• Journal of applied mathematics & informatics
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• v.29 no.5_6
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• pp.1421-1433
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• 2011

In this paper, using a fixed point approach, the generalized Hyeres-Ulam stability of the following quadratic functional equation $f(x+y+z)+f(x+{\sigma}(y))+f(y+{\sigma}(z))+f(x+{\sigma}(z))=3(f(x)+f(y)+f(z))$ will be studied, where f is a function from abelian group G into a quasi-${\beta}$-normed space and ${\sigma}$ is an involution on the group G. Next, we consider its pexiderized equation of the form $f(x+y+z)+f(x+{\sigma}(y))+f(y+{\sigma}(z))+f(x+{\sigma}(z))=g(x)+g(y)+g(z)$ and its generalized Hyeres-Ulam stability.

• Journal of Korean Institute of Industrial Engineers
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• v.17 no.1
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• pp.51-58
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• 1991

This paper presents a single-echelon, single item, stochastic lead time and static demand inventory model for situations in which, during the stockout period, a fraction ${\beta}$ of the demand is backordered and the remaining fraction $(1-{\beta})$ is lost. In this situations, an objective function representing the average annual cost of inventory system is obtained by defining a time-proportional backorder cost and a fixed penalty cost per unit lost. The optimal operating policy variables minimizing the average annual cost are calculated iteratively. At the extremet ${\beta}=1$, the model presented reduces to the usual backorder case. A numerical example is solved to illustrate the algorithm developed.

• Journal of the Korean Mathematical Society
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• v.54 no.4
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• pp.1175-1187
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• 2017

The spectral problem $$-y^{{\prime}{\prime}}+q(x)y={\lambda}y,\;0 < x < 1, \atop y(0)cos{\beta}=y^{\prime}(0)sin{\beta},\;0{\leq}{\beta}<{\pi};\;{\frac{y^{\prime}(1)}{y(1)}}=h({\lambda})$$ is considered, where ${\lambda}$ is a spectral parameter, q(x) is real-valued continuous function on [0, 1] and $$h({\lambda})=a{\lambda}+b-\sum\limits_{k=1}^{N}{\frac{b_k}{{\lambda}-c_k}},$$ with the real coefficients and $a{\geq}0$, $b_k$ > 0, $c_1$ < $c_2$ < ${\cdots}$ < $c_N$, $N{\geq}0$. The sharpened asymptotic formulae for eigenvalues and eigenfunctions of above-mentioned spectral problem are obtained and the uniform convergence of the spectral expansions of the continuous functions in terms of eigenfunctions are presented.

• Bulletin of the Korean Mathematical Society
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• v.55 no.4
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• pp.1231-1240
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• 2018

In this paper, we characterize the conformal transformations between two almost regular (${\alpha},{\beta}$)-metrics. Suppose that F is a non-Riemannian (${\alpha},{\beta}$)-metric and is conformally related to ${\widetilde{F}}$, that is, ${\widetilde{F}}=e^{{\kappa}(x)}F$, where ${\kappa}:={\kappa}(x)$ is a scalar function on the manifold. We obtain the necessary and sufficient conditions of the conformal transformation between F and ${\widetilde{F}}$ preserving the mean Landsberg curvature. Further, when both F and ${\widetilde{F}}$ are regular, the conformal transformation between F and ${\widetilde{F}}$ preserving the mean Landsberg curvature must be a homothety.

• Toxicological Research
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• v.27 no.3
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• pp.167-172
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• 2011

We demonstrate that glycoprotein isolated from Dioscorea batatas (GDB) activates macrophage function. Analysis of the infiltration of macrophages into peritoneal cavity showed GDB treatment significantly increased the recruitment of macrophages into the peritoneal cavity. In order to further confirm and investigate the mechanism of GDB on macrophage activation, we analyzed the effects of GDB on the cytokine expression including IL-$1{\beta}$, TNF-${\alpha}$, and IL-6 in mouse peritoneal macrophages. GDB increased the expression of IL-$1{\beta}$, TNF-${\alpha}$, and IL-6. Cytokine induction by GDB was further confirmed by RT-PCR and ELISA in mouse macrophage cell line, RAW264.7 cells. Treatment of RAW264.7 cells with GDB produced strong induction of NF-${\kappa}B$ DNA binding and MAPK phosphorylation, markers for macrophage activation and important factors for cytokine gene expression. Collectively, this series of experiments indicates that GDB stimulates macrophage activation.

