• 대한수학회지
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• 제53권6호
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• pp.1331-1345
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• 2016

A K-g-frame is a generalization of a g-frame. It can be used to reconstruct elements from the range of a bounded linear operator K in Hilbert spaces. K-g-frames have a certain advantage compared with g-frames in practical applications. In this paper, the interchangeability of two g-Bessel sequences with respect to a K-g-frame, which is different from a g-frame, is discussed. Several construction methods of K-g-frames are also proposed. Finally, by means of the methods and techniques in frame theory, several results of the stability of K-g-frames are obtained.

• Journal of Applied and Pure Mathematics
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• 제4권1_2호
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• pp.9-26
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• 2022

The purpose of this work is to study the existence and continuous dependence on neutral stochastic partial integrodifferential equations with impulsive effects, perturbed by a fractional Brownian motion with Hurst parameter $H{\in}({\frac{1}{2}},\;1)$. We use the theory of resolvent operators developed in Grimmer [19] to show the existence of mild solutions. Further, we establish a new impulsive-integral inequality to prove the exponential stability of mild solutions in the mean square moment. Finally, an example is presented to illustrate our obtained results.

• 대기
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• 제24권2호
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• pp.197-206
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• 2014

The effects of different averaging operators and atmospheric stability on the turbulent fluxes are investigated using the vertical velocity, air temperature, carbon dioxide concentration, and absolute humidity data measured at 10 Hz by a 3-dimensional sonic anemometer and an open-path $CO_2/H_2O$ infrared gas analyzer installed at a height of 18.5 m on the rooftop of the Jungnang KT building located at a typical residential area in Seoul, Korea. For this purpose, 7 different averaging operators including block average, linear regression, and moving averages during 100 s, 300 s, 600 s, 900 s, and 1800 s are considered and the data quality control procedure such as physical limit check and spike removal is also applied. It is found that as the averaging interval becomes shorter, turbulent fluxes computed by the moving average become smaller and the ratios of turbulent fluxes computed by the 100 s moving average to the fluxes by the 1800 s moving average under unstable stability are smaller than those under neutral stability. The turbulent fluxes computed by the linear regression are 85~92% of those computed by the 1800 s moving average and nearly the same as those computed by 900 s moving average, implying that the adequate selection of an averaging operator and its interval will be very important to estimate more accurate turbulent fluxes at urban area.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1987년도 한국자동제어학술회의논문집(한일합동학술편); 한국과학기술대학, 충남; 16-17 Oct. 1987
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• pp.729-733
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• 1987

Stability of Co Semigroups perturbed via the steady state Riccati equation (SSRE) is studied. We consider an infinite dimensional system : .chi. over dot = A.chi. + Bu, in, (A), domain of A, where A is the infinitesimal generator of a Co semigroup [T(t), t.geq.0] in H. If the original Co semigroup [T(t), t.geq.0] has a lower bound : vertical bar T(t).chi. vertical bar .geq. k vertical bar .chi. vertical bar, for all .chi. in H. t.geq. 0 and k>0, then the perturbed Co semigroup via the SSRE, where the feedback operator B is compact, cannot be exponentially stable. Physical interpretation of this result is as follows : in real applications, a finite number of actuators are available, therefore the operator B is compact. When the original system is inherently unstable, that is, has an infinite number of unstable modes, the perturbed system via the SSRE cannot be stable with a uniform decay rate.

• 제어로봇시스템학회논문지
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• 제22권3호
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• pp.204-209
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• 2016

In this paper, an unmanned delivery service using drone was proposed and verified the feasibility. The multicopter has GPS for autopilot and a camera for remote control by human operator. The gripper for manipulation of delivery object was designed and evaluated. The multicopter flies to a given position automatically based on GPS, and approaches to the prepared delivery desk by remote control of human operator using the received image from the multicopter. GPS sensor verification and experimental PID tuning were performed to ensure the flight stability. The flight tests were carried out to verify the feasibility of delivery service.

