• Bulletin of the Korean Mathematical Society
• /
• v.53 no.2
• /
• pp.411-421
• /
• 2016

In this paper, we investigate the problem of transcendental entire functions that share two values with one of their derivative. Let f be a transcendental entire function, n and k be two positive integers. If $f^n-Q_1$ and $(f^n)^{(k)}-Q_2$ share 0 CM, and $n{\geq}k+1$, then $(f^n)^{(k)}{\equiv}{\frac{Q_2}{Q_1}}f^n$. Furthermore, if $Q_1=Q_2$, then $f=ce^{\frac{\lambda}{n}z}$, where $Q_1$, $Q_2$ are polynomials with $Q_1Q_2{\not\equiv}0$, and c, ${\lambda}$ are non-zero constants such that ${\lambda}^k=1$. This result shows that the Conjecture given by W. $L{\ddot{u}}$, Q. Li and C. Yang [On the transcendental entire solutions of a class of differential equations, Bull. Korean Math. Soc. 51 (2014), no. 5, 1281-1289.] is true. Also we exhibit some examples to show that the conditions of our result are the best possible.

• Journal of the Chungcheong Mathematical Society
• /
• v.21 no.4
• /
• pp.455-466
• /
• 2008

In, [7], Th.M. Rassias proved that the norm defined over a real vector space V is induced by an inner product if and only if for a fixed integer $n{\geq}2$ $$n{\left\|{\frac{1}{n}}{\sum\limits_{i=1}^{n}}x_i{\left\|^2+{\sum\limits_{i=1}^{n}}\right\|}{x_i-{\frac{1}{n}}{\sum\limits_{j=1}^{n}x_j}}\right\|^2}={\sum\limits_{i=1}^{n}}{\parallel}x_i{\parallel}^2$$ holds for all $x_1,{\cdots},x_{n}{\in}V$. Let V,W be real vector spaces. It is shown that if a mapping $f:V{\rightarrow}W$ satisfies $$(0.1){\hspace{10}}nf{\left({\frac{1}{n}}{\sum\limits_{i=1}^{n}}x_i \right)}+{\sum\limits_{i=1}^{n}}f{\left({x_i-{\frac{1}{n}}{\sum\limits_{j=1}^{n}}x_i}\right)}\\{\hspace{140}}={\sum\limits_{i=1}^{n}}f(x_i)$$ for all $x_1$, ${\dots}$, $x_{n}{\in}V$ $$(0.2){\hspace{10}}2f\(\frac{x+y}{2}\)+f\(\frac{x-y}{2} \)+f\(\frac{y}{2}-x\)\\{\hspace{185}}=f(x)+f(y)$$ for all $x,y{\in}V$. Furthermore, we prove the generalized Hyers-Ulam stability of the functional equation (0.2) in real Banach spaces.

• Bulletin of the Korean Mathematical Society
• /
• v.22 no.2
• /
• pp.121-126
• /
• 1985

D.K. Harrison [5] has shown that if R and S are fields of characteristic different from 2, then two Witt rings W(R) and W(S) are isomorphic if and only if W(R)/I(R)$^{3}$ and W(S)/I(S)$^{3}$ are isomorphic where I(R) and I(S) denote the fundamental ideals of W(R) and W(S) respectively. In [1], J.K. Arason and A. Pfister proved a corresponding result when the characteristics of R and S are 2, and, in [9], K.I. Mandelberg proved the result when R and S are commutative semi-local rings having 2 a unit. In this paper, we prove the result when R and S are 2-fold full rings. Throughout this paper, unless otherwise specified, we assume that R is a commutative ring having 2 a unit. A quadratic space (V, B, .phi.) over R is a finitely generated projective R-module V with a symmetric bilinear mapping B: V*V.rarw.R which is nondegenerate (i.e., the natural mapping V.rarw.Ho $m_{R}$ (V, R) induced by B is an isomorphism), and with a quadratic mapping .phi.:V.rarw.R such that B(x,y)=(.phi.(x+y)-.phi.(x)-.phi.(y))/2 and .phi.(rx)= $r^{2}$.phi.(x) for all x, y in V and r in R. We denote the group of multiplicative units of R by U(R). If (V, B, .phi.) is a free rank n quadratic space over R with an orthogonal basis { $x_{1}$, .., $x_{n}$}, we will write < $a_{1}$,.., $a_{n}$> for (V, B, .phi.) where the $a_{i}$=.phi.( $x_{i}$) are in U(R), and denote the space by the table [ $a_{ij}$ ] where $a_{ij}$ =B( $x_{i}$, $x_{j}$). In the case n=2 and B( $x_{1}$, $x_{2}$)=1/2, we reserve the notation [ $a_{11}$, $a_{22}$] for the space.the space.e.e.e.