• Food Science and Preservation
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• v.5 no.1
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• pp.13-21
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• 1998

Korean medicinal herb extracts(KMHE) were applied to the preservation of greenhouse produce in order to prove their effectiveness. KMHE showed remarkable antimicrobial effects against Bacillus cereus, Peudomonas syringae, and Corynebacterium xerosis causing the postharvest decay of greenhouse produce. Among KMHE the extracts of Rheum palmatum L. and Coptis chinensis Franch most obviously inhibited the growth of microorganims causing the Postharvest decay of greenhouse produce, which destroyed to undetectable levels when treated with more than 500ppm of KMHE. The activities of KMHE were stable in the wide spectrum of pH and temperature. Direct visualization of microbial cells by using both transmission electron microscope and scanning electron microscope showed microbial cell membrane the function of which was destroyed by treating with the dilute solutions of KMHE. This change of cellular membrane permeability could be identified in the experiment that O-nitrophenyl-$\beta$-D-galactopyranoside(ONPG), the artificial substrate of $\beta$-galactosidase, was hydrolyzed in the presence of KMHE, indicating that the membrane was perturbed by KMHE.

• Proceedings of the KIEE Conference
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• 2001.07c
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• pp.1433-1435
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• 2001

The mechanical and phase transformation of the cold isostatically pressed $\beta$-SiC ceramic were investigated as a function of the sintering temperature. The result of phase analysis revealed 6H, 4H, 3C and phase transformation between 3C and 4H showed over 2000$^{\circ}C$ and the $\beta$ ${\rightarrow}$ $\alpha$ phase transformation was in saturation at 2200$^{\circ}C$. The relative density and the mechanical properties of $\alpha$-SiC ceramic was increased with increased sintering temperature. The flexural strength showed the highest value of 230 MPa at 2200$^{\circ}C$. This reason is because crack was propagated through surface flaw. The fracture toughness showed the highest value of 4.2 $MPa{\cdot}m^{1/2}$ at 2200$^{\circ}C$.

• ETRI Journal
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• v.39 no.1
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• pp.21-29
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• 2017

This paper addresses the problem of unsupervised speech separation based on robust non-negative matrix factorization (RNMF) with ${\beta}$-divergence, when neither speech nor noise training data is available beforehand. We propose a robust version of non-negative matrix factorization, inspired by the recently developed sparse and low-rank decomposition, in which the data matrix is decomposed into the sum of a low-rank matrix and a sparse matrix. Efficient multiplicative update rules to minimize the ${\beta}$-divergence-based cost function are derived. A convolutional extension of the proposed algorithm is also proposed, which considers the time dependency of the non-negative noise bases. Experimental speech separation results show that the proposed convolutional RNMF successfully separates the repeating time-varying spectral structures from the magnitude spectrum of the mixture, and does so without any prior training.

• Biomolecules & Therapeutics
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• v.19 no.4
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• pp.390-397
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• 2011

G protein-coupled receptor kinases (GRKs) and ${\beta}$-arrestins have been known as regulators of G protein-coupled receptors. However, it has been recently reported that GRKs and ${\beta}$-arrestins mediate receptor-mediated cellular responses in a G proteinin-dependent manner. In this scheme, GRKs work as a mediator or a scaffold protein. Among 7 members of the GRK family (GRK1-GRK7), GRK2 is the most extensively studied in vitro and in vivo. GRK2 is involved in cellular migration, insulin signaling, and cardiovascular disease. GRK6 in concert with ${\beta}$-arrestin 2 mediates chemoattractant-stimulated chemotaxis of T and B lymphocytes. GRK5 shuttles between the cytosol and nucleus, and regulates the activities of transcription factors. GRK3 and GRK4 do not seem to have striking effects on cellular responses other than receptor regulation. GRK1 and GRK7 play specific roles in regulation of rhodopsin function. In this review, these newly discovered functions of GRKs are briefly described.

• Journal of applied mathematics & informatics
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• v.18 no.1_2
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• pp.339-350
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• 2005

A space-time fractional advection-dispersion equation (ADE) is a generalization of the classical ADE in which the first-order time derivative is replaced with Caputo derivative of order $\alpha{\in}(0,1]$, and the second-order space derivative is replaced with a Riesz-Feller derivative of order $\beta{\in}0,2]$. We derive the solution of its Cauchy problem in terms of the Green functions and the representations of the Green function by applying its Fourier-Laplace transforms. The Green function also can be interpreted as a spatial probability density function (pdf) evolving in time. We do the same on another kind of space-time fractional advection-dispersion equation whose space and time derivatives both replacing with Caputo derivatives.