• 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.

• The Pure and Applied Mathematics
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• v.17 no.1
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• pp.1-27
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• 2010

Wu and Zhao [17] provided a semilocal convergence analysis for a Newton-type method on a Banach space setting following the ideas of Frontini and Sormani [9]-[11]. In this study first: we point out inconsistencies between the hypotheses of Theorem 1 and the two examples given in [17], and then, we provide the proof in affine invariant form for this result. Then, we also establish new convergence results with the following advantages over the ones in [17]: weaker hypotheses, and finer error estimates on the distances involved. A numerical example is also provided to show that our results apply in cases other fail [17].

• The Pure and Applied Mathematics
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• v.20 no.4
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• pp.243-249
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• 2013

Let A be an algebra and D a derivation of A. Then D is called algebraic nil if for any $x{\in}A$ there is a positive integer n = n(x) such that $D^{n(x)}(P(x))=0$, for all $P{\in}\mathbb{C}[X]$ (by convention $D^{n(x)}({\alpha})=0$, for all ${\alpha}{\in}\mathbb{C}$). In this paper, we show that any algebraic nil derivation (possibly unbounded) on a commutative complex algebra A maps into N(A), where N(A) denotes the set of all nilpotent elements of A. As an application, we deduce that any nilpotent derivation on a commutative complex algebra A maps into N(A), Finally, we deduce two noncommutative versions of algebraic nil derivations inclusion range.

• Journal of the Korean Mathematical Society
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• v.41 no.1
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• pp.65-76
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• 2004

An entire function $f\;{\in}\;H(\mathbb{C})$ is called universal with respect to translations if for any $g\;{\in}\;H(\mathbb{C}),\;R\;>\;0,\;and\;{\epsilon}\;>\;0$, there is $n\;{\in}\;{\mathbb{N}}$ such that $$\mid$f(z\;+\;n)\;-\;g(z)$\mid$\;<\;{\epsilon}$ whenever $$\mid$z$\mid$\;{\leq}\;R$. Similarly, it is universal with respect to differentiation if for any g, R, and $\epsilon$, there is n such that $$\mid$f^{(n)}(z)\;-\;g(z)$\mid$\;<\;{\epsilon}\;for\;$\mid$z$\mid$\;{\leq}\;R$. In this note, we review G. MacLane's proof of the existence of universal functions with respect to differentiation, and we give a simplified proof of G. D. Birkhoff's theorem showing the existence of universal functions with respect to translation. We also discuss Godefroy and Shapiro's extension of these results to convolution operators as well as some new, related results and problems.

• Bulletin of the Korean Mathematical Society
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• v.57 no.6
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• pp.1383-1392
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• 2020

Let H_n be the n-th harmonic number and let ν_n be its denominator. Shiu proved that there are infinitely many positive integers n with ν_n = ν_n+1. Recently, Wu and Chen proved that the set of positive integers n with ν_n = ν_n+1 has density one. They also proved that the same result is true for the denominators of alternating harmonic numbers. In this paper, we prove that the result is true for the denominators of 𝜀-harmonic numbers, where 𝜀 = {𝜀_i}^∞_i=1 is a pure recurring sequence with 𝜀_i ∈ {-1, 1}.

• Bulletin of the Korean Chemical Society
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• v.7 no.2
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• pp.102-105
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• 1986

Samples with the nominal composition of $Co_{9-x}M_xS_8$(M = Ni, Rh, Ru, and Fe) were prepared, and their magnetic properties were measured. X-ray diffraction analysis showed that small amount of the elements Ni, Rh, and Fe could be incorporated into $Co_9S_8$ forming a homogeneous ${\pi}$-phase, whereas the Ru-incorporated sample could not be prepared in a single phase. The lattice parameter was observed to increase as other elements were incorporated into $Co_9S_8$. Samples incorporated with the elements of Ni, Rh, and Ru showed Pauli-paramagnetism while the Fe-incorporated sample exhibited weak ferromagnetism. The values of magnetic susceptibility for the Ni, Rh, Ru-incorporated samples were nearly the same as that of pure $Co_9S_8$.

• Proceedings of the Korean Society of Sericultural Science Conference
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• 2004.04a
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• pp.45-46
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• 2004

• Kyungpook Mathematical Journal
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• v.61 no.3
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• pp.645-660
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• 2021

This paper examines the behavior of a 3-dimensional trans-Sasakian manifold equipped with a gradient generalized quasi-Yamabe soliton. In particular, It is shown that α-Sasakian, β-Kenmotsu and cosymplectic manifolds satisfy the gradient generalized quasi-Yamabe soliton equation. Furthermore, in the particular case when the potential vector field ζ of the quasi-Yamabe soliton is of gradient type ζ = grad(ψ), we derive a Poisson's equation from the quasi-Yamabe soliton equation. Also, we study harmonic aspects of quasi-Yamabe solitons on 3-dimensional trans-Sasakian manifolds sharing a harmonic potential function ψ. Finally, we observe that 3-dimensional compact trans-Sasakian manifold admits the gradient generalized almost quasi-Yamabe soliton with Hodge-de Rham potential ψ. This research ends with few examples of quasi-Yamabe solitons on 3-dimensional trans-Sasakian manifolds.

• The Journal of Fisheries Business Administration
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• v.52 no.1
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• pp.23-46
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• 2021

The purpose of this study is to understand the production efficiency of individual fishing communities and provide directions for improvement. The subject of the study is aquaculture type Ochon-Gye in Goheung-gun. The analysis method used bootstrap-DEA to overcome the statistical reliability problem of the traditional DEA analysis technique. In addition, data mining-GIS was applied to identify the spatial productivity of fishing communities. The values of technology efficiency, pure technology efficiency, and scale efficiency were estimated for 32 aquaculture-type fishing villages. Then, using the benchmarking reference set and weights, the projection was presented through adjustment of the input factor excess, and furthermore, the confidence interval of the efficiency values considering statistical significance was estimated using bootstrap.

• Natural Product Sciences
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• v.25 no.3
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• pp.181-199
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• 2019

Angelica decursiva Fr. et Sav. (Umbelliferae) has traditionally been used to treat different diseases due to its antitussive, analgesic, and antipyretic activities. It is also a remedy for thick phlegm, asthma, and upper respiratory infections. Recently, the leaf of A. decursiva has been consumed as salad without showing any toxicity. This plant is a rich in different types of coumarin derivatives, including dihydroxanthyletin, psoralen, dihydropsoralen, hydroxycoumarin, and dihydropyran. Its crude extracts and pure constituents possess anti-inflammatory, anti-diabetic, anti-Alzheimer disease, anti-hypertension, anti-cancer, antioxidant, anthelmintic, preventing cerebral stroke, and neuroprotective activities. This valuable herb needs to be further studied and developed not only to treat these human diseases, but also to improve human health. This review provides an overview of current knowledge of A. decursiva metabolites and their biological activities to prioritize future studies.