• The Pure and Applied Mathematics
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• v.14 no.3
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• pp.203-221
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• 2007

We introduce a new two-point iterative method to approximate solutions of nonlinear operator equations. The method uses only divided differences of order one, and two previous iterates. However in contrast to the Secant method which is of order 1.618..., our method is of order two. A local and a semilocal convergence analysis is provided based on the majorizing principle. Finally the monotone convergence of the method is explored on partially ordered topological spaces. Numerical examples are also provided where our results compare favorably to earlier ones [1], [4], [5], [19].

• Kyungpook Mathematical Journal
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• v.55 no.2
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• pp.345-353
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• 2015

Subnormality of bounded weighted composition operators on $L^2({\Sigma})$ of the form $Wf=uf{\circ}T$, where T is a nonsingular measurable transformation on the underlying space X of a ${\sigma}$-finite measure space (X, ${\Sigma}$, ${\mu}$) and u is a weight function on X; is studied. The standard moment sequence characterizations of subnormality of weighted composition operators are given. It is shown that weighted composition operators are subnormal if and only if $\{J_n(x)\}^{+{\infty}}_{n=0}$ is a moment sequence for almost every $x{{\in}}X$, where $J_n=h_nE_n({\mid}u{\mid}^2){\circ}T^{-n}$, $h_n=d{\mu}{\circ}T^{-n}/d{\mu}$ and $E_n$ is the conditional expectation operator with respect to $T^{-n}{\Sigma}$.

• Proceedings of the Korean Society of Broadcast Engineers Conference
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• 1997.06a
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• pp.107-112
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• 1997

This paper proposes the regularized constrained iterative image restoration algorithms which apply new space-adaptive methods to degraded image signals, and analyzes the convergence condition of the proposed algorithm. First, we introduce space-adaptive regularization operators which change according to edge characteristics of local images in order to effectively prevent the restored edges and boundaries from reblurring. And, pseudo projection operator is used to reduce the ringing artifact which results from extensive amplification of noise components in the restoration process. The analysed algorithm is stable convergent to the fixed point. According to the experimental results for various signal-to-noise ratios(SNR) and blur models, the proposed algorithms other methods and is robust to noise effects and edge reblurring by regularization especially.

• Journal of KSNVE
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• v.4 no.2
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• pp.177-185
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• 1994

In this study, the effect of parameter errors on the closed-loop behavior of flexible structure is analyzed for IMSC(Independent Modal Space Control) with PPF(Positive Position Feedback). If the control force designed on the basis of structure model with the parameter errors is applied to control the actual system, the closed-loop performance of the actural system will be degraded depending on the degree of the errors. An asymptotic stability condition has been derived, using Lyapunov approach, which is independent of the dynamic characteristics of the structure being controlled. The extent of deviation of the closed-loop performance from the designed one is also derived and evaluated using operator techniques. It has been found that the extent of the deviation is proportational to the magnitude of the parameter errors, and that the proportional coefficient depends on the control algorithm.

• Nuclear Engineering and Technology
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• v.37 no.2
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• pp.127-138
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• 2005

Approaches to several recent issues in the operation of nuclear power plants using computational intelligence are discussed. These issues include 1) noise analysis techniques, 2) on-line monitoring and sensor validation, 3) regularization of ill-posed surveillance and diagnostic measurements, 4) transient identification, 5) artificial intelligence-based core monitoring and diagnostic system, 6) continuous efficiency improvement of nuclear power plants, and 7) autonomous anticipatory control and intelligent-agents. Several changes to the focus of Computational Intelligence in Nuclear Engineering have occurred in the past few years. With earlier activities focusing on the development of condition monitoring and diagnostic techniques for current nuclear power plants, recent activities have focused on the implementation of those methods and the development of methods for next generation plants and space reactors. These advanced techniques are expected to become increasingly important as current generation nuclear power plants have their licenses extended to 60 years and next generation reactors are being designed to operate for extended fuel cycles (up to 25 years), with less operator oversight, and especially for nuclear plants operating in severe environments such as space or ice-bound locations.

• The Pure and Applied Mathematics
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• v.14 no.2 s.36
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• pp.127-137
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• 2007

The classical Bohr's inequality states that $|z+w|^2{\leq}p|z|^2+q|w|^2$ for all $z,\;w{\in}\mathbb{C}$ and all p, q>1 with $\frac{1}{p}+\frac{1}{q}=1$. In this paper, Bohr's inequality is generalized to the setting of n-inner product spaces for all positive conjugate exponents $p,\;q{\in}\mathbb{R}$. In. In particular, the parallelogram law is recovered and an interesting operator inequality is obtained.

• The Pure and Applied Mathematics
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• v.16 no.4
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• pp.405-416
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• 2009

In this study we are concerned with the problem of approximating a locally unique solution of an equation in a Banach space setting using Newton's and modified Newton's methods. We provide weaker convergence conditions for both methods than before [5]-[7]. Then, we combine Newton's with the modified Newton's method to approximate locally unique solutions of operator equations. Finer error estimates, a larger convergence domain, and a more precise information on the location of the solution are obtained under the same or weaker hypotheses than before [5]-[7]. The results obtained here improve our earlier ones reported in [4]. Numerical examples are also provided.

• Journal of the Korean Mathematical Society
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• v.58 no.1
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• pp.91-107
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• 2021

A bounded linear operator T on a separable infinite dimensional Banach space X is called strongly hypercyclic if $$X{\backslash}\{0\}{\subseteq}{\bigcup_{n=0}^{\infty}}T^n(U)$$ for all nonempty open sets U ⊆ X. We show that if T is strongly hypercyclic, then so are Tn and cT for every n ≥ 2 and each unimodular complex number c. These results are similar to the well known Ansari and León-Müller theorems for hypercyclic operators. We give some results concerning multiplication operators and weighted composition operators. We also present a result about the invariant subset problem.

• Journal of Applied and Pure Mathematics
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• v.4 no.3_4
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• pp.151-184
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• 2022

In the article, we handle with the existence and controllability results for fractional impulsive neutral functional integro-differential equation in Banach spaces. We have used advanced phase space definition for infinite delay. State dependent infinite delay is the main motivation using advanced version of phase space. The results are acquired using Schaefer's fixed point theorem. Examples are given to illustrate the theory.

• Bulletin of the Korean Mathematical Society
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• v.60 no.1
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• pp.123-135
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• 2023

The goal of this article is to introduce the concept of pseudo-weighted Browder spectrum when the underlying Hilbert space is not necessarily separable. To attain this goal, the notion of α-pseudo-Browder operator has been introduced. The properties and the relation of the weighted spectrum, pseudo-weighted spectrum, weighted Browder spectrum, and pseudo-weighted Browder spectrum have been investigated by extending analogous properties of their corresponding essential pseudo-spectrum and essential pseudo-weighted spectrum. The weighted spectrum, pseudo-weighted spectrum, weighted Browder, and pseudo-weighted Browder spectrum of the sum of two bounded linear operators have been characterized in the case when the Hilbert space (not necessarily separable) is a direct sum of its closed invariant subspaces. This exploration ends with a characterization of the pseudo-weighted Browder spectrum of the sum of two bounded linear operators defined over the arbitrary Hilbert spaces under certain conditions.