• Journal of the Korean Mathematical Society
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• v.36 no.2
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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.

• Communications of the Korean Mathematical Society
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• v.26 no.4
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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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• v.28 no.4
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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.

• Communications of the Korean Mathematical Society
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• v.27 no.3
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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: $$\bar{cp}(8n+7){\equiv}0(mod\;64)\;and\;\bar{cp}(9m+3){\equiv}0(mod\;3)$$.

• Honam Mathematical Journal
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• v.39 no.3
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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.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.19 no.9
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• pp.2029-2036
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• 2015

Hadoop MR(MapReduce) uses a partition function for passing the outputs of mappers to reducers. The partition function determines target reducers after calculating the hash-value from the key and performing mod-operation by reducer number. The legacy partition function doesn't divide the job effectively because it is so sensitive to key distribution. If the job isn't divided effectively then it can effect the total processing time of the job because some reducers need more time to process. This paper proposes the VPT(Virtual Partition Table) and has tested appling the VPT with a preponderance of data. The applied VPT improved three seconds on average and we figure it will improve more when data is increased.

• 전기의세계
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• v.23 no.4
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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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• v.5 no.2
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• pp.77-82
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• 1973

A method of obtaining the partition function for a system of electrons is developed by defining a new density matrix, in which the Fermi statistics is explicitly incorporated. The corresponding Bloch equation is formulated and a practical method of solving the equation is obtained for weak potential. This theory is applied to structurally disordered ststems which might be reasonable models for liquid metals.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1998.10a
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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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• v.1 no.1
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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.