• Communications of the Korean Mathematical Society
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• v.21 no.4
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• pp.665-673
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• 2006

In a recent paper, Domokos and $Kolumb\'{a}}n$ [2] gave an interesting interpretation of variational inequalities (VI) and vector variational inequalities (VVI) in Banach space settings in terms of variational inequalities with operator solutions (in short, OVVI). Inspired by their work, in a former paper [4], we proposed the scheme of generalized vector variational inequality with operator solutions (in short, GOVVI) which extends (OVVI) into a multivalued case. In this note, we further develop the previous work [4]. A more general pseudomonotone operator is treated. We present a result on the existence of solutions of (GVVI) under the weak pseudomonotonicity introduced in Yu and Yao [8] within the framework of (GOVVI) by exploiting some techniques on (GOVVI) or (GVVI) in [4].

• Communications of the Korean Mathematical Society
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• v.38 no.3
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• pp.821-835
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• 2023

Hankel operators and their variants have abundant applications in numerous fields. For a non-zero complex number r, the r-Hankel operators on a Hilbert space 𝓗 define a class of one such variant. This article introduces and explores some properties of two other variants of Hankel operators namely k^th-order (C, r)-Hankel operators and k^th-order (R, r)-Hankel operators (k ≥ 2) which are closely related to r-Hankel operators in such a way that a k^th-order (C, r)-Hankel matrix is formed from r^k-Hankel matrix on deleting every consecutive (k - 1) columns after the first column and a k^th-order (R, r^k)-Hankel matrix is formed from r-Hankel matrix if after the first column, every consecutive (k - 1) columns are deleted. For |r| ≠ 1, the characterizations for the boundedness of these operators are also completely investigated. Finally, an appropriate approach is also presented to extend these matrices to two-way infinite matrices.

• Journal of the Institute of Electronics Engineers of Korea SP
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• v.39 no.4
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• pp.455-461
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• 2002

This paper presents a new parametric log line equation of polar form for Hough transform in log-polar plane, in which it can remove the well-known unboundedness problem of Hough parameters. Bolduc's method is used to generate a log-polar image dividing the fovea and periphery from a Cartesian image. Edges of the fovea and periphery are detected by using the Sobel mask and the proposed space-variant gradient mask, and are combined in the log-polar plane. The sampled points that might constitute a log line are quite sparse in a deep peripheral region due to severe under-sampling, which is an inherent property of LPM. To cope with such under-sampling, we determine the values of cumulative cells in Hough space by using the space-variant weighting. In our experiments, the proposed method demonstrates its validity of detecting not only the lines passing through both the fovea and periphery but also the lines in a deep periphery.

• Journal of the Korean Mathematical Society
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• v.49 no.3
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• pp.571-583
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• 2012

Let $G$ be a metrizable, ${\sigma}$-compact locally compact abelian group with a compact open subgroup. In this paper we define the Gramian and the dual Gramian operators for shift invariant subspaces of $L^2(G)$ and we use them to characterize shift generated dual frames for shift in- variant spaces, which forms a frame for a subspace of $L^2(G)$. We present necessary and sufficient conditions for which standard dual is a unique SG-dual frame of type I and type II.

• The Korean Journal of Air & Space Law and Policy
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• v.30 no.2
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• pp.403-425
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• 2015

The Chicago Convention and Annexes have become the basis of aviation safety regulations for every contracting state. Generally, the State's aviation safety regulations refer to the Standards and Recommended Practices(SARPs) provided in the Annexes of the Chicago Convention. In order to properly reflect international aviation safety regulations, constant studies of the aviation fields are of paramount importance. This Paper is intended to identify the main differences between korean and foreign regulation and suggest a few amendment proposals on Mixed-fleet Flying(at or more two aircraft type operation) of flight crew. Comparing with these regulations, the korean regulations and implementations have some insufficiency points. I suggest some amendment proposals of korean regulations concerning Mixed-fleet Flying that flight crew operate aircraft of different types. Basically an operator shall not assign a pilot-in-command or a co-pilot to operate at the flight controls of a type of airplane during take-off and landing unless that pilot has operated the flight controls during at least three take-offs and landings within the preceding 90 days on the same type of airplane or in a flight simulator. Also, flight crew members are familiarized with the significant differences in equipment and/or procedures between concurrently operated types. An operator shall ensure that piloting technique and the ability to execute emergency procedures is checked in such a way as to demonstrate the pilot's competence on each type or variant of a type of airplane. Proficiency check shall be performed periodically. When an operator schedules flight crew on different types of airplanes with similar characteristics in terms of operating procedures, systems and handling, the State shall decide the requirements for each type of airplane can be combined. In conclusion, it is necessary for flight crew members to remain concurrently qualified to operate multiple types. The operator shall have a program to include, as a minimum, required differences training between types and qualification to maintain currency on each type. If the Operator utilizes flight crew members to concurrently operate aircraft of different types, the operator shall have qualification processes approved or accepted by the State. If applicable, the qualification curriculum as defined in the operator's Advanced Qualification Program could be applied. Flight crew members are familiarized with the significant differences in equipment and/or procedures between concurrently operated types. The difference among different types of airpcrafts decrease and standards for these airpcrafts can be applied increasingly because function and performance have been improved by aircraft manufacture company in accordance to basic aircraft system in terms of developing new aircrafts for flight standard procedure and safety of flight. Also, it becomes more necessary for flight crews to control multi aircraft types due to various aviation business and activation of leisure business. Nevertheless, in terms of flight crew training and qualification program, there are no regulations in Korea to be applied to new aircraft types differently in accordance with different levels. In addition, it has no choice different programs based on different levels because there are not provisions to restrict or limit and specific standards to operate at or more than two aircraft types for flight safety. Therefore the aviation authority introduce Flight Standardization and/or Operational Evaluation Board in order to analysis differences among aircraft types. In addition to that, the aviation authority should also improve standard flight evaluation and qualification system among different aircraft types for flight crews to apply reasonable training and qualification efficiently. For all the issue mentioned above, I have studied the ICAO SARPs and some state's regulation concerning operating aircraft of different types(Mixed-fleet flying), and suggested some proposals on the different aircraft type operation as an example of comprehensive problem solving. I hope that this paper is 1) to help understanding about the international issue, 2) to help the improvement of korean aviation regulations, 3) to help compliance with international standards and to contribute to the promotion of aviation safety, in addition.