• Journal of the Korean Mathematical Society
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• v.54 no.3
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• pp.867-876
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• 2017

Let $\mathcal{A}$ and $\mathcal{B}$ be two $C^*$-algebras such that $\mathcal{A}$ is prime. In this paper, we investigate the additivity of maps ${\Phi}$ from $\mathcal{A}$ onto $\mathcal{B}$ that are bijective and satisfy $${\Phi}(A^*B+{\eta}BA^*)={\Phi}(A)^*{\Phi}(B)+{\eta}{\Phi}(B){\Phi}(A)^*$$ for all $A,B{\in}\mathcal{A}$ where ${\eta}$ is a non-zero scalar such that ${\eta}{\neq}{\pm}1$. Moreover, if ${\Phi}(I)$ is a projection, then ${\Phi}$ is a ${\ast}$-isomorphism.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2007.04a
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• pp.209-212
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• 2007

Non-additive measures and their corresponding Choquet integrals are very useful tools which are used in both insurance and financial markets. In both markets, it is important to to update prices to account for additional information. The update price is represented by the Choquet integral with respect to the conditioned non-additive measure. In this paper, we consider a price functional H on interval-valued risks defined by interval-valued Choquet integral with respect to a non-additive measure. In particular, we prove that if an interval-valued pricing functional H satisfies the properties of monotonicity, comonotonic additivity, and continuity, then there exists an two non-additive measures ${\mu}_1,\;{\mu}_2$ such that it is represented by interval-valued choquet integral on interval-valued risks.

• Proceedings of the Korean Society of Computational and Applied Mathematics Conference
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• 2003.09a
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• pp.7-7
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• 2003

We studied closed set-valued Choquet integrals in two papers(1997, 2000) and convergence theorems under some sufficient conditions in two papers(2003), for examples : (i) convergence theorems for monotone convergent sequences of Choquet integrably bounded closed set-valued functions, (ii) covergence theorems for the upper limit and the lower limit of a sequence of Choquet integrably bounded closed set-valued functions. In this presentation, we consider fuzzy number-valued functions and define Choquet integrals of fuzzy number-valued functions. But these concepts of fuzzy number-valued Choquet inetgrals are all based on the corresponding results of interval-valued Choquet integrals. We also discuss their properties which are positively homogeneous and monotonicity of fuzzy number-valued Choquet integrals. Furthermore, we will prove convergence theorems for fuzzy number-valued Choquet integrals. They will be used in the following applications : (1) Subjectively probability and expectation utility without additivity associated with fuzzy events as in Choquet integrable fuzzy number-valued functions, (2) Capacity measure which are presented by comonotonically additive fuzzy number-valued functionals, and (3) Ambiguity measure related with fuzzy number-valued fuzzy inference.

• Journal of the Korean Statistical Society
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• v.34 no.3
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• pp.219-233
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• 2005

The 3-way balanced multi-level rotation design has been discussed (Park Kim and Kim, 2003), where the 3-way balancing is done on interview time, in monthly sample and rotation group and recall time. A greater advantage of 3-way balanced design is accomplished by an estimator. To obtain the advantage, we generalized previous generalized composite estimator (GCE). We call this as l-step GCE. The variance of the l-step GCE's of various characteristics of interest are presented. Also, we provide the coefficients which minimize the variance of the l-step GCE. Minimizing a weighted sum of variances of all concerned estimators of interest, we drive one set of the compromise coefficient of l-step GCE's to preserve additivity of estimates.

• Transactions of the Korean Society of Automotive Engineers
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• v.7 no.6
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• pp.198-206
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• 1999

An automobile outside rear view mirror system has been analyzed and designed to reduce vibration with a finite element model. model analysis is conducted for the calculation of natural frequencies. harmonic analysis is utilized to estimate the displacements of the glass surface under dynamic loads. The model is verified with the vibration experiment of the parts and the assembled body. The structure of the mirror system is optimized for the robustness defined by the Taguchi concept. At first, many potential design variables are defined. Final design variables are selected based on the amount of contribution on the objective function. That is, sensitive variables are chose. The SN ratio in the Taguchi method is replaced by an objective function with the mean and the standard deviation of the quality characteristic. The defined objective function is appropriate in the structural design in that the vibration displacements are minimized while the robustness is improved.

