• Honam Mathematical Journal
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• v.38 no.4
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• pp.795-807
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• 2016

More general form of an (${\in},{\in}{\vee}q_k$)-fuzzy subsemigroup is considered. The notions of (${\in},q^{\delta}_k$)-fuzzy subsemigroup, ($q^{\delta}_0,{\in}{\vee}q^{\delta}_k$)-fuzzy subsemigroup and (${\in},{\in}{\vee}q^{\delta}_k$)-fuzzy subsemigroup are introduced, and related properties are investigated. Characterizations of an (${\in},{\in}{\vee}q^{\delta}_k$)-fuzzy subsemigroup are considered. Conditions for an (${\in},{\in}{\vee}q^{\delta}_k$)-fuzzy subsemigroup to be a fuzzy subsemigroup are provided. Relations between ($q^{\delta}_0,{\in}{\vee}q^{\delta}_k$)-fuzzy subsemigroup, (${\in},q^{\delta}_k$)-fuzzy subsemigroup and (${\in},{\in}{\vee}q^{\delta}_k$)-fuzzy subsemigroup are discussed.

• Honam Mathematical Journal
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• v.39 no.4
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• pp.527-559
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• 2017

The main motivation of this article is to generalized the concept of fuzzy ideals, (${\alpha},{\beta}$)-fuzzy ideals, (${\in},{\in}{\vee}q_k$)-fuzzy ideals of semigroups. By using the concept of $q^{\delta}_K$-quasi-coincident of a fuzzy point with a fuzzy set, we introduce the notions of (${\in},{\in}{\vee}q^{\delta}_k$)-fuzzy left ideal, (${\in},{\in}{\vee}q^{\delta}_k$)-fuzzy right ideal of a semigroup. Special sets, so called $Q^{\delta}_k$-set and $[{\lambda}^{\delta}_k]_t$-set, condition for the $Q^{\delta}_k$-set and $[{\lambda}^{\delta}_k]_t$-set-set to be left (resp. right) ideals are considered. We finally characterize different classes of semigroups (regular, left weakly regular, right weakly regular) in term of (${\in},{\in}{\vee}q^{\delta}_k$)-fuzzy left ideal, (${\in},{\in}{\vee}q^{\delta}_k$)-fuzzy right ideal and (${\in},{\in}{\vee}q^{\delta}_k$)-fuzzy ideal of semigroup S.

• Journal of the Korean Mathematical Society
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• v.55 no.6
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• pp.1381-1388
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• 2018

Let ${\Delta}$ be a simplicial complex, $I_{\Delta}$ its Stanley-Reisner ideal and $K[{\Delta}]$ its Stanley-Reisner ring over a field K. Assume that ${\Gamma}(R)$ denotes the zero-divisor graph of a commutative ring R. Here, first we present a condition on two reduced Noetherian rings R and R', equivalent to ${\Gamma}(R){\cong}{\Gamma}(R{^{\prime}})$. In particular, we show that ${\Gamma}(K[{\Delta}]){\cong}{\Gamma}(K^{\prime}[{\Delta}^{\prime}])$ if and only if ${\mid}Ass(I_{\Delta}){\mid}={\mid}Ass(I_{{{\Delta}^{\prime}}}){\mid}$ and either ${\mid}K{\mid}$, ${\mid}K^{\prime}{\mid}{\leq}{\aleph}_0$ or ${\mid}K{\mid}={\mid}K^{\prime}{\mid}$. This shows that ${\Gamma}(K[{\Delta}])$ contains little information about $K[{\Delta}]$. Then, we define the squarefree zero-divisor graph of $K[{\Delta}]$, denoted by ${\Gamma}_{sf}(K[{\Delta}])$, and prove that ${\Gamma}_{sf}(K[{\Delta}){\cong}{\Gamma}_{sf}(K[{\Delta}^{\prime}])$ if and only if $K[{\Delta}]{\cong}K[{\Delta}^{\prime}]$. Moreover, we show how to find dim $K[{\Delta}]$ and ${\mid}Ass(K[{\Delta}]){\mid}$ from ${\Gamma}_{sf}(K[{\Delta}])$.

• Journal of the Korean Chemical Society
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• v.7 no.4
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• pp.238-244
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• 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
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• v.25 no.3
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• pp.152-159
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• 1981

The rates of solvolysis for p-nitrobenzyl chloride have been measured by the electric conductivity method in aqueous ethanol from 0.0 to 0. 5 mole fraction of ethanol under various pressures up to 1200bar at 50 and $60{\circ}C$. The activation parameters, ${\Delta}V_\0^{\neq},\ {\Delta}H^{\neq}$ and ${\Delta}S^{\neq}$ are evaluated from the rate constants. The results indicated that ${\Delta}V_\0^{\neq}$ exhibits an extremum behaviors near 0.3 mole fraction of ethanol and ${\Delta}H^{\neq}$ and ${\Delta}S^{\neq}$ near 0.1 mole fraction of ethanol. This behaviors are discussed in terms of solvent structure variation and the pressure dependences of ${\Delta}H^{\neq},\ {\Delta}H^{\neq}$ and ${\Delta}S^{\neq}$ are also discussed individually. The signs of the pressure dependence of ${\Delta}H^{\neq}$${\Delta}S^{\neq}$ are shown to be consistent with those required by the Maxwell relationships for classical thermodynamic systems.

• East Asian mathematical journal
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• v.23 no.2
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• pp.159-174
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• 2007

In this paper, the concepts of pairwise fuzzy $G_{\delta}$-connected spaces and pairwise fuzzy $G_{\delta}$-extremally disconnected spaces are introduced. The concept of pairwise fuzzy $G_{\delta}$-basically disconnected spaces is defined. Characterizations of the above spaces are given besides giving several examples. Interrelations among the spaces introduced are discussed and some relevant counter examples are given.

• Journal of the Korean Chemical Society
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• v.7 no.3
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• pp.211-215
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• 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 Chemical Society
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• v.36 no.2
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• pp.180-184
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• 1992

Kinetic studies for the reaction of pyridine with substituted benzoyl chlorides were conducted under various pressures (1-1000 bar) in acetonitrile. From rate constants, the activation parameters (${\Delta}V^{\neq}$, ${\Delta}{\beta}^{\neq}$,${\Delta}H^{\neq}$, ${\Delta}S^{\neq}$ and ${\Delta}G^{\neq}$) were evaluated. Rates of these reaction increased with an increase in the pressure. The activation volume, the activation compressibility coefficient and the activation entropy were negative. From substituents effect and these results, it was found that these reactions proceed through $S_N2$ mechanism, but the structure of transition state was slightly changed with substituents and pressure.

• 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.

• Journal of the Korean Chemical Society
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• v.42 no.2
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• pp.150-155
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• 1998

Kinetic studies on the reaction of isoquinoline with para-substituted benzylbromides were conducted under various pressures (1 ~1000 bar) in acetonitrile. From the rate constants obtained, the activation parameters such as$\DeltaV^{\neq}, \Delta\beta^{\neq}, \DeltaH^{\neq}, \DeltaS^{\neq}, \DeltaG^{\neq}$ and Ea were evaluated. Reaction rate increasing the pressure and temperature. The activation compressibility coefficient and the activation entropy showed negative values. From the substituent effect and the results, it was found that the reaction proceeds through $S_N2$ mechanism, but the structure of transition state was slightly changed with substituents and pressure.