• Journal of Mechanical Science and Technology
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• v.16 no.10
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• pp.1264-1275
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• 2002

This paper is concerned with the investigation on the stability and convergence characteristics of the Crank-Nicolson-Galerkin scheme that is widely being employed for the numerical approximation of parabolic-type partial differential equations. Here, we present the theoretical analysis on its consistency and convergence, and we carry out the numerical experiments to examine the effect of the time-step size △t on the h- and P-convergence rates for various mesh sizes h and approximation orders P. We observed that the optimal convergence rates are achieved only when △t, h and P are chosen such that the total error is not affected by the oscillation behavior. In such case, △t is in linear relation with DOF, and furthermore its size depends on the singularity intensity of problems.

• Journal of the Chungcheong Mathematical Society
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• v.25 no.2
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• pp.267-275
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• 2012

We present new results for the local convergence of Newton's method to a unique solution of an equation in a Banach space setting. Under a flexible gamma-type condition [12], [13], we extend the applicability of Newton's method by enlarging the radius and decreasing the ratio of convergence. The results can compare favorably to other ones using Newton-Kantorovich and Lipschitz conditions [3]-[7], [9]-[13]. Numerical examples are also provided.

• Kyungpook Mathematical Journal
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• v.55 no.3
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• pp.667-678
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• 2015

The aim of this paper is to prove strong convergence theorem by a modified three step iterative process with errors for three nonexpansive mappings in the frame work of uniformly smooth Banach spaces. The main feature of this scheme is that its special cases can handle both strong convergence like Halpern type and weak convergence like Ishikawa type iteration schemes. Our result extend and generalize the result of S. H. Khan, Kim and Xu and many other authors.

• 한국IT서비스학회:학술대회논문집
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• 2009.05a
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• pp.588-592
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• 2009

The latest advances in great revolution for digital media and contents industries with Ubiquitous era. Because of spread and supply of various multimedia devices with combination digital with network, we need various type of digital contents. The Digital contents consists of Middleware industries, network business, contents service presenters and users. For supporting digital media. contents and media devices have been converging Digital contents convergence has been proceeding rapidly in media, broadcast and communication field. And also, whole Environment for these industries has been changing, too. Wee need another digital contents convergence for new type of products and services because of convergence of IT and broadcast. In addition, new business trends is very important about these new industrial change and developments with digital contents convergence.

• Journal of Multimedia Information System
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• v.7 no.4
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• pp.249-256
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• 2020

Learning methods using various assistive and smart devices have been developed to enable independent learning of the disabled. Pointer control is the most important consideration for the disabled when controlling a device and the contents of an existing graphical user interface (GUI) environment; however, difficulties can be encountered when using a pointer, depending on the disability type; Although there are individual differences depending on the blind, low vision, and upper limb disability, problems arise in the accuracy of object selection and execution in common. A multimodal interface pilot solution is presented that enables people with various disability types to control web interactions more easily. First, we classify web interaction types using digital devices and derive essential web interactions among them. Second, to solve problems that occur when performing web interactions considering the disability type, the necessary technology according to the characteristics of each disability type is presented. Finally, a pilot solution for the multimodal interface for each disability type is proposed. We identified three disability types and developed solutions for each type. We developed a remote-control operation voice interface for blind people and a voice output interface applying the selective focusing technique for low-vision people. Finally, we developed a gaze-tracking and voice-command interface for GUI operations for people with upper-limb disability.

• The Journal of Korea Robotics Society
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• v.17 no.2
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• pp.183-190
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• 2022

Accurate kinematic parameters of mobile robots are essential because inaccurate kinematic model produces considerable uncertainties on its odometry and control. Especially, kinematic parameters of caster type mobile robots are important due to their complex kinematic model. Despite the importance of accurate kinematic parameters for caster type mobile robots, few research dealt with the calibration of the kinematic model. Previous study proposed a calibration method that can only calibrate double-wheeled caster type mobile robot and requires direct-measuring of robot center point and distance between casters. This paper proposes a calibration method based on geometric approach that can calibrate single-wheeled caster type mobile robot with two or more casters, does not require direct-measuring, and can successfully acquire all kinematic parameters required for control and odometry. Simulation and hardware experiments conducted in this paper validates the proposed calibration method and shows its performance.

• Journal of the Korean Mathematical Society
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• v.58 no.2
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• pp.327-349
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• 2021

In this paper, we main study the strong law of large numbers and complete convergence for weighted sums of asymptotically almost negatively associated (AANA, in short) random variables, by using the Marcinkiewicz-Zygmund type moment inequality and Roenthal type moment inequality for AANA random variables. As an application, the complete consistency for the weighted linear estimator of nonparametric regression models based on AANA errors is obtained. Finally, some numerical simulations are carried out to verify the validity of our theoretical result.

• Nonlinear Functional Analysis and Applications
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• v.27 no.4
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• pp.903-920
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• 2022

In this paper, we propose and study an implicit iteration process for a finite family of total asymptotically quasi-nonexpansive mappings and a finite family of asymptotically quasi-nonexpansive mappings in the intermediate sense in convex metric spaces and establish some strong convergence results. Also, we give some applications of our result in the setting of convex metric spaces. The results of this paper are generalizations, extensions and improvements of several corresponding results.

• Nonlinear Functional Analysis and Applications
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• v.28 no.4
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• pp.1127-1143
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• 2023

The purpose of this paper, we prove convergence theorems of the modified viscosity inexact Mann iteration process for a family of asymptotically quasi-nonexpansive type mappings in CAT(0) spaces. We also show that the limit of the modified viscosity inexact Mann iteration {x_n} solves the solution of some variational inequality.

• Bulletin of the Korean Mathematical Society
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• v.51 no.5
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• pp.1269-1279
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• 2014

The equations arising from the thermoelastic theory are analyzed in a linear approximation. First, we establish the convergence result on the coefficient c. Next, we establish that the solution depends continuously on changes in the coefficient c. The main tool used in this paper is the energy method.