• The Journal of the Korea institute of electronic communication sciences
• /
• v.12 no.4
• /
• pp.621-628
• /
• 2017

The efficiency of implementation of the arithmetic operations in finite fields depends on the choice representation of elements of the field. It seems that from this point of view normal bases are the most appropriate, since raising to the power 2 in $GF(2^n)$ of characteristic 2 is reduced in these bases to a cyclic shift of the coordinates. We, in this paper, introduce our algorithm to transform fastly the conventional bases to normal bases and present the result of H/W implementation using the algorithm. We also propose our algorithm to calculate the multiplication and inverse of elements with respect to normal bases in $GF(2^n)$ and present the programs and the results of H/W implementations using the algorithm.

• Journal of the Korean Chemical Society
• /
• v.36 no.6
• /
• pp.906-913
• /
• 1992

The polymeric compound [{$W(NO)_2Cl_2$}$_n$] were prepared by reductive nitrosylation of $WNaNO_2$ and acidified $WFeSO_4$ with $WWCl_6$ at room temperature. The reactions of [{$W(NO)_2Cl_2$}$_n$] with unidentate and bidentate ligands afforded neutral monomeric [$W(NO)_2Cl_2L_2$(or L-L)] in a relative high yields (70$\sim$90%). 3,5-lutidine, ${\gamma}$-cyanopyridine, 1,2-phenylenediamine, 1,10-phenanthroline, sym-diphenylethylenediamine, 9,10-phenanthrenequinone, 1,3-bis(diphenylphosphino)propane, 1,1'-bis(diphenylphosphino)ferrocene and 8-hydroxyquinoline were used as coordinating ligands. These dinitrosyltungsten complexes were characterized by elemental analysis, $^1H$-NMR, infrared, and UV-visible spectroscopy are reported. The spectral data indicated that geometric structures of the products were cis-dinitrosyl-trans-dichloro-cis-$L_2$ of $C_{2v}$ symmetry.

• Journal of the Korean Institute of Electrical and Electronic Material Engineers
• /
• v.13 no.3
• /
• pp.214-219
• /
• 2000

In this paper the structural dielectric and piezoelectric properties of Pb［(M $g_{1}$2// $W_{1}$2/)$_{x}$-(N $i_{1}$3//N $b_{2}$3/)$_{0.15-x-(Zr_{0.5})}$ $Ti_{0.5}$)$_{0.85}$］ $O_3$ (x=0.0~0.10) ceramic were investigated with the substitution of Pb(M $g_{1}$2// $W_{1}$2/) $O_3$. According to the substitution of Pb(M $g_{1}$2//W/1/2/) $O_3$ curie temperatures were slightly decrease due to the decrease of the tetrag-onality of crystal structure and coercive fields were decreased. Up to the substitution of Pb(M $g_{1}$2// $W_{1}$2/) $O_3$ 3mol%,remnant polarization dielectric constant piezoelectric constant were increased. Dielectric constant and electro-mechanical coupling factor( $k_{p}$, $k_{31}$ ) were appeared the highest value of 2230, 0.64, and 0.38 and piezoelectric constant( $d_{33}$ , $d_{31}$ ) was the largest value of 418, 202($\times$10$^{-12}$ /C/N), respectively, when the substitution amount of Pb(M $g_{1}$2// $W_{1}$2/N) respectively, when the substitution amount of Pb(M $g_{1}$2// $W_{1}$2/) $O_3$ was 3mol%.s 3mol%.%.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
• /
• 2010.06a
• /
• pp.370-370
• /
• 2010

