• Nonlinear Functional Analysis and Applications
• /
• v.26 no.2
• /
• pp.331-345
• /
• 2021

Let p(z)be a polynomial of degree n. Then Bernstein's inequality [12,18] is $${\max\limits_{{\mid}z{\mid}=1}}\;{\mid}p^{\prime}(z){\mid}\;{\leq}\;n\;{\max_{{\mid}z{\mid}=1}{\mid}(z){\mid}}$$. For q > 0, we denote $${\parallel}p{\parallel}_q=\{{\frac{1}{2{\pi}}}{\normalsize\displaystyle\smashmargin{2}{\int\nolimits_{0}}^{2{\pi}}}\;{\mid}p(e^{i{\theta}}){\mid}^qd{\theta}\}^{\frac{1}{q}}$$, and a well-known fact from analysis [17] gives $${{\lim_{q{\rightarrow}{{\infty}}}}\{{\frac{1}{2{\pi}}}{\normalsize\displaystyle\smashmargin{2}{\int\nolimits_{0}}^{2{\pi}}}\;{\mid}p(e^{i{\theta}}){\mid}^qd{\theta}\}^{\frac{1}{q}}={\max\limits_{{\mid}z{\mid}=1}}\;{\mid}p(z){\mid}$$. Above Bernstein's inequality was extended by Zygmund [19] into L^q norm by proving ║p'║_q ≤ n║p║_q, q ≥ 1. Let p(z) = a₀ + ∑ⁿ_𝜈=𝜇 a_𝜈z^𝜈, 1 ≤ 𝜇 ≤ n, be a polynomial of degree n having no zero in |z| < k, k ≥ 1. Then for 0 < r ≤ R ≤ k, Aziz and Zargar [4] proved $${\max\limits_{{\mid}z{\mid}=R}}\;{\mid}p^{\prime}(z){\mid}\;{\leq}\;{\frac{nR^{{\mu}-1}(R^{\mu}+k^{\mu})^{{\frac{n}{\mu}}-1}}{(r^{\mu}+k^{\mu})^{\frac{n}{\mu}}}\;{\max\limits_{{\mid}z{\mid}=r}}\;{\mid}p(z){\mid}}$$. In this paper, we obtain the L^q version of the above inequality for q > 0. Further, we extend a result of Aziz and Shah [3] into L^q analogue for q > 0. Our results not only extend some known polynomial inequalities, but also reduce to some interesting results as particular cases.

• Journal of the Korean Institute of Electrical and Electronic Material Engineers
• /
• v.31 no.5
• /
• pp.324-329
• /
• 2018

Red phosphor in glasses (PiGs) for automotive light-emitting diode (LED) applications were fabricated with 620-nm $CaAlSiN_3:Eu^{2+}$ phosphor and Pb-free silicate glass. PiGs were synthesized and mounted on high-power blue LED to make a monochromatic red LED. PiGs were simple mixtures of red phosphor and transparent glass powder. After being fabricated with uniaxial press and CIP at 300 MPa for 20 min, the green bodies were thermally treated at $550^{\circ}C$ for 30 min to produce high dense PiGs. As the phosphor content increased, the density of the sintered body decreased and PiGs containing 30% phosphor had a full sintered density. Changes in photoluminescence spectra and color coordination were studied by varying the thickness of plates that were mounted after optical polishing. As a result of the optical spectrum and color coordinates, PiG plate with $210{\mu}m$ thickness showed a color purity of 99.7%. In order to evaluate the thermal stability, the thermal quenching characteristics were measured at temperatures of $30{\sim}150^{\circ}C$. The results showed that the red PIG plates were 30% more thermally stable compared to the AlGaInP red chip.

• Polymer(Korea)
• /
• v.34 no.5
• /
• pp.480-484
• /
• 2010

A series of poly(amic acid)s(PAAs) was prepared by reacting 4,4'-(4,4'-isopropylidenediphenoxy) bis(phthalic anhydride)(BPADA) as the anhydride monomer and 2,2'-bis(trifluoromethyl) benzidine (TFB), bis(3-aminophenyl)sulfone (APS), 4,4'-methylenebis-(2-methylcyclohexylamine) (MMCA), or bis[4-(3-aminophenoxy) phenyl] sulfone (BAPS) as the amine monomer with 5 mol% melamine in N,N-dimethylacetamide (DMAc). Colorless and transparent polyimide (PI) films were obtained by casting the PAAs at various heat treatment temperatures. The thermo-mechanical properties and optical transparency of the PI films were investigated. The thermal properties of the PI films were examined using differential scanning calorimetry (DSC), thermogravimetric analysis (TGA), and thermomechanical analysis (TMA), and their optical transparency were measured by spectrophotometry. The coefficient of thermal expansion (CTE) and yellow index (YI) values of all samples were in the range of $48.53-64.24ppm/^{\circ}C$ and < 3.0, respectively.

