• Journal of the Korean Chemical Society
• /
• v.7 no.4
• /
• pp.238-244
• /
• 1963

Linear relationships between thermodynamic parameters, ,${\Delta}{\Delta}H^{\neq}=a{\sigma}+b{\Delta}{\Delta}S^{\neq}$, and $\Delta{\Delta}F^\neq=a\sigma+(b-T)\Delta{\Delta}S^\neq$, which were derived in the previous report have been tested with 57 reactions from literature. Linearities of plots $\Delta{\Delta}H^\neq-a\sigma$ vs. $\Delta{\Delta}S^\neq$ were generally good and the average correlation coefficient was 0.983 and the average of standard deviations from regression lines was 0.11. For 15 out of 57 reactions, Hammett plots were unsatisfactory and most of the reaction did not satisfy the Leffler equation. The general applicability of the new equations has been confirmed by the analysis of each reaction for which existing equations failed to correlate.

• Journal of the Korean Chemical Society
• /
• v.7 no.3
• /
• pp.211-215
• /
• 1963

Inter-relationship between the Hammett equation and the linear enthalpy-entropy effect has been discussed by deriving a new set of equations; ${\Delta}{\Delata}H^{\neq}=a{\sigma}+b{\Delta}{\Delta}S^{\neq}$ and ${\Delta}{\Delta}F^{\neq}=a{sigma}+(b-T){\Delta}{\Delta}S^{\neq}$ where a = -1.36p. Theoretical analysis show that the Hammett, Leffler and Brown equations are special limited forms of these general equations. A necessary and sufficient test of substituent effect can thus be provided by the plot of $({\Delta}{\Delta}H^{\neq}-a{\sigma)$ versus ${\Delta}{\Delta}S^{\neq}$.

• Journal of the Korean Mathematical Society
• /
• v.42 no.1
• /
• pp.111-127
• /
• 2005

Let B and S be the unit ball and the unit sphere in $\mathbb{C}^n$, respectively. Let ${\sigma}$ be the normalized Lebesgue measure on S. Define the Privalov spaces $N^P(B)\;(1\;<\;p\;<\;{\infty})$ by $$N^P(B)\;=\;\{\;f\;{\in}\;H(B) : \sup_{0 where H(B) is the space of all holomorphic functions in B. Let ${\varphi}$ be a holomorphic self-map of B. Let ${\mu}$ denote the pull-back measure ${\sigma}o({\varphi}^{\ast})^{-1}$. In this paper, we prove that the composition operator $C_{\varphi}$ is metrically bounded on $N^P$(B) if and only if ${\mu}(S(\zeta,\delta)){\le}C{\delta}^n$ for some constant C and $C_{\varphi}$ is metrically compact on $N^P(B)$ if and only if ${\mu}(S(\zeta,\delta))=o({\delta}^n)$ as ${\delta}\;{\downarrow}\;0$ uniformly in ${\zeta}\;\in\;S. Our results are an analogous results for Mac Cluer's Carleson-measure criterion for the boundedness or compactness of $C_{\varphi}$ on the Hardy spaces $H^P(B)$.

• Maxillofacial Plastic and Reconstructive Surgery
• /
• v.34 no.5
• /
• pp.311-319
• /
• 2012

Purpose: The aim of this study is to evaluate the vertical changes of the lip and perioral soft tissue, following orthognathic surgery in skeletal class III patients by a cephalometric analysis of a cone beam computed tomography (CBCT). Methods: A total of 20 skeletal class III patients, who had bimaxillary surgery with Le Fort 1 osteotomy and bilateral sagittal split ramus osteotomy, were included in this study. The surgical plan for maxilla was posterosuperior impaction with the anterior nasal spine, as the rotation center. Further, the surgical plan for mandible was also posterosuperior movement. The soft tissue changes between lateral cephalogram and CBCT were compared. And the correlations between independent variables and dependent variables were evaluated. Results: There were no significant differences of the soft tissues changes between lateral cephalogram and CBCT. Upper lip philtrum length (SnLs), nasolabial angle increased and upper lip vermilion length (LsStms), lower lip length (StmiB'), lower lip vermilion length (StmiLi), lower lip philtrum length (LiB') and soft tissue lower facial height (SnMe') decreased after surgery. Change of SnLs (${\Delta}$SnLs) was influenced by vertical change of menton (${\Delta}$MeV), and change of LsStms (${\Delta}$LsStms) was influenced by upper lip thickness (ULT). Change of StmiLi' (${\Delta}$StmiLi') were influenced by preoperative overjet. Change of StmiB' (${\Delta}$StmiB') were influenced by preoperative overjet, vertical change of lower incisor (${\Delta}$L1V) and horizontal change of posterior nasal spine (${\Delta}$PNSH). Change of LiB' (${\Delta}$LiB') was influenced by ${\Delta}$L1V and ${\Delta}$PNSH. Change of SnMe' (${\Delta}$SnMe') was influenced by ${\Delta}$MeV, horizontal change of upper incisor (${\Delta}$U1H) and horizontal change of lower incisor (${\Delta}$L1H). ${\Delta}$Nasolabial angle was influenced by change of ULT (${\Delta}$ULT). Conclusion: Both soft tissues and hard tissues can be evaluated by CBCT. Posterosuperior rotation of maxillomandibular complex resulted in increase of upper lip philtrum length and nasolabial angle, while the upper lip vermilion length, lower lip philtrum length, lower lip vermilion length, and soft tissue lower facial height showed a decrease.

