• Korean Journal of Mathematics
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• v.18 no.4
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• pp.395-407
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• 2010

In this paper, we prove the generalized Hyers-Ulam stability of the following quadratic functional equations $$cf\(\sum_{i=1}^{n}x_i\)+\sum_{j=2}^{n}f\(\sum_{i=1}^{n}x_i-(n+c-1)x_j\)\\=(n+c-1)\(f(x_1)+c\sum_{i=2}^{n}f(x_i)+\sum_{i<j,j=3}^{n}\(\sum_{i=2}^{n-1}f(x_i-x_j\)\),\\Q\(\sum_{i=1}^{n}d_ix_i\)+\sum_{1{\leq}i<j{\leq}n}d_id_jQ(x_i-x_j)=\(\sum_{i=1}^{n}d_i\)\(\sum_{i=1}^{n}d_iQ(x_i)\)$$ in random normed spaces.

• Journal of the Korean Mathematical Society
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• v.53 no.4
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• pp.929-967
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• 2016

Let p(t, x) be the fundamental solution to the problem $${\partial}^{\alpha}_tu=-(-{\Delta})^{\beta}u,\;{\alpha}{\in}(0,2),\;{\beta}{\in}(0,{\infty})$$. If ${\alpha},{\beta}{\in}(0,1)$, then the kernel p(t, x) becomes the transition density of a Levy process delayed by an inverse subordinator. In this paper we provide the asymptotic behaviors and sharp upper bounds of p(t, x) and its space and time fractional derivatives $$D^n_x(-{\Delta}_x)^{\gamma}D^{\sigma}_tI^{\delta}_tp(t,x),\;{\forall}n{\in}{\mathbb{Z}}_+,\;{\gamma}{\in}[0,{\beta}],\;{\sigma},{\delta}{\in}[0,{\infty})$$, where $D^n_x$ x is a partial derivative of order n with respect to x, $(-{\Delta}_x)^{\gamma}$ is a fractional Laplace operator and $D^{\sigma}_t$ and $I^{\delta}_t$ are Riemann-Liouville fractional derivative and integral respectively.

• Journal of IKEEE
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• v.23 no.2
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• pp.425-430
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• 2019

This work describes the design and characterization of a X-band power amplifier (PA) monolithic microwave integrated circuit (MMIC) using a $0.25{\mu}m$ gate length gallium nitride (GaN) high electron mobility transistor (HEMT) technology. The developed X-band power amplifier MMIC has small signal gain of over 22.7 dB and saturated output power of 43.02 dBm (20.04 W) over the entire band of 9 to 10 GHz. Maximum saturated output power is a 43.84 dBm (24.21 W) at 9.5 GHz. Its power added efficiency (PAE) is 41.0~51.24% and the chip dimensions are $3.7mm{\times}2.3mm$, generating the output power density of $2.84W/mm^2$. The developed GaN power amplifier MMIC is expected to be applied in a variety of X-band radar applications.

• The Pure and Applied Mathematics
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• v.17 no.1
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• pp.87-92
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• 2010

Let R be a 2-torsion free $\sigma$-prime ring with an involution $\sigma$, U a nonzero square closed $\sigma$-Lie ideal, Z(R) the center of Rand d a derivation of R. In this paper, it is proved that d = 0 or $U\;{\subseteq}\;Z(R)$ if one of the following conditions holds: (1) $d(xy)\;-\;xy\;{\in}\;Z(R)$ or $d(xy)\;-\;yx\;{\in}Z(R)$ for all x, $y\;{\in}\;U$. (2) $d(x)\;{\circ}\;d(y)\;=\;0$ or $d(x)\;{\circ}\;d(y)\;=\;x\;{\circ}\;y$ for all x, $y\;{\in}\;U$ and d commutes with $\sigma$.