• Molecules and Cells
• /
• v.24 no.2
• /
• pp.294-300
• /
• 2007

The mammalian glycosylphosphatidylinositol (GPI) anchor consists of three mannoses attached to acylated GlcN-(acyl)PI to form $Man_3$-GlcN-(acyl)PI. The first of the three mannose groups is attached to an intermediate to generate Man-GlcN-(acyl)PI by the first mannosyltransferase (GPI-MT-I). Mammalian and protozoan GPI-MT-I have different substrate specificities. PIG-M encodes the mammalial GPI-MT-I which has 423 amino acids and multiple transmembrane domains. In this work we cloned PIG-M homologues from humans, Plasmodium falciparum (PfPIG-M), and Saccharomyces cerevisiae (GPI14), to test whether they could complement GPI-MT-I-deficient mammalian cells, since this biosynthetic step is likely to be a good target for selective screening of inhibitors against many pathogenic organisms. PfPIG-M partially restored cell surface expression of the GPI-anchored protein CD59 in PIG-M deficient mammalian cells, and first mannose transfer activity in vitro; however, this was not the case for GPI14.

• Journal of Korean Vacuum Science & Technology
• /
• v.4 no.1
• /
• pp.1-5
• /
• 2000

The C 1s photoelectron energy loss spectra of tris (8-hydroxy-quinoline) aluminum (Alq$_3$) and N,N'-diphenyl-N,N'-bis (3-methyl phenyl)-1,1'-bi-phenyl-4,4'-diamine (TPD) thin films have been investigated. Two major loss structures, namely the plasmon dominated loss lines and shake-up satellites, have been observed. The shake-up spectrum of the C 1s photoelectron line is directly related to the $\pi$-$\pi$$\^$*/ energy gap of the molecule which plays an important role in organic electroluminescent materials. The molecular orbitals of Alq$_3$ and TPD and their major components, quinolime and benzene, have been calculated with the AMI semi-empirical method. The amount of the plasma-dominated loss of Alq$_3$ and TPD, which has to do with the delocalization of electrons through the molecule, was about 24 eV, alike in both cases. The main peak of the C 1s shake-up spectrum of Alq$_3$ and TPD, however, was 5.2 eV and 6.8 eV respectively. It was found that the main shake-up peak reflects more the local $\pi$\longrightarrow$\pi$$\^$*/ transition of quinoline and benzene component rather than the excitation of the whole molecule of Alq$_3$ and TPD. The C 1s shake-up spectra, however, revealed some correlation with the optical energy gap of the organic eletroluminescent materials.

• Analytical Science and Technology
• /
• v.8 no.1
• /
• pp.47-53
• /
• 1995

The aggregation of Pyronin G($PG^+$) with tetraphenylborate($TPB^-$) anion has been investigated in aqueous solution by absorption and fluorescence spectrophotometries. The addition of 1,4-dioxane in aqueous solution of $PG^+$ and $TPB^-$ dissociates the aggregates of PG-TPB due to the increased hydrophobicity of the mixed solvent as compared to pure water, and yields higher $PG^+$ momomer concentration than aqueous $PG^+$ solution. The aggregation is not observed in any organic solvents except in water. The absorption maxima of $PG^+$ are correlated relatively well with ${\pi}^*$ scale and $(n^2-1)/(2n^2+1)$ funtion. But better linear relationship was obtained with ${\pi}^*$ scale for alcohols.

• Bulletin of the Korean Chemical Society
• /
• v.21 no.9
• /
• pp.891-895
• /
• 2000

Transmission of substituent effects through 5-membered heteroaromaticrings isinvestigated theoretically at the RHF/6-31+G* and B3LYP/6-31+G* levelsusing the deprotonation equilibria of phenol analogues with heteroatoms Y = NH, O, PHand S. The incr ease in the resonance delocalization of the $\pilone-pair$ on the phe-nolic oxygen atom, $n\pi(O)$, accompanied with the deprotonation depends on the heteroatom Y,in the order NH < O < PH < S. This represents the $\pielectron$ accepting ability, or conversely reverse order of the $\pielectron$ donating ability of the $\pilone-pair$ on Y, $n\pi(Y).$ The transmission efficiency of substituenteffects is, however,in the reverse order NH > O > S, which represents the order of delocalizability of $n\pi(Y).$ A better correlation is obtained with ${\sigma}p$ - than with ${\sigma}p$ for the Hammett type plots with the positive slope, $\rho-$ > 0, of the magnitude in the same order as that for the delocalizability of $n\pi(Y).$ Thedeprotonation energy, ΔG = [G(PA) + G(H+)] -G(P), decreases with the increasein the extence delocalization in the order NH > O > PH > S.