• Proceedings of the Korean Society for Emotion and Sensibility Conference
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• 2000.04a
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• pp.407-411
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• 2000

Color reproduction n CRT monitors needs colorimetric characterization concluding two stages with 3x3 matrix and three TRCs (Tone-Reproduction Characteristics). The 3x3 matrix is based on the additivity of RGB emissions, and the TRC represents the non-linearity between the input digital counts and the output luminance. The objective of this project is to evaluate the accuracy of color reproduction on LCD monitors using conventional CRT model(GOG model). For two different manufacturers, colorimetric characterizations of desktop LCDs have been performed. Because the transfer function for LCD is very differ from TRC of CRT, some researchers had reported that GOG model is inadequate for the colorimetric characterization of LCDs. However in our experiment, the degree of accuracy was dependent on the shape of electro-optical transfer functions of LCD. It has been founded that the GOG model could be applied for LCD monitors having monotonically increased Electro-optical transfer function.

• International Journal of Safety
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• v.2 no.1
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• pp.28-33
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• 2003

Thermal decomposition characteristics of ethyl methacrylate (EMA) and Styrene (St.) copolymer was investigated with synthesis at 8$0^{\circ}C$ in a continuous stirred tank reacto (CSTR) using toluene and benzoyl peroxide(BPO) as solvent and initiator, respectively. The thermal decomposition was considered to be side scission at below 30$0^{\circ}C$ and estimated 2nd-order reaction kinetics of EMA/St. copolymer. The activation energies of decomposition on this copolymers were in the ranges of 38-43 kcal/mol for EMA/St. and a good additivity rule was observed in each composition. The thermogravimetric trace curves agreed well with the theoretical calculation.

• Korean Journal of Mathematics
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• v.26 no.3
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• pp.459-465
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• 2018

Recently, Li et al proved that ${\Phi}$ which satisfies the following condition on factor von Neumann algebras $${\Phi}([[A,B]_*,C]_*)=[[{\Phi}(A),B]_*,C]_*+[[A,{\Phi}(B)]_*,C]_*+[[A,B]_*,{\Phi}(C)]_*$$ where $[A,B]_*=AB-BA^*$ for all $A,B{\in}{\mathcal{A}}$, is additive ${\ast}-derivation$. In this short note we show the additivity of ${\Phi}$ which satisfies the above condition on prime ${\ast}-algebras$.

• Bulletin of the Korean Mathematical Society
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• v.51 no.4
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• pp.1127-1133
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• 2014

Let S be a nonempty subset of a ring R. A map $f:R{\rightarrow}R$ is called strong commutativity preserving on S if [f(x), f(y)] = [x, y] for all $x,y{\in}S$, where the symbol [x, y] denotes xy - yx. Bell and Daif proved that if a derivation D of a semiprime ring R is strong commutativity preserving on a nonzero right ideal ${\rho}$ of R, then ${\rho}{\subseteq}Z$, the center of R. Also they proved that if an endomorphism T of a semiprime ring R is strong commutativity preserving on a nonzero two-sided ideal I of R and not identity on the ideal $I{\cup}T^{-1}(I)$, then R contains a nonzero central ideal. This short note shows that the conclusions of Bell and Daif are also true without the additivity of the derivation D and the endomorphism T.

• Journal of the Korean Applied Science and Technology
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• v.19 no.4
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• pp.273-280
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• 2002

Thermal decomposition of the copolymer of butyl methacylate(BMA) with styrene(St) was investigated. The copolymer Was obtained at 80 $^{\circ}C$ in a continuous stirred tank reactor(CSTR) using toluene and benzoyl peroxide(BPO), as solvent and initiator, respectively. The reactor volume was 0.3 liters and residence time was 3 hours. The thermal decomposition followed the second order kinetics for BMA/St copolymer. The activation energies of thermal decompositon were in the ranges of 38 ${\sim}43$ kcal/mol for BMA with St copolymer and a good additivity rule was observed with the composition of copolymer. The thermogravimetric trace curve agreed well with the theoretical calculation.