• Nonlinear Functional Analysis and Applications
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• v.27 no.4
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• pp.813-837
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• 2022

In this paper we consider inverse problem for a general class of nonlinear stochastic differential equations on Hilbert spaces whose generating operators (drift, diffusion and jump kernels) are unknown. We introduce a class of function spaces and put a suitable topology on such spaces and prove existence of optimal generating operators from these spaces. We present also necessary conditions of optimality including an algorithm and its convergence whereby one can construct the optimal generators (drift, diffusion and jump kernel).

• Korean Journal of Mathematics
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• v.29 no.2
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• pp.227-237
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• 2021

Opial inequality and its consequences are useful in establishing existence and uniqueness of solutions of initial and boundary value problems for differential and difference equations. In this paper we analyze Opial-type inequalities for convex functions. We have studied different versions of these inequalities for a generalized integral operator. Further difference of Opial-type inequalities are utilized to obtain generalized mean value theorems, which further produce various interesting derivations for fractional and conformable integral operators.

• Journal of the Korean Mathematical Society
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• v.59 no.3
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• pp.469-494
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• 2022

In this paper, we study the boundedness of a class of inhomogeneous Journé's product singular integral operators on the inhomogeneous product Lipschitz spaces. The consideration of such inhomogeneous Journé's product singular integral operators is motivated by the study of the multi-parameter pseudo-differential operators. The key idea used here is to develop the Littlewood-Paley theory for the inhomogeneous product spaces which includes the characterization of a special inhomogeneous product Besov space and a density argument for the inhomogeneous product Lipschitz spaces in the weak sense.

• Journal of Korea Society of Industrial Information Systems
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• v.24 no.5
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• pp.121-127
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• 2019

This paper proposes an operator-centric velocity generation and control algorithm for differential-drive mobile robots, which are widely used in many industrial applications. Most of the previous works use a robot centric velocity generation and control for the operators to control the differential-drive mobile robots, which makes the robot control difficult for the operators. Such robot-centric control can cause the increase of accidents and the decrease of work efficiency. The experimental results with a real differential-drive mobile robot testbed demonstrate the efficiency of operator-centric mobile robot control.

• IEMEK Journal of Embedded Systems and Applications
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• v.15 no.2
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• pp.95-101
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• 2020

In situations where mobile robots are operated either by autonomous systems or human operators, such as smart factories, priority-based teleoperation is crucial for the multiple operators with different priority to take over the right of the robot control without conflict. This paper proposes a priority-based teleoperation system for multiple operators to control the robots. This paper also introduces an efficient joystick-based robot control command generation algorithm for differential-drive mobile robots. The proposed system is implemented with ROS (Robot Operating System) and embedded control boards, and is applied to Pioneer 3AT mobile robot platform. The experimental results demonstrate the effectiveness of the proposed joystick control command algorithm and the priority-based control input selection.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.12 no.2
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• pp.162-166
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• 2012

The instantaneous amplitude (IA) based on the higher order differential energy operator is proposed. And its general form for arbitrary order is also proposed. The various definitions of the IA and the instantaneous frequency (IF) estimators are considered. The IA and IF estimators based on the energy operators need less computational cost than the conventional IF and IA estimators exploiting the Hilbert transform. The IF and IA estimators are compared in terms of the frequency and amplitude tracking accuracy of the AM-FM signals. For noiseless case, the IA and IF estimators based on the Teager-Kaiser energy operator show better tracking performance than the IF and IA estimators based on the higher energy operators. However, under noisy condition, the IF and IA estimator based on the higher order energy operators with the order 3 and 4 show better tracking than the Teager-Kaiser energy based estimators. The IF and IA estimators are applied to signals in the various power anomalies to show their usefulness as the disturbance detectors.

• Journal of Communications and Networks
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• v.18 no.4
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• pp.658-669
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• 2016

The tremendous increase in mobile data traffic coupled with fierce competition in wireless industry brings about spectrum scarcity and bandwidth fragmentation. This inevitably results in asymmetric-valued long term evolution (LTE) spectrum allocation that stems from different timing for twice improvement in capacity between competing operators, given spectrum allocations today. This motivates us to study the economic effects of asymmetric-valued LTE spectrum allocation. In this paper, we formulate the interactions between operators and users as a hierarchical dynamic game framework, where two spiteful operators simultaneously make spectrum acquisition decisions in the upper-level first-price sealed-bid auction game, and dynamic pricing decisions in the lower-level differential game, taking into account user subscription dynamics. Using backward induction, we derive the equilibrium of the entire game under mild conditions. Through analytical and numerical results, we verify our studies by comparing the latest result of LTE spectrum auction in South Korea, which serves as the benchmark of asymmetric-valued LTE spectrum auction designs.

• Communications of the Korean Mathematical Society
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• v.37 no.4
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• pp.1055-1072
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• 2022

Our aim is to establish certain image formulas of the (p, 𝜈)-extended Gauss' hypergeometric function F_p,𝜈(a, b; c; z) by using Saigo's hypergeometric fractional calculus (integral and differential) operators. Corresponding assertions for the classical Riemann-Liouville(R-L) and Erdélyi-Kober(E-K) fractional integral and differential operators are deduced. All the results are represented in terms of the Hadamard product of the (p, 𝜈)-extended Gauss's hypergeometric function F_p,𝜈(a, b; c; z) and Fox-Wright function _rΨ_s(z). We also established Jacobi and its particular assertions for the Gegenbauer and Legendre transforms of the (p, 𝜈)-extended Gauss' hypergeometric function F_p,𝜈(a, b; c; z).

• Communications of the Korean Mathematical Society
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• v.38 no.3
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• pp.755-772
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• 2023

Our aim is to establish certain image formulas of the (p, q)-extended modified Bessel function of the second kind M_ν,p,q(z) by employing the Marichev-Saigo-Maeda fractional calculus (integral and differential) operators including their composition formulas and using certain integral transforms involving (p, q)-extended modified Bessel function of the second kind M_ν,p,q(z). Corresponding assertions for the Saigo's, Riemann-Liouville (R-L) and Erdélyi-Kober (E-K) fractional integral and differential operators are deduced. All the results are represented in terms of the Hadamard product of the (p, q)-extended modified Bessel function of the second kind M_ν,p,q(z) and Fox-Wright function _rΨ_s(z).

• Bulletin of the Korean Mathematical Society
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• v.26 no.2
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• pp.203-209
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• 1989

Recently many authors [2,3,5,6] proved the existence of zeros of accretive operators and estimated the range of m-accretive operators or compact perturbations of m-accretive operators more sharply. Their results could be obtained from differential equations in Banach spaces or iteration methods or Leray-Schauder degree theory. On the other hand Kirk and Schonberg [9] used the domain invariance theorem of Deimling [3] to prove some general minimum principles for continuous accretive operators. Kirk and Schonberg [10] also obtained the range of m-accretive operators (multi-valued and without any continuity assumption) and the implications of an equivalent boundary conditions. Their fundamental tool of proofs is based on a precise analysis of the orbit of resolvents of m-accretive operator at a specified point in its domain. In this paper we obtain a sufficient condition for m-accretive operators to have a zero. From this we derive Theorem 1 of Kirk and Schonberg [10] and some results of Morales [12, 13] and Torrejon[15]. And we further generalize Theorem 5 of Browder [1] by using Theorem 3 of Kirk and Schonberg [10].