• The KIPS Transactions:PartA
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• v.18A no.3
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• pp.81-92
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• 2011

There has been a number of attempts to apply 3D CAD data created in the design stage of product life cycle to various applications of the other stages in related industries. But, 3D CAD data requires a large amount of computing resources for data processing, and it is not suitable for post applications such as distributed collaboration, marketing tool, or Interactive Electronic Technical Manual because of the design information security problem and the license cost. Therefore, various lightweight visualization formats and application systems have been suggested to overcome these problems. However, most of these lightweight formats are dependent on the companies or organizations which suggested them and cannot be shared with each other. In addition, product structure information is not represented along with the product geometric information. In this paper, we define a dataset called prod-X3D(Enhanced X3D Dataset for Web-based Visualization of 3D CAD Product Model) based on the international standard graphic format, X3D, which can represent the structure information as well as the geometry information of a product, and propose a translation method from 3D CAD data to an prod-X3D.

• Bulletin of the Korean Chemical Society
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• v.35 no.7
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• pp.1927-1928
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• 2014

• The Korean Journal of Zoology
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• v.26 no.3
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• pp.181-192
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• 1983

Cytosol protein patterns of two strains of A. proteus, tD and xD strain, were compared by two dimensional gel electrophoresis. Among the 200 major polypeptides that could be stained by silver stain method, tD strain contained a cell specific protein whose molecular weight was 45,000 dalton, pI 5.9. On the other hand, the cytosol and the symbiotic vesicles of xD strain contained a symbiosis specific protein (M.W. 29,000; pI 5.5). The fate of the symbiosis specific protein depended on the presence of symbiotic bacteria in the experiment of high temperature effect and of experimental infection. The significance of these results is discussed in relation to their function in organismic association on the basis of the previous findings.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.2
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• pp.273-286
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• 2011

Using the fixed point method, we prove the Hyers-Ulam stability of the following quadratic functional equations $${cf\left({\displaystyle\sum_{i=1}^n\;xi}\right)+{\displaystyle\sum_{i=2}^nf}{\left(\displaystyle\sum_{i=1}^n\;x_i-(n+c-1)x_j\right)}\\ {=(n+c-1)\;\left(f(x_1)+c{\displaystyle\sum_{i=2}^n\;f(x_i)}+{\displaystyle\sum_{i in fuzzy Banach spaces.

• Kyungpook Mathematical Journal
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• v.59 no.1
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• pp.1-11
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• 2019

Let R be a prime ring with involution of the second kind and centre Z(R). Suppose R admits a generalized derivation $F:R{\rightarrow}R$ associated with a derivation $d:R{\rightarrow}R$. The purpose of this paper is to study the commutativity of a prime ring R satisfying any one of the following identities: (i) $F(x){\circ}x^*{\in}Z(R)$ (ii) $F([x,x^*]){\pm}x{\circ}x^*{\in}Z(R)$ (iii) $F(x{\circ}x^*){\pm}[x,x^*]{\in}Z(R)$ (iv) $F(x){\circ}d(x^*){\pm}x{\circ}x^*{\in}Z(R)$ (v) $[F(x),d(x^*)]{\pm}x{\circ}x^*{\in}Z(R)$ (vi) $F(x){\pm}x{\circ}x^*{\in}Z(R)$ (vii) $F(x){\pm}[x,x^*]{\in}Z(R)$ (viii) $[F(x),x^*]{\mp}F(x){\circ}x^*{\in}Z(R)$ (ix) $F(x{\circ}x^*){\in}Z(R)$ for all $x{\in}R$.

• Bulletin of the Korean Mathematical Society
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• v.52 no.5
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• pp.1489-1493
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• 2015

For a subset $E{\subseteq}\mathbb{R}^d$ and $x{\in}\mathbb{R}^d$, the local Hausdorff dimension function of E at x and the local packing dimension function of E at x are defined by $$dim_{H,loc}(x,E)=\lim_{r{\searrow}0}dim_H(E{\cap}B(x,r))$$, $$dim_{P,loc}(x,E)=\lim_{r{\searrow}0}dim_P(E{\cap}B(x,r))$$, where $dim_H$ and $dim_P$ denote the Hausdorff dimension and the packing dimension, respectively. In this note we give a short and simple proof showing that for any pair of continuous functions $f,g:\mathbb{R}^d{\rightarrow}[0,d]$ with $f{\leq}g$, it is possible to choose a set E that simultaneously has f as its local Hausdorff dimension function and g as its local packing dimension function.