• Journal of the Korean Chemical Society
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• v.24 no.2
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• pp.108-114
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• 1980

By using electrostatic model and simple bond additivity scheme a reasonable and simple method was developed for the estimation of standard enthalpy of formation $({\Delta}H_f\;^{\circ})$ of very polar compounds. The bond contributions to the enthalpy of formation for halomethanes were; ${\Delta}H_f\;^{\circ}(C-F)=-36.44\;kcal/mole,\;{\Delta}H_f\;^{\circ}(C-Cl)=-2.57\;kcal/mole,\;{\Delta}H_f\;^{\circ}(C-Br)=5.32\;kcal/mole,\;{\Delta}H_f\;^{\circ}(C-I)=19.18\;kcal/mole,\;and\;{\Delta}H_f\;^{\circ}(C-H)=-3.61\;kcal/mole$, respectively. Using these values and calculated electrostatic energies, the estimated ${\Delta}H_f\;^{\circ}$ values were estimated and found to be in good agreement with observed values.

• Journal of the Korean Chemical Society
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• v.38 no.2
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• pp.108-121
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• 1994

The retention indices of branched-chain alkane, benzene ring, alcohol, amine, ketone, aldehyde and cyclic compounds were measured at 150, 180 and $210^{\circ}C$ on OV-1701 and OV-1 capillary columns. The group retention factors (GRF) of the substituents and the st` ructure retention factors (SRF) of the molecular structure change are derived from the retention indices of reference compounds and series of homologues. The $GRF_f$ equation of `f'th substituent is $GRF_f\;=\;I_{obs}-(100Z + \sum\limits_{i{\neq}f}GRF_i$ + {\sum}$SRF_i$)and the SRFf equation of `f'th molecular structure group is $SRF_f\;=\;I_{obs}-(100Z + {\sum}GRFi + \sum\limits_{i{\neq}f}SRF_i$). The predicted retention indices for those compound were in agreement, within the error of $\pm2$ and $\pm3%$, with the observed values that were obtained using the OV-1701 and OV-1 capillary column, respectively. The $\Delta$ xi of the substituents and $\Delta$ yi of the molecular structure change according to temperature change are derived from the $\Delta'/^{\circ}C$ of reference compounds and series of homologues. The $\Delta$ xi equation of the `f'th substituent is ${\Delta}x_f = {$\Delta}'/^{\circ}C+ \sum\limits_{i{\neq}f}\Delta$ xi + {\sum}{\Delta}yi\;and\;{\Delta}yi$ equation of the `f'th molecular structure group is ${\Delta}y_f$ = {\Delta}'/^{\circ}C+{\sum}{\Delta}xi +\sum\limits_{i{\neq}f}{\Delta}yi$. The predicted $\Delta'/^{\circ}C$ for these compounds were in agreement, within the error of ${\pm}18%$ and 17%, with the observed values that were obtained using the OV-1701 and OV-1 capillary column, respectively.

• Journal of the Korean Mathematical Society
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• v.15 no.1
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• pp.59-61
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• 1978

Let $X_1$, $X_2$, ${\cdots}$, $X_n$ be i.i.d. uniform (0,1) random variables. Let $f_n(x)$ denote the probability density function (p.d.f.) of $T_n={\sum}^n_{i=1}X_i$. Consider a set S(x ; ${\delta}$) of lattice points defined by S(x ; ${\delta}$) = $x{\mid}x={\delta}+j$, j=0, 1, ${\cdots}$, n-1, $0{\leq}{\delta}{\leq}1$} The lattice distribution induced by the p.d.f. of $T_n$ is defined as follow: (1) $f_n^{(\delta)}(x)=\{f_n(x)\;if\;x{\in}S(x;{\delta})\\0\;otherwise.$. In this paper we show that $f_n{^{(\delta)}}(x)$ is a probability function thus we obtain a family of lattice distributions {$f_n{^{(\delta)}}(x)$ : $0{\leq}{\delta}{\leq}1$}, that the mean and variance of the lattice distributions are independent of ${\delta}$.

• Journal of the Chungcheong Mathematical Society
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• v.10 no.1
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• pp.43-56
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• 1997

In this paper, we introduce a new class of ${\delta}$-frames and study its properties. To do so, we introduce ${\delta}$-filters, almost Lindel$\ddot{o}$f frames and Lindel$\ddot{o}$f frames. First, we show that a complete chain or a complete Boolean algebra is a ${\delta}$-frame. Next, we show that a ${\delta}$-frame L is almost Lindel$\ddot{o}$f iff for any ${\delta}$-filter F in L, ${\vee}\{x^*\;:\;x{\in}F\}{\neq}e$. Last, we show that every regular Lindelof ${\delta}$-frame is normal and a Lindel$\ddot{o}$f ${\delta}$-frame is preserved under a ${\delta}$-isomorphism which is dense and codense.

