• Journal of applied mathematics & informatics
• /
• v.14 no.1_2
• /
• pp.493-498
• /
• 2004

In this paper, we try to construct the variation of the Green's function and investigate some operator properties of the Green's function. Also, we discuss the variation of the operator of the Green's function G(x, t) when the operator is varied.

• Bulletin of the Korean Mathematical Society
• /
• v.61 no.1
• /
• pp.207-216
• /
• 2024

This note is devoted to establishing the variation continuity of the one-dimensional discrete uncentered multilinear maximal operator. The above result is based on some refine variation estimates of the above maximal functions on monotone intervals. The main result essentially improves some known ones.

• Bulletin of the Korean Mathematical Society
• /
• v.50 no.2
• /
• pp.675-685
• /
• 2013

We prove, under some general assumptions, that a generator of any uniformly bounded Nemytskij operator, mapping a subset of space of functions of bounded variation in the sense of Wiener-Young into another space of this type, must be an affine function with respect to the second variable.

• Journal of the Korean Mathematical Society
• /
• v.49 no.2
• /
• pp.395-404
• /
• 2012

Our first aim of this paper is to define maximal operators a-quadratic variation and of a-conditional quadratic variation for vectorvalued tree martingales and to show that these maximal operators and maximal operators of vector-valued tree martingale transforms are all sublinear operators. The second purpose is to prove that maximal operator inequalities of a-quadratic variation and of a-conditional quadratic variation for vector-valued tree martingales hold provided 2 ${\leq}$ a < $\infty$ by means of Marcinkiewicz interpolation theorem. Based on a result of reference [10] and using Marcinkiewicz interpolation theorem, we also propose a simple proof of maximal operator inequalities for vector-valued tree martingale transforms, under which the vector-valued space is a UMD space.

• Journal of Electrical Engineering and Technology
• /
• v.9 no.4
• /
• pp.1210-1216
• /
• 2014

This paper deals with an application of Teager Energy Operator (TEO) and Energy Separation Algorithm(ESA) to detect and determine various voltage waveform distortions like harmonics, inter-harmonics and frequency variation. Because the TEO and DESA algorithm was initially proposed for speech or communication analysis, its applications are limited to some types of waveform in the power quality analysis area. For example, an undistorted voltage signal is similar with a pure sinusoid. A voltage fluctuation is very similar with an amplitude-modulated signal, from the viewpoint of signal theory. And a continuous frequency variation is similar with a frequency-modulated signal, which is also known as a chirp signal. This paper is written to show that the TEO and DESA algorithm can be used for detecting occurrences of the representative waveform distortions and determining their instantaneous information of amplitude and frequency.

• Bulletin of the Korean Mathematical Society
• /
• v.52 no.2
• /
• pp.649-659
• /
• 2015

The space $BV^2_{\alpha}(I)$ of all the real functions defined on interval $I=[a,b]{\subset}\mathbb{R}$, which are of bounded second ${\alpha}$-variation (in the sense De la Vall$\acute{e}$ Poussin) on I forms a Banach space. In this space we define an operator of substitution H generated by a function $h:I{\times}\mathbb{R}{\rightarrow}\mathbb{R}$, and prove, in particular, that if H maps $BV^2_{\alpha}(I)$ into itself and is globally Lipschitz or uniformly continuous, then h is an affine function with respect to the second variable.

• Journal of Institute of Control, Robotics and Systems
• /
• v.13 no.8
• /
• pp.777-782
• /
• 2007

Human Robot Interaction(HRI) through a haptic interface plays an important role in controlling robot systems remotely. The augmented usage of bio-signals in the haptic interface is an emerging research area. To consider operator's state in HRI, we used bio-signals such as ECG and blood pressure in our proposed force reflection interface. The variation of operator's state is checked from the information processing of bio-signals. The statistical standard variation in the R-R intervals and blood pressure were used to adaptively adjust force reflection which is generated from environmental condition. To change the pattern of force reflection according to the state of the human operator is our main idea. A set of experiments show the promising results on our concepts of human adaptive interface.

• Kyungpook Mathematical Journal
• /
• v.45 no.4
• /
• pp.571-577
• /
• 2005

The aim of this paper is to establish the rate of convergence of Baskakov-Durrmeyer operators for bounded variation function. We have given the better estimate over the results due to Guo ([4]), Anial and Teberska ([1]) and Gupta and Srivastava ([8]).

• Bulletin of the Korean Mathematical Society
• /
• v.59 no.6
• /
• pp.1539-1555
• /
• 2022

In this paper, we establish the boundedness and continuity for variation operators for θ-type Calderón-Zygmund singular integrals and their commutators on the Triebel-Lizorkin spaces. As applications, we obtain the corresponding results for the Hilbert transform, the Hermit Riesz transform, Riesz transforms and rough singular integrals as well as their commutators.

• Journal of applied mathematics & informatics
• /
• v.30 no.1_2
• /
• pp.173-181
• /
• 2012

In this paper, we study the control problems governed by the semilinear parabolic type equation in Hilbert spaces. Under the Lipschitz continuity condition of the nonlinear term, we can obtain the sufficient conditions for the approximate controllability of nonlinear functional equations with nonlinear monotone hemicontinuous and coercive operator. The existence, uniqueness and a variation of solutions of the system are also given.