• Journal of the Korean Mathematical Society
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• v.33 no.2
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• pp.333-346
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• 1996

Let $A(\zeta, \partial)$ be a second order uniformly elliptic operator $$ A(\zeta, \partial )u = -\sum_{j, k = 1}^{n} \frac{\partial\zeta_i}{\partial}(a_{jk}(\zeta)\frac{\partial\zeta_k}{\partial u}) + \sum_{j = 1}^{n}b_j(\zeta)\frac{\partial\zeta_j}{\partial u} + c(\zeta)u $$ with real, smooth coefficients $a_{j, k}, b_j$, c defined on $\zeta \in \Omega, \Omega$ a bounded domain in $R^n$ with a sufficiently smooth boundary $\Gamma$.

• Journal for History of Mathematics
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• v.23 no.1
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• pp.53-66
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• 2010

This study concerns with partial sum of Fourier series, Fourier coefficients and the $L^1$-convergence of Fourier series. First, we introduce the $L^1$-convergence results. We consider equivalence relations of the partial sum of Fourier series from the early 20th century until the middle of. Second, we investigate the minor lineage of $L^1$-convergence theorem from W. H. Young to G. A. Fomin. Finally, we compare and reinterpret the $L^1$-convergence theorems.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.9 no.1
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• pp.280-295
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• 2015

Block cipher ARIA was first proposed by some South Korean experts in 2003, and later, it was established as a Korean Standard block cipher algorithm by Korean Agency for Technology and Standards. In this paper, we focus on the security evaluation of ARIA block cipher against the recent zero-correlation linear cryptanalysis. In addition, Partial-sum technique and FFT (Fast Fourier Transform) technique are used to speed up the cryptanalysis, respectively. We first introduce some 4-round linear approximations of ARIA with zero-correlation, and then present some key-recovery attacks on 6/7-round ARIA-128/256 with the Partial-sum technique and FFT technique. The key-recovery attack with Partial-sum technique on 6-round ARIA-128 needs $2^{123.6}$ known plaintexts (KPs), $2^{121}$ encryptions and $2^{90.3}$ bytes memory, and the attack with FFT technique requires $2^{124.1}$ KPs, $2^{121.5}$ encryptions and $2^{90.3}$ bytes memory. Moreover, applying Partial-sum technique, we can attack 7-round ARIA-256 with $2^{124.6}$ KPs, $2^{203.5}$ encryptions and $2^{152}$ bytes memory and 7-round ARIA-256 employing FFT technique, requires $2^{124.7}$ KPs, $2^{209.5}$ encryptions and $2^{152}$ bytes memory. Our results are the first zero-correlation linear cryptanalysis results on ARIA.

• Journal of the Korean Mathematical Society
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• v.33 no.3
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• pp.601-607
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• 1996

For functions $f(z) = \sum_{n = 0}^{\infty}a_n z^n$ and $g(z) = \sum_{n = 0}^{\infty} b_n z^n$ analytic in the unit disk $\Delta = {z : $\mid$z$\mid$ < 1}$, the convolution $f * g$ is defined by $(f * g)(z) = \sum_{n = 0}^{\infty}a_n b_n z^n$. Let S denote the family of functions $f(z) = z + \cdots$ analytic and univalent in $\Delta$ and K, St, C the subfamilies that are respectively convex, starlike, and close-to-convex.

• Bulletin of the Korean Mathematical Society
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• v.52 no.5
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• pp.1729-1735
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• 2015

It is known that the partial sum of the Taylor series of an holomorphic function of one complex variable converges in norm on $H^p(\mathbb{D})$ for 1 < p < ${\infty}$. In this paper, we consider various type of partial sums of a holomorphic function of several variables which also converge in norm on $H^p(\mathbb{B}_n)$ for 1 < p < ${\infty}$. For the partial sums in several variable cases, some variables could be chosen slowly (fastly) relative to other variables. We prove that in any cases the partial sum converges to the original function, regardlessly how slowly (fastly) some variables are taken.

• Journal of the Korea Computer Industry Society
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• v.5 no.1
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• pp.147-156
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• 2004

In this paper, a new fast motion estimation algorithm which is based on the Block Sum Pyramid Algorithm(BSPA) is presented. The Spiral Diamond Mesh Search scheme and Partial Distortion Elimination scheme of Efficient Multi-level Successive Elimination Algorithm were improved and then the improved schemes were applied to the BSPA. The motion estimation accuracy of the proposed algorithm is nearly 100% and the cost of Block Sum Pyramid Algorithm was reduced in the proposed algorithm. The efficiency of the proposed algorithm was verified by experimental results.

• Journal of applied mathematics & informatics
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• v.30 no.3_4
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• pp.647-653
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• 2012

In this paper, we consider fuzzy random sets as (measurable) mappings from a probability space into the set of fuzzy sets and prove a uniform strong law of large numbers for sequences of independent and identically distributed fuzzy random sets. Our results generalize those of Bass and Pyke(1984)and Jang and Kwon(1998).

• Journal of the Chungcheong Mathematical Society
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• v.28 no.3
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• pp.409-417
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• 2015

In this paper, some $L_p$-convergences and complete convergences of the maximum of the partial sum for negatively superadditive dependent random variables are obtained. The proofs of the results are based on a new Rosenthal type inequality concerning negatively superadditive dependent random variables.

• Journal of the Korean Mathematical Society
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• v.32 no.1
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• pp.141-149
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• 1995

Let N denote the set of positive integers. Fix $d_1, d_2 \in N with d = d_1 + d_2$. Let X and Y be real random variables and let ${X_i : i \in N^d_1} and {Y_j : j \in N^d_2}$ be independent families of independent identically distributed random variables with $L(X) = L(X_i) and L(Y) = L(Y_j)$, where $L(\cdot)$ denote the law of $\cdot$.

• Journal of the Korean Mathematical Society
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• v.41 no.6
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• pp.1023-1034
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• 2004

In this paper we establish limsup and liminf theorems for the increments of partial sum processes of a dependent stationary Gaussian sequence.