The effects of adding higher-valence impurities on the bipolar resistive switching characteristics of Pt/$NiO_{1+x}$/TiN MIM stacks and physical properties were investigated. $NiO_{1+x}$ films with 14% W deposited at 20% oxygen partial pressure exhibited the bipolar resistance switching characteristics in Pt/$NiO_{1+x}$/TiN MIM stacks, while $NiO_{1+x}$ films with 8.2% W show unipolar resistance switching behavior. The relationship of W-doping and the crystallinity was studied by X-ray diffraction. The metallic Ni contents and $WO_x$ binding states with W amount was investigated by XPS. Our result showed that the metallic Ni, $WO_x$ binding states, and crystallinity in $NiO_{1+x}$ played an important role on the bipolar resistive switching.

• Bulletin of the Korean Mathematical Society
• /
• v.53 no.5
• /
• pp.1585-1596
• /
• 2016

In this paper we investigate the existence of nontrivial solutions for the following fractional boundary value problem (FBVP) $$\{_tD_T^{\alpha}(_0D_t^{\alpha}u(t))={\nabla}W(t,u(t)),\;t{\in}[0,T],\\u(0)=u(T)=0,$$ where ${\alpha}{\in}(1/2,1)$, $u{\in}{\mathbb{R}}^n$, $W{\in}C^1([0,T]{\times}{\mathbb{R}}^n,{\mathbb{R}})$ and ${\nabla}W(t,u)$ is the gradient of W(t, u) at u. The novelty of this paper is that, when the nonlinearity W(t, u) involves a combination of superquadratic and subquadratic terms, under some suitable assumptions we show that (FBVP) possesses at least two nontrivial solutions. Recent results in the literature are generalized and significantly improved.

• Journal of the Korean Institute of Electrical and Electronic Material Engineers
• /
• v.16 no.1
• /
• pp.1-4
• /
• 2003

The SiH$_4$soak step is widely used to prevent the WF$_{6}$ attack to the underlayer metal using the chemical vapor deposition (CVD) method. Reduction or skipping of the SiH$_4$soak process time if lead to optimizing W-plug deposition process on via. The electrical characteristics including via resistance and the structure of W-film are affected by the time of SiH$_4$soak process. The possibility of elimination of SiH$_4$soak process is confirmed In the case of W- film grown on the stable Ti/TiN underlayer.

• Journal of the Korean institute of surface engineering
• /
• v.32 no.3
• /
• pp.416-422
• /
• 1999

The characteristics of inductively coupled Cl$_2$/BCl$_3$ plasmas during the GaN etching were studied using plasma mass spectrometry by measuring the relative amounts of reactive ions, neutrals, and etch products. GaN etch rates increased with the increase of pressure and showed a maximum near 25mTorr for the pure $Cl_2$ and near 30mTorr for $Cl_2$$BCl_3$. The addition of$ BCl_3$ to $Cl_2$ also was increased GaN etch rates until 50%BCl$_3$ was mixed to $Cl_2$. The GaN etching with pure $Cl Cl_2$ appears to be related to the combination of Cl$_2^{+}$ ion bombardment and the chemical reaction of Cl radicals. In the case of the GaN etching with Cl$_2$/BCl$_3$, in addition to the combined effect of$_2^{ +}$ ions and Cl radicals, $_BCl2^{+ }$ ions appear to be responsible for some of GaN etching even though they do not have significant effect on the GaN etching compared to $Cl_2^{+}$ and Cl. $Ga^{+ }$ , $GaCl^{+}$ , $GaCl_2^{+}$ , and $N_2^{+}$ were observed as the positive ions of etch products, and the intensities of these etch products showed the same trends as those of GaN etch rate. Among the etch products, Ga and $N_2$ appear to be the main etch products.