 밀도행렬을 정의함으로써 전자들의 Partition 함수를 구하는 방법이 마련되었다. 새 밀도행렬에 대응하는 Bloch방정식이 형성되었고 약한 Potential에 대하여 이것을 푸는 방법이 얻어겼다. 이 이론은 액체금속의 모델이 될 수 있는 구조적 불규칙계에 적용되었다.

• 한국지능시스템학회:학술대회논문집
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• 한국퍼지및지능시스템학회 1998년도 추계학술대회 학술발표 논문집
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• pp.433-439
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• 1998

In this paper, we present an approach to the structure identification based on the input space partition methods and to the parameter identification by hybrid learning method in neuro-fuzzy system. The structure identification can automatically estimate the number of membership function and fuzzy rule using grid partition, tree partition, scatter partition from numerical input-output data. And then the parameter identification is carried out by the hybrid learning scheme using back-propagation and least squares estimate. Finally, we sill show its usefulness for neuro-fuzzy modeling to truck backer-upper control.

• Journal of Electrical Engineering and information Science
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• 제1권1호
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• pp.164-172
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• 1996

The partitioning of related objects should be performed before clustering for an efficient access in object-oriented databases. In this paper, a horizontal partition of related objects in object-oriented databases is presented. All subclass nodes in a class inheritance hierarchy of a schema graph are shrunk to a class node in the graph that is called condensed schema graph because the aggregation hierarchy has more influence on the partition than the class inheritance hierarchy. A set function and an accessibility function are defined to find a maximal subset of related objects among the set of objects in a class. A set function maps a subset of the domain class objects to a subset of the range class objects. An accessibility function maps a subset of the objects of a class into a subset of the objects of the same class through a composition of set functions. The algorithm derived in this paper is to find the related objects of a condensed schema graph using accessibility functions and set functions. The existence of a maximal subset of the related objects in a class is proved to show the validity of the partition algorithm using the accessibility function.