• Journal of the Chungcheong Mathematical Society
• /
• v.17 no.1
• /
• pp.85-101
• /
• 2004

Let A be a Hopf algebra with a linear form ${\sigma}:k{\rightarrow}A{\otimes}A$, which is convolution invertible, such that ${\sigma}_{21}({\Delta}{\otimes}id){\tau}({\sigma}(1))={\sigma}_{32}(id{\otimes}{\Delta}){\tau}({\sigma}(1))$. We define Hopf algebras, ($A_{\sigma}$, m, u, ${\Delta}_{\sigma}$, ${\varepsilon}$, $S_{\sigma}$). If B and C are opposite skew copaired Hopf algebras and $A=B{\otimes}_kC$ then we find Hopf algebras, ($A_{[{\sigma}]}$, $m_B{\otimes}m_C$, $u_B{\otimes}u_C$, ${\Delta}_{[{\sigma}]}$, ${\varepsilon}B{\otimes}{\varepsilon}_C$, $S_{[{\sigma}]}$). Let H be a finite dimensional commutative Hopf algebra with dual basis $\{h_i\}$ and $\{h_i^*\}$, and let $A=H^{op}{\otimes}H^*$. We show that if we define ${\sigma}:k{\rightarrow}H^{op}{\otimes}H^*$ by ${\sigma}(1)={\sum}h_i{\otimes}h_i^*$ then ($A_{[{\sigma}]}$, $m_A$, $u_A$, ${\Delta}_{[{\sigma}]}$, ${\varepsilon}_A$, $S_{[{\sigma}]}$) is the dual space of Drinfeld double, $D(H)^*$, as Hopf algebra.

• Journal of the Korean Chemical Society
• /
• v.10 no.1
• /
• pp.11-14
• /
• 1966

The thermodynamic parameters for the solvolysis of the p-nitrobenzyl chloride which take place in the ethanol-water mixture media were determined. From the application of this data to the formula ${\delta}_M{\Delta}H^{\neq} = a'Y + b{\delta}_M{\Delta}S^{\leq}$ the following conclusion was obtained. The substrate constant a' for this reaction was not varied in the media which contain more than 50% alcohol and less than 50% alcohol. From this, it is clear that the mechanism of this reaction is the same both in the water-rich solvent and in the alcohol-rich solvent.

• Membrane Journal
• /
• v.11 no.4
• /
• pp.143-151
• /
• 2001

We have fabricated mixed-ionic conducting membranes, L $a_{0.6}$S $r_{0.4}$ $Co_{0.2}$F $e_{0.8}$ $O_{3-}$$\delta$/ and L $a_{0.7}$S $r_{0.3}$G $a_{0.6}$F $e_{0.4}$ $O_{3-}$$\delta$/ by the solid state method. Ceramic membranes consisted of perovskite-type structures and exhibited high relative density, >95%. Especially, dense L $a_{0.6}$S $r_{0.4}$Co $O_{3-}$$\delta$/ layer was coated on the L $a_{0.7}$S $r_{0.3}$G $a_{0.6}$F $e_{0.4}$ $O_{3-}$$\delta$/ membranes by using screen printing technique in order to improve oxygen ion flux. We measured oxygen ion flux on uncoated L $a_{0.6}$S $r_{0.4}$ $Co_{0.2}$F $e_{0.8}$ $O_{3-}$$\delta$/, uncoated L $a_{0.7}$S $r_{0.3}$G $a_{0.6}$F $e_{0.4}$ $O_{3-}$$\delta$/, and coated L $a_{0.7}$S $r_{0.3}$G $a_{0.6}$F $e_{0.4}$ $O_{3-}$$\delta$/ membranes. The L $a_{0.6}$S $r_{0.4}$ $Co_{0.2}$F $e_{0.8}$ $O_{3-}$$\delta$/ membranes showed the highest flux, 0.26 mL/min.$\textrm{cm}^2$ at 90$0^{\circ}C$, after steady state had been reached. The oxygen flux of coated L $a_{0.7}$S $r_{0.3}$G $a_{0.6}$F $e_{0.4}$ $O_{3-}$$\delta$/ membranes showed higher value, 0.19 mL/min.$\textrm{cm}^2$ at 95$0^{\circ}C$. This flux was as much as 2 or 3 times higher than those of uncoated L $a_{0.7}$S $r_{0.3}$G $a_{0.6}$F $e_{0.4}$ $O_{3-}$$\delta$/ membranes. 3-$\delta$/ membranes.X> 3-$\delta$/ membranes.membranes.

