• Bulletin of the Korean Mathematical Society
• /
• v.56 no.4
• /
• pp.885-898
• /
• 2019

This paper gives a counterexample to show that the first order commutator $C_2$ is not bounded from $H^1({\mathbb{R}}){\times}H^1({\mathbb{R}})$ into $L^{1/2}({\mathbb{R}})$. Then we introduce the atomic definition of abstract weighted Hardy spaces $H^1_{ato,{\omega}}$$({\mathbb{R}})$ and study its properties. At last, we prove that $C_2$ maps $H^1_{ato,{\omega}}$$({\mathbb{R}}){\times}H^1_{ato,{\omega}}$$({\mathbb{R}})$ into $L^{1/2}_{\omega}$$({\mathbb{R}})$.

• Bulletin of the Korean Mathematical Society
• /
• v.56 no.2
• /
• pp.471-477
• /
• 2019

Let (R, m) be a commutative Noetherian ring, I an ideal of R and M a non-zero finitely generated R-module. We show that if M and $H_0(I,M)$ are aCM R-modules and $I=(x_1,{\cdots},x_{n+1})$ such that $x_1,{\cdots},x_n$ is an M-regular sequence, then $H_i(I,M)$ is an aCM R-module for all i. Moreover, we prove that if R and $H_i(I,R)$ are aCM for all i, then R/(0 : I) is aCM. In addition, we prove that if R is aCM and $x_1,{\cdots},x_n$ is an aCM d-sequence, then depth $H_i(x_1,{\cdots},x_n;R){\geq}i-1$ for all i.

• 제어로봇시스템학회:학술대회논문집
• /
• 1994.10a
• /
• pp.364-368
• /
• 1994

Algebraic matrix Riccati equations of the form, FP+PF$^{T}$ -PRP+Q=0. are analyzed with reference to the stability of closed-loop system F-PR. Here F, R and Q are n * n real matrices with R=R$^{T}$ and Q=Q$^{T}$ .geq.0 (nonnegative-definite). Such equations have been playing key roles in optimal control and filtering problems with R .geq. 0. and also in the solutions of in H$_{\infty}$ control problems with R taking the form R=H$_{1}$$^{T}$ H$_{1}$-H$_{2}$$^{T}$ H$_{2}$. In both cases an existence of stabilizing solution, i.e. the solution yielding asymptotically stable closed-loop system, is an important problem. First, we briefly review the typical results when R is of definite form, namely either R .geq. 0 as in LQG problems or R .leq. 0. They constitute two extrence cases of Riccati to the cases H$_{2}$=0 and H$_{1}$=0. Necessary and sufficient conditions are shown for the existence of nonnegative-definite or positive-definite stabilizing solution. Secondly, we focus our attention on more general case where R is only assumed to be symmetric, which obviously includes the case for H$_{\infty}$ control problems. Here, necessary conditions are established for the existence of nonnegative-definite or positive-definite stabilizing solutions. The results are established by employing consistently the so-called algebraic method based on an eigenvalue problem of a Hamiltonian matrix.x.ix.x.

• Journal of Information Display
• /
• v.11 no.1
• /
• pp.24-27
• /
• 2010

A novel stereo 3D LCD for passive interference filter glasses is presented. A demonstrator based on a standard 120Hz LCD was set up. Stereoscopic image separation was realized in a time-sequential mode using a LED-based scanning backlight with two complementary spectra. A stereo brightness of 3 cd/$m^2$ and a channel separation of 30:1 were achieved.