• Korean Journal of Mathematics
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• v.24 no.3
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• pp.409-445
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• 2016

The class $\mathcal{W}^{\delta}_{\beta}({\alpha},{\gamma})$ defined in the domain ${\mid}z{\mid}$ < 1 satisfying $Re\;e^{i{\phi}}\((1-{\alpha}+2{\gamma})(f/z)^{\delta}+\({\alpha}-3{\gamma}+{\gamma}\[1-1/{\delta})(zf^{\prime}/f)+1/{\delta}\(1+zf^{\prime\prime}/f^{\prime}\)\]\)(f/z)^{\delta}(zf^{\prime}/f)-{\beta}\)$ > 0, with the conditions ${\alpha}{\geq}0$, ${\beta}$ < 1, ${\gamma}{\geq}0$, ${\delta}$ > 0 and ${\phi}{\in}{\mathbb{R}}$ generalizes a particular case of the largest subclass of univalent functions, namely the class of $Bazilevi{\check{c}}$ functions. Moreover, for 0 < ${\delta}{\leq}{\frac{1}{(1-{\zeta})}}$, $0{\leq}{\zeta}$ < 1, the class $C_{\delta}({\zeta})$ be the subclass of normalized analytic functions such that $Re(1/{\delta}(1+zf^{\prime\prime}/f^{\prime})+1-1/{\delta})(zf^{\prime}/f))$ > ${\zeta}$, ${\mid}z{\mid}$<1. In the present work, the sucient conditions on ${\lambda}(t)$ are investigated, so that the non-linear integral transform $V^{\delta}_{\lambda}(f)(z)=\({\large{\int}_{0}^{1}}{\lambda}(t)(f(tz)/t)^{\delta}dt\)^{1/{\delta}}$, ${\mid}z{\mid}$ < 1, carries the fuctions from $\mathcal{W}^{\delta}_{\beta}({\alpha},{\gamma})$ into $C_{\delta}({\zeta})$. Several interesting applications are provided for special choices of ${\lambda}(t)$. These results are useful in the attempt to generalize the two most important extremal problems in this direction using duality techniques and provide scope for further research.

• Bulletin of the Korean Mathematical Society
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• v.51 no.3
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• pp.659-666
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• 2014

Let $\mathcal{A}$ be the class of analytic functions f in the open unit disk $\mathbb{U}$={z : ${\mid}z{\mid}$ < 1} with the normalization conditions $f(0)=f^{\prime}(0)-1=0$. If $f(z)=z+\sum_{n=2}^{\infty}a_nz^n$ and ${\delta}$ > 0 are given, then the $T_{\delta}$-neighborhood of the function f is defined as $$TN_{\delta}(f)\{g(z)=z+\sum_{n=2}^{\infty}b_nz^n{\in}\mathcal{A}:\sum_{n=2}^{\infty}T_n{\mid}a_n-b_n{\mid}{\leq}{\delta}\}$$, where $T=\{T_n\}_{n=2}^{\infty}$ is a sequence of positive numbers. In the present paper we investigate some problems concerning $T_{\delta}$-neighborhoods of function in various classes of analytic functions with $T=\{2^{-n}/n^2\}_{n=2}^{\infty}$. We also find bounds for $^{\delta}^*_T(A,B)$ defined by $$^{\delta}^*_T(A,B)=jnf\{{\delta}&gt;0:B{\subset}TN_{\delta}(f)\;for\;all\;f{\in}A\}$$ where A, B are given subsets of $\mathcal{A}$.

• Journal of dental hygiene science
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• v.17 no.2
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• pp.116-122
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• 2017

The purpose of this study was to evaluate the detection ability of secondary caries using qunatitative light-induce fluorescence-digital (QLF-D) device. Twenty bovine teeth with cavity on surface were demineralized during 21 days for secondary caries lesion of cavity wall. After 21 days, cavity was filled using composite resin and cut the specimen in half with disc. Fluorescence loss of lesion on surface by time flow, cross sectional lesion, and lesion of filled or unfilled surface were analyzed using analysis software. ${\Delta}F$ (value of fluorescence loss) of the lesion on surface assessed by the QLF-D increased significantly over time up to 21 days. And ${\Delta}F$ value of lesion of filled surface is significantly lower than that of unfilled surface (p<0.001). ${\Delta}F$ of filled surface is 1.31 times of cross section lesion. The correlation of between ${\Delta}F$ of filled surface lesion and ${\Delta}F$ of cross section lesion was showed low agreement (0.026) and correlation of between ${\Delta}F$ of unfilled surface lesion and ${\Delta}F$ of cross section lesion was showed high agreement (0.613). In conclusion, secondary caries can be detected on surface using QLF-D. However, interference of fluorescence of filling material is the points to be especially considered for exact analysis of secondary caries lesion.

