• Korean Journal of Mathematics
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• v.26 no.1
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• pp.103-127
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• 2018

This paper is dedicated to studying some Hausdorff operators on the Heisenberg group ${\mathbb{H}}^n$. The sharp bounds on the strong-type weighted Lorentz spaces ${\Lambda}^p_u(w)$ and the weak-type weighted Lorentz spaces ${\Lambda}^{p,{\infty}}_u(w)$ are investigated. Especially, the results cover the classical power weighted space $L^{p,q}_{\alpha}$. The results are also extended to the product spaces ${\Lambda}^{p_1}_{u_1}(w_1){\times}{\Lambda}^{p_2}_{u_2}(w_2)$, especially for $L^{p_1,q_1}_{{\alpha}_1}{\times}L^{p_2,q_2}_{{\alpha}_2}$. Our proofs are quite different from those in previous documents since the duality principle, and some well-known inequalities concerning the weights are adopted. The results recover the existing results as well as we obtain new results in the new and old settings.

• Korean Journal of Culture and Social Issue
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• v.12 no.3
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• pp.49-68
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• 2006

The present study was attempted to compare duality in value structure and judgment system between youth, adults and North Korean defectors. A questionnaire was administered to 150 college students(Men: 89, Women: 61), 155 adults(Men: 80, Women: 75) and 80 North Korean defectors(Men: 39, Women: 41). Participants rated their values, behavior and South Korean behavior (or North Korean behavior for North Korean defectors) as a whole both on the 7 dimensions relevant to characteristics indigenous to Korean society and on their opposite 7 dimensions characteristic of Western culture. Results indicated that defectors marked the highest score on the traditional value dimensions, and yet youth ranked the first for the western value systems. Also, duality in value systems was the most severe for the defectors. In relation to dual judgement system in behavior, both young and old generation judged Korean behavior more negatively than their own. This was also the case for the North Korean defectors. Those findings were discussed in terms of cultural changes in Korean society.

• Bulletin of the Korean Mathematical Society
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• v.37 no.1
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• pp.153-169
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• 2000

Let E be a real q-uniformly smooth Banach space which admits a weakly sequentially continuous duality map, and K a nonempty closed convex subset of E. Let T : K -> K be a mapping such that $F(T)\;=\;{x\;{\in}\;K\;:\;Tx\;=\;x}\;{\neq}\;0$ and (I - T) satisfies the accretive-type condition: $\;{\geq}\;{\lambda}$\mid$$\mid$x-Tx$\mid$$\mid$^2$, for all $x\;{\in}\;K,\;x^*\;{\in}\;F(T)$ and for some ${\lambda}\;>\;0$. The weak and strong convergence of the Ishikawa iteration method to a fixed point of T are investigated. An application of our results to the approximation of a solution of a certain linear operator equation is also given. Our results extend several important known results from the Mann iteration method to the Ishikawa iteration method. In particular, our results resolve in the affirmative an open problem posed by Naimpally and Singh (J. Math. Anal. Appl. 96 (1983), 437-446).

• Korean Journal of Mathematics
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• v.24 no.3
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• pp.409-445
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• 2016

The class $\mathcal{W}^{\delta}_{\beta}({\alpha},{\gamma})$ defined in the domain ${\mid}z{\mid}$ < 1 satisfying $Re\;e^{i{\phi}}\((1-{\alpha}+2{\gamma})(f/z)^{\delta}+\({\alpha}-3{\gamma}+{\gamma}\[1-1/{\delta})(zf^{\prime}/f)+1/{\delta}\(1+zf^{\prime\prime}/f^{\prime}\)\]\)(f/z)^{\delta}(zf^{\prime}/f)-{\beta}\)$ > 0, with the conditions ${\alpha}{\geq}0$, ${\beta}$ < 1, ${\gamma}{\geq}0$, ${\delta}$ > 0 and ${\phi}{\in}{\mathbb{R}}$ generalizes a particular case of the largest subclass of univalent functions, namely the class of $Bazilevi{\check{c}}$ functions. Moreover, for 0 < ${\delta}{\leq}{\frac{1}{(1-{\zeta})}}$, $0{\leq}{\zeta}$ < 1, the class $C_{\delta}({\zeta})$ be the subclass of normalized analytic functions such that $Re(1/{\delta}(1+zf^{\prime\prime}/f^{\prime})+1-1/{\delta})(zf^{\prime}/f))$ > ${\zeta}$, ${\mid}z{\mid}$<1. In the present work, the sucient conditions on ${\lambda}(t)$ are investigated, so that the non-linear integral transform $V^{\delta}_{\lambda}(f)(z)=\({\large{\int}_{0}^{1}}{\lambda}(t)(f(tz)/t)^{\delta}dt\)^{1/{\delta}}$, ${\mid}z{\mid}$ < 1, carries the fuctions from $\mathcal{W}^{\delta}_{\beta}({\alpha},{\gamma})$ into $C_{\delta}({\zeta})$. Several interesting applications are provided for special choices of ${\lambda}(t)$. These results are useful in the attempt to generalize the two most important extremal problems in this direction using duality techniques and provide scope for further research.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.24 no.8
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• pp.1022-1029
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• 2020

