• The Pure and Applied Mathematics
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• v.15 no.2
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• pp.169-178
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• 2008

In this paper we generalize the superstability of the exponential functional equation proved by J. Baker et al. [2], that is, we solve an exponential type functional equation $$f(x+y)\;=\;a^{xy}f(x)f(y)$$ and obtain the superstability of this equation. Also we generalize the stability of the exponential type equation in the spirt of R. Ger[4] of the following setting $$|{\frac{f(x\;+\;y)}{{a^{xy}f(x)f(y)}}}\;-\;1|\;{\leq}\;{\delta}.$$

• The Pure and Applied Mathematics
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• v.29 no.2
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• pp.179-188
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• 2022

In this paper we investigate the Hyers-Ulam stability of the s-variable additive and l-variable quadratic functional equations of the form $$f\(\sum\limits_{i=1}^{s}x_i\)+\sum\limits_{j=1}^{s}f\(-sx_j+\sum\limits_{i=1,i{\neq}j}^{s}x_i\)=0$$ and $$f\(\sum\limits_{i=1}^{l}x_i\)+\sum\limits_{j=1}^{l}f\(-lx_j+\sum\limits_{i=1,i{\neq}j}^{l}x_i\)=(l+1)$$$\sum\limits_{i=1,i{\neq}j}^{l}f(x_i-x_j)+(l+1)\sum\limits_{i=1}^{l}f(x_i)$ (s, l ∈ N, s, l ≥ 3) in quasi-Banach spaces.

• Journal of the Ergonomics Society of Korea
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• v.25 no.4
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• pp.9-22
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• 2006

1/f fluctuation characteristics can be seen in various natural phenomena, such as breezes, streams, candle flames and the luminous patterns of fireflies. It is said that the 1/f fluctuation are comfortable for human beings. And they are introduced into many industrial products, such as an air conditioner, music, lighting, etc. This study focused on verifying the effects of 1/f fluctuation sound on comfort sensibility. Stimulus were divided into three groups(Group 1, 2, 3) by sound generation methodology. Fluctuation patterns of group 1, 2 were given by three types of fluctuation, 1/f0, 1/f1, 1/f2, and its of group 3 were given by two types of pure tone, 1/f1. In order to verify the effects, we measured the physiological responses of the subjects such as EEG(Electroencephalogram), ERP(Event-Related Potential), and these physiological responses were compared with subjective assessments, free answers. Consequently, we found that factor which had an effect on comfort sensibility was cognitive factor(for stimulus) rather than 1/f fluctuation sound pattern.

• Bulletin of the Korean Chemical Society
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• v.28 no.4
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• pp.581-588
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• 2007

To enhance the photodecomposition of concentrated ammonia into N2, Pt/V-TiO2 photocatalysts were prepared using solvothermal and impregnation methods. Nanometer-sized particles of 0.1, 0.5 and 1.0 mol% V-TiO2 were prepared solvothermally, and then impregnated with 1.0 wt% Pt. The X-ray diffraction (XRD) peaks assigned to V2O5 at 30.20 (010) and Pt metal at 39.80 (111) and 46.20 (200) were seen in the 1.0 wt% Pt/ 10.0 mol% V-TiO2. The particle size increased in the order: pure TiO2, V-TiO2 and Pt/V-TiO2 after thermal treatment at 500 °C, while their surface areas were in the reverse order. On X-ray photoelectron spectroscopy (XPS), the bands assigned to the Ti2p3/2 and Ti2p1/2 of Ti4+-O were seen in all the photocatalysts, and the binding energies increased in the order: TiO2 < Pt/V-TiO2 < V-TiO2. The XPS bands assigned to the V2p3/2 (517.85, 519.35, and 520.55 eV) and V2p1/2 (524.90 eV) in the V3+, V4+ and V5+ oxides appeared over V-TiO2, respectively, while the band shifted to a lower binding energy with Pt impregnation. The Pt components of Pt/ V-TiO2 were identified at 71.60, 73.80, 75.00 and 76.90 eV, which were assigned to metallic Pt 4f7/2, PtO 4f7/2, PtO2 4f7/2, and PtO 4f5/2, respectively. The UV-visible absorption band shifted closer towards the visible region of the spectrum in V-TiO2 than in pure TiO2 and; surprisingly, the Pt/V-TiO2 absorbed at all wavelengths from 200 to 800 nm. The addition of vanadium generated a new acid site in the framework of TiO2, and the medium acidic site increased with Pt impregnation. The NH3 decomposition increased with the amount of vanadium compared to pure TiO2, and was enhanced with Pt impregnation. NH3 decomposition of 100% was attained over 1.0 wt% Pt/1.0 mol% V-TiO2 after 80 min under illumination with 365 nm light, although about 10% of the ammonia was converted into undesirable NO2 and NO. Various intermediates, such as NO2, -NH2, -NH and NO, were also identified in the Fourier transform infrared (FT-IR) spectra. From the gas chromatography (GC), FT-IR and GC/mass spectroscopy (GC/MS) analyses, partially oxidized NO and NO2 were found to predominate over V-TiO2 and pure TiO2, respectively, while both molecules were reduced over Pt/V-TiO2.