• Journal of Environmental Science International
• /
• v.5 no.1
• /
• pp.93-102
• /
• 1996

Hydrodynamic characteristics such as gas holdup, liquid circulation velocity and bed expansion in a hexagonal inverse fluidized bed were investigated using air-water system by changing the ratio ($A_d$/$A_r$) of cross-sectional area between the riser and the downcomer, the liquid level($H_1$/H), and the superficial gas velocity($U_g$). The gas holdup and the liquid circulation velocity were steadily increased with the superficial gas velocity increasing, but at high superficial gas velocity, some of gas bubbles were carried over to a downcomer and circulated through the column. When the superficial gas velocity was high, the $A_d$/$A_r$ ratio in the range of 1 to 2.4 did not affect the liquid circulation velocity, but the maximum bed expansion was obtained at $A_d$/$A_r$ ratio of 1.25. The liquid circulation velocity was expressed as a model equation below with variables of the cross-sectional area ratio($A_d$/$A_r$) between riser to downcomer, the liquid level($H_1$/H), the superficial gas velocity($U_g$), the sparser height[(H-$H_s$)/H], and the draft Plate level($H_b$/H). $U_{ld}$ = 11.62U_g^{0.75}$${(\frac{H_1}{H})}^{10.30}$${(\frac{A_d}{A_r})}^{-0.52}$${(\frac({H-H_s}{H})}^{0.91}$${(\frac{H_b}{H})}^{0.13}$

• Journal of the Institute of Electronics Engineers of Korea TC
• /
• v.45 no.6
• /
• pp.27-33
• /
• 2008

Given a polynomial ${\hbar}(x){\in}F_q[x]$ of degree h, it is an important problem to determine the size of multiplicative subgroup of $\(F_q[x]/({\hbar(x))\)*$ generated by $x-s_1,\;x-s_2,\;{\cdots},\;x-s_n$, where $\{s_1,\;s_2,\;{\cdots},\;s_n\}{\sebseteq}F_q$, and for all ${\hbar}(x){\neq}0$. So far the best known asymptotic lower bound is $(rh)^{O(1)}\(2er+O(\frac{1}{r})\)^h$, where $r=\frac{n}{h}$ and e(=2.718...) is the base of natural logarithm. In this paper, we exploit the coding theory connection of this problem and prove a better lower bound $(rh)^{O(1)}\(2er+{\frac{e}{2}}{\log}r-{\frac{e}{2}}{\log}{\frac{e}{2}}+O{(\frac{{\log}^2r}{r})}\)^h$, where log stands for natural logarithm We also discuss about the limitation of this approach.

• The Journal of the Petrological Society of Korea
• /
• v.27 no.1
• /
• pp.1-15
• /
• 2018

The characteristics of the rock cleavage of Jurassic Geochang granite were analysed using the distribution of microcrack lengths and spacings. The length and spacing-cumulative diagrams for the six directions of rock cleavages were arranged in increasing order ($H2{\rightarrow}R1$) on the density (${\rho}$) of microcrack length. The various parameters were extracted through the combination of above two types of diagrams. The evaluation for the six directions of rock cleavages was performed using the four groups (I~IV) of parameters such as (I) intersection angle (${\alpha}-{\beta}$), exponent difference (${\lambda}_S-{\lambda}_L$), length of line (ol and ll'), length ratio (ol/os and ll'/sl'), mean length ((ss'+ll')/2), area of right-angled triangle (${\Delta}oaa_a^{\prime}$ and ${\Delta}obb_a^{\prime}$) and area difference (${\Delta}obb^{\prime}-{\Delta}oaa^{\prime}$ and ${\Delta}obb_a^{\prime}-{\Delta}oaa_a^{\prime}$), (II) length of line (oa and os) and area (${\Delta}oaa^{\prime}$), (III) length of line (sl') and length ratio (ss'/ll') and (IV) length of line (ob, ss' and ls') and area (${\Delta}obb^{\prime}$, ${\Delta}ll^{\prime}s^{\prime}$, ${\Delta}ss^{\prime}l^{\prime}$ and ⏢ll'ss'). The results of correlation analysis between the values of parameters for three rock cleavages and those for three planes are as follows. The values of parameters for three rock cleavages are in orders of (I) H(hardway, (H1 + H2)/2) < G(grain, (G1 + G2)/2) < R(rift, (R1 + R2)/2), (II) R < G < H, (III) G < H < R and (IV) H < G < R. On the contrary, the values of parameters for three planes are in orders of (I) R' < G' < H', (II) H' < G' < R' and (III and IV) R' < H' < G'. Especially the values of parameters belonging to group I and group II show mutual reverse orders. In conclusion, this type of correlation analysis is useful for discriminating three quarrying planes.