We investigate the joint selection problem of the transmit power level and the best access point for multi-access points. We further reduce the transmit power by jointly optimizing the transmit power and the access point selection. Our aim is to minimize the total transmit power, while each terminal maintains minimum signal to interference ratio requirement. We observe that the optimum solution can be achieved through proposed iterative algorithm for both TA link and AT link. Simulation results show that proposed algorithm (joint optimization of transmit power level and access point) outperforms the algorithm which optimizes the transmit power only. We also observe that the duality between the TA link and AT link does not hold in multi-access points environment. Accordingly, the resulting power vectors and the access point vectors for TA link and AT link are different in general.

• Journal of applied mathematics & informatics
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• v.27 no.1_2
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• pp.59-68
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• 2009

In this paper we present an iterative scheme for finding a common element of the set of zero points of accretive mappings and the set of fixed points of nonexpansive mappings in Banach spaces. By using viscosity approximation methods and under suitable conditions, some strong convergence theorems for approximating to this common elements are proved. The results presented in the paper improve and extend the corresponding results of Kim and Xu [Nonlinear Anal. TMA 61 (2005), 51-60], Xu [J. Math. Anal. Appl., 314 (2006), 631-643] and some others.

• Journal of applied mathematics & informatics
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• v.27 no.1_2
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• pp.13-23
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• 2009

Some strong convergence theorems of explicit iteration scheme for asymptotically nonexpansive semi-groups in Banach spaces are established. The results presented in this paper extend and improve some recent results in [T. Suzuki. On strong convergence to common fixed points of nonexpansive semigroups in Hilbert spaces, Proc. Amer. Math. Soc. 131(2002)2133-2136; H. K. Xu. A strong convergence theorem for contraction semigroups in Banach spaces, Bull. Aust. Math. Soc. 72(2005)371-379; N. Shioji and W. Takahashi. Strong convergence theorems for continuous semigroups in Banach spaces, Math. Japonica. 1(1999)57-66; T. Shimizu and W. Takahashi. Strong convergence to common fixed points of families of nonexpansive mappings, J. Math. Anal. Appl. 211(1997)71-83; N. Shioji and W. Takahashi. Strong convergence theorems for asymptotically nonexpansive mappings in Hilbert spaces, Nonlinear Anal. TMA, 34(1998)87-99; H. K. Xu. Approximations to fixed points of contraction semigroups in Hilbert space, Numer. Funct. Anal. Optim. 19(1998), 157-163.]

• Journal of the Korean Operations Research and Management Science Society
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• v.28 no.1
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• pp.79-95
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• 2003

This paper investigates how the weights of performance measures vary depending on corporate life cycle, such as birth, growth, maturity, revival, and decline. Balanced Scorecard performance measures are employed for this investigation. Balanced Scorecard has been widely used for measuring a corporate Performance by incorporating financial and non-financial measures simultaneously. Because these performance measures are related to the compensation and promotion of employees, research of weights of performance measures would be instrumental. Questionnaires from 218 companies are analyzed. Depending on the corporate life cycle, our survey results demonstrate that the weights of the business Performance measures differ In the four Perspectives - financial. customer, Internal Process, and learning/growth. Our results can be used for enhancing the Duality of performance measurement systems.

• Journal of applied mathematics & informatics
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• v.14 no.1_2
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• pp.397-403
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• 2004

Cutler showed some duality results about Hausdorff and packing dimensions of a measure on a compact set in Euclidean space if its s-dimensional Hausdorff measure or packing measure is positive. We show that the similar results in a perturbed Cantor set hold according to its quasi s-dimensional Hausdorff measure or packing measure and we find concrete measures in this case while Cutler showed the existence of such measures. Finally under some strong condition, we give a concrete measure whose Hausdorff and packing dimensions are the same as those of the perturbed Cantor set without the condition that it has positive s-dimensional Hausdorff or packing measures.

• Journal of KSNVE
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• v.10 no.6
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• pp.1017-1021
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• 2000

This paper addresses experimental results carried out to investigate the characteristics of dynamic mass for Korean. Vertical seat vibration in the frequency range of 0.5-30 Hz was applied to a seated Korean male subject. To examine the intra-variable effects on dynamic mass, five different postures and three different vibration excitation levels were considered. The applied acceleration and transmitted force to the hip of the seated subject were measured simultaneously. Detailed experimental results of measured dynamic mass are illustrated for each posture and/or vibration excitation level. Maximum peaks of around 5 Hz were observed for most experimental cases. They are found to allow the identification of dynamic characteristics of Korean seated body for various real vibration environments. Furthermore, they are expected to be very useful in designing new seats for automotive and railway vehicles and in improving their vibration ride duality.