• Kyungpook Mathematical Journal
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• 제48권2호
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• pp.281-286
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• 2008

In this note we prove that if A and $B^*$ are subnormal operators and is a bounded linear operator such that AX - XB is a Hilbert-Schmidt operator, then f(A)X - Xf(B) is also a Hilbert-Schmidt operator and $${\parallel}f(A)X\;-\;Xf(B){\parallel}_2\;\leq\;L{\parallel}AX\;-\;XB{\parallel}_2$$, for f belonging to a certain class of functions. Furthermore, we investigate the similar problem in the case that S, T are hyponormal operators and $X\;{\in}\;\cal{L}(\cal{H})$ is such that SX - XT belongs to a norm ideal (J, ${\parallel}\;{\cdot}\;{\parallel}_J$) and prove that f(S)X - Xf(T) $\in$ J and ${\parallel}f(S)X\;-\;Xf(T){\parallel}_J\;\leq\;C{\parallel}SX\;-\;XT{\parallel}_J$, for f in a certain class of functions.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2013년도 추계학술대회 논문집
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• pp.331-337
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• 2013

Acoustic Emission technique is widely applied to develop the early fault detection system, and the problem about a signal processing method for AE signal is mainly focused on. In the signal processing method, envelope analysis is a useful method to evaluate the bearing problems and Wavelet transform is a powerful method to detect faults occurred on rotating machinery. However, exact method for AE signal is not developed yet. Therefore, in this paper two methods which are Hilbert transform and DET for feature extraction. In addition, we evaluate the classification performance with varying the parameter from 2 to 15 for feature selection DET, 0.01 to 1.0 for the RBF kernel function of SVR, and the proposed algorithm achieved 94% classification accuracy with the parameter of the RBF 0.08, 12 feature selection.

• Kyungpook Mathematical Journal
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• 제59권1호
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• pp.83-99
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• 2019

In this paper, we introduce a hybrid subgradient method for finding an element common to both the solution set of a class of pseudomonotone equilibrium problems, and the set of fixed points of a finite family of ${\kappa}$-strictly presudononspreading mappings in a real Hilbert space. We establish some weak and strong convergence theorems of the sequences generated by our iterative method under some suitable conditions. These convergence theorems are investigated without the Lipschitz condition for bifunctions. Our results complement many known recent results in the literature.

• Nonlinear Functional Analysis and Applications
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• 제29권1호
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• pp.225-258
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• 2024

In this paper, we study the problem of finding a common solution to a fixed point problem involving a finite family of ρ-demimetric operators and a split monotone inclusion problem with monotone and Lipschitz continuous operator in real Hilbert spaces. Motivated by the inertial technique and the Tseng method, a new and efficient iterative method for solving the aforementioned problem is introduced and studied. Also, we establish a strong convergence result of the proposed method under standard and mild conditions.

• 한국수학사학회지
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• 제25권3호
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• pp.15-27
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• 2012

이 글의 목적은 튜링이 태어난 지 100주년을 맞이하여 튜링의 삶을 살펴보고 그의 업적 중 특히 '멈춤정리' 에 주목하여 철학적 함의를 궁구하는 것이다. 튜링은 멈춤문제가 해결불가능하다는 것을 증명함으로써 힐베르트의 결정문제를 부정적으로 해결했다. 본고에서는 멈춤문제의 해결불가능성이 이성의 한계를 함축한다고 파악하고 인식이나 행위에 있어서 여백을 가지는 것이 필요하다는 것을 주장한다.

• Korean Journal of Mathematics
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• 제24권2호
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• pp.199-213
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• 2016

The resolvent operator approach of [2] is applied to solve a set-valued variational inclusion problem in ordered Hilbert spaces. The resolvent operator under consideration is called relaxed resolvent operator and we demonstrate some of its properties. To obtain the solution of a set-valued variational inclusion problem, an iterative algorithm is developed and weak-RRD set-valued mapping is used. The problem as well as main result of this paper are more general than many previous problems and results available in the literature.

• Nonlinear Functional Analysis and Applications
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• 제27권1호
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• pp.149-167
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• 2022

In this paper, we propose a viscosity iterative algorithm for approximating a common solution of finite family of variational inequality problem and fixed point problem for finite family of multi-valued type-one demicontractive mappings in real Hilbert spaces. A strong convergence result of the aforementioned problems were proved and some consequences of our result was also displayed. In addition, we discuss an application of our main result to convex minimization problem. The result presented in this article complements and extends many recent results in literature.

• 대한수학회보
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• 제55권3호
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• pp.899-911
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• 2018

In this paper, we consider the second-order nonlinear differential equation with the nonlocal boundary conditions. We first reformulate this boundary value problem as a fixed point problem for a Fredholm integral equation operator, and then present a result on the existence and uniqueness of the solution by using the contraction mapping theorem. Furthermore, we establish a sufficient condition on the functions ${\mu}$ and $h_i$, i = 1, 2 that guarantee a unique solution for this nonlocal problem in a Hilbert space. Also, accurate analytic solutions in series forms for this boundary value problems are obtained by the Adomian decomposition method (ADM).

• 전기의세계
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• 제31권3호
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• pp.209-217
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• 1982

This paper considers a finite spectrum assignment Problem for a functional retarded linear differential system with delays in control only. In this problem, by generalizing from an abstract linear system characterized by Semigroups on a Hilbert space to a finite dimensional linear system, we unify the relationship between a control-delayed system and its non-delayed system, and then by using the spectrum of the generator-decomposition of Semigroup, we try to get a feedback law which yields a finite spectrum of the closed-loop system, located at an arbitrarily preassigned sets of n points in the complex plane. The comparative examinations between the standard spectrum assignment method and the method of spectral projection for the feedback law which consists of proportional and finite interval terms over present and past values of control variables are also considered. The analysis is carry down to the elementary spectral projection level because, in spite of all the research efforts, so far there has been no significant attempt to obtain the feedback implementation directly from the abstract representation forms in the case of multivariables.

• 대한수학회지
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• 제35권1호
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• pp.115-126
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• 1998

We study the optimal control problem of system governed by retarded functional differential $$ x'(t) = A_0 x(t) + A_1 x(t - h) + \\ulcorner\ulcorner\ulcorner_{-h}^{0} a(s)A_2 x(t + s)ds + B_0 u(t) $$ in Hilbert space H. After the fundamental facts of retarded system and the description of condition so called a weak backward uniqueness property are established, the technically important maximal principle and the bang-bang principle are given. its corresponding linear system.