• Kyungpook Mathematical Journal
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• 제63권1호
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• pp.45-60
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• 2023

In this paper we suggest an enhanced Geraghty-type contractive mapping for examining the existence properties of classical nonlinear operators with or without prior degenerates. The nonlinear operators are proved to exist with the imposition of the Geraghty-type condition in a non-empty closed subset of complete metric spaces. To showcase some efficacies of the Geraghty-type condition, convergent rate and stability are deduced. The results are used to study some asymptotic properties of perturbed integral and hypergeometric operators. The results also extend and generalize some existing Geraghty-type conditions.

• Nonlinear Functional Analysis and Applications
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• 제29권1호
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• pp.83-98
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• 2024

In this paper, we investigate the existence and uniqueness of solutions to a new class of integro-differential equation boundary value problems (BVPs) with ㄒ-Hilfer operator. Our problem is converted into an equivalent fixed-point problem by introducing an operator whose fixed points coincide with the solutions to the given problem. Using Banach's and Schauder's fixed point techniques, the uniqueness and existence result for the given problem are demonstrated. The stability results for solutions of the given problem are also discussed. In the end. One example is provided to demonstrate the obtained results

• The Journal of Advanced Prosthodontics
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• 제7권1호
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• pp.51-55
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• 2015

PURPOSE. Bone density at implant placement site is a key factor to obtain the primary stability of the fixture, which, in turn, is a prognostic factor for osseointegration and long-term success of an implant supported rehabilitation. Recently, an implant motor with a bone density measurement probe has been introduced. The aim of the present study was to test the objectiveness of the bone densities registered by the implant motor regardless of the operator performing them. MATERIALS AND METHODS. A total of 3704 bone density measurements, performed by means of the implant motor, were registered by 39 operators at different implant sites during routine activity. Bone density measurements were grouped according to their distribution across the jaws. Specifically, four different areas were distinguished: a pre-antral (between teeth from first right maxillary premolar to first left maxillary premolar) and a sub-antral (more distally) zone in the maxilla, and an interforaminal (between and including teeth from first left mandibular premolar to first right mandibular premolar) and a retroforaminal (more distally) zone in the lower one. A statistical comparison was performed to check the inter-operators variability of the collected data. RESULTS. The device produced consistent and operator-independent bone density values at each tooth position, showing a reliable bone-density measurement. CONCLUSION. The implant motor demonstrated to be a helpful tool to properly plan implant placement and loading irrespective of the operator using it.

• 대한기계학회논문집A
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• 제20권11호
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• pp.3549-3559
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• 1996

In this study, the effect of parameter and modal filter errors on the vibration control characteristics of flexible structures is analyzed for IMSC ( Independent Modal Space Control). If the control force is designed on the basis of the mathematical model with the parameter and modal filter errors, the closed-loop performance of the vibration control system will be degraded depending on the magnitude of the errors. An asymptotic stability condition of the system with parameter and modal filter errors has more significant effect on the stability condition of the system with parameter and modal filter errors has been drived using Lyapunov approach. It has been found that modal filter error has more significant effect on the stability of closed-loop system than parameter error does. The extent of the response deviation of the closed-loop system is also derived and evaluated using operator thchniques.

• Journal of Mechanical Science and Technology
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• 제15권1호
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• pp.1-9
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• 2001

The recent spread of scaled telemanipulation into microsurgery and the nano-world increasingly requires the identification of the possible operation region as a main system specification. A teleoperation system is a complex cascaded system since the human operator, master, slave, and communication are involved bilaterally. Hence, a small time delay inside a master and slave system can be critical to the overall system stability even without communication time delay. In this paper we derive an upper bound of the scaling product of position and force by using Llewellyns unconditional stability. This bound can be used for checking the validity of the designed bilateral controller. Time delay from the sample and hold of computer control and its effects on stability of scaled teleoperation are modeled and simulated based on the transfer function of the teleoperation system. The feasible operation region in terms of position and force scaling decreases sharply as the sampling rate decreases and time delays inside the master and slave increase.