• Bulletin of the Korean Mathematical Society
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• v.56 no.1
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• pp.187-200
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• 2019

Truncated Hankel operators are compressions of classical Hankel operators to model spaces. In this paper we describe matrix representations of truncated Hankel operators on finite-dimensional model spaces. We then show that the obtained descriptions hold also for some infinite-dimensional cases.

• Bulletin of the Korean Mathematical Society
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• v.59 no.6
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• pp.1595-1603
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• 2022

We show how some of well-known recurrent operators such as recurrent curvature operator, recurrent Ricci operator, recurrent Jacobi operator, recurrent shape and Weyl operators have the significant role for biharmonic hypersurfaces to be minimal in the Euclidean space.

• Journal of the Korean Institute of Intelligent Systems
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• v.14 no.5
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• pp.563-570
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• 2004

Genetic algorithms have been successfully applied to various optimization problems belonging to NP-hard problems. The sequential ordering problems(SOP) and the job shop scheduling problems(JSP) are well-known NP-hard problems with strong influence on industrial applications. Both problems share some common properties in that they have some imposed precedence constraints. When genetic algorithms are applied to this kind of problems, it is desirable for genetic operators to be designed to produce chromosomes satisfying the imposed precedence constraints. Several genetic operators applicable to such problems have been proposed. We call such genetic operators precedence-preserving genetic operators. This paper presents three existing precedence-preserving genetic operators: Precedence -Preserving Crossover(PPX), Precedence-preserving Order-based Crossover (POX), and Maximum Partial Order! Arbitrary Insertion (MPO/AI). In addition, it proposes two new operators named Precedence-Preserving Edge Recombination (PPER) and Multiple Selection Precedence-preserving Order-based Crossover (MSPOX) applicable to such problems. It compares the performance of these genetic operators for SOP and JSP in the perspective of their solution quality and execution time.

• Computers and Concrete
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• v.11 no.6
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• pp.541-569
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• 2013

There is a wide variety of existing Genetic Algorithms (GA) operators and parameters in the literature. However, there is no unique technique that shows the best performance for different classes of optimization problems. Hence, the evaluation of these operators and parameters, which influence the effectiveness of the search process, must be carried out on a problem basis. This paper presents a comparison for the influence of GA operators and parameters on the performance of the damage identification problem using the finite element model updating method (FEMU). The damage is defined as reduction in bending rigidity of the finite elements of a reinforced concrete beam. A certain damage scenario is adopted and identified using different GA operators by minimizing the differences between experimental and analytical modal parameters. In this study, different selection, crossover and mutation operators are compared with each other based on the reliability, accuracy and efficiency criteria. The exploration and exploitation capabilities of different operators are evaluated. Also a comparison is carried out for the parallel and sequential GAs with different population sizes and the effect of the multiple use of some crossover operators is investigated. The results show that the roulettewheel selection technique together with real valued encoding gives the best results. It is also apparent that the Non-uniform Mutation as well as Parent Centric Normal Crossover can be confidently used in the damage identification problem. Nevertheless the parallel GAs increases both computation speed and the efficiency of the method.

• Korean Journal of Remote Sensing
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• v.32 no.1
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• pp.13-24
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• 2016

This paper presents a method to evaluate the performance of subpixel localization operators using target image data. Subpixel localization of edges is important to extract the precise shape of objects from images. In this study, each target image was designed to provide reference lines and edges to which the localization operators can be applied. We selected two types of moment-based operators: Gray-level Moment (GM) operator and Spatial Moment (SM) operator for comparison. The original edge localization operators with kernel size 5 are tested and their extended versions with kernel size 7 are also tested. Target images were collected with varying Camera-to-Object Distance (COD). From the target images, reference lines are estimated and edge profiles along the estimated reference lines are accumulated. Then, evaluation of the performance of edge localization operators was performed by comparing the locations calculated by each operator and by superimposing them on edge profiles. Also, enhancement of edge localization by increasing the kernel size was also quantified. The experimental result shows that the SM operator whose kernel size is 7 provides higher accuracy than other operators implemented in this study.

• Korean Journal of Mathematics
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• v.22 no.1
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• pp.1-28
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• 2014

We consider the hypergeometric translation operator associated to the Cherednik operators and the Heckman-Opdam theory attached to the root system of type $B_2$. We prove in this paper that these operators are positivity preserving and allow positive integral representations. In particular we deduce that the product formulas of the Opdam-Cherednik and the Heckman-Opdam kernels are positive integral transforms, and we obtain best estimates of these kernels. The method used to obtain the previous results shows that these results are also true in the case of the root system of type $C_2$.

• Honam Mathematical Journal
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• v.42 no.2
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• pp.251-268
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• 2020

In this paper, we estimate the degree of approximation by means of the complete modulus of continuity, the partial modulus of continuity, the Lipschitz-type class and Petree's K-functional for the bivariate Szász-Kantorovich operators based on Brenke-type polynomials. Later, we construct Generalized Boolean Sum operators associated with combinations of the Szász-Kantorovich operators based on Brenke-type polynomials. In addition, we obtain the rate of convergence for the GBS operators with the help of the mixed modulus of continuity and the Lipschitz class of the Bögel continuous functions.

• Journal of the Korean Mathematical Society
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• v.55 no.1
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• pp.225-251
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• 2018

The m-isometry of a single operator in Agler and Stankus [3] was naturally generalized to the m-isometric tuple of several commuting operators by Gleason and Richter [22]. Some examples of m-isometric tuples including the recently much studied Arveson-Drury d-shift were given in [22]. We provide more examples of m-isometric tuples of operators by using sums of operators or products of operators or functions of operators. A class of m-isometric tuples of unilateral weighted shifts parametrized by polynomials are also constructed. The examples in Gleason and Richter [22] are then obtained by choosing some specific polynomials. This work extends partially results obtained in several recent papers on the m-isometry of a single operator.

• Journal of Institute of Control, Robotics and Systems
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• v.14 no.11
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• pp.1110-1116
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• 2008

In this paper, we suggest GP operators based on tree structure considering tree distributions in structure space and structural difficulties. The main idea of the proposed genetic operators is to place generated offspring into the specific region which nodes and depths are balanced and most of solutions exist. To enable that, the proposed operators are designed to utilize region information where parents belong and node/depth rates of selected subtree. To demonstrate the effectiveness of our proposed approach, experiments of binomial-3 regression, multiplexer and even parity problem are executed. The experiments results show that the proposed operators based on tree structure is superior to the results of standard GP for all three test problems in both success rate and number of evaluations.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2000.11a
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• pp.647-652
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• 2000

This paper presents a study on the position tracking control of robot system on the uncertain elastic base. The elastic base is modeled as a virtual robot which has passive joints and the control strategy is using approximate Jacobian operators. Jacobian operators represent the overall robot system including base movement. However, because we don't know the base movement we can't estimate the jacobian operators directly. The control algorithm is proposed which uses only Jacobian operators of a real robot as approximate Jacobian operators. The measured errors from external sensor are compensated by approximate Jacobian operators. The simulation results of a single-axis robot system show that the control strategy can be used for position tracking.