• KSII Transactions on Internet and Information Systems (TIIS)
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• 제8권10호
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• pp.3624-3637
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• 2014

At SAC 2004, Junod and Vaudenay designed the FOX family based on the Lai-Massey scheme. They noted that it was impossible to find any useful differential characteristic or linear trail after 8 rounds of FOX64 or FOX128. In this paper, we provide the lower bound of differentially active S-boxes in consecutive rounds of the Lai-Massey scheme that has SPS as its F-function, and we propose the necessary conditions for the reachability of the lower bound. We demonstrate that similar results can be obtained with respect to the lower bound of linearly active S-boxes by proving the duality in the Lai-Massey scheme. Finally, we apply these results to FOX64 and FOX128 and prove that it is impossible to find any useful differential characteristics or linear trail after 6 rounds of FOX64. We provide a more precise security bound for FOX128.

• Journal of the Optical Society of Korea
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• 제14권4호
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• pp.438-443
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• 2010

In this paper, behaviors of photonic crystal (PC) radiative structures and antenna arrays have been compared for two types of uniform and binomial excitations. Appropriate duality has been shown between them. These results can be generalized to other types of excitation and arrangement of photonic crystal radiative arrays such as linear, planar and circular arrays of three dimensional (3D) photonic crystal termination resonators. Using these results in designing photonic circuits has some advantages for shaping a particular radiative beam at the photonic crystal exit, for instance reducing the divergence angle of the main lobe in order to enhance the directivity, for better coupling, or for splitting the emitted beam, for dividing the output beam to the next devices in photonic integrated circuits (PIC). For analysis and simulation of the photonic crystal structures, the finite difference time domain (FDTD) method has been employed.

• Korean Journal of Mathematics
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• 제30권3호
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• pp.475-489
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• 2022

This paper focuses on a robust semi-infinite interval-valued optimization problem with uncertain inequality constraints (RSIIVP). By employing the concept of LU-optimal solution and Extended Mangasarian-Fromovitz Constraint Qualification (EMFCQ), necessary optimality conditions are established for (RSIIVP) and then sufficient optimality conditions for (RSIIVP) are derived, by using the tools of convexity. Moreover, a Wolfe type dual problem for (RSIIVP) is formulated and usual duality results are discussed between the primal (RSIIVP) and its dual (RSIWD) problem. The presented results are demonstrated by non-trivial examples.

• 대한수학회논문집
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• 제20권1호
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• pp.71-78
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• 2005

In this paper, the iterative solution is studied for equation Tx = f with a uniformly continuous ${\varphi}$-strongly accretive operators in arbitrary real Banach spaces. Our results extend, generalize and improve the corresponding results obtained by Zeng [11].

• 자원ㆍ환경경제연구
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• 제22권3호
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• pp.499-520
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• 2013

기존 연구에서는 이산화탄소의 한계저감비용을 추정할 경우 쌍대성 이론에 근거하여 임의로 설정된 하나의 방향성 벡터(directional vector) 설정하였으나 본 연구에서는 이러한 한계를 극복하고자 다양한 형태의 방향성 벡터를 사용하여 이산화탄소의 한계저감비용을 추정하였다. 기존의 방법론에서는 임의로 설정된 방향성 벡터가 한계저감비용 추정에 결정적인 역할을 하여 선택된 방향성 벡터에 따라 한계저감 비용 추정치가 상당한 차이가 있음을 알 수 있다. 그리고 $45^{\circ}$의 방향성 벡터를 설정하는 경우에는 실제 이산화탄소 배출량 수준과는 다른 배출량 수준에서의 한계저감비용을 추정하게 되지만 본 연구에서 제안한 방법론에 의하여 추정된 한계저감비용은 실제 이산화탄소 배출량 수준에서 한계저감비용을 추정하여 보다 더 현실을 정확하게 반영하는 추정치이다. 새로운 방법론을 서유럽 국가에 적용하여 추정한 이산화탄소의 한계저감비용은 기존 방법론을 사용하는 경우에 비하여 적은 것으로 추정되었다.

• 대한수학회지
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• 제54권4호
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• pp.1063-1079
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• 2017

Two standard Bessel sequences in a Hilbert $C^*$-module are approximately duals if the distance (with respect to the norm) between the identity operator on the Hilbert $C^*$-module and the operator constructed by the composition of the synthesis and analysis operators of these Bessel sequences is strictly less than one. In this paper, we introduce (a, m)-approximate duality using the distance between the identity operator and the operator defined by multiplying the Bessel multiplier with symbol m by an element a in the center of the $C^*$-algebra. We show that approximate duals are special cases of (a, m)-approximate duals and we generalize some of the important results obtained for approximate duals to (a, m)-approximate duals. Especially we study perturbations of (a, m)-approximate duals and (a, m)-approximate duals of modular Riesz bases.

• Journal of applied mathematics & informatics
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• 제13권1_2호
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• pp.85-97
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• 2003

An indefinite stochastic linear-quadratic(LQ) optimal control problem with cross term over an infinite time horizon is studied, allowing the weighting matrices to be indefinite. A systematic approach to the problem based on semidefinite programming (SDP) and .elated duality analysis is developed. Several implication relations among the SDP complementary duality, the existence of the solution to the generalized Riccati equation and the optimality of LQ problem are discussed. Based on these relations, a numerical procedure that provides a thorough treatment of the LQ problem via primal-dual SDP is given: it identifies a stabilizing optimal feedback control or determines the problem has no optimal solution. An example is provided to illustrate the results obtained.

• Journal of applied mathematics & informatics
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• 제33권3_4호
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• pp.235-246
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• 2015

In this paper, a vector optimization problem over cones is considered, where the functions involved are $\eta$-semidifferentiable. Necessary and sufficient optimality conditions are obtained. A dual is formulated and duality results are proved using the concepts of cone $\rho$-semilocally preinvex, cone $\rho$-semilocally quasi-preinvex and cone $\rho$-semilocally pseudo-preinvex functions.

• The Journal of Asian Finance, Economics and Business
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• 제8권3호
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• pp.341-350
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• 2021

This study tested the effect of the board of directors' (BOD) characteristics on the corporate performance of the Jordanian industrial and service companies listed on the Amman Stock Exchange (ASE) during the period 2015-2019. The characteristics of the BOD were measured through the following variables: MO = managerial ownership; CEODU = CEO duality; BI = board independence; GD = gender diversity; ND = nationality diversity; AE = advanced education; BM = board meetings; BSIZ = board size; CSIZ = corporate size; CA = corporate age. The corporate performance was measured by return on assets (ROA) and return on equity (ROE). The corporate size and corporate age were used as control variables. The study sample consisted of 85 industrial and service companies with 425 observations to identify the nature of the effect of the BOD characteristics on performance. This study applied time-series data (panel data), and the multiple linear regression method was used to achieve study objectives. Results showed a positive effect of the study variables on performance, while the corporate age and the education level (BOD members) have a negative effect on performance.

• Korean Journal of Mathematics
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• 제4권2호
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• pp.83-88
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• 1996

In 1994 Z.Liang constructed an iterative method for the solution of nonlinear equations involving m-accretive operators in uniformly smooth Banach spaces. In this paper we apply the slight variants of Liang's iterative methods and generalize the results of Z.Liang. Moreover our proof is more simple than Liang's proof.