• The Pure and Applied Mathematics
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• v.24 no.3
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• pp.179-190
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• 2017

In this paper, we introduce and solve the following quadratic (${\rho}_1$, ${\rho}_2$)-functional inequality (0.1) $$N\left(2f({\frac{x+y}{2}})+2f({\frac{x-y}{2}})-f(x)-f(y),t\right){\leq}min\left(N({\rho}_1(f(x+y)+f(x-y)-2f(x)-2f(y)),t),\;N({\rho}_2(4f(\frac{x+y}{2})+f(x-y)-2f(x)-2f(y)),t)\right)$$ in fuzzy normed spaces, where ${\rho}_1$ and ${\rho}_2$ are fixed nonzero real numbers with ${{\frac{1}{{4\left|{\rho}_1\right|}}+{{\frac{1}{{4\left|{\rho}_2\right|}}$ < 1, and f(0) = 0. Using the fixed point method, we prove the Hyers-Ulam stability of the quadratic (${\rho}_1$, ${\rho}_2$)-functional inequality (0.1) in fuzzy Banach spaces.

• Journal of the Korean Chemical Society
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• v.43 no.1
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• pp.52-57
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• 1999

The anionic complexes, [ln($C_6F_5)_4$]-, which are thermal and moisture sensitive, have been prepared by the reaction of In($C_6F_5)_3{\cdot}D(D=CH_3CN$, O($C_2H_5)_2$) with the system ($CH_3)_3SiC_6F_5$/CsF, $C_6F_5$MgBr or Cd($C_6F_5)_2$. The stable anionic indium(III) complexes are obtained through cation exchange with PNPCI ([PNP]= bis(triphenylphosphino)ammonium). The pure substance is obtained by column chromatography. These new anionic complexes are unambiguously identifed by NMR-spectroscopy, IR spectroscopy, molecular weight, DTA/TG and elemental analysis.

• Journal of the Korean Society of Tobacco Science
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• v.3 no.1
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• pp.49-57
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• 1981

To obtain genetic information for breeding aromatic tobacco, broad sense heritabilities, phenotypic, and genotypic correlations were obtained for the following characters : days to frowert, plant height, number of leaves, leaf shape and nicotine. Six pure line varieties and the first and second generations of 5 crosses among them were employed in this study. The heritabilities for number of leaves and nicotine were very high in pure line varieties. However, the heritabilities for days to flower and yield were low in six varieties as well as in F2. Genotypic correlations had higher values than phenotypic did. Heritabilities calculated from segregating generations were lower than those from pure varieties, regardless of crosses involved. Positive phenotypic correlations between yield and plant height were observed in all crosses. Same phenomenon was observed with correlations between days to flower and number of leaves. The genotypic and phenotypic variances and covariances entering into the computation of correlations were used to construct the seletion indices for yield. The use and limitation of selection index was also discussed.

• Steel and Composite Structures
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• v.10 no.5
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• pp.415-428
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• 2010

Proper material constitutive models for concrete-filled tube (CFT) columns of circular cross section and subjected to pure bending moment are proposed. These material models are implemented into the Abaqus finite element program and verified against experimental data. It has been shown that the steel tube does not provide good confining effect to the concrete core when the CFT columns is subjected to pure bending moment. When the diameter-to-thickness ratio of the CFT columns is small, the behavior of the CFT column is the same as the steel tube without a concrete core.

• Communications of the Korean Mathematical Society
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• v.33 no.3
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• pp.721-739
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• 2018

In this paper, we investigate the problem of describing the form of Jordan generalized derivations on trivial extension algebras. One of the main results shows, under some conditions, that every Jordan generalized derivation on a trivial extension algebra is the sum of a generalized derivation and an antiderivation. This result extends the study of Jordan generalized derivations on triangular algebras (see [12]), and also it can be considered as a "generalized" counterpart of the results given on Jordan derivations of a trivial extension algebra (see [11]).

• The Pure and Applied Mathematics
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• v.27 no.4
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• pp.171-186
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• 2020

Long back in 1972, it was shown that the sum of the squares of vertex degrees and the sum of cubes of vertex degrees of a molecular graph both have large correlations with total 𝜋-electron energy of the molecule. Later on, the sum of squares of vertex degrees was named as first Zagreb index and became one of the most studied molecular graph parameter in the field of chemical graph theory. Whereas, the other sum remained almost unnoticed until recently except for a few occasions. Thus it got the name "forgotten" index or F-index. This paper investigates extremal graphs with respect to F-index among the class of bicyclic graphs with n vertices and k pendant vertices, 0 ≤ k ≤ n - 4. As consequences, we obtain the bicyclic graphs with largest and smallest F-indices.