• Bulletin of the Korean Chemical Society
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• v.18 no.12
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• pp.1281-1285
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• 1997

The time-dependent tracking inversion method is developed to extract the potential of the excited state from frequency-domain measurements, such as the absorption profile. Based on the relay of the regularized inversion procedure and time-dependent wave-packet propagation, the algorithm extract the underlying potential piece by piece by tracking the time-dependent data which can be synthesized from frequency-domain measurements. We have demonstrated the algorithm to extract the potential of excited state for a model diatomic molecule. Finally, we describe the merits of the time-dependent tracking inversion method compared to the time-dependent inversion and discuss several extensions of the algorithm.

• Kyungpook Mathematical Journal
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• v.59 no.3
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• pp.445-464
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• 2019

In this paper, we propose a new iterative algorithm generated by a finite family of accretive operators in a q-uniformly smooth Banach space. We prove the strong convergence of the proposed iterative algorithm. The results presented in this paper are interesting extensions and improvements of known results of Qin et al. [Fixed Point Theory Appl. 2014(2014): 166], Kim and Xu [Nonlinear Anal. 61(2005), 51-60] and Benavides et al. [Math. Nachr. 248(2003), 62-71].

• Communications of the Korean Mathematical Society
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• v.36 no.4
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• pp.705-714
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• 2021

The Whittaker function and its diverse extensions have been actively investigated. Here we aim to introduce an extension of the Whittaker function by using the known extended confluent hypergeometric function 𝚽_p,v and investigate some of its formulas such as integral representations, a transformation formula, Mellin transform, and a differential formula. Some special cases of our results are also considered.

• Honam Mathematical Journal
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• v.41 no.1
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• pp.89-99
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• 2019

The Steffensen's Inequality was discovered in 1918 by Johan Frederic Steffensen (1873-1961). This inequality is very popular in the research environment and attracted the attention of many people working in similar area. Various extensions and generalisations have been provided concerning the inequality. This paper presents some further refinements of the Steffensen's Inequality on Time scales using methods of convexity, differentiability and monotonicity.

• Kyungpook Mathematical Journal
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• v.61 no.3
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• pp.461-472
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• 2021

We study a new ring property called axis-commutativity. Axis-commutative rings are seated between commutative rings and duo rings and are a generalization of division rings. We investigate the basic structure and several extensions of axis-commutative rings.

• Nonlinear Functional Analysis and Applications
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• v.26 no.1
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• pp.165-175
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• 2021

In this article we derive some best approximation theorems for multimaps in abstract convex metric spaces. We are based on generalized KKM maps due to Kassay-Kolumbán, Chang-Zhang, and studied by Park, Kim-Park, Park-Lee, and Lee. Our main results are extensions of a recent work of Mitrović-Hussain-Sen-Radenović on G-convex metric spaces to partial KKM metric spaces. We also recall known works related to single-valued maps, and introduce new partial KKM metric spaces which can be applied our new results.

• Bulletin of the Korean Mathematical Society
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• v.59 no.4
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• pp.843-852
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• 2022

In this paper, we study some properties of Bézout and weakly Bézout rings. Then, we investigate the transfer of these notions to trivial ring extensions and amalgamated algebras along an ideal. Also, in the context of domains we show that the amalgamated is a Bézout ring if and only if it is a weakly Bézout ring. All along the paper, we put the new results to enrich the current literature with new families of examples of non-Bézout weakly Bézout rings.

• Korean Journal of Mathematics
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• v.29 no.4
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• pp.741-747
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• 2021

The Cayley-Bacharach theorem says that every cubic curve on an algebraically closed field that passes through a given 8 points must contain a fixed ninth point, counting multiplicities. Ren et al. introduced a concrete formula for the ninth point in terms of the 8 points [4]. We would like to consider a different approach to find the ninth point via the theory of truncated moment problems. Various connections between algebraic geometry and truncated moment problems have been discussed recently; thus, the main result of this note aims to observe an interplay between linear algebra, operator theory, and real algebraic geometry.

• Honam Mathematical Journal
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• v.45 no.1
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• pp.71-81
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• 2023

In this paper, we deal with some geometric properties including starlikeness and convexity of order 𝛽 of Ramanujan-type entire functions which are natural extensions of classical Ramanujan entire functions. In addition, we determine some conditions on the parameters such that the Ramanujan-type entire functions belong to the Hardy space and to the class of bounded analytic functions.

• Nonlinear Functional Analysis and Applications
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• v.27 no.4
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• pp.903-920
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• 2022

In this paper, we propose and study an implicit iteration process for a finite family of total asymptotically quasi-nonexpansive mappings and a finite family of asymptotically quasi-nonexpansive mappings in the intermediate sense in convex metric spaces and establish some strong convergence results. Also, we give some applications of our result in the setting of convex metric spaces. The results of this paper are generalizations, extensions and improvements of several corresponding results.