• East Asian mathematical journal
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• v.12 no.1
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• pp.125-145
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• 1996

• East Asian mathematical journal
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• v.11 no.1
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• pp.7-26
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• 1995

• Korean Journal of Mathematics
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• v.23 no.2
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• pp.231-248
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• 2015

In this paper, we solve the following quadratic $\rho$-functional inequalities ${\parallel}f(\frac{x+y+z}{2})+f(\frac{x-y-z}{2})+f(\frac{y-x-z}{2})+f(\frac{z-x-y}{2})-f(x)-x(y)-f(z){\parallel}\;(0.1)\\{\leq}{\parallel}{\rho}(f(x+y+z+)+f(x-y-z)+f(y-x-z)+f(z-x-y)-4f(x)-4f(y)-f(z)){\parallel}$ where $\rho$ is a fixed complex number with ${\left|\rho\right|}<\frac{1}{8}$, and ${\parallel}f(x+y+z)+f(x-y-z)+f(y-x-z)+f(z-x-y)-4f(x)-4f(y)-4f(z){\parallel}\;(0.2)\\{\leq}{\parallel}{\rho}(f(\frac{x+y+z}{2})+f(\frac{x-y-z}{2})+f(\frac{y-x-z}{2})+f(\frac{z-x-y}{2})-f(x)-f(y)-f(z)){\parallel}$ where $\rho$ is a fixed complex number with ${\left|\rho\right|}$ < 4. Using the fixed point method, we prove the Hyers-Ulam stability of the quadratic $\rho$-functional inequalities (0.1) and (0.2) in complex Banach spaces.

• 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.

• Korean Institute of Interior Design Journal
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• v.23 no.3
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• pp.108-116
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• 2014

Postmodernism, a cultural movement which occurred in the mid-20th century, avoided functional form, one of the features of modernism, and pursued post-rational and post-centric pluralistic thought which puts human emotions in importance. Postmodernism set a high value on emotional instincts of humans and focused on creation of empathy. It includes scepticism of rationalism and indicates the significance of emotional and psychological instincts of humans, or 'emotions'. Along with the big change in that time, more dynamic and unprecedented indoor spaces had appeared. Nigel Coates, who had taken various kinds of artistic activity from the early 1980s to the late 1990s, had tried to make a new approach of objet-focused emotional spaces. Such an approach made in the time when science and technology had rapidly developed and social structure had changed was considerably fresh, liberal, and futuristic. He interpreted spaces by escaping from realistic intentions and communicating with drawings, and designed object-focused emotional spaces by actively employing objets on the basis of ideas. He tried to make emotional sharing between the public and spaces through objet, and showed unique spaces in his own way by reinterpreting the meanings of spaces and stimulating human emotion. This study was intended to look into his artworks to show his way of approaching objets, and to find an application plan and the future possibility of the plan.

• The Pure and Applied Mathematics
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• v.19 no.4
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• pp.397-407
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• 2012

Let X and Y be vector spaces. We introduce a new type of a cubic functional equation $f$ : $X{\rightarrow}Y$. Furthermore, we assume X is a vector space and (Y, N) is a fuzzy Banach space and then investigate a fuzzy version of the generalized Hyers-Ulam stability in fuzzy Banach space by using fixed point method for the cubic functional equation.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.4
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• pp.671-681
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• 2013

In this paper, we prove the generalized Hyers-Ulam stability of the additive functional inequality $${\parallel}f(x-y)+f(y-z)+f(z){\parallel}{\leq}{\parallel}f(x){\parallel}$$ in Banach spaces.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.4
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• pp.707-721
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• 2013

In this paper, we investigate a fuzzy version of stability theory for the following functional equation f(x+y)+f(x-y)-2f(x)-f(y)-f(-y)=0 in the sense of M. Mirmostafaee and M. S. Moslehian.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.15 no.4
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• pp.253-265
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• 2011

In this paper, we study the existence of mild solutions for double perturbed impulsive neutral functional evolution equations with infinite delay in Banach spaces. The existence of mild solutions to such equations is obtained by using the theory of the Hausdorff measure of noncompactness and Darbo fixed point theorem, without the compactness assumption on associated evolution system. An example is provided to illustrate the theory.

• Journal of the Chungcheong Mathematical Society
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• v.28 no.3
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• pp.397-408
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• 2015

In this paper, we solve the Hyers-Ulam stability problem for the following cubic type functional equation $$f(rx+sy)+f(rx-sy)=rs^2f(x+y)+rs^2f(x-y)+2r(r^2-s^2)f(x)$$in quasi-Banach space and non-Archimedean space, where $r={\neq}{\pm}1,0$ and s are real numbers.