• The Pure and Applied Mathematics
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• v.12 no.1
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• pp.65-73
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• 2005

Let g = g(A) = (equation omitted) + be a symmetrizable Kac-Moody Lie algebra of type D/sub l//sup (1) with W as its Weyl group. We construct a sequence of root spaces with certain conditions. We also find the number of terms of this sequence is less then or equal to the hight of θ, the highest root.

• Honam Mathematical Journal
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• v.43 no.1
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• pp.47-58
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• 2021

In this paper, we introduce rough statistical convergence of difference double sequences in normed linear spaces as an extension of rough convergence. We define the set of rough statistical limit points of a difference double sequence and analyze the results with proofs.

• Kyungpook Mathematical Journal
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• v.55 no.2
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• pp.355-372
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• 2015

In the present paper, by using the Fibonacci difference matrix, we introduce the almost convergent sequence space $\hat{c}^f$. Also, we show that the spaces $\hat{c}^f$and $\hat{c}$ are linearly isomorphic. Further, we determine the ${\beta}$-dual of the space $\hat{c}^f$ and characterize some matrix classses on this space. Finally, Fibonacci core of a complex-valued sequence has been introduced, and we prove some inclusion theorems related to this new type of core.

• Bulletin of the Korean Mathematical Society
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• v.56 no.3
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• pp.757-777
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• 2019

In this paper, we study the convergence analysis of the sequences generated by the proximal point method for an infinite family of pseudo-monotone equilibrium problems in Banach spaces. We first prove the weak convergence of the generated sequence to a common solution of the infinite family of equilibrium problems with summable errors. Then, we show the strong convergence of the generated sequence to a common equilibrium point by some various additional assumptions. We also consider two variants for which we establish the strong convergence without any additional assumption. For both of them, each iteration consists of a proximal step followed by a computationally inexpensive step which ensures the strong convergence of the generated sequence. Also, for this two variants we are able to characterize the strong limit of the sequence: for the first variant it is the solution lying closest to an arbitrarily selected point, and for the second one it is the solution of the problem which lies closest to the initial iterate. Finally, we give a concrete example where the main results can be applied.

• Communications of the Korean Mathematical Society
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• v.21 no.4
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• pp.679-687
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• 2006

The purpose of this paper is to obtain a new common fixed point theorem by using a new contractive condition in intuitionistic fuzzy metric spaces. Our result generalizes and extends many known results in fuzzy metric spaces and metric spaces.

• Korean Journal of Mathematics
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• v.30 no.4
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• pp.679-686
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• 2022

In this study, the concept of lacunary statistical convergence is studied in G-metric spaces. The G-metric function is based on the concept of distance between three points. Considering this new concept of distance, we examined the relationships between GS, GS_θ, Gσ₁ and GN_θ sequence spaces.

• Korean Journal of Mathematics
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• v.29 no.4
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• pp.665-677
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• 2021

The main object of this study is to introduce the spaces $c_0({\hat{F}^q)$ and $c({\hat{F}^q)$ derived by the matrix ${\hat{F}^q$ which is the multiplication of Riesz matrix and Fibonacci matrix. Moreover, we find the 𝛼-, 𝛽-, 𝛾- duals of these spaces and give the characterization of matrix classes (${\Lambda}({\hat{F}^q)$, Ω) and (Ω, ${\Lambda}({\hat{F}^q)$) for 𝚲 ∈ {c₀, c} and Ω ∈ {ℓ₁, c₀, c, ℓ_∞}.

• Korean Journal of Mathematics
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• v.32 no.1
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• pp.109-120
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• 2024

The aim of this research is to describe lacunary ∆^m-statistically convergent sequences with respect to metrics on generalised metric spaces (g-metric spaces) and to look into the fundamental characteristics of this statistical form of convergence. Also, the relationship between strong summability and lacunary ∆^m-statistical convergence in g-metric space is established at the end.

• Proceedings of the Korean Society for Applied Microbiology Conference
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• 2001.06a
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• pp.77-80
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• 2001

A variety of different methods to generate diverse proteins, including random mutagenesis and recombination, are currently available, and most of them accumulate the mutations on the target gene of a protein, whose sequence space remains unchanged. On the other hand, a pool of diverse genes, which is generated by random insertions, deletions, and exchange of the homologous domains with different lengths in the target gene, would present the protein lineages resulting in new fitness landscapes. Here we report a method to generate a pool of protein variants with different sequence spaces by employing green fluorescent protein (GFP) as a model protein. This process, designated functional salvage screen (FSS), comprises the following procedures： a defective GFP template expressing no fluorescence is firstly constructed by genetically disrupting a predetermined region(s) of the protein, and a library of GFP variants is generated from the defective template by incorporating the randomly fragmented genomic DNA from E. coli into the defined region(s) of the target gene, followed by screening of the functionally salvaged, fluorescence-emitting GFPs. Two approaches, sequence-directed and PCR-coupled methods, were attempted to generate the library of GFP variants with new sequences derived from the genomic segments of E. coli. The functionally salvaged GFPs were selected and analyzed in terms of the sequence space and functional property. The results demonstrate that the functional salvage process not only can be a simple and effective method to create protein lineages with new sequence spaces, but also can be useful in elucidating the involvement of a specific region(s) or domain(s) in the structure and function of protein.

• Bulletin of the Korean Mathematical Society
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• v.26 no.1
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• pp.83-94
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• 1989