• Korean Journal of Mathematics
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• v.17 no.4
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• pp.461-471
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• 2009

Let ${\Omega}$ be a bounded subset of $R^n$ with smooth boundary and H be a Sobolev space $W_0^{1,2}({\Omega})$. Let $I{\in}C^{1,1}$ be a strongly definite functional defined on a Hilbert space H. We investigate the conditions on which the functional I satisfies the Palais-Smale condition. Palais-Smale condition is important for determining the critical points for I by applying the critical point theory.

• The Pure and Applied Mathematics
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• v.22 no.1
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• pp.1-11
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• 2015

The present paper is concerned with the notions of Lipschitz and asymptotic for perturbed functional differential system knowing the corresponding stability of functional differential system. We investigate Lipschitz and asymptotic stability for perturbed functional differential systems. The main tool used is integral inequalities of the Bihari-type, and all that sort of things.

• Bulletin of the Korean Chemical Society
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• v.15 no.10
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• pp.881-888
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• 1994

The approximate rates and stoichiometry of the reaction of excess sodium tris(diethylamino)aluminum hydride (ST-DEA) with selected organic compounds containing representative functional groups under standardized conditions(tetrahydrofuran, $0{\circ}$) were studied in order to characterize the reducing characteristics of the reagent for selective reductions. The reducing ability of STDEA was also compared with those of the parent sodium aluminum hydride (SAH) and lithium tris(diethylamino)aluminum hydride (LTDEA). The reagent appears to be milder than LTDEA. Nevertheless, the reducing action of STDEA is very similar to that observed previously for LTDEA, as is the case of the corresponding parent sodium and lithium aluminum hydrides. STDEA shows a unique reducing characteristics. Thus, benzyl alcohol, phenol and 1-hexanol evolved hydrogen slowly, whereas 3-hexanol and 3-ethyl-3-pentanol, secondary and tertiary alcohols, were essentially inert to STDEA. Primary amine, such as n-hexylamine, evolved only 1 equivalent of hydrogen slowly. On the other hand, thiols examined were absolutely stable. STDEA reduced aidehydes and ketones rapidly to the corresponding alcohols. The stereoselectivity in the reduction of cyclic ketones by STDEA was similar to that by LTDEA. Quinones, such as p-benzoquinone and anthraquinone, were reduced to the corresponding 1,4-dihydroxycyclohexadienes without evolution of hydrogen. Carboxylic acids and anhydrides were reduced very slowly, whereas acid chlorides were reduced to the corresponding alcohols readily. Esters and epoxides were also reduced readily. Primary carboxamides consumed hydrides for reduction slowly with concurrent hydrogen evolution, but tertiary amides were readily reduced to the corresponding tertiary amines. The rate of reduction of aromatic nitriles was much faster than that of aliphatic nitriles. Nitrogen compounds examined were also reduced slowly. Finally, disulfide, sulfoxide, sulfone, and cyclohexyl tosylate were readily reduced without evolution of hydrogen. In addition to that, the reagent appears to be an excellent partial reducing agent: like LTDEA, STDEA converted ester and primary carboxamides to the corresponding aldehydes in good yields. Furthermore, the reagent reduced aromatic nitriles to the corresponding aldehydes chemoselectively in the presence of aliphatic nitriles. Consequently, STDEA can replace LTDEA effectively, with a higher selectivity, in most organic reductions.

• Bulletin of the Korean Chemical Society
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• v.18 no.8
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• pp.890-895
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• 1997

The approximate rates and stoichiometry of the reaction of excess lithium tripiperidinoaluminum hydride (LTPDA), an alicyclic aminoaluminum hydride, with selected organic compounds containing representative functional groups under the standardized conditions (tetrahydrofuran, 25°) were examined in order to define the reducing characteristics of the reagent for selective reductions. The reducing ability of LTPDA was also compared with those of the parent lithium aluminum hydride (LAH) and lithium tris(diethylamino)aluminum hydride (LTDEA), a representative aliphatic aminoaluminum hydride. In general, the reactivity of LTPDA toward organic functionalities is weaker than LTDEA and much weaker than LAH. LTPDA shows a unique reducing characteristics. Thus, benzyl alcohol, phenol and thiols evolve a quantitative amount of hydrogen rapidly. The rate of hydrogen evolution of primary, secondary and tertiary alcohols is distinctive. LTPDA reduces aldehydes, ketones, esters, acid chlorides and epoxides readily to the corresponding alcohols. Quinones, such as p-benzoquinone and anthraquinone, are reduced to the corresponding diols without hydrogen evolution. Tertiary amides and nitriles are also reduced readily to the corresponding amines. The reagent reduces nitro compounds and azobenzene to the amine stages. Disulfides are reduced to thiols, and sulfoxides and sulfones are converted to sulfides. Additionally, the reagent appears to be a good partial reducing agent to convert primary carboxamides into the corresponding aldehydes.

• Journal of The Korea Institute of Healthcare Architecture
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• v.10 no.1
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• pp.39-45
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• 2004

This thesis is a case study of hospital design corresponding to substance of hospital components. The substance of each divisions and functional elements of hospital architecture is analyzed and the appropriate forms corresponding to each substance are tried in design. The researcher is convinced, that healthcare facilities for patients must be differently designed from post-modernism or deconstructivism. He suggests new design method in designing of jeju university hospital competition.

• Bulletin of the Korean Mathematical Society
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• v.38 no.3
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• pp.495-504
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• 2001

In this paper we consider the (generalized) autoregressive model with conditional heteroscedasticity (ARCH/GARCH models). We willing give conditions under which strict stationarity, ergodicity and the functional central limit theorem hold for the corresponding models.

