• 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: $$\bar{cp}(8n+7){\equiv}0(mod\;64)\;and\;\bar{cp}(9m+3){\equiv}0(mod\;3)$$.

• Communications of the Korean Mathematical Society
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• v.32 no.3
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• pp.565-566
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• 2017

An error in the proof of Theorem 1 of "On partition congruences for overcubic partition pairs" [Commun. Korean Math. Soc. 27 (2012), no. 3, 477-482] is corrected.

• Korean Journal of Mathematics
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• v.23 no.4
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• pp.637-642
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• 2015

We study congruence properties of the number of cubic partition pairs weighted by the parity of the crank. If we define such number to be c(n), then $c(5n+4){\equiv}0$ (mod 5) and $c(7n+2){\equiv}0$ (mod 7), for all nonnegative integers n.

• Journal of the Korean Mathematical Society
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• v.57 no.2
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• pp.471-487
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• 2020

We find congruences modulo 32, 64 and 128 for the partition function ${\overline{PP}_o}(n)$, the number of overpartition pairs of n into odd parts, with the aid of Ramamnujan's theta function identities and some known identities of t_k(n), for k = 6, 7, where t_k(n) denotes the number of representations of n as a sum of k triangular numbers. We also find two Ramanujan-like congruences for ${\overline{PP}_o}(n)$ modulo 128.

• Journal of the Korean Mathematical Society
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• v.42 no.4
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• pp.857-869
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• 2005

Let $(X,\;B,\;{\mu},\;T)$ be a dynamical system and (Y, A, v, S) be a factor. We investigate the relative sequence entropy of a partition of X via the maximal compact extension of (Y, A, v, S). We define relative sequence entropy pairs and using them, we find the relative topological ${\mu}-Kronecker$ factor over (Y, v) which is the maximal topological factor having relative discrete spectrum over (Y, v). We also describe the topological Kronecker factor which is the maximal factor having discrete spectrum for any invariant measure.

• Bulletin of the Korean Chemical Society
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• v.23 no.10
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• pp.1381-1391
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• 2002

The solvent sublation using ion pairs of metal-2-naphthoate(2-HNph) and tetrabutyl ammonium ($TBA^+$) ion has been studied for the concentration and determination of ultra trace Bi(III), In(III) and Tl(Ⅲ) ions in water samples. The partition coefficients ($K_p$) and the extraction percentages of 2-HNph and the ion pairs to methyl isobutyl ketone (MIBK) were obtained as basic data. After the ion pair $TBA^+$·M$(Nph)_4^-$ was formed in water samples, the analytes were concentrated by the solvent sublation and the elements were determined by GF-AAS. The pH of the sample solution, the amount of the ligand and counter ion added and stirring time were optimized for the efficient formation of the ion pair. The type and amount of optimum surfactant, bubbling time with nitrogen and the type of solvent were investigated for the solvent sublation as well. 10.0 mL of 0.1 M 2-HNph and 2.0 mL of 0.1 M $TBA^+$ were added to a 1.0 L sample solution at pH 5.0. After 2.0 mL of 0.2%(w/v) Triton X-100 was added, the ion pairs were extracted into 20.0 mL MIBK in a flotation cell by bubbling. The analytes were determined by a calibration curve method with measured absorbances in MIBK, and the recovery was 80-120%.

• Journal of KIISE:Databases
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• v.31 no.4
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• pp.352-361
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• 2004

Spatial joins find all pairs of spatial objects that satisfy a given spatial relationship. In this paper, we propose the transformation-based spatial partition join algorithm (TSPJ), a new spatial join algorithm that performs join in the transform space without using indexes. Since the existing algorithms deal with extents of spatial objects in the original space, they either need to replicate the spatial objects or have a relatively complex partition structure-resulting in degrading performance. In contrast, TSPJ transforms objects in the original space into points in the transform space and deals only with points having no extents. The transformation does not incur any additional overhead. Thus, our algorithm has advantages over existing ones in that it obviates the need for replicating spatial objects, and its partition structure is simple. As a result, it always has better performance compared with existing algorithms. Extensive experiments show that TSPJ improves performance by 20.5∼38.0% over the existing algorithms compared.

• Journal of the Institute of Electronics Engineers of Korea SD
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• v.41 no.10
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• pp.9-16
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• 2004

The state assignment for a finite state machine greatly affects the delay, area, power dissipation, and testabilities of the sequential circuits. In order to improve the testabilities and power consumption, a new state assignment technique based on m-block partition is introduced in this paper. The algorithm minimizes the dependencies between groups of state variables are minimized and reduces switching activity by grouping the states depending on the state transition probability. In the sequel the length and number of feedback cycles are reduced with minimal switching activity on the state variables. Experiment shows significant improvement in testabilities and Power dissipation for benchmark circuits.

• Communications of the Korean Mathematical Society
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• v.13 no.3
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• pp.445-459
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• 1998

Let λ be a partition with all distinct parts. In this paper we give a bijection between the set $\Gamma$$_{λ}$(X) of pairs (equation omitted) satisfying a certain condition and the set $\pi_{λ}$(X) of circled permutation tableaux of shape λ on the set X, where P$\frac{1}{2}$ is a tail circled shifted rim hook tableaux of shape λ and (equation omitted) is a barred permutation on X. Specializing to the partition λ with one part, this bijection gives a combinatorial proof of the Schur identity: $\Sigma$2$\ell$(type($\sigma$)) = 2n! summed over all permutation $\sigma$ $\in$ $S_{n}$ with type($\sigma$) $\in$ O $P_{n}$ . .

• Korean Journal of Mathematics
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• v.24 no.3
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• pp.469-487
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• 2016

In [6] Schensted constructed the Schensted algorithm, which gives a bijection between permutations and pairs of standard tableaux of the same shape. Stanton and White [8] gave analog of the Schensted algorithm for rim hook tableaux. In this paper we give a generalization of Stanton and White's Schensted algorithm for rim hook tableaux. If k is a fixed positive integer, it shows a one-to-one correspondence between all generalized hook permutations $\mathcal{H}$ of size k and all pairs (P, Q), where P and Q are semistandard k-rim hook tableaux and k-rim hook tableaux of the same shape, respectively.