• KSII Transactions on Internet and Information Systems (TIIS)
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• v.8 no.10
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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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• v.14 no.4
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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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• v.30 no.3
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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.

• Communications of the Korean Mathematical Society
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• v.20 no.1
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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].

• Environmental and Resource Economics Review
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• v.22 no.3
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• pp.499-520
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• 2013

This study proposes an iterative approach to the estimation of the marginal abatement costs of undesirable outputs by computing the slope of the efficient production possibilities frontier on the basis of the efficient projection points generated by the directional output distance function approach due to Fare et al. (2005) based on duality theory. In case of the latter methodology, the estimated marginal abatement costs differ significantly depending on the choice of the directional output vector. In addition, depending on the curvature of the underlying PPF the efficient projection points may be located at a significant distance away from their actually observed counterparts. While it would be more logical to estimate marginal abatement costs as a PPF slope at a point corresponding to the actually observed emissions level, the methodology based on duality theory is likely to produce unstable results due to the problems associated with applying the theorem of implicit function differentiation. Since our methodology is not based on duality theory, our results are immune to both of these problems. We apply our methodology to a sample of Western European countries for the period of 1995-2011 to illustrate our approach.

• Journal of the Korean Mathematical Society
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• v.54 no.4
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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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• v.13 no.1_2
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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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• v.33 no.3_4
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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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• v.8 no.3
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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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• v.4 no.2
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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.