• Bulletin of the Korean Chemical Society
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• v.16 no.5
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• pp.416-421
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• 1995

The approximate rates and stoichiometry of the reaction of excess lithium gallium hydride with selected organic compounds containing representative functional groups were examined under the standard conditions (diethyl ether, 0 $^{\circ}C)$ in order to compare its reducing characteristics with lithium aluminum hydride and lithium borohydride previously reported, and enlarge the scope of its applicability as a reducing agent. Alcohols, phenol, and amines evolve hydrogen rapidly and quantitatively. However lithium gallium hydride reacts with only one active hydrogen of primary amine. Aldehydes and ketones of diverse structure are rapidly reduced to the corresponding alcohols. Conjugated aldehyde and ketone such as cinnamaldehyde and methyl vinyl ketone are rapidly reduced to the corresponding saturated alcohols. p-Benzoquinone is mainly reduces to hydroquinone. Caproic acid and benzoic acid liberate hydrogen rapidly and quantitatively, but reduction proceeds slowly. The acid chlorides and esters tested are all rapidly reduced to the corresponding alcohols. Alkyl halides and epoxides are reduced rapidly with an uptake of 1 equiv of hydride. Styrene oxide is reduced to give 1-phenylethanol quantitatively. Primary amides are reduced slowly. Benzonitrile consumes 2.0 equiv of hydride rapidly, whereas capronitrile is reduced slowly. Nitro compounds consumed 2.9 equiv of hydride, of which 1.9 equiv is for reduction, whereas azobenzene, and azoxybenzene are inert toward this reagent. Cyclohexanone oxime is reduced consuming 2.0 equiv of hydride for reduction at a moderate rate. Pyridine is inert toward this reagent. Disulfides and sulfoxides are reduced slowly, whereas sulfide, sulfone, and sulfonate are inert under these reaction conditions. Sulfonic acid evolves 1 equiv of hydrogen instantly, but reduction is not proceeded.

• Bulletin of the Korean Chemical Society
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• v.31 no.3
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• pp.678-682
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• 2010

A doubly tethered chiral stationary phase (CSP) based on (+)-(18-crown-6)-2,3,11,12-tetracarboxylic acid were applied to the liquid chromatographic resolution of racemic tocainide, an antiarrhythmic agent, and its analogues. The chiral recognition efficiency of the doubly tethered CSP for tocainide and its analogues was generally greater than that of the corresponding singly tethered CSP especially in terms of the resolution ($R_S$). The resolution of tocainide and its analogues on the doubly tethered CSP were dependent on the content and the type of the organic and acidic modifiers in aqueous mobile phase and the column temperature. Especially, the retention behaviors of analytes on the doubly tethered CSP with the variation of the content of organic modifier in aqueous mobile phase were opposite to those on the corresponding singly tethered CSP and these opposite retention behaviors were rationalized by the lipophilicity differences of the two CSPs.

• Journal of the Korean Chemical Society
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• v.55 no.5
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• pp.751-755
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• 2011

A doubly tethered chiral stationary phase (CSP) based on (+)-(18-crown-6)-2,3,11,12-tetracarboxylic acid was applied to the resolution of various aryl ${\alpha}$-aminoalkyl ketones with the use of 80% ethanol in water containing 10 mM sulfuric acid as a mobile phase. The chiral resolution was quite successful, the separation factors (${\alpha}$) and the resolutions ($R_S$) being in the range of 1.39-2.05 and 3.18-5.22, respectively. The separation factors (${\alpha}$) on the doubly tethered CSP were slightly worse than those on the corresponding singly tethered CSP. However, the resolutions ($R_S$) on the doubly tethered CSP were generally greater than those on the corresponding singly tethered CSP. The chromatographic behaviors for the resolution of aryl ${\alpha}$-aminoalkyl ketones on the doubly tethered CSP were demonstrated to be dependent on the type and the content of the organic and acidic modifiers in aqueous mobile phase and the column temperature.

• Bulletin of the Korean Chemical Society
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• v.18 no.3
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• pp.274-280
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• 1997

The rates and stoichiometry of the reaction of gallane-trimethylamine with selected organic compounds containing representative functional groups were examined in tetrahydrofuran solution under standardized conditions (THF, 0 ℃). And its reducing characteristics were compared with those of aluminum hydride-triethylamine(AHTEA). The rate of hydrogen evolution from active hydrogen compounds varied considerably with the nature of the functional group and the structure of the hydrocarbon moiety. Alcohols, phenol, amines, thiols evolved hydrogen rapidly and quantitatively. Aldehydes and ketones were reduced moderately to the corresponding alcohols. Cinnamaldehyde was reduced to cinnamyl alcohol, which means that the conjugated double bond was not attacked by gallane-trimethylamine. Carboxylic acids, esters, and lactones were stable to the reagent under standard conditions. Acid chlorides also were rapidly reduced to the corresponding alcohols. Epoxides and halides were inert to the reagent. Caproamide and nitrile were stable to the reagent, whereas benzamide was rapidly reduced to benzylamine. Nitropropane, nitrobenzene and azoxybenzene were stable to the reagent, whereas azobenzene was reduced to 1,2-diphenylhydrazine. Oximes and pyridine N-oxide were reduced rapidly. Di-n-butyl disulfide and dimethyl sulfoxide were reduced only slowly, but diphenyl disulfide was reduced rapidly. Finally, sulfones and sulfonic acids were inert to the reagent under the reaction.