• 대한수학회지
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• 제33권2호
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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 $\Gamma$.

• 한국수학사학회지
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• 제23권1호
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• pp.53-66
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• 2010

본 논문에서는 푸리에 급수의 $L^1$-수렴성에 대한 20세기 초부터 중반(W. H. Young부터 G. A. Fomin)까지 고전적인 연구 결과를 고찰하고 연구자들의 소계보를 조사한다. 푸리에 급수 부분합의 수렴성 문제를 동치관계인 푸리에 계수 성질을 이용하여 수렴성을 보인 결론들의 상호 연계성을 재해석한다.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제9권1호
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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.

• 대한수학회지
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• 제33권3호
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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.

• 대한수학회보
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• 제52권5호
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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.

• 한국컴퓨터산업학회논문지
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• 제5권1호
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• pp.147-156
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• 2004

본 논문에서는 블록 합 피라미드 알고리즘에 기초한 빠른 움직임 추정 알고리즘을 제안하였다. Efficient Multi-level Successive Elimination Algorithm의 Spiral Diamond Mesh Search 기법과 Partial Distortion Elimination 기법을 개선하여 이들을 블록 합 피라미드 알고리즘에 적용하였다. 제안된 알고리즘의 움직임 추정 정확도는 거의 100%이고 블록 합 피라미드 알고리즘의 연산량을 효과적으로 줄였다. 실험을 통하여 제안된 알고리즘의 효율성을 확인하였다.

• Journal of applied mathematics & informatics
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• 제30권3_4호
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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).

• 충청수학회지
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• 제28권3호
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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.

• 대한수학회지
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• 제32권1호
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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 $\cdot$.

• 대한수학회지
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• 제41권6호
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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.