• Transactions of the Korean Society of Mechanical Engineers B
• /
• v.28 no.12
• /
• pp.1484-1493
• /
• 2004

In this study, it induced to a conclusion below by experiment consideration to regarding an effective supercooling ends method of the flow cooling water in a tube of continuous ice making method and the static cooling water in a tube of continuous ice making method which used magneticfluid in a dynamic type ice storage system. Continuous ice making in a tube of the flow cooling water was shortened about 12 minutes until supercooling ends that case which gave vertical eccentricity rotation magnetic field 120rpm than did not provide magnetic field by experimental result that was tested to supercooling ends effect from shape control of magneticfluid. Continuous ice making method in a tube of the static cooling water compared with and reviewed the case that was not provided with the magnetic field and exposed cooling surface instantaneously by magnetic field. It confirmed that supercooling degree $\Delta$ $T_{c}$, $\Delta$ $T_{s}$, and $\Delta$ $T_{w}$ became lower because of heat transfering increasing by the occurrence of natural convection between after cooling starting progress time 1∼3 minutes if it did not give a magnetic field, and peformed the supercooling ends when natural convection occurred confirmed that refrigerating capacity was better. That relation $\Delta$ $T_{c}$, and $t_{e}$/($\Delta$ $T_{c}$-$\Delta$ $T_{s}$) after convection occurred, was not depended on $T_{b}$ and initial temperature if the depth of water and thickness of magneticfluid were regular and it was possible to verify conjecture of tp from $\Delta$ $T_{s}$ and $\Delta$ $T_{c}$.lar and it was possible to verify conjecture of tp from $\Delta$ $T_{s}$ and $\Delta$ $T_{c}$.c}$.>.

• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.11 no.6
• /
• pp.411-420
• /
• 1986

Quantization noise of nonadaptive Linear Delta Modulation(LDM) and adaptive Constant Factor Delta Modulation(CFDM) systems is studied. The formulas for quantization noise of CFDM system are derived on the basis of the rusults of LDM. And the output signal-to-quantization noise ratios(SNR) in LDM and CFDM systems are calculated in the range of bit rates from 16[Kb/s] to 96[Kb/s]. By comparing LDM and CFDM, it is known that the adaptive DM is superior to non-adaptive DM by 8[dB] when bit rate is 20[Kb/s] and SNR advantage increases to 14[dB] when bit rate is 56[Kb/s]. All the theoretical results agree well with the experimental results.

• Bulletin of the Korean Mathematical Society
• /
• v.36 no.2
• /
• pp.225-231
• /
• 1999

Let Mf(x) be the Hardy-Littlewood maximal function on $\mathbb{R}^n$. Let $\Phi$ and $\Psi$ be functions satisfying $\Phi$(t) = ${\int^t}_0$a(s)ds and $\Psi(t)$ = ${\int^t}_0$b(s)ds, where a(s) and b(s) are positive continuous such that ${\int^\infty}_0\frac{a(s)}{s}ds$ = $\infty$ and b(s) is quasi-increasing. We show that if there exists a constant $c_1$ so that ${\int^s}_0\frac{a(t)}{t}dt\;c_1b(c_1s)$ for all $s\geq0$, then there exists a constant $c_1$ such that(0.1) $\int_{\mathbb{R^{n}}$ $\Phi(Mf(x))dx\;\leq\;c_2$ $\int_\mathbb{R^{n}}$$\Psi(c_2\midf(x)\mid)dx$ for all $f\epsilonL^1(R^n_$. Conversely, if there exists a constant $c_2$ satisfying the condition (0.1), then there exists a constant $c_1$ so that ${\int^s}_\delta\frac{a(t)}{t}dt=;\leq\;c_1b(c_1s$ for all $\delta$ > 0 and $s\geq\delta$.