• Honam Mathematical Journal
• /
• v.1 no.1
• /
• pp.1-9
• /
• 1979

Positive Local Coordmate($(x^1,x^2,{\cdots}x^n)$)을 갖는 Oriented Manifold M을 생각한다. M이 Compact Carrier를 갖는 경우, M위의 n차(次) Differential Form ${\phi}^{(n)}$의 적분(積分)을 $${\int}{\phi}^{(n)}=\sum_{\alpha}{\int}_{-{\infty}}^{\infty}{\cdots}{\int}_{-{\infty}}^{\infty}f_{\alpha}{\phi}^{(n)}dx^1{\cdots}dx^n$$로 정의(定義)하며 (정의(定義) 7), M위의 p 차(次)의 Differential form $\beta^{(p)}$와 Differential simplex $S^{(p)}=(S^{(p)},\;{\pi},\;{\varepsilon})$에 대하여 $S^{(p)}$위의 $\beta^{(p)}$의 적분(積分)을 $${\int}_{^{(p)}S}{\beta}^{(p)}={\int}_{S^{(p)}}{\varepsilon}{\pi}^*{\beta}^{(p)}={\int}_{E^p}f{\cdot}{\varepsilon}{\cdot}{\pi}^*{\beta}^{(p)}$$로 정의(定義)한다 (정의(定義) 9). 단(但) $\bar{S}^{(p)}$는 $S^{(p)}=(p_0{\cdot}p_1{\cdots}p_p)$에 의(依)하여 Spanning 되는 $E^p$의 Subspace이고 f는 $\bar{S}^{(p)}$의 특성함수(特性函數)이다. 이때 (n-1)차(次)의 Differential Form ${\beta}^{(n-1)}$이 Compart인 Carrier를 가지면 ${\int}d{\beta}^{(n-1)}=0$이 됨을 고찰(考察)하며(정리(定理 8), (p-1)차(次) Differential Form ${\beta}^{(p-1)$과 p차(次) Differential Chain $C^{(p)}$에 관(關)하여 $${\int}_{C^{(p)}}d{\beta}^{(p-1)}={\int}_{{\partial}C^{(p)}}{\beta}^{(p-1)}$$이 성립(成立)함을 구명(究明)하려 한다(정리(定理) 10).

• Sleep Medicine and Psychophysiology
• /
• v.19 no.2
• /
• pp.68-76
• /
• 2012

Objectives: Sleep disorders cause changes of autonomic nervous system (ANS) which affect cardiovascular system. Primary insomnia (PI) makes acceleration of sympathetic nervous system (SNS) tone by sleep deficiency and arousal. Obstructive sleep apnea syndrome (OSAS) sets off SNS by frequent arousals and hypoxemias during sleep. We aimed to compare the changes of heart rate variability (HRV) indices induced by insomnia or sleep apnea to analyze for ANS how much to be affected by PI or OSAS. Methods: Total 315 subjects carried out nocturnal polysomnography (NPSG) were categorized into 4 groups - PI, mild, moderate and severe OSAS. Severity of OSAS was determined by apnea-hypopnea index (AHI). Then we selected 110 subjects considering age, sex and valance of each group's size [Group 1 : PI (mean age=$41.50{\pm}13.16$ yrs, AHI <5, n=20), Group 2 : mild OSAS (mean age=$43.67{\pm}12.11$ yrs, AHI 5-15, n=30), Group 3 : moderate OSAS (mean age $44.93{\pm}12.38$ yrs, AHI 16-30, n=30), Group 4 : severe OSAS (mean age=$45.87{\pm}12.44$ yrs, AHI >30, n=30)]. Comparison of HRV indices among the four groups was performed with ANCOVA (adjusted for age and body mass index) and Sidak post-hoc test. Results: We found statistically significant differences in HRV indices between severe OSAS group and the other groups (PI, mild OSAS and moderate OSAS). And there were no significant differences in HRV indices among PI, mild and moderate OSAS group. In HRV indices of PI and severe OSAS group showing the most prominent difference in the group comparisons, average RR interval were $991.1{\pm}27.1$ and $875.8{\pm}22.0$ ms (p=0.016), standard deviation of NN interval (SDNN) was $85.4{\pm}6.6$ and $112.8{\pm}5.4$ ms (p=0.022), SDNN index was $57.5{\pm}5.2$ and $87.6{\pm}4.2$ (p<0.001), total power was $11,893.5{\pm}1,359.9$ and $18,097.0{\pm}1,107.2ms^2$(p=0.008), very low frequency (VLF) was $7,534.8{\pm}1,120.1$ and $11,883.8{\pm}912.0ms^2$ (p=0.035), low frequency (LF) was $2,724.2{\pm}327.8$ and $4,351.6{\pm}266.9ms^2$(p=0.003). Conclusions: VLF and LF which were correlated with SNS tone showed more increased differences between severe OSAS group and PI group than other group comparisons. We could suggest that severe OSAS group was more influential to increased SNS activity than PI group.

• Communications of the Korean Mathematical Society
• /
• v.12 no.1
• /
• pp.157-163
• /
• 1997

Based on a n-regular polygon $P_n$, we show that $r_n = 1/(2 \sum^{[(n-4)/4]+1}_{j=0}{cos 2j\pi/n)}$ is the ratio of contractions $f_i(1 \leq i \leq n)$ at each vertex of $P_n$ yielding a symmetric gasket $G_n$ associated with the just-touching I.F.S. $g_n = {f_i $\mid$ 1 \leq i \leq n}$. Moreover we see that for any odd n, the ratio $r_n$ is still valid for just-touching I.F.S $H_n = {f_i \circ R $\mid$ 1 \leq i \leq n}$ yielding another symmetric gasket $H_n$ where R is the $\pi/n$-rotation with respect to the center of $P_n$.