• Bulletin of the Korean Chemical Society
• /
• v.20 no.1
• /
• pp.65-68
• /
• 1999

Novel mononuclear group 13 metal complexes with the formula (R2M){NC5H4C(CH3)NNC(S)NH(C6H5)} (M=Al, R=iC4H9 (1); M=Ga, R=iC4H9 (2); M=Al, R=CH2SiMe3 (3); M=Ga, R=CH2SiMe3 (4)) result when 2-acetyl pyridine 4-phenyl-thiosemicarbazone ligand is mixed with trialkyl aluminum or trialkylgallium. These compounds 1-4 are characterized by microanalysis, NMR (1H, 13C) spectroscopy, mass spectra, and singlecrystal X-ray diffraction. X-ray single-crystal diffraction analysis reveals that 1 is mononuclear metal compound with coordination number of 5 and N, N, S-coordination mode.

• Communications of the Korean Mathematical Society
• /
• v.27 no.1
• /
• pp.69-76
• /
• 2012

Let R be a ring, and ${\alpha}$ be an endomorphism of R. An additive mapping H : R ${\rightarrow}$ R is called a left ${\alpha}$-multiplier (centralizer) if H(xy) = H(x)${\alpha}$(y) holds for all x,y $\in$ R. In this paper, we shall investigate the commutativity of prime and semiprime rings admitting left ${\alpha}$-multiplier satisfying any one of the properties: (i) H([x,y])-[x,y] = 0, (ii) H([x,y])+[x,y] = 0, (iii) $H(x{\circ}y)-x{\circ}y=0$, (iv) $H(x{\circ}y)+x{\circ}y=0$, (v) H(xy) = xy, (vi) H(xy) = yx, (vii) $H(x^2)=x^2$, (viii) $H(x^2)=-x^2$ for all x, y in some appropriate subset of R.

• The Korean Journal of Physiology and Pharmacology
• /
• v.23 no.1
• /
• pp.37-45
• /
• 2019

To study the effect of nicorandil pretreatment on ketone body metabolism and Acetyl-CoA acetyltransferase (ACAT1) activity in hypoxia/reoxygenation (H/R)-induced cardiomyocytes. In our study, we applied H9c2 cardiomyocytes cell line to evaluate the cardioprotective effects of nicorandil. We detected mitochondrial viability, cellular apoptosis, reactive oxygen species (ROS) production and calcium overloading in H9c2 cells that exposed to H/R-induced cytotoxicity. Then we evaluated whether nicorandil possibly regulated ketone body, mainly ${\beta}$-hydroxybutyrate (BHB) and acetoacetate (ACAC), metabolism by regulating ACAT1 and Succinyl-CoA:3-ketoacid coenzyme A transferase 1 (OXCT1) protein and gene expressions. Nicorandil protected H9c2 cardiomyocytes against H/R-induced cytotoxicity dose-dependently by mitochondria-mediated anti-apoptosis pathway. Nicorandil significantly decreased cellular apoptotic rate and enhanced the ratio of Bcl-2/Bax expressions. Further, nicorandil decreased the production of ROS and alleviated calcium overloading in H/R-induced H9c2 cells. In crucial, nicorandil upregulated ACAT1 and OXCT1 protein expressions and either of their gene expressions, contributing to increased production of cellular BHB and ACAC. Nicorandil alleviated cardiomyocytes H/R-induced cytotoxicity through upregulating ACAT1/OXCT1 activity and ketone body metabolism, which might be a potential mechanism for emerging study of nicorandil and other $K_{ATP}$ channel openers.