• Journal of applied mathematics & informatics
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• v.24 no.1_2
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• pp.357-366
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• 2007

Let G(V, E) be a simple graph, and let f be an integer function on V with $1{\leq}f(v){\leq}d(v)$ to each vertex $v{\in}V$. An f-edge cover-coloring of a graph G is a coloring of edge set E such that each color appears at each vertex $v{\in}V$ at least f(v) times. The f-edge cover chromatic index of G, denoted by ${\chi}'_{fc}(G)$, is the maximum number of colors such that an f-edge cover-coloring of G exists. Any simple graph G has an f-edge cover chromatic index equal to ${\delta}_f\;or\;{\delta}_f-1,\;where\;{\delta}_f{=}^{min}_{v{\in}V}\{\lfloor\frac{d(v)}{f(v)}\rfloor\}$. Let G be a connected and not complete graph with ${\chi}'_{fc}(G)={\delta}_f-1$, if for each $u,\;v{\in}V\;and\;e=uv{\nin}E$, we have ${\chi}'_{fc}(G+e)>{\chi}'_{fc}(G)$, then G is called an f-edge covered critical graph. In this paper, some properties on f-edge covered critical graph are discussed. It is proved that if G is an f-edge covered critical graph, then for each $u,\;v{\in}V\;and\;e=uv{\nin}E$ there exists $w{\in}\{u,v\}\;with\;d(w)\leq{\delta}_f(f(w)+1)-2$ such that w is adjacent to at least $d(w)-{\delta}_f+1$ vertices which are all ${\delta}_f-vertex$ in G.

• The Korean Journal of Ecology
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• v.4 no.3_4
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• pp.59-67
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• 1981

Stomatal resistances of the leaves in Heteromeres arbutifolia and of the stems in Ferocactus acanthodes were studied to estimate active and passive behaviors of the guard cells on a theoretical basis. Active and passive stomatal responses to light and water deficit were observed. When the change rate of existent water due to variation of osmotic potential in the guard cells and the loss rate of transpirational water from the guard cells are $\Delta$wi-$\Delta$wt and leaded to active behaviors for opening and closing stomata. However, when stems of F. acanthodes with stomata closecd under the solar irradiation were covered with black cloth and then taken off, behaviors of the guard cells occurred in the condition of $\Delta$wi<$\Delta$wt and were passive. Under the conditiion of $\Delta$wi<$\Delta$wt due to cutout from stems, passive behaviors of the guard cells in H. arbutifolia and F. acanthodes always occurred in spite of the solar irradiation and darkness, respectively. The transpirational resistance coefficients of the guard cells in stems of F. acanthodes (0.380) and Opuntia bigelovii (0.135) wer emuch higher than in leaves of H. arbutifolia (0.034). Moreover, stomatal opening in stems of F. acanthodes during the daytime could be induced by watering. Those results are interpreted as that since the guard cells in desert Crassulacean acid metabolism (CAM) plants always exist in the state of stomatal opening, nocturnal stomatal opening and daytime stomatal closing are exhibited by passive behaviors of the guard cells in the alternant conditioins of $\Delta$wi>$\Delta$wt and $\Delta$wi<$\Delta$wt, respectively.

• Journal of the Korea Society of Computer and Information
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• v.17 no.11
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• pp.189-196
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• 2012

This paper proposes Swap algorithm for solving Dynamic Economic Dispatch (DED) problem. The proposed algorithm initially balances total load demand $P_d$ with total generation ${\Sigma}P_i$ by deactivating a generator with the highest unit generation cost $C_i^{max}/P_i^{max}$. It then swaps generation level $P_i=P_i{\pm}{\Delta}$, (${\Delta}$=1.0, 0.1, 0.01, 0.001) for $P_i=P_i-{\Delta}$, $P_j=P_j+{\Delta}$ provided that $_{max}[F(P_i)-F(P_i-{\Delta})]$ > $_{min}[F(P_j+{\Delta})-F(P_j)]$, $i{\neq}j$. This new algorithm is applied and tested to the experimental data of Dynamic Economic Dispatch problem, demonstrating a considerable reduction in the prevalent heuristic algorithm's optimal generation cost and in the maximization of economic profit.